NBS SPECIAL PUBLICATION 484

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

Flow Measurement in Open Channels

and Closed Conduits

Volume 2

r

...
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and

technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to pro- mote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Institute for Computer Sciences and Technology, the Office for Information Programs, and the

Office of Experimental Technology Incentives Program.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis wMiin the United States of a complete and consist- ent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry,

and commerce. The Institute consists of the Office of Measurement Services, and the following center and divisions:

Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics — Center for Radiation Research — Laboratory Astrophysics 2 — Cryogenics* — Electromagnetics* — Time and Frequency".

THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to improved methods of measurement, standards, and data on the properties of well-characterized materials needed! by insfastry, commerce, educational insti- tutions, and Government; provides advisory and research services to other Government agencies; and develops, produces, and

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3 Located at Boulder, Colorado 80302.
iflqnat Bureau 6? Stan3ardf

NOV 8 1977

Flow Measurement in Open Channels

;r\ and Closed Conduits

Volume 2 >/pg-cu i kkk^Jypu /to* V<f^

no

Proceedings of the Symposium on Flow Measurement

in Open Channels and Closed Conduits held at the

National Bureau of Standards in Gaithersburg,

Maryland on February 23-25, 1977

Lafayette K. Irwin, Editor

Mechanics Division

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

Vj v S , NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued October 1977
Library of Congress Cataloging in Publication Data

Symposium on Flow Measurement in Open Channels and Closed

Conduits, National Bureau of Standards, 1977. Flow measurement in open channels and closed conduits.

(National Bureau of Standards special publication ; 484)

Includes index. Supt. of Docs, no.: C13.10:484

1. Flow meters—Congresses. I. Irwin, Lafayette K. II. Title. III.

Series: United States. National Bureau of Standards. Special publication ; 484. QC100.U57 no. 484 [TC177] 602'. Is [6a0.1'064] 77-14243

National Bureau of Standards Special Publication 484/2

Nat. Bur. Stand. (U.S.), Spec. Publ. 484/2, 490 pages (Oct. 1977)

CODEN. XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1977

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 - Price $12.25 per 2 part set ; sold In sets only

Stock No. 003-003-01845-7
PREFACE

These Proceedings include most of the papers presented at the threeday symposium on fluid flow measurements held at the National Bureau of

Standards, Gaithersburg, Maryland, on February 23, 24, and 25, 1977. The

papers dealt with flow in open channels and closed conduits and a special

related session on international standards.

The impetus to hold the symposium came from several sources. These

included (1) continuing requests for the information presented at the 1974

Flow Measurement Conference held to establish connections between flow

measurement and national needs (conference presentations not published)

,

(2) increasing use of measurement technology by regulators to monitor or

enforce the effects of their rule making, and (3) rising awareness of

the importance of international standards to this nation, particularly,

for quantifying energy-related fluids. The purpose of the symposium was

to bring together a significant group of the producers and users of flow

measurement technology, to provide a forum for presenting and discussing

both the new and the proven ideas for making useful flow measurements,

and to assemble and disseminate the resulting information.

Initially, the theme was to emphasize identification and assessment

of sources of errors, formulation of error analysis techniques and

recommendations for resolving the uncertainties for flow measurement.

The strong interests of investigators in presenting related research,

of instrument developers in describing the performance of flow measurement devices and systems, and of users in discussing applications

resulted in a broader spectrum and larger number of papers than was

envisioned. An optimum ordering of papers in the resulting two volumes

has not evolved.

Lafayette K. Irwin, Editor

iii
Conversions for Customary to International System (SI) Units

Reflecting the transitional stage of the measurement units in this

technological area, both U. S. customary and SI units of measurement are

used in different papers of these Proceedings. The U.S.A. is a member

of the General Conference on Weights and Measures which gave official

status to the SI metric units in 1960. Conversion factors for selected

units in these Proceedings are:

Quantity

Length

Area

Volume

Conversion

customary to SI

inch (in) to meter (m)

foot (ft) to meter (m)

inch2 (in2

) to meter 2 (m2

) foot 2 (ft 2

) to meter2 (m2

)

inch 3 (in 3

) to meter 3 (m 3

) foot 3 (ft 3

) to meter 3 (m 3

) gallon"^ (gal) to meter 3 (m3

)

Factor

,

approximate

0.02541

"

0.3048+

0.0006452

0.09290

0.00001639

0.02832

0.003785

Mass pound, avoirdupois (lb) to kilogram (kg) 0.4536

Force

Pressure, or

Stress

Velocity

Acceleration

Density

Flow

Temperature

pound (lbf) to newton (N)

kilogram (kgf) to newton (N)

pound/inch2 (psi) to newton/meter2 (N/m2

) inch of mercury, 60 °F (inHg) to newton/meter2 (N/m2

) inch of water, 60 °F (inH-20) to newton/meter2 (N/m2

) millimeter of mercury, 0 °C (mmHg) to

newton/meter2 (N/m2

)

inch/second (in/s) to meter/second (m/s)

foot/second (ft/s) to meter/second (m/s)

foot/second2 (ft/s 2

) to meter/second2 (m/s 2

) free fall, standard (g) to meter/second2 (m/s 2

)

pound/foot 3 (lb/ft 3

) to kilogram/meter 3 (kg/m3

) pound/gallon^"^ (lb/gal) to kilogram/meter 3 (kg/m 3

)

foot 3 /second (ft 3 /s) to meter 3 /second (m 3 /s)

foot 3 /minute (ft 3 /min) to meter 3 /second (m 3 /s)

gallon

-^/minute (gal/min) to meter 3 /second (m 3 /s)

pound/second (lb/s) to kilogram/second (kg/s)

degree Fahrenheit to degree Celsius

4.448

9.807

6895

3377

248.8

133.3

0.02541

"

0.3048+

0.3048+ 9.807

16.02

119.8

0.02832

0.0004719

0.00006309

0.4536

t 0 =(t c -32)1.

t

See NBS SP330, 1977 ed. , The International System of Units (SI) and

ASTM E380-76, Metric Practice Guide for more complete information.

Exact

++ U. S. liquid
TABLE OF CONTENTS - Volume 1

PREFACE iii

Conversions for Customary to International (SI) Units iv

ABSTRACT ix

Measuring the Repeatability of Flowmeters 1

A. T. J. Hayward

The Navy Liquid Flow Correlation Program 25

J. H. Tabler and C. G. Kullman

A Laboratory Study of Turbine Meter Uncertainty 33

G. Mattingly, P. Pontius, H. Allion, and E. Moore

Evolution of a Modern Petroleum Measurement Manual 55

L. M. Davis

Building Blocks Towards Flowmeter Reliability 61

Dezsoe Halmi

Open Channel Flow Monitoring or Metering, That is the Question ... 83

Kenneth W. Martig, Jr.

Instrument Errors in Open Channel Flow Measurement Systems 91

D. M. Grant

Marine Dynamics and Its Effects on Current Measuring Transducers . 109

Thomas Mero, Gerald Appell, and Raul S. McQuivey

Some Error Sources in Price and Pygmy Current Meter Traverses .... 123

G. Kulin

Flow Measurements in the Canals of Power Plant Closed Loop Cooling

Systems 145

Joseph F. O'Brien, James Skridulis, John Annett, G. Wayne Singley

and Harold L. Koenig

Errors in Flow Measurement and Their Importance in Infiltration/

Inflow Analysis 173

D. L. Guthrie, D. R. Washington and C. Vincenty

Rating Broad-Crested V-Notch Weirs with Narrow, Sloping Approach

Channels and Sediment Deposits 187

James F. Ruff, Keith Saxton and Clement Dang

Compensating for Construction Errors in Critical-Flow Flumes and

Broad-Crested Weirs 201

John A. Replogle

v
Table of Contents - Volume 1 (Continued)

Numerical Modeling of Two-Dimensional Flumes 219

Ronald W. Davis

The Design of Open Channel Acoustic Flowmeters for Specified Accuracy:

Sources of Error and Calibration Test Results 243

Francis C. Lowell, Jr.

Application Considerations & Performance Capability of the Time

Differential Clamp-On Ultrasonic Flowmeter 267

J . Baumoel

Theoretical and Experimental Assessment of Uncertainties in NonIntrusive, Ultrasonic Flow Measurement 277

Ronald F. Bruner

A New Ultrasonic Flowmeter for the Natural Gas Industry 293

N. E. Pedersen, J. E. Bradshaw, L. C. Lynnworth and P. F. Morel

A New Non- Intrusive Flowmeter 319

R. S. Flemons

Reconstructing Three-Dimensional Fluid Velocity Vector and Temperature Fields from Acoustic Transmission Measurements 335

S. A. Johnson, J. F. Greenleaf, M. Tanaka, and G. Flandro

Validation of Use of Dye-Dilution Method for Flow Measurement in

Large Open and Closed Channel Flows 361

W. H. Morgan, D. Kempf, R. E. Phillips

Dilution Method of Discharge Measurement in Pipes 395

E. R. Holley

Application of a Fluorescence Technique to Dye-Concentration Measurements in a Turbulent Jet 423

Hsien-Ta Liu, Jung-Tai Lin, Donald P. Delisi and Frank A. Robben

The Application of Monte Carlo and Bayesian Probability Techniques

to Flow Prediction and Determination 447

Frank J. Berte*

Author Index 470-A

TABLE OF CONTENTS - Volume 2

Laser Doppler Anemometry for Flow Measurement 471

William W. Durgin and Lawrence C. Neale

On Improving the Pitot-Tube Determination of Flows in Large Pipes. 479

J. M. Robertson and M. E. Clark

Numerical Modeling and Turbulent Flow Through Thin Orifice Plates. 491

R. W. Davis and G. E. Mattingly

vi
Table of Contents - Volume 2 (Continued)

Studies of Pulsating Incompressible Flow Through Orifice Meters . . 523

R. A. Bajura and M. T. Pellegrin

A Vortex Flowmeter - Calibration Results and Application Experiences 549

R. W. Miller, J. P. DeCarlo, and J. T. Cullen

Temperature Field Measurements in Turbulent Thermals 571

Mohamed Gad-el-Hak

Flow Measurement Up-Date 597

Robert B. Suhoke

Near Wall Velocity Measurements for Wall Shear Inference in Turbulent Flows 621

F. J. Pierce and D. S. Gold

On Reduction of Errors Arising in Hot-Wire Anemometry of Thin Turbulent Shear Layers 649

J. Gaviglio and J. P. Dussauge

Probe and Method for Simultaneous Measurements of 'True' Instantaneous Temperature and Three Velocity Components in Turbulent

Flow 659

Gracio Fabris

Measurement of Boundary Layer Transition Using Acoustic Techniques 687

Donald C. Sachs, Thomas F. V. Meagher, and Vernon D. Peckham

Measurement of Recirculating Flow Behind a Cylinder with Spray

Cooling 705

R. S. Rudland

A New Type of Velocity Probe 719

W. B. Brower, Jr. and Alan Servoz

The Influence of Turbulence on Static and Total Pressure Probes . . 737

V. E. Scottron

Determination and Elimination of Errors in Velocity Readings at

Ventilation Tubing Inlets 755

Robert A. Haney

Indirect Two-Phase Flow Measurement: Analysis and Reduction of

Methods Errors 765

N. N. Kondic

vii
Table of Contents - Volume 2 (Continued)

Measurements of Density and Density Gradient With an Oscillating

Conductivity Probe 783

Donald P. Delisi and Robert H. Kirchhoff

New Techniques for Automotive Fuel Flow Measurements 803

Milton Baker

A New Digital Technique for Temperature and Viscosity Compensation

of Turbine and Positive-Displacement Flow Transducers 821

Roger Jennings

Viscosity Effects on the Turbine Flowmeter 847

John M. Ball

Turbine Meters for the Measurement of Gaseous Hydrocarbons 871

Paul J. LaNasa

On a New Method of Gas Flow Measurement Using Cryogenic Techniques 881

D. B. Mann and J. A. Brennan

An Anatomy of the International Standards Producing System - Flow

Measurement 895

L. K. Irwin

OIML and EEC, Their Impact on the International Standards Producing

System 921

D. E. Edgerly

The Interface Between Industrial, National and International

Standards 929

Wallace N. Seward

The Adequacy of the Data Bases Available for Promulgating International Standards 935

H. H. Dijstelbergen

Equitable Implementation of National and International Allocation

Programs - Summary of Remarks 945

James A. West

Of Form and Substance for Effective Standards 947

E. A. Spencer

Comments On: Role of International Standards in Measuring and

Allocating Hydrocarbons - A Program for Solution of our Present

Problems 957

F. H. Abernathy

Author Index 960

viii
ABSTRACT

The wide range and complexity of problems and potential solutions that

must be considered for useful flow measurements are emphasized by the

papers contained in these proceedings. Fifty-three presentations cover:

characteristics of new and improved instruments; applications of traditional and new measuring devices in field environments; procedures for

identifying and analyzing errors or uncertainties in data under specific

conditions; uses of physical and numerical models; politico-economic

changes that affect international standards for flow measurement; and

philosophical bases for making measurements. The fluids of most interest

are water and waste water, petroleum and related refined products, air,

natural gas and stack gas.

Experimental and analytical investigations on instrument performance

and interpretation of results include innovative applications of traditional

and new flow measurement techniques to fluid flows in open channels and

closed conduits. The traditional devices or techniques include weirs,

flumes, current meters, orifice plates, turbines, hot-wires, pitot-static

tubes, velocity traverses, dye-dilution, and others. More recent instrumentation developments and procedures such as laser doppler anemometry,

acoustic and thermal imaging, acoustic pulse velocity and doppler anemometry, numerical modeling, vortex shedding and digital computation are

covered for particular measurement purposes.

The most significant trend reflected in these presentations is the

general awareness that uncertainties in measured quantities at the lowest

point in the measurement chain, i.e., in the field or plant, are more

important than accuracy statements derived from controlled laboratory

studies. Other trends in evidence are the rising importance of turbine

meters for use as transfer standards and in-line measurements of liquids

and gases in filled pipes and the increasing number of applications for

acoustics and laser technology for flow measurements in both open channels

and closed conduits.

Key Words: Acoustic flow meters; closed conduit flows; current meters;

dye-dilution methods ; errors in flow measurement ; flow

measurement; fluid flow modeling; fluid velocity; flumes;

gas flow standard; hot-wire anemometry; international flow

standards; laser anemometry; open channel flows; orifice

meters; pitot-static meters; turbine meters; weirs.

ix
DISCLAIMER:

Certain trade names and company products are identified in order

to adequately specify the experimental procedure. In no case does such

identification imply recommendation or endorsement by the National

Bureau of Standards, nor does it imply that the products are necessarily

the best available for the purpose.

x
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

LASER DOPPLER ANEMOMETRY FOR

FLOW MEASUREMENT

William W. Durgin

Alden Research Laboratories

Worcester Polytechnic Institute

Holden, Massachusetts

Lawrence C. Neale

Charles T . Main , Inc . Boston, Massachusetts

Laser doppler anemometers are non-invasive, linear, and

inherently precise. Calibration, in the usual sense, is not

necessary; length and frequency measurements suffice to

establish velocity at a spatial point. Measurements were

made at points in the cross-sections of two square ducts

containing water flow. The points were selected in conformance with a numerical integration scheme to be used

for volumetric flow rate determination from the velocity

measurements . The experiments were performed in a

primary calibration facility at flows up to 1.25 m

3 /sec

using ducts with sides 46 and 92 cm . The anemometer

,

operating in forward scatter differential mode with a 15

mw He Ne laser , was positioned with a special traversing

frame . Windows in the ducts allowed transmission of the

beams into the flow and reception of scattered light. Two

grid patterns, 4 x 11 and 11 x 11, were used so that 44 and

121 velocities were measured for each test. A total of eight

tests were conducted covering a Reynolds number range

from 1.1 to 3.9 x 10 6

. After accounting for errors due to

the discreet integration scheme of 0.61% and 0.13% for the

4 x 11 and 11 x 11 schemes, respectively, comparison with

the calibration facility indicated extreme errors of +0.81/

-0.16 and +0.84/-0.61. The major limitation of the set-up

used was the time required to move the anemometer and

obtain a new velocity value. It was pointed out that either

better mechanical positioning or optical scanning could be

employed to reduce the time required for a flow determination .

471
1 . Introduction

As part of a test program to evaluate the performance of a four path acoustic

flow meter, it was necessary to establish the velocity distribution at the

metering section. The measurements were made using a laser doppler

anemometer and a pattern which allowed numerical integration for volumetric

flow rate . The experiments were set up in a primary flow calibration facility

using gravimetric determination of water flow rate. Square ducts were used

with windows provided for the anemometer. A traversing mechanism was

used to position the anemometer measuring volume at spatial locations where

velocity measurements were made. The facilities, procedures, and results

of the entire program are reported in [1, 2] *, while this paper discusses

only those aspects pertaining to determination of flow rate from laser

doppler measurements .

2. Test Facility

Square ducts (46 and 92 cm) were installed in the large primary calibration

facility at the Alden Research Laboratories, Figure 1. This facility consisted

of a sump with a capacity of 760 m

3 of water, which was maintained at temperatures from 30C to 40C, a pumping capacity of 1 . 27 m

3 /s at a head of 37 m, a

straight pipe run of 25 m, and a weigh tank with capacity of 45,000 kg. A

diverter was provided to allow static weighing for all tests and a timing activator for mid-stroke operation. At the maximum flow rate, the filling time for a weigh tank run was approximately 30 seconds.

The weighing system was a Toledo beam scale arranged with a direct reading

dial and nine individual drop weights . Timing was accomplished by a photoelectric system mounted on the diverter which activated a 100 KH counter

synchronized with a precision time base. Dead weight calibration of the scale

and load cell was carried out on a routine basis every 6 months, while the

time base was checked on a continuing basis each week. The culmative error

associated with this facility was known to be approximately 0.1% so that it

formed a good primary standard for the LDA flow measurements

.

3. Laser Doppler Anemometer

A laser doppler anemometer (LDA) operating in the forward scatter differential mode was used. The light beam from a 15 mw He Ne laser was split

into two beams which passed into the test section through a plane window,

Figure 2. The beams were brought to a focus at the crossing point where

the velocity measurement was made . A photomultiplier on the opposite side

of the duct detected light scattered from particles in the measuring volume

modulated at the doppler frequency. Figure 3 shows the 46 cm test section,

traversing frame, laser, and transmission optics. The receiving optics were

also mounted on the frame , but out of view . Figure 4 shows the measuring

volume just inside the window on the 92 cm duct.

*Figures in brackets indicate the literature references at the end of this paper.

472
The instantaneous particle velocity, u, was given by the equation

u

2 sin 9/2

where X was the wavelength of the laser radiation, was the doppler frequency , and G was the beam angle . The radiation wavelength was known

accurately, and the beam angle was determined by projecting the two beams

onto a distant screen and using careful geometrical measurements . The

accuracy of a velocity measurement thus hinged on measurement of the

doppler frequency. This measurement was made with a frequency tracker

which utilized a voltage controlled oscillator and an error detector to track

the doppler signal. Either the control voltage or the VCO output could be

monitored as an indication of velocity . The measurements of mean velocity

reported here were made using a digital voltmeter with variable time

constants , although it was later found that a frequency meter monitoring

the VCO gave better results. In either case, the system was conveniently

and accurately calibrated using a crystal frequency source.

Thus , all quantities associated with a velocity measurement were accurately

and easily traceable. Furthermore, the velocity and signal output were

linearly related, which simplified subsequent processing. An error analysis

indicated that the accuracy of the velocity measurements was approximately

±0.18%.

4. Integration for Flowrate

The traversing mechanism provided for the LDA facilitated positioning the

measuring volume at specific locations in the cross-section. The positions

were chosen as 4 x 11 and 11 x 11 matrices such that the flow rate could

be obtained from the mean velocities using Gaussian quadrature [3] .

The volumetric flowrate was determined as

11 4, 11

Q = 4A I I u. u. u.. *i r

3 i]

3

where

A = duct area

x. , x. = fractional location of point from centerline

1

3

U., Uj = weights

u„ = measured velocity at i , j

473
The Gaussian weights and fractional locations are given in Table I.

TABLE I

11 POINTS 4 POINTS

i, i x. |i. x. u.

1 0.978 0.056 0.861 0.348

2 0.887 0.126 0.340 0.652

3 0.730 0.186 0.340 0.652

4 0.519 0.233 0.861 0.348

5 0.269 0.263

6 0.000 0.273

7 0.269 0.263

8 0.519 0.233

9 0.730 0.186

10 0.887 0.126

11 0.978 0.056

To the extent that velocity profiles could be represented by Legendre polynomials , the integration would be exact. For more realistic profiles, the

accuracy was checked by integrating over a theoretical velocity distribution

derived from a law of the wall . An exact integration was made and compared

to the 4 x 11 and 11 x 11 schemes corresponding to the measurements. Based

on this calculation, the 4 x 11 and 11 x 11 schemes should have overestimated

the flow rate by 0 . 61% and 0.13%, respectively

.

5 . Results

Mean and rms velocity measurements were made at each of the 165 grid points.

Each measurement required approximately two minutes to insure proper time

averaging. A flow rate determination was made after each 11 measurements

and slight temporal variations accounted for in subsequent data reduction.

Three useful runs were made using the smaller duct, while five were made

for the larger. The results are summarized in Table II.

TABLE II

Test Test

Size cm No. Date

3 Flow m /s % 11 x 11 % 4 x 11 TR x 10

46 x 46 4 1/29/75 1.2013 +0.37 +0. 70 3.5

46 x 46 5 2/05/75 1.2098 -0.01 +0. 45 3.9

46 x 46 6 2/07/75 0.5955 +0.30 +0. 73 1.9

92 x 92 7 5/06/75 1.2470 -0.24 +0. 83 1.8

92 x 92 8 5/12/75 0.6370 -0.12 +0. 68 1.0

92 x 92 9 5/19/75 1.2418 +0.97 +1. 42 2.0

92 x 92 10 5/20/75 0.6222 +0.65 +1. 16 1.1

92 x 92 11 6/17/75 1.2498 -0.48 +0. 59 1.8

-6

474
Keeping in mind that errors of 0.61% and 0.13% should be expected for the

4 x 11 and 11 x 11 schemes, respectively, because of the integration method,

it can be seen that flow rate determinations using the LDA are quite good.

In fact, after accounting for the integration error , the maximum percentage

flow rate error for the 4 x 11 scheme was +0.81/-0.16 while the 11 x 11

scheme was +0.84/-0.61. Similarly, the mean errors were +0.21% and -0.35%,

respectively

.

The precision of the system, including the LDA and the integration, was good.

The system required no calibration other than a tape measure to determine

beam angle and a frequency standard to calibrate the tracker. The possibility

of using standards other than volume or mass in connection with flow metering

is thus open. The major limitation is seen to be the length of time required to

make a flow rate determination. It is speculated, however, that suitable hardware could be arranged to provide fast scanning of the flow cross-section.

Much of the work described herein was originally supported by the Oceanic

Division of Westinghouse Electric Corporation in connection with the development of their LEFM flow meter . Matching funds from an internal development

fund enabled acquisition of the laser Doppler system.

[1] Tassinari, P.J. , "Fluid Flow Characteristics in Square Ducts at High

Reynolds Numbers," M.S. Thesis, Worcester Polytechnic Institute,

(May 1975).

[2] Tassinari, P.J. andW.W. Durgin, "Flow Measurement in Rectangular

Ducts," Report 87-75/M91F, Alden Research Laboratories, Worcester

Polytechnic Institute, (November 1975).

6 . Conclusions

7. Acknowledgements

8 . References

Benedict, R.P. and J. Wyler, "Determining Flow Rate from Velocity

Measurements," Instruments and Control Systems , pp. 47-50,

February 1974.

475
FIGURE 1 TEST FACILITY

FIGURE 2 TEST SECTION

476
FIGURE 3 46 cm DUCT, LDA, AND TRAVERSING FRAME

National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

ON IMPROVING THE PITOT-TUBE DETERMINATION

OF FLOWS IN LARGE PIPES

J. M. Robertson and M. E. Clark

Department of Theoretical and Applied Mechanics

University of Illinois at Urbana- Champaign

Urbana, Illinois 61801

Reliable and accurate flow measurements in large pipes are

becoming increasingly important in assessing the performance of

power plant equipment in these days of energy crises. Since the

Pitot- static tubes that are used for the determination of flows in

large (diameters from 4 to 8 ft) pipes are being calibrated in a

smaller (24-in. ) pipe, various uncertainties arise in the use of the

Pitot and in the interpretation of its coefficient. These uncertainties

include the correction for the area blockage by the Pitot tube, the

effect of tip proximity to the wall on velocity indications, and the

effect of asymmetric velocity profiles on the accuracy of the flow

rate prediction. Additionally, the problems associated with fluctuating manometer readings and vibration of the Pitot tube can be

significant. Studies and considerations of these uncertainties are

reported. Specifically, the blockage correction has been studied

via traverses with several Pitot tubes in the 24-in. pipeline and

with a reduced- size model in 8- and 24-in. pipelines. Test results indicate that this type of correction is necessary to achieve

true flow rate predictions but that it needs a better definition and

is not unique. Velocity gradients and proximity to the far wall also

significantly affect velocity indications. Conventional integration

techniques applied to asymmetric velocity profiles, obtained from

laboratory measurements following a pipe bend, are shown to yield

inaccurate flow rate predictions. A study of Pitot tube vibration

effects suggests that the resultant over-indicated velocities should

be discarded from the average and more appropriate values, estimated from the trend of the profile, should be substituted for them.

Key Words: Pipe flow; Pitot tubes; flow metering; velocity indication; flow in large pipes.

1 . Introduction

The flow rate in large pipelines can be found using several methods (integral

flow meters, dilution methods, velocity probes, etc). Because of the small initial

cost and the relative ease in conducting the test in the field, the current conventional method of choice involves the integration of velocity profiles obtained by traversing a Pitot- static head mounted at the end of a cylindrical rod cantilevered into the

pipe. Usually a pair of orthogonal traverses are used with velocities taken at the

centroids of ten or more annular areas of equal increments of the cross section.

The geometries of the commercial Pitot- static heads deviate considerably from that

of the optimum Pitot design which gives a direct indication of velocity. This difference is commonly accounted for by attaching a coefficient to each Pitot tube with

this coefficient taken as a unique constant. Calibration is thus required and is

479
usually accomplished in a pipe appreciably smaller than the pipeline in the field.

Specifically, the authors have been calibrating standard Pitot tubes in a 24- in. pipe

for use in pipelines with diameters of 4 to 8 ft. This paper addresses questions

which arise on using the coefficient obtained in the smaller pipe to evaluate the flow

rate in the large pipelines.

Uncertainties. Various uncertainties arise in the use of the Pitot tube. The cantilevered device introduces a variable blockage (reduction in flow area) as it is

extended into the pipe. How should a correction for this blockage be introduced

when one is using the calibration determined in a small pipe to obtain flow rates

in large pipes? When the Pitot head is near a wall, the flow patterns and, hence,

the velocity indications are modified. Since these modifications depend upon tip

size, how do they affect the establishing of calibration coefficients for pipes of various sizes? Evaluation of average pipe velocity from two orthogonal traverses can

involve serious errors when the velocity profiles are appreciably distorted by upstream fittings. Periodic flow separation from the rod can cause the cantilevered

Pitot tube to vibrate, or "sing". Unsteady separation of the flow about the Pitot

head or turbulence can cause appreciable fluctuations in the manometer readings.

Thus, it is difficult to interpret the indicated velocities. Results of studies of these

factors are presented in what follows. The objective of these continuing studies is

to improve the Pitot head, our methods of using it, and our methods of interpreting

its indications so that more reliable flow- rate measurements can be achieved in

large pipelines.

Background. Since its invention by Henri de Pitot in 1732, the Pitot or Pitot -static

tube has been extensively studied, modified, and used. The 1955 review of this

device by Folsom [ l] 1 indicates the status of our knowledge of it. Folsom and

others note that the real reason why the Pitot-tube fails as an absolute velocityindicating device lies in the measurement of the static or reference pressure. The

impact pressure or total head is usually obtained with sufficient accuracy. A number of designs for Pitot heads are indicated in Fig. 1. Two long heads with coefficients near unity are (a) the Prandtl tube and (b) the NPL-type tube; this latter

tube seems to be much like that developed by Gregory in 1903. These elongated

tubes, however, tend to be unsuitable for introduction into pipelines through moderate-sized valves or corporation cocks. Various compact heads, which can be

inserted through openings about the size of their support rods, are illustrated by

Fig. lc, d and e. The typical one of Fig. lc was used for traversing flow in

4-in. pipes at the University of Illinois [2] and in 10-in. pipes at the Pennsylvania

State University [3]. The Pitot-static head commonly used for large pipeline flow

measurements (see Fig. le) is compact enough to be moved through openings less

than one -inch in diameter. Information on the design of this specific head, which

has a coefficient of about 0. 8, is not available in the literature. The reference

pressure taps of this head are half way around a circular cylinder in a region particularly susceptible to flow separation and to oscillations due to variations in the

flow direction. In another type of standardized Pitot head - the Pitometer of Cole

[4] - the Darcy scheme of getting the reference pressure from an 'opening at the

rear was adopted and, according to Cole, this led to much more consistent calibrations.

Figures in brackets indicate the literature references at the end of this paper.

480
L d/3 L d v.

• • o

• 00

0.56d

(a) Prandtl (1921)

C = 1.00

0.035"

•0.375"V ©

(b) NPL Tapered (1912)

C = 1.00

0.040 .jC

}«~2.0^

2" x

1" Elliptical

Rod

Typical Compact (d) CTWT Design

(UITAM 1937, PSU 1946) (PSU 1949)

C = 0.60 - 0.80 C = 0.97/1.01

3 O

0.625' diam.

*-0. 875 CD

Common (Simplex)

C £ 0. 82

Fig. 1. Various Long and Compact Pitot- Static Heads

The design of a larger head (see Fig. Id) capable of being moved through a

2-in. opening, has been reported [5]. This head was mounted on a one- by two-in.

elliptical cantilever rod. It was designed for use in large circular conduits (up to

12-ft diameter) and for large velocities (80 fps in 4-ft pipe). In towing-tank calibration, it had a coefficient of 1.010, four percent above the design value -- presumably due to errors in placing the static holes in the head. Such a tube would be

difficult to fabricate in a size that would move through a one-inch hole. The cantilevered Pitot cylinder of Winternitz [4] on the other hand is quite simple in geometry

but exhibits a considerable wall-interference effect.

An alternative design to the cantilever arrangement is the transverse Pitot

tube, which may consist simply of a cylinder completely spanning the pipe along a

diameter [5,6] with static reference pressures obtained from wall-piezometer taps.

A more sophisticated device of this type with integral reference pressure taps has

been developed by Numachi, et al [7]. Unfortunately, it is not always convenient

or easy to drill the holes and to mount such transverse tubes and wall piezometers

are affected by wall roughness.

2. Errors and Corrections

Blockage Correction. Since the Pitot head and support rod assembly reduces the

pipe flow area and thereby increases the velocity, some correction for blockage

481
is necessary. This effect is localized near the rod, so that for Pitot tubes with long

heads (Fig. la or lb), it should be negligible; Hubbard [10] has noted that a long

head could produce a significant blockage only if it was large relative to the pipe.

Cole [2] gave lengthy consideration to the blockage effect for the cantilevered Pitometer and detailed various experiments which yielded a correction factor of between

one and one and a half times the projected area of the Pitometer (extended to the pipe

center). Additional work by Cole and Cole [11] in pipes of various sizes indicated

a correction of about 1.2 times the projected area of the Pitometer. The blockage

correction certainly depends upon the geometry of the Pitot head and, hence, studies

are reported here of the design shown in Fig. le which is often used for flow measurements in large pipelines.

The Pitot tube of Fig. le (Simplex design) has a cylindrical head, one inch

long and 0.625 in. in diameter, mounted at the end of a oval rod having a thickness

normal to the flow of 0.34 in. When introduced into a 24-in. pipe to indicate the

centerline velocity, the flow area is reduced by one percent. In a 4-ft pipe, the

reduction is 0.48 percent and, in a 6 -ft pipe, 0.31 percent. This rod is also

used in long lengths but then it is stiffened against vibration by encasing it in a 1.5-

in. steel cylinder. When stiffened to within 11 in. of the pressure taps, the blockage in the 2-ft pipe is then 1.3 percent and, in the 4- and 6-ft pipes, is 1.4 and

1.0 percent, respectively.

The blockage acts to increase the average velocity indicated by the Pitot

tube. If C is defined as the true Pitot coefficient obtained by calibration with a

blockage correction based on the projected area of the tube extended to give the

centerline velocity, the flow rate can be calculated by the following relation.

(1) Q = (A - Aw

) C V

p

= A (1 - B) C V

p

I

where A is the actual cross -sectional area of the pipe, A^ = B A is the projected

Pitot tube area when extended to give the centerline velocity, B is the fractional

blockage (A^j/A), and V is the average uncorrected velocity indicated by the Pitot

traverse. The nominal coefficient for the tube is defined, ignoring the blockage, as

follows

< 2> C

nom

= "V = C (1 - B)

AV

P

For a Pitot of true coefficient C = 0. 820, the nominal coefficient in pipes of 2- to

8-ft diameter would be as listed in Table I. The variation in Cn0m is appreciable.

If blocking were the only factor, calculation of a true C from Cnom would be relatively simple; unfortunately, other factors varying with pipe size also enter.

Experiments with the Simplex Pitot in a 24-in. pipe and a model (0. 59 times

as large) of it in 24- and 8-inch pipes have been made to further evaluate the problem. The coefficient values found from these tests (via Eq. 1) are presented in

Table II together with the associated pipe and skewness factors. Some of the results were found from single traverses (not one or more pairs at 90 degrees, as

for the others). Included are results for the reinforced Pitot rod with different

lengths (Y) of non- reinforced end. The trends of these results are qualitatively

as indicated by Eq. 2 and Table I, but there is much scatter. As an example, the

coefficient for the model varies from 0.81 in the 8 -in. pipe to 0.83 in the 24-in.

pipe. Other factors must affect the coefficient, as will be noted in later sections.

482
If blockage were the only factor affecting the coefficient, then the C values should

be the same no matter what Pitot or pipe size was involved.

Table I. Variation in Nominal Coefficient

with Pipe Size for C = 0. 820

C

nom

Pipe

Diameter Std. Simplex Reinf. Simplex

Y = 11 in.

2 ft 0.812 0.810

4 ft 0.816 0.809

6 ft 0.817 0.812

8 ft 0.818 0.813

1

Table II. Pitot Coefficients and Flow Factors Found for Two

Sizes of the Simplex Pitot Tube in Two Pipes

B_ —

Coefficients Flow Factors

Pipe Pitot

C

nom C P S

24 in. Reinf. Simplex

Pitot A

Y = 11 in.

Y = 5 in*

0.013

0.028

0.812

0.794

0.823

0.817

0.866

0.864

1.082

1. 116

Pitot B

Y = 5 in. 0.028 0.808 0. 831 0.873 1. 160

24 in. Simplex** 0. 0097 0.796

to 0. 824

0. 804

to 0. 832

0.85

to 0. 87

1.08

to 1. 14

24 in.

8 in.

Model Simplex

Model Simplex

0. 0055

0.018

0.826

0.795

0.831

0.810

0. 843

0.847

1.076

1.141

* Single Traverse

**Six Pitots /23 Traverses

In addition to the Pitot coefficient, certain other ratios or factors characterizing the flow also indicate effects of blockage. These are the pipe factor and the

skewness of the velocity profiles. The ratio of average to centerline velocity —

dubbed the pipe factor P by Cole [2] is a useful indicator of the nature of the flow,

483
as well as a direct factor for flow metering. At a sufficient distance downstream of

flow disturbances, this factor is a unique function of Reynolds number and the relative roughness of the pipe [ 10, 11]. However, for a Pitot of finite size, blockage

effects result in an over- indication of the velocities. In Table II, there is a definite

tendency for these data for the 24-in. pipe to increase with B. The model Pitot traverses in the 8-in. pipe gave a value somewhat above the value of 0. 83 which was

established earlier [11] in the same pipe using a Pitot with negligible blockage.

Since the blockage is larger when the Pitot is extended to indicate far-wall

velocities than for near-wall velocities, the ratio of velocities equidistant from but

on opposite sides of the centerline depends on blockage when the pipe flow is symmetrical. The skewness factor S of Table II is thus taken as the ratio of the two

velocities found at wall distances of 0.09D. These factors are seen to increase with

B, but not in a simple linear fashion. Calculations of S, based on blockage alone,

yield values of 1.05 and 1.015 for values of B equal to 0.028 and 0.0097, respectively. As can be seen from the table, the experimentally-determined values

are considerably larger but the trends are as predicted.

Wall- Proximity and Velocity -Gradient Effects. The specialized flow field about the

end of a Pitot tube is affected by wall-proximity and by transverse velocity gradients.

These two effects will be considered separately, although in practice they occur

simultaneously since steep velocity gradients appear near walls.

The extensive study of Pitot tube errors by Hubbard [ 10] did not consider

the effect of wall proximity on the the flow and on corresponding velocity indications

but, on a reciprocity basis, his studies of the rod effects on wall piezometer taps

would infer an effect of the wall on the tip pressure field leading to near-wall errors

in the reference static pressure. Winternitz [4] in his study of a round tip on the

end of a cylindrical cantilever tube found a significant wall -interference effect; errors in static pressure, up to the order of ten percent, occurred near walls and were

of different signs for the near and far walls. Since the wall-proximity effect must

depend greatly on the Pitot head design, the common Pitot tube (Fig. le) has been

investigated for its wall effect. Changes in the velocity indicated by this tube in uniform flow (except for a boundary layer about 0.06-in. thick) near a flat plate in an

air stream are summarized in Fig. 2. From this figure, the Pitot is seen to significantly over-indicate velocities when the tip is within a few inches of the far wall.

In fact, for a flow- rate evaluation (using a 14 -point concentric-area integration) the

two velocity indications nearest the wall would be 1.0 and 0.5 percent too high.

Studies have yet to be made of near-wall effects; there the wall opening through

which the tube enters the pipeline will also disturb the flow field.

An error -- tantemount to a shift in the effective location of the measuring

tip -- appears in the indicated velocity of Pitots, even the elongated forewardpointing types, when measurements are made in transverse velocity gradients. This

effect was first studied by Young and Maas [ 14] and later by Livesey [ 15], Davies

[ 16] and Dhawan and Vasudeva [17]. No studies of the common pipeline Pitot seem

to have been made and the authors' experiments in shear flows away from walls are

still in the planning stage. Further studies of this effect and that of wall interference

seem necessary.

Pulsation and Support- Rod Vibration Effects. Turbulent flow is inherently unsteady

so that a manometer connected to a Pitot in a pipeline will show pulsations. Additionally, pulsation can result from unsteady flow about the Pitot head due to vortexstreet occurrences. Both Cole [4] and Hubbard [ 10] have considered this problem

484
Boundary Layer

6 = 0. 06 ~3_ y >">7\>> 1, ) )))})> i /

of properly interpreting the

manometer indication in the

presence of pulsations. Cole's

suggestion that the readings be

taken over a full cycle of variation is fine except that the variations are generally random

and one is not able to define the

cycle. The authors have observed less manometer pulsation

with one Pitot design that with

another, but ferretting out the

explanation for this and optimizing it is difficult.

Rod vibration effects are

more easily recognized. Cole

[4], Cole and Cole [11] and

Bean [18] have all noted effects

of vibration. These effects are

small when the amplitude of

vibration is small but the overindication becomes large with

increase in amplitude. Winter- nitz [19] has studied this problem extensively and explains it

on the basis of the streaming

flow near the reference staticpressure taps as induced by the

lateral vibration of the Pitot rod

assembly. The vibration is due

to fluid-dynamic forces generated by the oscillating vortex

street behind the cantilevered

rod. When the frequency of

these oscillations matches the

natural frequency of the Pitot

tube system (including the

support mechanism), resonance

occurs. Except to make the rod

and its support as stiff as possible not a lot can be done to prevent these vibrations.

Common fluid-dynamic fixes, in the form of strakes or trailing plates, are not feasible since they must be applied to the outside surface of the rod and this would lead

to difficulties with packing seals. For the common pipeline Pitot tube (Fig. le), the

authors have noted "singing" (forced vibration evidenced by an audible hum) in their

24-in. pipeline at velocities between 5. 6 and 7. 2 fps when the tube was extended

1.71ft from the near wall and at velocities between 7.4 and 10. 0 fps when extended 1.27 ft. These speeds must certainly depend upon the rigidity of the Pitot

in its support. The resultant increase of indicated velocity is generally only a few

percent but this debilitates the validity of a flow- rate evaluation. As an operational

procedure, the authors suggest that elevated readings, caused by vibration effects,

be reduced in calculating an average velocity. Generally, one can smooth the velocity profile, taking the trend of the curve below the values indicated by the vibrating

+2 +3

Velocity Error - %

Fig. 2. Wall Proximity Effects on Simplex

Pitot in Uniform Air Flow of 86 fps

485
Cube. To quantify the correction requires correlation of the error with the amplitude of vibration; this has not been done. An alternative approach is to have two

Pitot tubes or support geometries of significantly different natural frequency (stiffness) so that the vibration region of one may be avoided with the other.

Flow Rate Evaluation in Disturbed Flow. It is sometimes necessary to make flow

measurements in the field at sites where the flow profiles have not been fully developed. The field engineer then asks, "How accurately can I determine the flow rate

by the probe method?" In an attempt to provide a partial answer to such a question

in a laboratory context where the actual flow rate was determinable, horizontal and

vertical traverses were taken in the 24- in. pipeline two diameters downstream of

a short- radius bend. The flow upstream of this bend was disturbed from the fullydeveloped profile by other bends. Vertical (in plane of bend) and horizontal 14-point

traverses were taken with the common Pitot; the resultant velocity profiles are

shown in Fig. 3. Both profiles are obviously skewed. The tube coefficient C,

determined in the same pipe with fully -developed flow according to standardized

procedures with the appropriate blockage correction, was 0. 823 for the average

of a horizontal and a vertical traverse. The 14-point averages of the Pitot tube

indications downstream from the elbow were 8.08 and 8.77 fps for horizontal

and vertical traverses, respectively; corresponding average velocities (obtained

through multiplication by C) were 6. 65 and 7.22 fps. Using the same amount of

blockage as used in the calibration calculations, the indicated flow rates were 20.74

and 22.51 cfs. The corresponding values of the flow rate, determined volumetrically, were 20.20 and 20.49 cfs; thus giving percentage errors in the flow rate of

2.7 and 11.4, respectively.

Fig. 3. Pitot Traverses Taken Downstream of a Pipe

Bend At a Flow Rate of 20 cfs.

486
From these results, it can be seen that some individual velocity traverses

taken in disturbed flow will give fair approximations to the true flow rate (e.g.

,

the horizontal traverse of Fig. 3 predicts a flow rate to within three percent of

the actual one). However, other traverses can give a poor prediction of flow rate.

In the single case investigated, both traverses over-predicted the flow rates. Hence,

other traverse directions should exist which would have under-predicted the flow

rate by comparable amounts. Only if the total cross -sectional area had been sufficiently probed to give a true average value of the velocity would the indicated flow

rate agree with the actual value. One would presume that two more orthogonal traverses midway between the horizontal and vertical traverses already taken would

have been sufficient to formulate a proper average. Without going through the additional work required to secure such data, however, the foregoing statement remains

a presumption. Under field conditions there would be no way to determine the validity of such a four-traverse result. Therefore, at a site where skewed profiles are

found, a sufficient number of traverses must be taken so as to obtain a trustworthy

average velocity. Otherwise, errors in flow rate of as much as 10 to 20 percent

can be expected.

Other Considerations. Certain significant features of the Pitot tube problem are

not addressed here. Thus Cole's [4] studies indicated a small, but finite, velocity

effect -- as a decrease in coefficient from 0. 89 to 0. 86 as the pipe velocity increased from 2 to 10 fps. The common Pitot (Fig. le) is usually taken to have a

coefficient invariant with velocity; the authors' limited studies tend to support this

view. Another feature of flow evaluations from velocity traverses involves the number of annular-area increments used for averaging the velocity profile. Often five

areas -- giving a ten-point average -- are used. Folsom [1] presents calculations

based on the one-seventh- power velocity profile of turbulent flows indicating overcalculation of the average velocity by 0. 91 percent for a six-point traverse, by

0.53 percent for a ten-point one and by 0.25 percent for 20 points. The authors

have compared 10-point and 14-point averages from an actual traverse in a 24-

in. pipe and have found a 0. 1 percent decrease (suggesting a larger Pitot coefficient) in the indicated average velocity with the larger number of points. The choice

of an optimum number of points involves such considerations modified by concern

for wall-proximity effects.

3. Summary

Obviously, this study of the Pitot tube commonly used in field measurements

of large pipeline flows is far from complete. Even though firm conclusions from

this study would be premature at this time, some of the uncertainties have been

clarified.

Blockage and wall- proximity effects on the Pitot tube significantly affect

flow rate evaluation in pipes of different size (larger) than those used for the calibration of the tube. Further study is needed to quantify the needed corrections.

Pitot vibration effects on indicated flows can be reduced with care in taking and

interpreting traverses. Flow rate evaluations at sites of disturbed flow require

more than the usual two orthogonal traverses, otherwise significant errors may be

encountered.

The results of numerous calibrations of the commonly-used Pitot in the

2-ft pipe are indicated as well as those of a 0. 59 model in the 2 -ft and in an 8-in.

487
pipe. These calibrations do not yield the unique coefficient one would expect

the variation certainly stems from the effects discussed but also presumably from

small dimensional differences between the measuring heads due, in part at least,

to rough handling in the field. The coefficient has a value of 0. 82 + 0.01. The

studies of this Pitot in uniform flow (see Fig. 2 at large values of y~) yield a coefficient of 0. 81. The difference between this value and 0. 82 is presumably due to

the characteristics of the pipe flow, i.e. , blockage, wall- proximity, turbulence,

etc.

Improvement of this type of measurement is not easy since the effects involved amount to only a few percent and are due to factors not always clearly understood. Improvement in the design of the Pitot measuring head is not imminent.

Changes in the geometry or in placement of the pressure ports affect the overall

performance only slightly and sometimes unpredictably.

References

[1], Folsom, R. G., "Review of the Pitot Tube", Trans. A.S.M.E., 78, 1447-

1460, (1956).

[2], Robertson, J. M. , "A Study of the Flow of Water Around Bends in Pipes",

B. S. Thesis in Civil Engineering, Univ. of Illinois, (1938).

[3], Turchetti, A. J., and Robertson, J. M. , "Design of Vaned-Turns for a

Large Water Tunnel", A.S.M.E. paper 48-SA-15, (1948).

[4]. Cole, E. S. , "Pitot Tube Practice", Trans. A.S.M.E., 57, 281-294, (1935).

[5]. Shuster, F. E., "Design of Pitot-Static Tube for a Large Water Tunnel",

M.S. Thesis in Civil Engineering, Penn. State Univ., (1949).

[6], Winternitz, F. A. L. , "Cantilevered Pitot Cylinder", The Engineer, May 27,

739-732, (1955).

[7]. Christensen, J. E., and French, O. C. , "Characteristics of Transverse

Pitot Tubes", Agricultural Engineering.

,

_18, 21-24, (1937).

[8]. Robertson, J. M. , and Shuster, F. E. , "Coefficient of a Pitot-Tube Flow

Detector", Instruments and Control Systems, 34, 645-647, (1961).

[9], Numachi, F. , Murai, H. , and Abe, S. , "Streamlined Pitot-Tube Bar for

Measuring Water Flow in Large Pipe", Trans. A.S.M.E., 78, 1079-1089,

(1956).

[10]. Hubbard, C. W. , "Investigation of Errors of Pitot Tubes", Trans. A.S.M.E.,

61, 477-506, (1939).

[11]. Cole, E. S. , and Cole, E. Shaw, "Pitot Tubes in Large Pipes", Trans.

A.S.M.E., 61, 465-475, (1939).

488
[12]. Folsom, R. G. , and Iverson, H. W. , "Pipe Factors for Quantity Rate FlowMeasurements with Pitot Tubes", A.S. M.E. paper 48-A35, (1948); abstract

in Mech. Engineering, 20, 1019-1020, (1948).

[13]. Robertson, J. M. , Martin, J. D. , and Burkhart,T."Turbulent Flow in Rough

Pipes", I&EC Fundamentals, 7, 253-265, (1968).

[ 14]. Young, A. D. , and Maas, J. N. , "The Behavior of a Pitot Tube in a Transverse Total Pressure Gradient", British Aero. Res. Council, R&M No.

1770, (1937).

[15], Livesey, J. L. , "The Behavior of Transverse Cylindrical and Forward Facing Total Pressure Probes in Transverse Total Pressure Gradients", Jour.

Aero. Sci.

,

23, 949-955, (1956).

[ 16]. Davies, P. O. A. L. , "The Behavior of a Pitot Tube in Transverse Shear",

Jour. Fluid Mchs.

,

3, 441-7, (1957).

[17]. Dhawan, S. , and Vasudeva, B. R. , "The Pitot Tube Displacement Effect in

Boundary Layer Flows", Jour. Aero. Soc. of India, 11 , 1-18, (1959).

[18], Bean, H. S. , discussion of reference 9, 473.

[19]. Winternitz, F. A. L. , "Effects of Vibration on Pitot Probe Readings", The

Engineer, 201 , 273-75, 282-290, (March 30 and April 6, 1956).

489

National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

NUMERICAL MODELING OF TURBULENT FLOW THROUGH

THIN ORIFICE PLATES

R. W. Davis and G. E. Mattingly

Mechanics Division, IBS

National Bureau of Standards

Department of Commerce

Washington, D.C. 20234

A study is presented which uses the twoequation turbulence model developed at Imperial

College, London to model high Reynolds number

flow through orifice plates. This turbulence

model employs the eddy viscosity concept for

the Reynolds stresses. Two transport equations

are solved for turbulence variables and are

combined to form a spatially dependent eddy

viscosity. This eddy viscosity is used in the

numerical solution of the time-averaged momentum

equations. The resulting solution is in terms

of velocities, pressure, and turbulence intensity.

The flow fields modeled are axisymmetric; the

orifice plates are infinitely thin with beta

ratios from 0.4 to 0.7. Reynolds numbers are

in the approximate range 10^ - 106

. The incoming

velocity profile at one pipe diameter upstream

of the orifice plate is varied to assess its

effect on meter performance. The results of

the calculations give such orifice flow features

as discharge coefficients for various tap

locations, vena contracta, points of minimum

pressure, and reattachment locations, and overall

pressure loss through the meter. The numerical

results are compared with available experimental

data, and the agreement between computed and

experimental discharge coefficients is within

4 percent. It is concluded that this type of

computer simulation can be extremely useful in

conjunction with experiments in future investigations of the performance of numerous types of

differential pressure meters.

Key Words: Closed conduit meter; differential

pressure; flow measurement; mathematical modeling;

meter performance; orifice meter; turbulence flow.

491
1. Introduction

There are two objectives in the present study. The first is to

test the feasibility of using turbulence modeling to study the flow

through orifice meters. The second is to establish a unified, comprehensive picture of orifice flow that will produce more reliable metering

with this widely used device.

Reliable and accurate flow meter performance becomes increasingly

important when, in our present world with its ever expanding population,

we envision equitable exchange, transmission and consumption of our

finite resources. An example of the economic impact that optimizing

flow meter performance can have can be taken from the natural gas

industry. Miller and Kneisel [l] 1 have shown that there is a significant bias in the measured values of flow coefficients for recently

manufactured orifice meters as compared with the published (and widely

used) values. Conservatively, the reported bias was more than 0.3

percent. Using this value, it was estimated [2] that in 1974 the daily

average error value associated with the uncertainty of orifice metering

natural gas amounted to $87,500 per day. Because orifice meters are

relatively inexpensive and hence widely used in industry the impact of

the effects of optimized orifice meter performance becomes more apparent.

In an earlier effort [3] we computed laminar orifice flow for a

variety of meter configurations. The present results for the turbulent

case include flow fields for the axisymmetric, incompressible flow

through four (4) different meters. In addition, the variations produced

by a range of velocity profiles and Reynolds numbers are described.

Critical to any effort directed toward optimizing orifice meter

performance is a thorough understanding of the flow field through the

meter and its interaction with the readout instrumentation. Furthermore,

it is essential to quantify the effects of well-known sources of variation such as upstream meter tube length, centeredness of the orifice

hole in the pipe, orifice lip shape and sharpness, orifice plate smoothness, orifice hole roundness, etc. To date, users are guided by recommended procedure and practice that have evolved over many years [4,5,6],

Orifice discharge coefficients have been tabulated for many meter and

pressure tap configurations. Values presented are the results of

averaging the massive amounts of data taken in experimental studies

over the past 80 years. In these studies, experimental control was not

uniformly proper and, as a result, variability is large and individual

effects such as those mentioned above cannot be determined. It is

therefore apparent that a new approach to orifice metering has to be

initiated and carried out according to proper measurement theory [7]

,

To do this, a dual effort is envisioned. One effort will consist of

conducting properly controlled experiments; the other will be producing,

via computer methods, the flow fields through meters. In this manner,

widely ranging parameters and meter variations can be introduced and

iBracketed numbers refer to references listed at the end of this paper.

492
evaluated using computer methods and, for selected cases, validation

experiments would demonstrate credibility. The results of this dual

approach should produce reliable flow measurements using orifice meters.

Orifice meter performance is based upon an obstruction to the fluid

flow in a pipe which is designed to produce a flow rate dependent change

in the fluid pressure across it. The general form of this obstruction

is a thin round plate with a hole in its center. The pressure difference

across this plate is monitored by means of a variety of schemes each

with its own advantages and disadvantages. The fluid pressures are

measured via pressure "taps" along the pipe wall. Figure 1 presents a

sketch of the flow through an orifice meter equipped with a particular

arrangement of taps. The salient features of the flow field are the

pressure distribution along the wall, the characteristics of the recirculating eddy downstream of the orifice plate, and the nature of the jet

flow through the orifice hole. Determining how these characteristics

change with the various factors affecting them is the central objective

of these efforts to reduce the variability attributed to the orifice

meter. Also significant in the operation of the orifice meter are the

positions along the pipe wall of the taps which measure the static

pressure difference across the orifice plate.

The four schemes most widely used in orifice installations are

corner, flange, so called "D-D/2," and vena contracta taps. Corner taps

(prevalent in Europe) are located in the corners produced by the pipe

wall and the up and downstream surfaces of the orficie plate. Flange

taps are placed one inch (2.54 cm) up and downstream of each surface of

the orifice plate. They have the advantage of being conveniently installed

via a radial hole drilled through flange discs that sandwich the orifice

plate in the pipe. Since for most large pipe sizes, flange taps are

located small fractions of a pipe diameter from the orifice plate, the

pressure difference they sense approximates that given by corner taps.

The major disadvantage with flange taps is that their location does not

scale with diameter according to the principles of geometric similitude.

Taps located one diameter up and one half diameter downstream from the

upstream surface of the orifice plate are referred to as D-D/2 taps.

The advantage of these taps is that they are displaced from the orifice

plate and give a smaller but "smoother" pressure difference, i.e., less

affected by pressure fluctuations than those obtained via the corner or

flange taps. Vena contracta taps are located one diameter upstream of

the upstream surface of the orifice and a variable distance downstream

from this surface. This variable distance is intended to align the

downstream tap with the minimum pressure which, at one time, was assumed

to occur at the vena contracta. Previous results [3,8] indicate that

the minimum wall pressure and the vena contracta occur at different

locations. In spite of this misalignment, the advantage of these taps

is that they render a smaller, but supposedly even "smoother" pressure

difference than that of the D-D/2 taps.

To properly assess orifice meter variability, consideration is

given: (a) to the primary device - the orifice meter and its associated

flow field and (b) to the secondary device - the readout system which

493
senses the pressure difference. Orifice metering practice will benefit

considerably when the combined variability of these two components of

the total variation is properly characterized.

The present study is to assess the variability of the primary device,

i.e., the orifice meter and its flow field. The particular turbulence

model that is used to simulate this flow field is the ke-model developed

at Imperial College, London [9]. This turbulence model is economical,

in wide use, and has given reasonable results in situations similar to

orifice flow [10,11,12].

2. Basic Equations

The momentum and continuity equations for turbulent incompressible

stationary flow are

p(q • V)q = - VP - Vx[u eff (Vxq) ] (1)

V • q = 0 (2)

in which q = (U, V) , where U and V are the mean velocity components in

the radial and axial directions in an axisymmetric cylindrical reference

frame; P is the mean pressure; p is the constant density; and Veff is

the sum of the laminar and turbulent viscosities. The turbulent viscosity,

y t

, is assumed to be a function of the turbulent kinetic energy, k, and

the dissipation rate, e, of k; i.e.,

V t = C..p k

2 /e (3)

where Cy = 0.09. The values of k and e to be inserted in (3) are

determined from the following transport equations written in axisymmetric

cylindrical coordinates (r,z):

n 8k 3k. 9 /eff 9k '

, 1 3 , ryeff 9k. , _ _ ... P(V

97

+ U

97} - 37 ("^lT 9l} + 7 37 ("7k- 37} + \

G " C

D

p£ (4)

„ /tt 3£ i tt 9e N 3 , y ef f 9e N ,13 ,TVe£f 3e, , p(v

37

+ u ^

= 37 37} + 7 37 (^7~ 97} +

cie g - c 2P \r (V

where ok

= 1.0, a £ = 1.3, CD= 1.0, Cj = 1.44, C2 = 1.92, and

494
G, 2[ (f)

2

+ (f)

2

+

(f)

2

, + [ f + f,

2

.

The justification for the values of the empirical constants is given

in [9].

3. Numerical Scheme

The SIMPLE finite difference scheme has been developed and

incorporated into the TEACH-T, Fortran computer code at the Department

of Mechanical Engineering, Imperial College of Science and Technology,

London, England. Since a complete description of TEACH-T is available

[13,14] and, also, of SIMPLE [15,16], only a brief review of the computer

code will be given here.

The system of equations (1) to (5) is finite differenced and solved

iteratively by underrelaxation. The convective terms in these equations

are differenced using a hybrid scheme [17] comprised of central and

conservative upwind differencing. At each iterative step, the finite

difference analogs of equation (1) are solved implicitly using a lineby-line procedure involving a tridiagonal matrix solver. The velocity

field resulting from this solution of the momentum equations for a given

iteration will probably not satisfy the continuity equation (2) . Using

this known (but probably incorrect) velocity field, equation (2) can be

transformed into an equation for the pressure correction required to

make the velocity field solenoidal. This pressure correction is calculated in the same implicit manner and is used to determine the final

velocity field for a given iteration. These velocities are then used in

the solution (by the usual implicit scheme) of equations (4) and (5) for

k and e. Finally, equation (3) for y t is updated and the next iteration

begins. The iterations proceed until the sum of the absolute values of

the residual mass and momentum sources is less than some predetermined

small value. This summation is performed separately for the mass flow

and each component of momentum, with the resulting sums to each be less

than some small percentage, 6, of the mass flow and largest component

of momentum, respectively, at the inlet to the computational test section.

4. Numerical Modeling of Orifice Flow

The computational test section containing the orifice plate is

shown in Figure 2. The mesh selected had 13 computational cells in the

radial direction and up to 68 cell axially. Variable mesh spacing was

used, with the radial cell dimension, Ar, only a function of r and the

axial cell dimension, Az, only a function of z. The variation in Ar

was from 0.05Ro to 0.10Ro , while that for Az was from 0,05Ro to 0.50Ro , where R0 is pipe radius. Cells were concentrated axially in the area

of the orifice plate and radially near the plate lip and pipe wall.

Normal velocities were specified along cell boundaries, and pressure,

turbulent kinetic energy, and dissipation rate were specified at cell

centers. An orifice plate of zero thickness was created by setting

axial velocities to zero along a strip of cell boundaries whose length

495
varied with 6 ratio. The inlet velocity profile was specified at a

distance of about 2R0 upstream of the orifice plate, while the outlet

profile was determined by setting axial gradients to zero. Inlet distributions of turbulent kinetic energy and dissipation rate were specified

via a pipe flow computation. This computation produced results which

satisfactorily agreed with available experimental data. For the orifice

flow computations, boundary conditions along the pipe wall were based on

the logarithmic law (i.e., the wall-function method [9]), and the radial

velocity and the radial derivative of the streamwise velocity were set

to zero along the axis. The value of the convergence criterion, 6, that

was chosen was five percent. Computation times on the NBS UNIVAC 1108

ranged up to 17 minutes, but were generally less than 10 minutes per

case.

5. Results and Discussion

The flow patterns through four orifice meters for values of 6, the

ratio of orifice hole to pipe diameter, in the range from 0.4 to 0.7 are

shown in Figure 3. The Reynolds number of 2 x 10 5 is based upon pipe

radius and average velocity. The inlet conditions (V,k,e) at a distance

of about 2R0 upstream of the orifice plate are based on the results of

200Ro -long straight, smooth pipe calculations using the same computer

program at the same Reynolds number. The exit conditions from these

pipe calculations were in good agreement with available experimental

data and were thus used to simulate fully-developed flow entering an

orifice meter. In what follows, all velocities are nondimensionalized

by average inlet velocity, Vg , pressure by Vq 2

, and all lengths by R0 thus producing R = r/R0 and Z = z/Rc

. To exhibit the flow patterns

through the orifice plate, the computational test section is only shown

axially for six radii; the actual computed test section extends for 14

to 17 radii depending on 3 ratio. In these plots are shown segmented

streamlines produced by the short line segments drawn from a point at

the center of each computational cell tangent to the local velocity

vector. The length of each segment is constant. Several radial rows

of cells located at axial locations adjacent to the plate are omitted

for clarity. With these exceptions, Figure 3 exhibits the general

distribution of cells in the portion of the flow field shown.

Shown via the segmented streamlines in Figure 3 is the way the

pipe flow is turned through the orifice hole and forms the jet flow

downstream of the plate. The shape of the eddy downstream of the plate

is also evident with its radial and axial dimensions perceived via the

streamline that could be drawn from the orifice lip to the reattachment

point on the pipe wall. The dynamics of the flow within this eddy can

also be seen.

The streamwise distributions of the mean static pressure along the

pipe wall and the centerline are shown in Figure 4 along with the centerline velocity. Evident here are the locations of the points of maximum

centerline velocity, minimum centerline and wall static pressures, and

the differences between centerline and wall pressures. From such distributions, one is able, with any particular choice of pressure taps, to

496
determine the corresponding discharge coefficient, C<j given by

-Vi

a

1*

2B 4 Ap

where Ap is the upstream - downstream pressure difference taken at the

respective tap locations. Discharge coefficients will be presented

below for particular tap configurations and compared with published

values.

Radial distributions of the streamwise component of velocity,

plotted at six axial locations, are shown in Figure 5. The inlet

profile plotted is the specified power law profile whose l/9th exponent

was determined via the pipe flow computation noted previously. Profiles

adjacent to the orifice plate are shown and exhibit the flow into and

out of the hole in the plate. The profile downstream of the plate

shows that the velocity distribution in the jet flow is not uniform.

In fact for the smaller B's, the maximum velocity in the profile is

located, not on the pipe centerline, but off of it, in the flow adjacent

to the orifice lip where the axial pressure gradients are large - an

effect that has been observed experimentally [18] . Velocity profiles

are also plotted at the maximum centerline velocity location, near the

reattachment point, and at the outlet of the computational test section.

This outlet profile is noted to have developed into one closely

resembling that at the inlet.

The axial location of the vena contracta, the point of maximum

orifice jet convergence, is found from radially integrating velocity

profiles downstream of the orifice plate. This location is where the

orifice jet radius is minimized. This minimum jet radius is then taken

as the vena contracta radius, Rv .c> and the axial location is considered

specified to within the local axial grid spacings and the tolerances

applied to the calculated results.

Figure 6 presents plots of the streamwise distribution of the shear

stress at the pipe wall. The plots show the axial extent of the recirculating eddy downstream of the orifice plate by virtue of the sign

change at the reattachment point.

The turbulent intensity, I, which is proportional to the square

root of the turbulent kinetic energy normalized by the square root of

the mean kinetic energy, is plotted against streamwise coordinate in

Figure 7. Shown here are the distributions along the wall and the pipe

centerline. The peaks in the wall intensity distributions are of

interest in that at these locations turbulent effects can be considered

locally significant relative to the mean flow dynamics. These peaks

occur adjacent to the orifice plate and in the region near the point

of reattachment. In fact, the turbulent intensity values near the

point of reattachment attain values which exceed scale limits and are,

therefore, omitted from these graphs.

497
That peaks in the turbulent intensity at the wall occur adjacent to

the orifice plate are interesting in that it is in these regions where

it is common practice to measure the pressure for the determination of

flow rate. It has been well established that pressure pulsations can

significantly limit the accuracy and precision of "head-type" meters by

the way they influence the pressure measuring instrumentation [19,20,21].

For example, the error attributed to pulsations is related to the ratio

of the streamwise component of the turbulent velocity to the average

streamwise velocity. This error, which is termed the square root error,

is such that the measured flow rate is greater than the actual. The

value of the error depends upon the nature of the pulsation. For a

single frequency of pulsation, the time averaged square root of the

pressure difference which is read is, where overbars are to indicate

time averages,:

and where Apr , Apa , and Ap denote, respectively, the recorded, the

oscillation amplitude, and the true mean differential pressures. This

relationship applies for small ratios of Apa to ApQ . It is apparent

that to reduce this square root error, that a small amplitude of pressure pulsation is preferable, i.e., the taps should not be placed in

regions where there are large pressure fluctuations.

Since pressure pulsation intensity is related to the square of the

intensity of the streamwise component of the pulsating velocity, the

present computer solutions can, in principle, be used as a guide. It

is conceivable that an optimal tap location might be found where both

the mean pressure difference across the orifice plate is maximized and

the detrimental pulsation effects are minimized. Judging from Figure 7

one would want to place taps away from regions where the intensity

distribution along the pipe wall is peaked. Figure 7 also illustrates

that the centerline values of turbulent intensity exhibit an increase

downstream of the reattachment point. This increase is also seen in

the experimental results of Turner and Lightning [22],

The effects of upstream velocity profile were demonstrated for the

3 = 0.7 orifice in Figures 8-12. In these, we have placed at the inlet

section three different velocity profiles to span a wide range possible

for axisymmetric flows. The average flow rate and Reynolds number are

the same for all three profiles. In Figure 8 are shown the segmented

streamline patterns for a portion of the flow field computed. In 8 (a)

is an admittedly unrealistic parabolic profile, in 8 (b) the realistic

l/9th power law profile, and in 8 (c) an admittedly unrealistic uniform

profile. The figure shows that the streamwise length of the large

recirculating eddy downstream of the orifice plate is increased as the

velocity profile approaches the uniform one.

498
It is also noted that, for the parabolic case, a small reversed

flow occurs in the corner produced by the upstream surface of the orifice

plate and the adjacent pipe wall. This reversed flow is undoubtedly due

to the presence of an eddy trapped in this corner and having sufficient

momentum to produce the small but visible reversed flow. Actually,

several radial rows of cells were not plotted for reasons of graphical

clarity at axial locations adjacent to the orifice plate. These omitted

cells confirm the presence of this eddy upstream of the plate. Figures

8(b) and 8(c) indicate that no such eddy is evident in the same corner;

the omitted cells in this region show no effects of reversed flow.

Figures 8(b) and 8(c) are noted to be quite similar. While this observation appears to indicate that these two profile variations do not

change the fluid flow pattern, it shall be found in what follows that

the detailed features of the two flows are different. More important

are the differences found in the discharge coefficients for the two

flows

.

Figure 9 presents streamwise distributions in the B = 0.7 meter of

centerline and wall static pressures and centerline velocity. It is

seen here that while the maximum values for centerline velocity are

essentially the same, the pressure distributions show significant

differences. The largest difference is noted between the parabolic

and uniform profiles. Comparing the wall pressure distributions for

the l/9th and the uniform profile, differences are found both upstream

and downstream of the plate. The increased inertial effects of the

uniform flow elevate the pressure levels upstream of the plate relative

to those of the l/9th profile. Downstream, the uniform flow calculation

exhibits reduced pressure levels. The head loss for the meter with the

parabolic flow is the smallest of the three while those of the l/9th and

uniform profiles are essentially the same.

Streamwise velocity distributions for the 3 = 0.7 meter with the

three different inlet velocity profiles are shown in Figure 10. Here

the different inlet profiles, with constant average velocities, are

clearly shown. The velocity profiles adjacent to the orifice plate

indicate the variation in velocity across the orifice jet, the edge

of which is located at R = 0.7. It is apparent that the orifice jet

velocity varies markedly in the parabolic case while in the other cases

the velocity is quite uniform over about 80 percent of the jet radius

with significant variation occurring over the remaining 20 percent.

Further downstream, the differences between the three cases are reduced

further due to turbulent diffusion. At the outlet, the three profiles

are practically the same.

The fluid shearing stress, xw at the pipe wall is shown in Figure

11 for the three profiles. Here, the parabolic flow produces a signifcantly different distribution from the other two. The l/9th and uniform

distributions exhibit slight differences in the region upstream of the

plate and otherwise are very similar. The orifice jet reattachment to

the pipe wall located via the zero stress point downstream of the plate

lies closest to the orifice plate for the parabolic profile. The

499
reattachment point for the uniform flow lies slightly downstream of

that for the l/9th profile.

In Figure 12 are shown streamwise distributions for turbulent

intensity. Again, the parabolic distribution stands out as the most

different of the three with increased levels of turbulent intensity

along the pipe wall upstream of the plate. In this region just upstream

of the orifice plate, a large peak in the intensity distribution is

observed. This is probably the result of the reduced velocity and

reversed flow resulting from the presence of an eddy in this corner.

Intensity distributions along the pipe centerline are quite similar for

all three inlet profiles.

In Table 1 are presented comparisons of the computed discharge

coefficient for two tap configurations i.e., corner and D-D/2 with

corresponding values taken from an ISO Draft International Standard

(ISO/DIS 5167) [6]. Table 1 shows that for constant diametral Reynolds

number, Rep = A x 10 5

, the computed discharge coefficients for corner

and D-D/2 taps behave quite differently. For corner taps, the discharge

coefficients decrease monotonically with increasing S and constant inlet

velocity profile. The corresponding ISO values are noted not to follow

this trend. For each 3> the deviations occurring between the sets of

values is nominally 2 percent or less. The effects of inlet velocity

profile on the 3 = 0.7 meter are considered especially significant since

the maximum variation is 23 percent for corner taps. The D-D/2 tap

configuration produces computed coefficients which, with increasing 3,

first decrease and then increase with constant inlet profile. It is

noted that this trend is not duplicated in the ISO results. However,

the differences here are small and may be insignificant. The effects

of profile variations on discharge coefficients can be estimated from

the computed values given. For D-D/2 taps, the maximum variation

attributed to the profiles examined in the 3 = 0.7 meter is 27 percent.

For both tap configurations, the discharge coefficients are found to

decrease as the velocity profile approaches uniform flow. At 3 = 0,5,

it is noted that for both corner and D-D/2 taps, the reduced Reynolds

number results indicate that the discharge coefficients increase

slightly. In Table 2, discharge coefficients obtained via computation

are compared with tabulated results for flange and D-D/2 taps taken

from the ASME Fluid Meters [4]. The computed results for flange taps

were produced by assuming a pipe diameter of 2 in. (^5 cm). The flange

taps comparison duplicates that noted from Table 1 for the case of

corner taps, i.e., the monotonically increasing trend in ASME values

follows that for the computed results only for 0,5 £ 3 £ 0,7, However

»

the difference between the computed flange tap coefficients for 3 = 0,4

and 0.5 is too small to be significant. As seen in Table 1, variations

in inlet profile for 3 = 0.7 produce significant variations in flange

tap coefficients. Trends similar to those noted in Table 1 are seen in

the ASME values for D/D/2 coefficients.

In view of the changes produced here by the different velocity

profiles, it seems pertinent to note that the oft repeated and conventional

process of calibrating orifice meters can lead to systematic errors.

500
When a meter is removed from its "native" pipeline and sent to a "foreign"

one for calibration, the differences in the inlet velocity profile conditions are not considered. If, for example, other sources of meter

variation such as upstream piping roughness, roundness, or vibration can

be neglected and inlet velocity characteristics are the major source of

differences, the present results indicate that such differences can be

important. In this regard, one can envision that a more precise calibration for an orifice meter could, in principle, be achieved by computer.

These calibrations by computer might be done by precisely determining

the inlet velocity profile and meter geometries, and then having the

calibration done via computer without removing the meter from its "native"

pipeline.

The present results permit tabulation of the salient features of

turbulent orifice flow and their respective locations in the flow field.

These individual features are shown in Table 3. Here, for constant

Rej) = 4 x 10 5 and the l/9th profile, the location of the vena contracta

as determined by mass flow integrations across the jet appears to lie

furthest downstream for the 8 = 0.5 meter. The radius of the orifice

jet at the vena contracta increases with 8 and is, typically, 90 percent

of the orifice radius. The maximum centerline velocity decreases with

increasing 8 ratio from a value of about 10 at B = 0.3 to a minimum of

about 3 at 8 - 0.7. The location of this maximum centerline velocity

occurs at X = 0.75 independent of 8 and lies downstream of the vena

contracta. This is due to the distribution of velocity in the orifice

jet. Along the pipe centerline, the static pressure decreases markedly

from that at the orifice plate for the lower 8 ratios. The minimum

centerline static pressure location is nominally one pipe radius downstream of the plate. Since liquid cavitation effects would begin wherever the local pressure reached vapor pressure levels, the location of

the minimum static pressure is one place where one could expect incipient

cavitation. Another place would be wherever mean pressure levels were

low and the turbulent component of the pressure was sufficiently large

to produce instantaneous values at the vapor pressure level. In this

event one would expect sporadic cavitation to occur. Given the distributions of pressure in these meters, the prospects for sporadic cavitation

could exist in or adjacent to the large recirculating eddy downstream of

the orifice plate. The reattachment location, Xr, gives the streamwise

length of the large recirculating eddy downstream of the orifice plate.

This eddy length decreases with increasing 8 ratio. The location of the

minimum static pressure along the pipe wall, Xpmw is also found to

decrease with increasing 8. It is also noted that the minimum static

pressure along the pipe wall occurs at or upstream of the minimum pressure

on the centerline.

To assess the accuracy of the computed results, it is necessary to

compare them with experimental values. The experimental results

available [4] for the overall pressure loss across thin-plate orifices

are shown in Figure 13. The agreement is considered good. At 8 = 0,7,

the three values shown for the present study represent the effects of

the different inlet velocity profiles. The parabolic value lies below

the line, the l/9th profile point lies just above the line, and the

501
uniform profile point gives the maximum loss.

An interesting comparison of the present computed values to graphical results given in [4] is shown in Figure 14. Here, spatial ranges

for the position of minimum static pressure along the pipe wall are

presented as they depend upon B ratio. These were obtained by averaging

data from "numerous experiments by different investigators over a wide

range of pipe sizes of 2 in or larger." The resulting range of minimum

pressure positions for any B ratio is interpreted to be due to the wide

range of Reynolds numbers and other pertinent parameters the graph is

undoubtedly intended to encompass, since no ranges are specified. As

stated further in [4], it is "the general assumption that this plane of

minimum pressure coincides with that of the vena contracta." The present

results for the minimum pressure along the pipe wall are observed to fall

considerable short of the ranges presented for the experimental data. In

addition, the computed results for vena contracta positions are graphed,

For the range of B ratios presented and, as shown in Table 3, the vena

contracta lies downstream of the minimum wall pressure for the higher

values of B, but it lies upstream for the lower values. Thus, the graphed

results for the presently computed values indicate the degree to which

the conventional assumption regarding the coincidence of minimum pressure

and vena contracta points is valid. Concurrently, it is concluded that

presently unexplained discrepancies exist between the experimental data

and the computed positions for these points. It is expected that further

experimental investigation of these features will properly resolve these

issues.

Conclusions

It has been demonstrated that the k,e - turbulence model can

provide a reasonably accurate description of the important features of

turbulent, incompressible flow through an axisymmetric , thin-plate

orifice meter. The effects of B ratio variation are described through

the range typically used in metering practice. A wide range of inlet

velocity profiles is used to determine this effect on a B = 0.7 meter,

and a limited range of Reynolds number is examined for a B = 0,5 meter.

The present results include radial and axial distributions of the

fluid velocities and pressure anywhere in the flow field. Consequently,

comparisons can be made with a wide variety of measurable quantities.

Such comparisons are made for quantities such as discharge coefficients,

pressure distributions, and the locations of salient features in the flow

field. The comparison of the computed discharge coefficients with

published values is considered reasonable. Generally, the trends found

in discharge coefficients parallel those published. Qualitatively, good

agreement is also found between computed and published axial pressure

distributions through these meters. However, quantitative discrepancies

are noted between computed and published values for the locations of

salient features of the flow such as minimum pressure points and the

vena contracta. The present computations have extended the range of

earlier efforts which have demonstrated that the vena contracta and the

points of minimum pressure along the pipe wall are not aligned, It is

502
shown here that for certain $ ratios, 0 > 0.6, the vena contracta lies

downstream of the point of minimum wall pressure while for £ < 0.6 the

vena contracta lies upstream of this point.

The present results show that numerical turbulence models are

capable of describing the complete orifice flow field and corresponding

meter performance. As such, computational methods have to be considered

a feasible and fertile complement to similarly directed theoretical and

experimental analyses. Furthermore, these methods are not intended to

be limited solely to orifice-type head meters. It seems only logical

to include other head meters such as nozzles and venturies, as well as

other types of meters operating in a wide variety of turbulent flow

conditions.

It is also concluded that, while there does exist a considerable

volume of experimental data pertaining to orifice meter characteristics,

further efforts are now required to firmly establish realistic tolerances

on much of the so-called "well-established" results such as discharge

coefficients and the locations of salient flow features. It is toward

this end that the full complement of numerical methods in conjunction

with the most recent developments in experimental measurement techniques

should be directed.

503
Acknowledgements

The authors gratefully acknowledge contributions of a wide variety

from several persons at the National Bureau of Standards. The efforts

of Ms. E. F. Moore, in maintaining the organization of and running the

computer programs and plotting routines, enabled this phase of the

present study to proceed with high efficiency. In addition, her efforts

in reducing the computed results to proper form for tabulation and

comparisons of the results are greatly appreciated. We are indebted

for several helpful discussions with Mr. L. K. Irwin and Mr. K. R. Benson.

The secretarial assistance provided by P. Beall, P. Gurewitz, and

J. Preet is also greatly appreciated.

504
References

[1] Miller, R. W. and Kneisel, 0. A., Comparison Between Orifice and

Flow Nozzle Laboratory and Published Coefficients, ASME Journal of

Fluids Engineering} Vol. 96, p. 139-149, June 1974.

API/Committee on Gas Measurement internal document, November 1975.

Mattingly, G. E. and Davis, R. W. , Numerical Solutions for Laminar

Orifice Flow (submitted, June 1976 for publication in the ASME

Journal of Fluids Engr.)

Bean, H. S., ed, Fluid Meters - Their Theory and Applications3 6th ed, ASME, New York, 1971.

American Gas Association - Report No. S. Orifice Metering of

Natural Gas3 Arlington, Va, 1972.

Measurement of Fluid Flow by Means of Orifice Plates, Nozzles, and

Venturi Tubes Inserted in Circular Cross-sectional Conduits

Running Full, ISO Draft International Standard 5167 , April 1976,

Pontius, P. E., Notes on the Fundamentals of Measurement and

Measurement as a Production Process, NBSIE 74-5453 1974.

Wilson, M. P. and Teyssandier, R. G. , The Paradox of the Vena

Contracta, Trans ASME3 Sept. 1975, pp 366-370.

Launder, B. E. and Spalding D. B. , The Numerical Computation of

Turbulent Flows, Computer Methods in Applied Mechanics and

Engineering3 Vol. 3, pp 269-289, 1974.

[10] Proceedings of Symposium on Turbulent Shear Flowss University Park,

Penn, April 18-20, 1977.

[11] Kubo, I. and Gouldin, F. C. , Numerical Calculations of Turbulent

Swirling Flow, ASME Journal of Fluids Engineerings Vol, 97, p, 310,

Sept. 1975.

[12] Moon, L. F., and Rudinger, G. , Velocity Distribution in an Abruptly

Expanding Circular Duct, ASME Journal of Fluids Engineerings Vol. 98, p. 226, March, 1977.

[13] Salimonu, Dauda 0. , Mathematical and Programming Details of the

TEACH T and L Recirculating Flow Code, Argonne National Laboratory

Technical Memorandum ANL-CT-76-22, October 1975,

[14] Gosman, A. D., Khalil, E. E., and Whitelaw, J, H, , The Calculation

of Two-Dimensional Turbulent Recirculating Flows, Proceedings of

Symposium on Turbulent Shear Flowss University Park, Penn, p, 13,35,

April 18-20, 1977.

505
[15] Caretto, L. S., Gosman, A. D. , Patankar, S. V., and Spalding, D. B.,

Two Calculation Procedures for Steady, Three-Dimensional Flows

with Recirculation, Proceedings of the Third International

Conference on Numerical Methods in Fluid Mechanics, ed. by Henri

Cabannes and Roger Temam, Vol. II, Springer-Verlag, New York, p. 60,

(1973)

.

[16] Patankar, S. V., Numerical Prediction of Three-Dimensional Flows,

Studies in Convection, Vol. 1, ed. by B. E. Launder, Academic

Press, New York, p. 1, (1975).

[17] Spalding, D. B., A Novel Finite Difference Formulation for

Differential Expressions Involving Both First and Second

Derivatives, International Journal for Numerical Methods in

Engineering, Vol. 4, pp 551-559, (1972).

[18] Pearson, J., An Experimental Investigation of Turbulent Flow

Through Orifice, Masters item submitted to the Dept. of Mech,

Engr. and Appl. Mech., University of Rhode Island, 1975.

[19] Sparks, C. W. , A Study of Pulsation Effects on Orifice Metering

of Compressible Flow, ASME Flow Measurement Symposium, Pittsburgh,

Pa., pp 124-138 (1966).

[20] Miller, R. W., Precise Measurements of Differential Pressure When

Calibrating a Head Class Flow Meter, Trans ASME, Dec, 1970,

pp 742-757.

[21] Watanabe, N. and Komiya, K. , Pulsating Gas Flow Measurement by

Orifice Meter, Bulletin of the National Research Laboratory of

Metrology Series No. 26, April 1972, pp 22-27.

[22] Turner, J. T. and Lightning, G. , Measurement of Mean Flow and

Turbulent Structure in an Axisymmetric Pipe Flow with High Initial

Shear, Proceedings of Symposium on Turbulent Shear Flows,

University Park, Pa., p. 8.29, April 1977.

506
Table 1. Comparisons of discharge coefficients with ISO [6] values

6 Re

D

Inlet* Profile

Ccorner

CD-D/2

Computed ISO Computed ISO

0.4 4-10 5 1/9 .616 .602 .615 .600

0.5 4-10u 1/7 .609 .609 .610 .609

0.5 4- 10 s 1/9 .607 .604 .609 .605

0.6 4-10 5 1/9 .602 .606 .616 .609

0.7 4-10 5 P .706 .788

0.7 «.10s 1/9 .591 .604 .637 .612

0.7 4. 10 s U .573 .622

"The inlet profile is that imposed at the entrance of the computed test section: "1/9" indicates a pover law profile with this exponent, "P" denotes a parabolic and "U" denotes a uniform profile.

Tabl« 2. Comparison of discharge coefficients for flange and D-D/2 taps [4]

Re

D

Inlet* flange

** CD-D/2"

6 Profile Computed ASME Computed ASHE

0.4 4 -10s 1/9 0.613 0.603 0.615 0.599

0.4 I>-10K 1/7 0.610 0.618 0.610 0.615

0.5 4 -10s 1/9 0.608 0.607 0.609 0.604

0.6 4-105 1/9 0.616 0.611 0.616 0.610

0.7 4-105 P 0.783 0.788

0.7 4 -10s 1/9 0.636 0.610 0.637 0.615

0.7 4-105 D 0.621 0.622

*The inlet profile is that imposed at the entrance of the computed test section. "1/9"

a power law profile with this exponent, "P" denotes a parabolic, and "U" denotes a uni

profile.

**To determine these coefficients, a 2 inch pipe size (" 5 cm) is assumed.

507
Table 3. Salient features and their locations* in turbulent orifice flow

Inlet U) (2) O) (4) C5) (6) (7) (8) C?) (10

0 Profile Xv.c. R

v.c.

VmaxX

v.m. Vt ^mXn Xpm h

X

pmw

0.4 4.10 s 1/9 0.46 0.37 9.93 0.75 -19.7 -49.7 1.05 4.75 1.05

0.5 4.10" 1/7 0.46 0.45 6.35 0.75 -8.12 -19.7 0.85 3.90 0.65

0.5 4.10 s 1/9 0.55 0.44 6.37 0.75 -8.08 0.9.8 1.05 4,12 0.65

0.6 4.10 s 1/9 0.46 0.53 4.29 0.75 -3.71 -8,59 0.85 3.21 0.45

0.7 4.10 s P 0.26 0.65 2.97 0.55 -1.39- -2.59 0.65 1.61 0.30

0.7 4.10 s 1/9 0.38 0.63 2.97 0.75 -1.79 -3.79 0.85 2.23 0.30

0.7 4.10 s U 0.38 0.63 2.99 0.75 -1.79 -3.96 0.85 2.32 0.30

All radial distances are given in pipe radii from the center of the pipe. Axial distances are given in

pipe radii from the orifice plate; upstream distances are negative; downstream are positive.

(1) The inlet profile in that imposed at the entrance of the computed test section: "1/9" indicates a power law profile with this exponent, "P" denotes a parabolic profile, and "U" denotes a uniform profile.

(2) X is the location of the vena contracta.

v.c.

(3) R is the radius of the orifice jet at the vena contracta.

v.c.

(4) V is the maximum centerline velocity. max

(5) X is the location of the maximum centerline velocity. vm

(6) ^p£t

* s tne centerline static pressure at the location of the orifice plate.

(7) P . is the centerline static pressure at the minimum pressure location. min

(8) X is the location of the minimum centerline static pressure. pm

(9) X^ is the location of the orifice jet reattachment to the pipe wall.

(10) X is the location of the minimum static pressure along the pipe wall, pmw

508
509
510
g

Q RjF ICE FL6N BJETfV-O . 4 . R E = 2 * 10

x5

R

= = = = = = Uf7 5 = =

1 1 i \ \ i /

l \ \ s = = r

- >• -« ^ / / \ \ N *» = = = = ==: = - s: <;

0 I

0

R

0

R

QRIFICE FLOW BETfl:=0.5, RE=2*10**5

_ - - »- /

0 1

Iff? 5 = S = S H = S 5 5 5 5 = = = S U \ X % - - „ , , >NV v^ - - - ~ - Ji;: = = = = = = = = = 5S!j =? 2? _> =

1 1 1 1 1 1 —r~ 3 4 5 6

0RIFICE FLQW BETn^O-6, RE=2*10**5

= = = = == ttil

0

5^5 = = = =•=• = = = 4. > _T* _> ==

-i r

0

R

QRIFICE FLOW BETflr0.7, RE=2*10**5

= = =

0

i^;= = £ / j s = = = = = = E

-i r

Fig 3. 8 effects on orifice flows.

511
P .V

12

-20

-36

-52

ORIFICE FLOW BETR=0.4. RE:2»I0"«5. T = 0 M I N I M I H4-H

I I I I I I I I I I I I

1 1 1 1 H

1 1 \ 1 1 1 (-

0 12 3 4 5 W6 7 8 9 10 11 12 13

Z (O CENTERL 1NE PRESSURE.* WALL PRESSURE . + CENTERL INE VELOCITY)

H IS 16 ^T7

ORIFICE FLOW BE T fl; 0 . 5 . RE = 2«10«5. T = 0

P .V

16

-24

*-H—I t

1 1 1 1—t—)

1 1-

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Z (O CENTERL1NE PRESSURE.* WALL PRESSURE . + CENTERL INE VELOCITY)

ORIFICE FLOW BETFU0.6. RE = 2«10"S. T = 0

1 1 1 1 1 1 1 1 h

P . V -S

10

•15

0 12 3 4 1

' 6 ' T 8 9 10 11 12

Z (O CENTERL I NE PRESSURE.* WRLL PRESSURE. + CENTERL INE VELOCITY)

13 14

P.V

ORIFICE FLOW 8ETA;0.7. RE = 2«M0«5. T = 0

^ I

1 1 1 1 f

0 1 2 3 4 S 6 T 8 9,10 11 12

Z iCD CENTERL I NE PRESSURE.* WALL PRESSURE. + CENTERL I NE VELOCITY)

13 14

Fig 4. 6 effects on the centerline and wall static pressures

and centerline velocity distributions.

512
0

0.2

0-4

0.6

0.8

1 .0

0

0.2

0-4

0.6

0.8

1 .0

0

0.2

0.4

0-6

0.8

1.0

0

0.2

0-4

0.6

0.8

1 .0

ORIFICE FLOW BETA=0.4. RE = 2«10«5.

T=0

2 0 2 4 6 8 10

V ORIFICE FLOW BETPt0.5. RE = 2»I0"5.

T = 0

-2-10 1 v4 5 6 7

ORIFICE FLOW BETH;0.6. RE-2«1C«"5.

T = 0

1 0

V ORIFICE FLOW BE1H=0.7. RE = 2" 1 0--5 . T = 0

0

0-2

0.4

0-6

0.8

1 .0

ORIFICE FLOW 8ETA-0.4. RE-2»10«5.

T=0

8 10

ORIFICE FLOW 8ETRr0.5. RE = 2«10"S.

TrO

ORIFICE FLOW BETP-0.6. RE = 2«10«5.

T = 0

•10 12 3 V I * I NLET . X UPSTREAM OF PLRTE. O DOWNSTREAM OF PLATE I

0

0-2

0.4

0.6

0.8

1 .0

ORIFICE FLOW BETA=0.7. RE=2»10«S.

T = 0

0 1 2

V I A VENA CONTRACTA

.

O REATTACHMENT . + OUTLET 1

Fig 5. 6 effects on radial profiles of the streamwise velocity

component

.

513
0 018 ORIFICE FLOW BE T fl = 0 4 . RE=2«10-"S. T = 0

xzemtw***-^*-'* * * * * * *

9 10 II 12 13 |4 IS

ORIFICE FLOW BE Tfl-0 • S . RE;2-I0.«5. TrO O.OIO

0 .005

0.000

0.005

0.010

*-xxx xxxxxx xxxx

0 I 2 3 4 5 6 7 8 9 10 1 1 12 13 14

ORIFICE FLOW BE Tfi = 0 .6 . RE-2-I0--5. TzO 0.005

0.003

0.001

0-001

0.003

1 2 3 4 S 6 7 B 9 10 II 12 13 14

ORIFICE FLOW BETflzO .7 . REr2-10--5. T = 0 0-004

0-002

0.000

•0-002

-0.004

SIS \xs ^ ^ /^

Fig 6. 6 effects on the wall shearing stress distribution.

514
0RIF1CF FLOW BUfi.0.4. RE-2»IO»»5. 1:0

0 I 2 3 _ 4 S 6 7 6 9 10 II 12 13 14

Z ( O CENTERL INE I . A WfiLL I 1

ORIFICE FLOW BE TflrO .5 . RE = 2.I0"S. 1=0

I .5

ORIFICE FLOW BETRr0.6. RE = 2«10"S. r=0

1 -5 ,

ORIFICE FLOW 8ETfiz0.7. RE:2»I0«»5. TzO

1-5 i

I lO CENTERLINE I . * WALL 1J

Fig 7. $ effects on the centerline and wall turbulent intensity

distributions.

515
0

R

ORIFICE FLGH BETR^O.7, RE=2*10**5

0

{{ /IJ/S S = ; S S H E i = | 5

(a)

0

R

0

ii::=^^js jrj:f ; = = = = = =

1 —"T 1 1 1 1 1 1-

(b)

0

R

0

= = = = === \i Vs- rNviri^s-S^SS = = = =

= = = = === ^JU: = =? > tr j > 2" JT J= ? H H = = = = = ——~ i —*"

i " 1——

T* i "* ~* r

~" "

\

t~ —t —j i "J" 1 2 3 4 5 6

(c)

Fig. 8 Inlet velocity profiles effects on a B = 0.7 orifice meter,

The profiles are: (a) parabolic, (b) "l/9"th power law,

and (c) uniform

.

516
ORIFICE FLOW BETflzO . 7 RE=2»10«»5. T;0

P .V

-3

-5

1 1 1 1 1 \ 1 h

(a)

O 1 2 3 4 5 6 7 8 9 10 11 12 1314

Z lO CENTERLINE PRESSURE.* WALL PRESSURE. + CENTERL 1 NE VELOCITY)

ORIFICE FLOW BE TfirO • 7 . RE=2«10»«5. TrO

< 1 1 1 1 M (-

P .V - 1

-3

(b)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Z [O CENTERLINE PRESSURE.* WALL PRESSURE. + CENTERLINE VELOCITTI

ORIFICE FLOW BE Tfi = 0 • 7 . RE = 2»10--5. T = 0

3 , -^-H-H-H+f+++.

< 1—I

1 1 h

P .V

-3

(c)

01' 2 '3 4 5 6 7 8 9 10 II 12 13 14

Z tO CENTERLINE PRESSURE.* WALL PRESSURE . + CENTERLINE VELOCITY)

Fig. 9. Inlet velocity profile effects on the centerline and wall

static pressures and the centerline velocity distribution

for a 6 = 0.7 orifice meter. The profiles are: (a) parabolic,

(b) "l/9"th power law, and (c) uniform.

517
Fig. 10. Inlet velocity profile effects on radial profiles of the

streamwise velocity component in a B = 0.7 orifice meter.

The profiles are: (a) parabolic, (b) "l/9"th power law,

and (c) uniform.

518
ORIFICE FLOW BE T Rz 0 • 7 . RE=2«10««5. T = 0 0-004

0-002

0-000

-0-002

-0-004

(a)

^XXX X—X—X—X—X—X—X—X X X

5 6 7

Z 0 12 3 4

ORIFICE FLOW BETAzO-7. RE = 2»10"5. T:0

6 9 10 11 12 13 14

0-004

0 .002

0 .000

-0-002

-0-004 0123456787

ORIFICE FLOW BE Tfi; 0 . 7 . RE=2"10«S. T = 0

Ni/ xiX ^/ \i/

9 10 11 12 13 14

0 .004

0-002

0 .000

-0 .002

-0-004

(c)

***** XXXXXXXXXX

2 3 4 5 6 7

Z 8 9 10 11 12 13 14

11. Inlet velocity profile effects on the wall shearing stress

distribution in a 6=0.7 orifice meter. The profiles are

(a) parabolic, (b) "l/9"th power law, and (c) uniform.

519
Fig. 12. Inlet velocity profile effects on the centerline and wall

turbulent intensity distributions in a 8 = 0.7 orifice meter.

The profiles are: (a) parabolic, (b) "l/9"th power law,

and (c) uniform.

520
OvEILALL P*EJJU»E LOSI AdOSI TBIK-PtATt OmFICEJ

(Per cent of mixlmurn differential pressure)

Fig. 13. Comparison of computed and experimental results for the

overall pressure loss across thin plate orifices. Symbols

A, 0, and D denote previous results [3]; denote present

results

.

521
Re = 2xlOtt X Minimum wall pressure

& Vena contracta location

Re = 2xl0 5 0 Minimum wall pressure

O Vena contracta location

Fig. 14. Comparison of computed and experimental results for the

locations of minimum wall pressure and vena contracta in

thin plate orifice flows.

522
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

STUDIES OF PULSATING INCOMPRESSIBLE FLOW

THROUGH ORIFICE METERS

R. A. Bajura and M. T. Pellegrin

Department of Mechanical Engineering and Mechanics

West Virginia University

Morgantown, West Virginia 26506

The differential pressure-flow relationship for standard ASME concentric sharp-edged orifice meters subjected to

pulsating incompressible flow was investigated experimentally

and analytically. Tests were conducted with water at pipe

Reynolds numbers between 8,000 and 24,000. Strouhal numbers

of pulsation were varied between 0 and 1.8. The source of

pulsation was located 15 diameters downstream of the orifice

and provided flow pulsation amplitudes of up to 30% of the

mean flow with differential pressure pulsation amplitudes of

up to 250% of the mean differential pressure across the

orifice. Three orifices with beta ratios of 0.35, 0.50 and

0.70 were used in the tests. A vortex shed from the edge of

the orifice during pulsatile flow distorts the downstream

flow channel as the vortex is convected away from the orifice.

A marked distortion of the orifice flow channel occurs for

pulsation conditions where the wavelength of the pulsation

is approximately equal to the bore diameter of the orifice.

The effect of the inertia of the fluid mass between pressure

taps was determined over a range of pulsation Strouhal numbers.

The effective discharge coefficient of the orifice decreases

during pulsatile flow conditions. An analytical model which

included the effects of fluid inertia and the increased

friction losses which occur during pulsatile flow was

developed and compared with the experimental data.

Key Words: Pulsating flow measurements; orifice meters; flow

metering error; pulsations; flow oscillations; jet flow;

vortex; differential pressure; turbulence.

1. Introduction

Orifices are the most common differential producers used in industrial

flow metering because of their ease of installation, low cost, accuracy,

and the interchangeability of orifice plates without the need for recalibration. The total flow metering system is comprised of three parts. The

first part, or primary element, consists of the orifice plate and the re-

• mainder of the metering run. The second part, or secondary system, consists of the impulse piping, the differential pressure sensor, and the

associated read-out devices and/or recording elements. An illustration

of these two hardware components is given by Figure 1. The third part of

the metering system is conceptual in nature and involves the formulation

and interpretation of system equations which relate the output from the

hardware elements to the flow rate for a given set of conditions.

523
The dimensionless equation for the one dimensional unsteady flow of

an incompressible fluid through an orifice can be represented by a relationship between the flow rate*, q(t), and the differential pressure,

Ah(t), which has the form:

d(

? (t) + CQ q

2

(t) = CP Ah(t) - CLOSS K (1) dt

The term CQ is a coefficient for the convective acceleration of the fluid,

CP is a coefficient related to the differential pressure, and CLOSS represents the effects of friction losses. Equation (1) is obtained by integrating the momentum equation between the upstream and downstream pressure

taps using suitable assumptions for the shape of the flow channel. One of

the most common assumptions is to require the shape of the flow channel to

remain constant during pulsation. Under this condition, no mass or momentum storage occurs in the flow channel due to changes in the size of the

control volume. A change in the size of the control volume can be interpreted as a capacitance effect which leads to a compressibility condition

that alters the propagation of flow signals through the downstream jet

region [1].** For steady flow, the dimensionless metering equation can

be reduced to a more elementary relationship, namely:

q = CD sqrt (Ah) (2)

Orifice meters can be calibrated to an accuracy of + 0.5% under steady

flow conditions. For unsteady flow, a calibration relationship such as

equation (2) will lead to inaccurate predictions of the flow rate. Flow

metering errors arise due to a number of reasons, such as neglecting the

effects of fluid inertia in the measurement volume and in the transmission

lines leading to the pressure transducer, and the introduction of acoustical effects due to the impedance of the orifice. Under the analytical

model known as square root theory [2,3], it is assumed that the inertial

effects may be neglected and the flow rate may be accurately predicted if

the square root of the differential pressure is obtained from the secondary

system before time-averaging the output signal. This quasi-steady flow

approximation is useful when the characteristic frequency of the unsteadiness is low and the differential pressure across the orifice is always

positive. When the characteristic frequency of the unsteadiness is large,

changes in the assumed flow channel for the orifice will occur, the inertial and friction loss terms become important, the flow coefficients

CP and CQ may vary during the cycle of the oscillation, and the differential pressure across the orifice may become negative. These conditions

lead to a strong non-linearity in the metering relationship which prohibits

obtaining an accurate flow rate estimate from a simple time-averaging of an

output differential pressure signal.

An indication of the degree of unsteadiness in the flow is given by

the Strouhal number, which is defined as:

S = fd/U (3)

*Terms are defined in the Nomenclature Section at the end of the paper.

**Numbers in brackets denote references in the Bibliography Section.

524
where f is the pulsation characteristic frequency, d is the orifice bore

diameter, and Uj is the maximum jet velocity downstream of the orifice.

The boundary between steady, quasi-steady, and unsteady flow is a function of the Strouhal number.

The objectives of the present research program are to determine the

characteristics of an orifice flow meter under pulsatile flow conditions.

Specific areas of investigation were defined in three broad categories:

1) the pressure and velocity fields near the orifice, 2) the response of

typical secondary systems under pulsatile flow conditions, and 3) the

development of an analytical model to accurately predict the flow rate

under pulsatile flow conditions. The present paper discusses results

obtained from studies of the pressure and velocity fields near the orifice

plate. A discussion of a one-dimensional, fixed flow channel analytical

model for the orifice is also presented.

2. Review of Literature

Flow metering with concentric orifices has long been a standard

practice to obtain flow rate measurements in pipelines. Accurate values

of the orifice calibration coefficients have been obtained from statistical- studies of the data of various experimenters and experimental facilities under steady flow conditions [4,5,6]. The dependence of the discharge coefficient on the Reynolds number and the pressure tap location

has been described by Halmi [7] and is documented in detail in flow metering reference books [8]. Minor corrections due to changes in the edge

sharpness [9,10] and in the approaching velocity profile [11,12], have

also been identified in order to account for scatter in discharge coefficient data. These analytical studies [11,12,13] which incorporate the

approaching velocity profile into the orifice flow model predict discharge

coefficients which are in close agreement with experimental data. In

summary, the main direction of the steady flow work has been to modify the

one-dimensional orifice hydraulic equation to account for the effects of

Reynolds number, pipe diameter and orifice diameter ratio, and the pressure tap location.

However, steady flow conditions often do not prevail in industrial

piping systems. Examples of severe pulsating flow and pressure conditions

have been given in several review papers [14,15,16]. Flow metering errors

have been observed under these conditions and were assumed to be dependent

on an unsteadiness parameter which took various forms such as the Hodgson

and Strouhal numbers [17,18] and an intensity parameter as proposed by

Head [19]. Some investigators [3,20,21] have suggested that the Strouhal

number is not a criterion for pulsating flow measurement.

Earlier attempts to explain the discrepancy between the actual mean

flow and the predicted flow based on the hydraulic equation focused on the

interpretation of the output of the secondary system when the readings

oscillated at large amplitudes due to the unsteadiness of the flow [17,22,

23]. Severe throttling of the impulse lines was often used to obtain

steady readings under the assumption that the output device would produce

the "true" differential pressure reading if the secondary system response

525
were linear. Later, "square root theory" was proposed as a possible solution to the problem of obtaining accurate flow measurements under pulsating

flow conditions [23,24]. Using this method, the output of the secondary

system is processed to obtain the square root of the differential pressure

before time-averaging the output signal. The basis of this method is the

square root relationship between the differential pressure and the flow

rate if the steady flow hydraulic equation is used as the correlation between these two variables. The square root method proved satisfactory in

most cases, but always produced a positive error in the measurement (i.e.,

the indicated flow rate was always greater than the actual flow rate)

.

This method is unsatisfactory if the differential pressure becomes negative

during a portion of the cycle of oscillation.

Much discussion has appeared in the literature concerning the causes

of the metering error and the difficulties of obtaining flow measurements

under conditions of pulsation [25,26,27,28,29,30,31]. Randall [32] examined

the operation of the orifice meter under unsteady conditions and noted in

summary that the error in measurement was attributable to the following

factors

:

1. The inertia of the fluid mass between pressure taps introduces an additional factor into the metering equation which

is not taken into account in steady flow calibrations.

2. The flow rate is related to the square root of the differential pressure if a quasi-steady flow relationship is

assumed for the pulsating flow condition.

3. The inertia of the fluid in the impulse piping and the output

transducer introduces additional factors into the response of

the secondary system which contribute to errors in flow

measurement

.

4. Acoustic waves which arrive out-of-phase at the measuring

taps due to the impedance of the orifice can impose negative

differential pressures across the orifice which are much

larger than the average differential pressure due to flow.

These observations suggest that a combination of factors such as orifice

beta ratio, the pulsation Strouhal number and amplitude ratio, the pressure

tap location, and the response characteristics of the secondary system must

all be considered in evaluating the error under pulsatile conditions.

Various investigators have measured the flow metering error under a wide

range of pulsation conditions. A summary of their results is presented

in Pellegrin [33]

.

While some insight into the characteristics of the error behavior may

be gained by calibration experiments, a physical understanding of the

orifice flow metering relationship cannot be developed without a careful

study of the dynamic flow field near the orifice plate. Experimental

data for the orifice flow field in steady flow have been obtained by

Teyssandier [34] and others; however, detailed flow field data under

pulsation are scarce.

526
Some of the characteristics of the downstream orifice jet flow can

be deduced from the behavior of free jets and shear layers. A large scale

organized vortex structure has been found in the transition region of free

jets between the nozzle and the fully developed zone [35,36,37]. The

natural excitation frequencies for this vortex structure lie in the

Strouhal number range of 0.3 to 0.6. The presence of bounding walls in

the orifice jet zone and the stagnation region at the upstream face of

the orifice introduce complicating factors which differentiate the orifice jet flow from the free jet flow case. Some observations of the

vortex structure for two dimensional slit orifices have been reported by

Rockwell [38] and Farr [39]. The authors present in this paper the results of a detailed study of the flow and pressure fields near the orifice under conditions of pulsation.

3. Experimental Facility

The metering run was constructed from 10.2 cm diameter clear acrylic

pipe in a manner consistent with ASME specifications. Orifice plates of

0.95 cm thickness were threaded so that they could be installed in the

metering run without the need for flanges which would impair flow visualization studies near the orifice. The three test orifices had beta ratios of

0.35, 0.50, and 0.70, respectively. Pressure tap arrangements corresponded

to the Flange, D-D/2, and Vena Contracta locations for each orifice. Velocity measurements were obtained from hot film and hot wire probes and

flow visualization techniques, including high speed movies. Pressure

measurements were made at the pipe wall using crystal pressure sensors.

The average differential pressure across the orifice was obtained from

manometers and capacitance-type pressure transducers. Signal averaging

techniques were used to obtain ensemble-averaged waveforms of the pulsating

differential pressure and velocity as a function of the phase angle of the

pulsation.

Most of the testing program was conducted with water except for a few

initial experiments with air. A schematic illustration of the orifice and

the water test facility is given by Figures 1 and 2, respectively. The

flow through the system was regulated by two upstream constant head reservoirs in order to attain a steady supply flow independent of any pressure

or flow disturbances from the pump. The water was recirculated through the

system to maintain constant temperature operation for the hot film probes.

Pulsations were induced from the downstream end of the metering run by a

rotating valve arrangement driven by a variable speed DC motor. The valve

rotation frequency range was 0-17 Hz. Velocity and flow rate variations

could be adjusted to rms levels of from 5% to 30% of the temporal mean

values of these parameters. Corresponding rms pressure oscillations approached 250% of the mean differential pressure across the orifice. Typical Reynolds numbers for the experiments were in the range of 8,000 to

24,000 (based on the metering run diameter of 10.2 cm and the volumetric

average velocity of the flow approaching the orifice)

.

527
4. Velocity Measurements Near the Orifice

A. Steady Flow . The flow approaching the orifice was determined to

be without swirl and corresponded to a fully developed power law profile

with an exponent of (1/6.6). The location of the maximum velocity in the

downstream orifice jet coincided with the predicted vena contracta region

for the 0.70 and 0.50 beta ratio orifices. The maximum velocity location

for the 0.35 beta ratio orifice was found to occur slightly upstream of

the predicted vena contracta region. Frequency spectra taken for the

lower flow rates near the edge of the shear zone in the contracting jet

region downstream from the orifice indicated that a laminar-turbulent

transition process was intermixed with lower frequency turbulent fluctuations convected from upstream. At higher flow rates, the upstream turbulence dominated the frequency spectra in this region and no regular

velocity fluctuations were observed.

B. Pulsatile Flow . The amplitude and waveform characteristics of

the pulsation were functions of the frequency of oscillation, the pulsator

valve design, and the overall resistance, capacitance and inductance of

the metering run. An example of the change in waveform with frequency for

low and high Reynolds number flows is given by Figure 3. In general,

higher oscillation frequencies produced lower amplitudes of flow fluctuation through the orifice.

The metering run was modeled using a lumped parameter description of

the resistive, inductive and capacitative elements of the system. Several

analytical functions describing the pulsator valve opening and closing

time history were studied using a computer analysis. Results from the

computer analysis were in qualitative agreement with the experimentallyobserved differential pressure and centerline velocity measurements. The

computer analysis also verified the experimentally-observed sensitivity

of" the system characteristics to different valve designs (area-of-opening

vs. angular position). The natural frequency of the metering run was in

the neighborhood of 4 Hz as determined from experiments and the lumped

parameter computer analysis. The system natural frequency was dominated

by the characteristics of the entire metering run and appeared to be only

slightly dependent on the beta ratio of the orifice being tested.

Figure 4 illustrates mean velocity profiles in pulsating flow at 4

positions along the metering run for the 0.50 beta ratio orifice. For

cases where the steady flow mean velocity profile differs from the pulsatile flow case, the steady flow mean velocity profiles are shown by the

dotted lines. The example of Figure 4 is typical of the velocity profile

characteristics for all three beta ratio orifices. Upstream of the orifice,

the mean velocity profiles were similar to the steady flow cases. In the

downstream region, time averaged velocity profiles were generally broader

than the corresponding profiles for steady flow conditions. The location

of the maximum velocity region also moved further upstream toward the

orifice under pulsating flow conditions.

528
The rms amplitude of the pulsation component, urms , appeared to be

constant over the core regions of the flow both upstream and downstream

of the orifice. Figure 4 illustrates the profiles for the fluctuating

velocity component in the lower portion of the figure. The fluctuating

velocity (rms magnitude) consists of both turbulence and the periodic

change in velocity due to the pulsation. The amplitude of the fluctuating

velocity is larger in the downstream shear layer than in the core region

at that location, partially due to the greater turbulence activity and

partially due to the characteristic response of the shear layer to the

pulsation. The larger amplitude of the fluctuating component of streamwise velocity was especially noted for Strouhal numbers between 0.4 and

0.8 where large variations in the orifice flow channel boundaries occurred.

The broadening of the mean velocity profile in pulsatile flow is due to

increased friction losses and also indicates that pressure recovery downstream from the orifice may occur sooner than for the steady flow condition.

Figure 5 gives an illustration of a conceptual model of the downstream flow channel for cases where the Strouhal number is such that the

wavelength of the pulsation corresponds with the dimensions of the orifice.

The model assumes that the shape of the flow channel (i.e., the flow channel

radius at any point along the centerline) varies with time. On the average,

however, the time mean flow channel does not correspond to a contracting

jet cylinder but retains this wavelike structure as shown by Figure 5. The

cause of the waviness in the flow channel is attributed to a well-defined

vortex which is shed from the lip of the orifice during each pulsation

cycle.

Due to the growth of the shear layer downstream, it is not possible

to define a zone in which all the fluid is moving at the centerline velocity. The velocity profiles at each station were analyzed to determine the

point for which the jet momentum flux was 25% of the momentum flux at the

centerline. In steady flow, this location corresponds to the point where

the velocity is one half of the centerline velocity. The time averaged

flow channel was defined as the locus of points where the jet momentum

flux was 25% of the centerline momentum flux. An analysis of the experimental data showed that this flow channel encompassed approximately 95% of

the total momentum flux of the jet velocity profile. Experimentally-determined shapes for the orifice flow channel boundary are shown on Figure 6.

A wavelike structure is seen in the locus of points defining the flow

channel. However, the shape of the flow channel changes with the Strouhal

number and the amplitude of the flow oscillation. This characteristic behavior was noted for all three orifice beta ratios.

The size and location of the starting vortex in relation to the shear

layer of the downstream jet flow is a function of the orifice beta ratio,

the Strouhal number, and the amplitude of the pulsation. The convection

velocity, Uc, of the vortex varied almost linearly between 0.4 Uj for

Strouhal numbers of 0.4 to approximately 0.8 Uj for Strouhal numbers of 1.5.

The optimum vortex formation was observed for Strouhal numbers between 0.4

and 0.8 where the wavelength of the pulsation was of the order of the bore

diameter of the orifice. Visual studies confirmed that the smaller vortices

occurred for the higher Strouhal number cases. This effect is partially due

529
to the fact that the amplitude of the oscillation decreased with increasing frequency due to the response characteristics of the metering

run. The smaller vortices tended to remain in the high velocity portion

of the shear layer and were therefore convected downstream at speeds

closer to the core region velocity. The larger vortices spread over more

of the shear layer and were convected downstream at a lower average speed.

For a given amplitude of pulsation, oscillations with Strouhal numbers in

the range of 0.4 to 0.8 produced large wavelike spatial variations in

the time-averaged cross-sectional area of the flow channel downstream from

the orifice. Regions where the flow channel cross-sectional area were

increased were coincident with regions where the rms velocity fluctuations

were decreased. The opposite effect was observed in regions where the

cross-sectional area was decreased. These observations were confined to

regions between the orifice plate and the furthest vena contracta tap

location downstream.

Figure 7 shows the velocity profile (ensemble average) at different

times in the cycle of oscillation at three downstream locations. The timemean velocity profile for pulsation is shown by the dotted line. These

profiles were obtained by signal averaging techniques, using the upstream

pressure signal as a trigger for the averaging process to ensure that the

zero phase angle for each profile coincided to the same reference time in

the cycle of oscillation. The effects of turbulence are averaged out of

the profiles in Figure 7. These data clearly show that the maximum swing

in the value of the velocity occurs in the shear layer region. The data

also show phase differences between stations which are due to the time lag

caused by the convective characteristics of the orifice vortex. These results show that the pressure and the flow rate do not coincide due to the

effects of both inertia and the convective lag, or capacitance effect,

caused by the orifice vortex. This latter effect has not been considered

in any analytical model for the orifice as a flow meter.

5. Pressure Measurements Near the Orifice

Static pressure measurements were obtained across the jet profile at

a location 5.1 cm downstream from the leading edge of the orifice. The

average static pressure at any radial location was found to be equal to

the pressure observed at the wall tap. The largest rms pressure fluctuation was observed in the shear layer for the steady flow case. In pulsatile flow, the system pressure level oscillation is so much larger than

the shear layer turbulent pressure fluctuations that the local static

pressure fluctuation is practically constant over the cross-section.

These results support the assumption that the pressure pulse is propagated

along the test section as a one-dimensional wave. Since the waveform of

the pressure signal was similar at both the upstream and downstream pressure taps, it was concluded that the orifice was not acting as an acoustic

impedence for the test conditions studied.

Analytical models for the orifice under pulsatile flow conditions show

that the inertial coefficient for the time dependent term should increase

as the spatial separation between pressure taps in increased. The major

530
contribution to the inertial coefficient is the length of the high kinetic

energy region in the downstream orifice jet zone. The downstream jet zone

may be hypothesized to be a cylinder in which the fluid behaves in a sluglike manner. This idealized flow channel is shown on Figure 5. Experiments with the 0.7 beta ratio orifice were in agreement with this concept.

The rms differential pressure was observed to increase as the distance

between the upstream and downstream pressure taps was increased. Velocity

measurements showed that the fluid moved through the 0.7 beta ratio orifice in a slug-like manner. The increase in the magnitude of the fluctuating differential pressure, Ap 1 , with tap separation is shown on

Figure 8a.

For the 0.5 beta ratio orifice, the rms differential pressure increased only slightly with increases in the tap separation distance. For

the 0.35 beta ratio orifice, the rms differential pressure decreased

slightly as the tap separation distance was increased. This behavior is

illustrated by Figures 8b and 8c, respectively.

The observations for the 0.35 beta ratio orifice are consistent with

the velocity profile experiments which show an increased turbulent dissipation. The slug-like motion of the fluid through the orifice under pulsatile

flow conditions is not as well-defined for the lower beta ratio orifices in

comparison with the high beta ratio orifice. Decreases in the level of the

flow oscillation in the test section were accompanied by corresponding decreases in the rms level of the differential pressure fluctuation.

6. Calibration Experiments

All three orifices were calibrated for both steady and pulsating flow

by collecting approximately 135 kg of water in a weigh tank. The tests

were repeatable to 0.3% differences for the same flow conditions. The

orifice calibration constants were in agreement with ASME standards (+ 0.5%

accuracy) for the 0.35 and the 0.50 beta ratio orifices in steady flow [8].

However, the 0.70 beta ratio orifice differed from the ASME standards for

flows in the Reynolds number range of 20,000 to 30,000 (based on the bore

of the orifice). The calibration constant was approximately 15% higher

than the recommended values in reference [8]. However, the behavior of

the 0.70 beta ratio data is in agreement with the data of Stearns, et al,

[40], Steady state values of the flow coefficients obtained by calibration were used in all cases for comparison with pulsatile flow results.

Each orifice was tested for metering error for various combinations

of Strouhal number and amplitude of oscillation. Data taken for the D-D/2

pressure tap combination are presented in Figure 9. In all cases, the

orifice passed less flow under pulsatile flow conditions than would be

predicted using the steady flow hydraulic equation, steady flow coefficients,

and the average value of the differential pressure across the orifice. The

amplitude parameter shown on Figure 9 is the oscillation in flow rate and

not the oscillation in the differential pressure across the orifice.

Square root theory was not used in calculating the flow rate since the

differential pressure across the orifice became negative for some portions

of the cycle of oscillation. The dashed lines on Figure 9 illustrate

531
three regions delineating flow pulsation amplitudes between 5 and 10%,

10 and 20%, and 20 to 30%, respectively. The data appear to be consistent

in that the magnitude of the error increases with increases in both the

amplitude of the oscillation and the Strouhal number. One data point,

for the 0.70 beta ratio orifice at high pulsation amplitudes, however,

indicates a significantly lower error than would be expected based upon

the general trends of the data. Two comments are in order here. First,

the error which would be obtained using the flange tap arrangement is

approximately 16% and is much greater than the 1% error predicted for the

D-D/2 taps. Second, the Strouhal number of the oscillation for this case

is in the range where the flow channel was markedly deformed by the orifice vortex. This deformation was also verified by visual observations

with dye streaks. Additional experiments are required to formulate the

overall relationship between the measurement error and the independent

parameters (Strouhal number, tap separation, flow pulsation amplitude,

orifice beta ratio, and Reynolds number).

7. Analytical Model

An analytical model was developed for the unsteady flow of an incompressible fluid through a sharp-edged orifice under the assumption

that the flow channel for the orifice did not vary with time. The orifice flow channel is idealized as shown by the cylindrical volumes on

Figure 5. Inputs from the experimental velocity profiles were used in

formulating estimates for the radius of the cylinders in the upstream and

downstream regions. The length of the control volume extends from the upstream to the downstream pressure taps. Values for the friction loss coefficient, CLOSS, were developed from the experimental data and some preliminary computations with the analytical model. An indication of the

variation in the friction loss coefficient is given by Figure 10.

One complete period of pulsation for the experimentally observed

differential pressure signal was obtained by time averaging techniques and

recorded on strip charts. This differential pressure trace was nondimensionalized and digitized to provide discrete values of the differential

pressure for 50 times in the cycle of pulsation. Numerical computations

were performed with this input signal to obtain a solution for the dimensionless velocity waveform through the orifice. These numerical predictions were compared with experimentally-determined velocity waveforms.

Two cases of analysis are shown in Figures 11 and 12, respectively.

Figure 11 illustrates the comparison between the model and the theory for

a Strouhal number of approximately 0.14. The dashed line represents the

solution obtained from another analytical model patterned after square

root theory. Note that the square root theory solution is similar to the

differential pressure signal, as should be expected. The analytical model

developed by the authors provides a better fit to the data than does the

square root theory model. Figure 12 illustrates the case of a Strouhal

number near 0.34. The agreement between the present analytical model and

the experimental data is still good while the square root theory solution

is clearly inadequate. These examples show that the inertia effects must

be taken into account in formulating a hydraulic equation for the orifice

532
which is applicable to pulsating flow. In those instances where the flow

channel was markedly deformed by the orifice vortex, the agreement between

the model and the experimental results was not as well-matched as the results illustrated by Figures 11 and 12. The amplitude of the waveform

predicted by the model was larger than the amplitude of the experimentallydetermined waveform, although predictions of phase angle were accurate.

In these instances, the fixed area flow channel assumption is questionable.

Simple arguments based upon the analytical model can be used to show

the dependence of the flow metering error upon the amplitude of oscillation

parameter and the Strouhal number. The analytical model can also be used

to show that the effective discharge coefficient for the orifice under

pulsating flow must be less than the steady flow discharge coefficient for

the same average differential pressure. This result is in agreement with

the experimental data for the flow metering error shown on Figure 9. The

data of Figures 11 and 12 also illustrate the relationship between the

differential pressure and the flow rate variable as a function of the

Strouhal number. Referring to equation (1), when the Strouhal number is

small, the inertia term may be eliminated and the pressure is related to

the square of the flow. For this case the extrema in the pressure and flow

curves should occur at approximately the same time in the cycle of oscillation. This condition is illustrated by the experimental data of Figure 11.

When the Strouhal number becomes large, the inertia term becomes dominant

and the convective acceleration term may be neglected. For this case, the

pressure variable and the time derivative of the flow variable should have

maxima and minima at corresponding times in the cycle of oscillation. The

higher Strouhal number case is illustrated on Figure 12, where the maximum

flow occurs at the location where the pressure is changing rapidly, and

vice versa.

8. Conclusions

When the wavelength of the pulsation is of the order of the bore diameter of the orifice, the vortex shed from the edge of the orifice distorts

the downstream flow channel sufficiently to introduce significant errors

in the one-dimensional flow metering equation. The orifice passes less

flow during pulsatile flow conditions than for steady flow at the same

average differential pressure. Reversal of flow through the orifice was

not observed even when the differential pressure became negative. A variable area flow channel analytical model is needed to predict the flow field

adequately when the Strouhal number is in the range of 0.4-0.8. The present

results suggest that the accurate prediction of the flow rate under unsteady

conditions may require information concerning the amplitude of the flow

fluctuation in addition to the more readily observed fluctuations in the

differential pressure.

Acknowledgments

This research program is sponsored by the National Science Foundation,

Fluid Mechanics Program, under Grant ENG-10399-A01 and is being conducted

533
as a cooperative effort with the Babcock & Wilcox Company, the DeLaval

Turbine Division, and West Virginia University. Project reports issued

by the investigators under this program of research are listed as

references [41,42,43].

Nomenclature

CD Discharge coefficient

CLOSS Friction coefficient

CP Differential pressure coefficient

CQ Convective acceleration coefficient

d Orifice bore diameter

D Pipe diameter (10.4 cm)

f Frequency, hz

Ah Dimensionless differential pressure

& Length of orifice jet zone between orifice and downstream

pressure tap.

p Pressure

Ap Average differential pressure

Ap Root mean square value of fluctuating differential pressure

rms

q Dimensionless volume flow rate

R Pipe radius (5.2 cm)

Rp Reynolds number based on pipe diameter and bulk velocity in pipe.

R^ Reynolds number based on orifice bore diameter and velocity

through orifice

S Strouhal number, fd/U.

3

t Dimensionless time

u Average velocity

U Vortex convection velocity

c

U\. Maximum velocity on centerline in downstream jet region

U

rms

R°om mean square of fluctuating velocity component

Velocity on centerline

x Axial location

y Radial position measured from centerline

3 Orifice beta ratio

A Wavelength of pulsation

9 Phase angle of pulsation

534
Bibliography

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presented to the Fluids Engineering Division Luncheon, ASME Winter

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Through Concentric Square Edged Orifices," ASME Paper 75-WA/FM-4, 1975.

535
14. H. Diederichs and W. D. Pomeroy, "The Occurrence and Elimination of

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15. E. G. Chilton and L. R. Handley, "Pulsations in Gas Compressor Systems,"

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17. A. K. Oppenheim and E. G. Chilton, "Pulsating-Flow Measurement —

A

Literature Survey," Transactions of ASME , p. 231, 1955.

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The Engineer , pp. 378-379, March, 1959.

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536
30. B. W. Imrie and R. A. Evans, "An Investigation of Resonance Conditions for Pulsating Flow of Air Through an Orifice in a Pipe,"

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a Sharp-Edged Orifice Meter," Ph.D. Dissertation, West Virginia

University, 1976.

34. R. G. Teyssandier and M. P. Wilson, Jr., "The Paradox of the Vena

Contracta," ASME Paper 73-WA/FM-9, 1973.

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Fluid Mechanics , v. 44, pp. 97-112, 1970.

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ASME Paper 76-WA/FLCS-ll, 1976.

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Virginia University, 1976.

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Measurement with Orifice Meters," Van Nostrand Company, New York, 1951.

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an Orifice," Available from NTIS, Springfield, Virginia, accession

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Available from NTIS, Springfield, Virginia, accession number PB 261147,

129 pages, July, 1976.

537
Threaded Insert Clear Acrylic Pipe

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Figure 1. Description of Orifice Meter and Flow Field.

538
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Velocity

Wove Form

(Center line)

o

time

Differentiol

Pressure

Wave Form

(Inverted)

Arbitrary

L

Figure 3. Characteristics of the Velocity and Differential Pressure Waveforms

for Two Pulsation Frequencies.

539
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' Pulsation Wavelength

£

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Figure 5. Conceptual Models of Flow Channel for an Orifice.

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Figure 7. Ensemble -Averaged Axial Velocity Profiles for Six Equally Spaced

Intervals in the Cycle of Pulsation for a 0.50 Beta Ratio Orifice

at R

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Figure 9. Metering Error as a Function of Strouhal Number and Amplitude of

Pulsation in Flow for D-D/2 Pressure Taps.

545
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Figure 10. Dependence of Friction Loss Coefficient on Strouhal Number and

Pulsation Amplitude.

546
Figure 11. Comparison of Analytical Models with Experimental Velocity Waveform

for a Strouhal Number of 0.14. Beta Ratio =0.5, 27% Flow Pulsation

Amplitude.

547
Figure 12. Comparison of Analytical Models with Experimental Velocity Waveforms

for a Strouhal Number of 0.34. Beta Ratio = 0.5, 14% Flow Pulsation

Amplitude

.

548
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

A VORTEX FLOWMETER - CALIBRATION RESULTS

AND APPLICATION EXPERIENCES

R. W. Miller, J. P. DeCarlo, and J. T. Cullen

The Foxboro Company

Foxboro, Massachusetts 02035 U.S.A.

Key Words: Vortex shedding; linearity; shedding frequency; vortex

flowmeter; vortex generating element.

1. Introduction

Over the past few years the vortex flowmeter has come into prominence

because of its potentially high degree of accuracy and low cost. Although

several meter manufacturers offer this type flowmeter, little calibration

data has been published to support specifications that are claimed.

The purpose of this paper is to present a substantial body of calibration data on a particular vortex flowmeter design. Over 1300 data

points on 167 meters in 2" (50 mm), 3" (75 mm), and 4" (100 mm) line sizes

were obtained in a high quality hydraulic test laboratory. These data are

statistically analyzed to arrive at specifications for this particular type

of vortex flowmeter. These results are not necessarily representative of

the performance of any other vortex flowmeter design.

This paper will not deal with the theoretical aspect of vortex shedding,

of which little is known, but will describe the broad fundamentals of vortex

shedding. Details of the experimental and fluid mechanic studies necessary

to design a practical industrial type flowmeter are left to the reader's

imagination.

2. General Description of Flowmeter

Generally, vortex flowmeters are made up of three parts: a vortex

generating element fully spanning a pipe, a sensor to convert the vortex

shedding energy into an electrical pulse signal, and a transmitter for

signal amplification and conditioning. The significant differences between

vortex flowmeter designs are the shape of the element, the complexity of

the sensor, and the location of the electronic transmitter. These three

factors affect performance, as well as cost.

Vortex flowmeters measure flow rate by detecting pressure or velocity

changes in the flow field resulting from the periodic generation and shedding

of vortices. Vortices are rotational flow zones that form and shed alternately, as shown in Figure 1, at a frequency proportional to the fluid

velocity [l]. 1 Associated with these vortices is a sinusoidal differential

pressure, which is created aft of the generating body. By sensing the

sinusoidal differential pressure, the frequency of vortex shedding and

hence the fluid velocity is determined. For a given line size, a vortex ——— i .—.

^Numbers in brackets refer to references given at the end of this paper,

549
flowmeter may then be considered a volumetric type flowmeter suitable for

both a flow rate measurement (gal/min;m3 /s) and totalizing (gals;m3 ).

The presence of the vortex generating element causes the separation of

fluid particles that form a shear layer, where a high velocity gradient

exists. The fluid within the shear layer is inherently unstable and breaks

down after some length of travel into well-formed vortices. At the outer

extremities of the vortices, called the edge of the wake, there exists a

zone of random fluid turbulence. The edge of the wake represents the

extrapolated path of the shear layer if the layer could remain stable without vortex formation.

The shear layer is a complex fluid mechanic phenomenon having a zero

velocity at the lower part of the layer and a large velocity gradient

through to the upper part of the layer. Some of the fluid necessary to

feed the vortex is drawn from the lower part of the layer, and it is this

fluid feed that is believed to lead to instability in the layer and to

initiate the vortex shedding.

A region extending upstream from the point where the shear layer breaks

down is normally referred to as "outside" the wake. The region inside the

lower part of the layer to the point of shear layer breakdown is commonly

referred to as "inside" the wake.

Within the shear layer and at its upper extremity random turbulence

exists. When the layer begins to break down, pressure and velocity changes

exist that are at the vortex shedding frequency, close to the shedding

frequency, or completely random in nature.

Consequently, detecting the vortex shedding frequency outside the wake,

particularly after the layer breakdown point, is difficult and requires

sophisticated filtering and sensitive detector schemes. Care also must be

taken to ensure that the detector configuration does not alter the basic

flow field.

3. The Foxboro Vortex Flowmeter [2]

The vortex generator shape was designed for detecting vortex shedding

inside the wake where the dominant vortex frequency exists. When viewed

from the inlet end, the vortex generator appears as a simple rectangular

plate with a width (h) to meter bore (D) ratio of approximately 0.27,

Figure 1. In terms of blockage, the net flow area approximates a 0.8

beta ratio orifice plate. When viewed in cross section, the vortex

generator appears as a flat plate with a centered tail, Figure 2. Vortex

shedding generates an alternating differential pressure across the differential pressure sensor located within the tail.

This vortex flowmeter uses a particular shape of vortex generating

element. Its shape evolved in conjunction with the type sensor employed.

The sensor, a rugged piezoelectric differential pressure detector, is completely sealed from the process fluid and located in a "quiet" fluid zone

on the vortex generating body. In addition, the location of the sensor is

protected from the impacting of any solid particles carried by the flow

stream. In the development phase, the type of sensor and sensor location

played just as important a role in determining the vortex generator shape as

did the performance potential of the shape itself.

550
A thorough research and development program was initiated to study

the effects of vortex generator body shapes on the performance of a vortex

flowmeter. Hundreds of tests and thousands of hours of data analysis

finally resulted in a vortex element shape that is essentially a flat

plate. However, a tail type section mounted downstream of the flat plate

proved to be a significant factor in the control of stable vortex shedding.

Specifically, the geometry of the end of the tail section proved to be a

critical vortex-stabilizing control parameter. In addition, the tail section

served as an excellent location for a sensor. The flow zone inside the wake

surrounding the tail is low in noise, consequently the signal-to-noise ratio

is high. Because the tail is behind the flat plate, the plate also acts as

a shield to prevent damage to the sensor.

The flowmeter's primary device, Figure 3, consists of a wafer-style

housing, a removable vortex element with integrally mounted differential

pressure sensor, and associated mounting hardware.

The integral secondary device consists of a two -compartment electrical

housing; the amplifier compartment contains the electronics; the junction

box compartment contains the wiring terminals and optional flow rate

indicator. The amplifier options are: (1) amplified and conditioned voltage

pulse output, or (2) a 4-20 mA analog output.

4. Flowmeter Performance

Vortex flowmeter performance is similar to that of a turbine meter.

The frequency of shedding is linear with pipeline velocity, and hence to

the volumetric flow rate for a given bore. In the case of a turbine flowmeter, the rotational speed of the blades is proportional to pipeline

velocity. By counting the blades passing a fixed point, the flow rate is

determined. Because of the similarity in both readout and the relationship

to volumetric flow rate, the accepted terminology and performance standards

for turbine meters [3] were selected to present the data. The ISO Standard

[4] is used to establish accuracy specifications.

The relationship between input (volumetric flow rate) and output (pulse

rate) defines the flow "coefficient". This relationship, expressed as the

ratio of pulse rate to volumetric flow rate, is called the K-factor. The

units are pulses/unit volume (pulses/gallon, pulses/cubic metre, etc.).

A plot of the K-factor against the pipe Reynolds number (R^) establishes

a signature curve. Because the K-factor remains essentially constant for

pipe Reynolds numbers greater than 10,000, a mean K-factor is used to

characterize the flow performance over a designated flow rate range. A

linearity band, expressed as a percentage, defines the performance over the

designated linearity range. This band is calculated from the maximum and

minimum K-factor determined by a flow calibration.

The mean K-factor is

K + K

Mean K-factor =

where K

max

is the maximum K-factor and K is the minimum K-factor over

the flowarate range, the values of each D*e?ng determined by a flow

calibration.

551
Two design flow rate ranges were of interest; first, a 1-10 ft. /sec.

(0.3 - 3 m/s) range, the normal operating range for most pipeline installations, and second, a 1-20 ft. /sec. (0.3 - 6 m/s) range encountered in

wide turn-down control, batching or totalizing. As is the case in turbine

meters, the linearity and "designated" linear range are specified in terms

of a water calibration factor. Adjustments to flow rate range limits, due

to viscosity effects (Reynolds number) or the minimum velocity the detector

would operate, is checked by a simple calculation procedure. Flow tests

using oil at varying viscosities confirmed the Reynolds number signature

curve, while the differential pressure created by the shedding was experimentally determined as a constant times the product of the fluid density

and the square of the pipeline velocity. These factors allow a water test

to fully define the operating characteristics and the operating flow rate

limits.

In Table 1, the parameters for defining the low velocity limit of the

flowmeter as a function of viscosity are presented.

5. Flow Laboratory

Ninety 2-inch (50 mm) , fifty-one 3-inch (75 mm) , and twenty-six 4-inch

(100 mm) flowmeters were calibrated to determine the mean K-factor and

linearity.

Calibration work was performed at the Engineering-Development Flow

Laboratory of The Foxboro Company, in Foxboro, Massachusetts. The meter

run and piping arrangement are illustrated in Figure 4.

Water is brought from a weir type head tank, located 55 feet above the

test facility, and similar to that described by Spencer and Hayward [5J, into

a 6-inch horizontal header located in the main facility. This header branches

into a permanently installed 4-inch (100 mm) test meter run. Flow straight

eners are located upstream of the meter test section. These flow straightener

are of the multiple-multiholed type [6]. They consist of three multiholed

1/4-inch (6.3 mm) thick circular plates mounted in series with approximately

2 inches (50 mm) between plates. Downstream of the meter run are 29 pipe

diameters of straight horizontal pipe. A vertical length of pipe with a

throttling valve leads to the flow nozzle diffuser and diverter system.

The diverter and nozzle diffuser are similar in construction to those

described by Shafer and Ruegg [7], The flow is directed into the 10,000 lbs.

(4536 kg) calibrated weigh receiver or returned to the reservoir by the

diverter system. The mass rate of flow is calculated as the collected mass,

corrected for buoyancy and scale calibration, divided by the measured test

time interval.

Eight calibration points were obtained on each flowmeter over a

velocity range of approximately 1-20 ft. /sec./ (0.3 - 6 m/s). The meter's

output pulses were gated and counted when the diverter directed the flow

into the calibrated weigh receiver. The count was stopped when the flow

was redirected into the reservoir.

552
The actual K-factor, at each flow rate point, is calculated as the

recorded pulses divided by the volume of water collected. Volume is derived

from the mass of collected water and the water density values given in ASME

Steam Tables [8] of water density as a function of temperature. It is

estimated that the random systematic error, in the determination of volumetric

flow rate, is ±0.1 percent and that the random uncertainties including counters,

timers, and scales are ±0.15 percent computed for a 95 percent confidence

level.

6. Data Analysis

A typical 2-inch (50 mm) flowmeter calibration plot is shown in Figure 5.

Similar plots were made for the 167 flowmeters tested to date. Plots were

generated on a high speed plotter after the laboratory data had been computercalculated to determine the actual K-factor at each flow rate point. The plus

symbols are actual test points plotted on the ordinate as a percentage deviation from the mean K-factor established over the range of velocities shown

on the abscissa. The upper and lower dashed lines run through the minimum

and maximum K-factors and represent the upper and lower linearity limit over

the entire test range. The average of these points is the mean K-factor, and

the percent deviation is the linearity over the designated flow rate range.

The calculated mean K-factor and linearity over three designated linear

ranges are indicated on each plot. Reading from left to right, the first is

for the complete range tested, the second a nominal 1-10 ft. /sec. range (0.3 -

3 m/s), and the third a 1-20 ft. /sec. (0.3 - 6 m/s). For this particular

flowmeter, the linearity (±.28 percent) and mean K-factor (24.187) are independent of the linear range selected. The linearity is expressed as a percent

of flow rate reading.

This was generally true of the 2-inch (50 mm) and 3-inch (75 mm) flowmeters, because the minimum and maximum K-factors occurred within the 1-10 ft./

sec. (0.3 - 3 m/s) range. This is not true, however, for the 4-inch (100 mm)

flowmeter where the minimum K-factor, because of a higher Reynolds number,

occurred at approximately 20 ft. /sec. (6 m/s).

In Figure 6 are shown all the data points (435) taken on fifty-one

3-inch (75 mm) flowmeters. These points are plotted as the percent difference of each point from the average of the mean K-factors for all fiftyone flowmeters over the entire flow rate range. The upper and lower dashed

lines are the uncertainty limit of the data (statistically referred to as

upper and lower range) calculated for a 95 percent confidence level (±2

sigma) . The 95 percent confidence level uncertainty limit was selected

because it is the international standard proposed for specifying flowmeter

uncertainties [4].

The standard deviation estimate was calculated in accordance with

ISO/DIS 5168 [4]. The range of values within which the mean K-factor and

linearity are expected to lie, at a 95 percent confidence level, is calculated as:

553
Range of Mean K-factors

R_ - K + t S

K

K

(1)

where : K

t

= Average Mean K-factor

= Student "t" value at a 95 percent confidence level. [4]

1=n 77,2-1 h

and

K

. p~ (K - to

2!

(2)

with: K = Mean K-factor for each flowmeter.

K = Average of Mean K-factors for (n) flowmeters.

n = Number of flowmeters.

Range of Linearity

\

= Z ± * S

L

where: L = Average Linearity of n flowmeters.

S = Standard deviation estimation calculated from Eq. 2.

Ju

Sigma was adjusted using the student's "t" method for the estimation

of sigma for a 51 sample size. These statistical calculations are covered

in detail in reference [4].

The ±0.71 percent two sigma value, computed for the 3-inch (75 mm)

flowmeters, includes not only linearity but the inherent systematic differences between flowmeters when tests are conducted on multiple flowmeters.

In the case of vortex flowmeters, as with turbine flowmeters, the

performance specifications are given as a mean K-factor, established by

flow calibration and a linearity specification over a specified linear flow

rate range. This linearity value may be based on the actual calibrated

curve or more generally as an upper limit value below which all the data is

expected to fall for a 95 percent confidence level.

If twice the standard deviation, corrected by the use of student "t"

for sample size, is computed, and the value of each flowmeter mean K-factor

is used to eliminate systematic differences between flowmeters, the data

point plot of Figure 7 is obtained.

The heavy lines represent the averaged linearity over the entire flow

rate range, and the dashed lines represent the lower and upper linearity

uncertainty limits. Within these two dashed lines, the linearity of 95

percent of all flowmeters tested, or the linearity of any future flowmeters,

are estimated to fall.

554
Similar plots and statistical computations made for each line size

and for two designated linear range (1-10 ft. /sec. and 1-20 ft. /sec;

.3 - 3 m/s and .3 - 6 m/s) are not presented here because of repetition

and lack of space. Table 2 lists the mean K-factors and linearities for

the 167 flowmeters.

Of the 167 flowmeters tested, two early production 2-inch (50 mm) and

one 3-inch (75 mm) flowmeters were outliers as indicated by the Thomson's

Tau (t) technique [4] or Dixon's illegitimate error test [4]. These flowmeters, marked by an asterisk in Table 2, were considered outliers and

excluded in the final computation of the mean and standard deviations of

both the mean K-factor and linearity values. It should be noted, however,

that their inclusion only affects the results by <±0.05 percent.

Table 3 summarizes the test results. The average mean K-factor (K)

and range of values within which the mean K-factors are expected to lie for

a 95 percent confidence level are presented for the two designated linear

ranges (1-10 and 1-20 ft. /sec. or 0.3 - 3 and 0.3-6 m/s).

For example, the 2" (50 mm) flowmeters have a mean K-factor of 24.129,

and the values range ±0.77 percent about this mean. Ninety-five percent of

these meters, or future meters, would be expected to have a mean K-factor

ranging between 23.943 and 24.315 if water tested over a 1-10 ft. /sec.

(0.3 - 3 m/s) range. This uncertainty in the mean K-factor is academic,

since each flowmeter was calibrated, and the mean K-factor established,

within the flow laboratory accuracy limits previously stated. However, if,

in the future, uncalibrated flowmeters are used, these values would be the

assigned mean K-factor "tolerance"; analogous to the tolerance assigned to

orifice, venturi, or flow nozzles.

It should be noted, however, that only one 2" (50 mm) meter was outside

this estimated range. Therefore, it is felt that the range limits presented

are conservative.

The lower half of Table 3 presents the mean linearity (L) and the random

uncertainty (tS^) over the two designated flow rate ranges. For example,

the 3" (75 mm) flowmeters had a mean linearity of ±0.43 percent with a

random uncertainty (tS^) of ±0.21 percent when tested over a nominal 1-10 ft./

sec. (0.3 - 3 m/s) flow rate range. Ninety-five percent of all 3-inch (75 mm)

flowmeters tested are estimated to have a linearity ranging between ±0.22

and ±0.64 percent. For a nominal 1-20 ft. /sec. (0.3 - 6 m/s) flow rate range

these values are ±0.25 to ±0.63 percent.

7. Flowmeter Accuracy Specifications

The accuracy of a measurement may be characterized by giving the random

uncertainty to be expected and the systematic uncertainty bounds [4, 9, 10].

For this particular test work, the laboratory and the mean linearity would

constitute the systematic errors, assuming these errors are randomized.

The random uncertain portion is the computed uncertainty (tS^) with respect

to the average linearity, with the assumption that the ±0.15 percent

laboratory random uncertainty is included in the estimated linearity

uncertainty (tS )

The overall uncertainty over a given flow rate range can be computed
. / 2 -2

Ve

S

Overall uncertainty - + \/e

s + L + ^1^95

with a random uncertainty of

(eR>95

= *V

where n = number of flowmeters tested in a given line size.

For example: the 3" (75 mm) flowmeter has an overall estimated uncertainty

over a 1-20 ft. /sec. (0.3 - 6 m/s) flow rate range of

= Vo.l2

+ .44

2

+ .19

2

Overall uncertainty = VO.l + .44 + .19 = ±0.0.49%

NOTE : To be conservative the random uncertainty (tS^) of 0.19 percent was

not reduced by \/ n In the above computation.

The random uncertainty would be:

(Ooc = .19/v/51= ±0.03%

Although recommended by IS0/DIS 5168, it is confusing to some readers

to give both components in an accuracy statement. The authors prefer to

algebraically add the overall uncertainty and the random uncertainty computed

above to arrive at a conservative estimate of the maximum errors to be expected, and to call this accuracy.

In Table 4, the accuracy specifications for the three line size flowmeters calibrated are presented to the nearest tenth of a percent.

8. Application Experiences

Since the release of the Foxboro Vortex Flowmeter, applications for

the device have been found in the five basic areas of batching, control,

totalizing, recording, and blending. Some examples of field trial applications are shown in Table 5.

Meters that were on field trial and used with such fluids as ammonia,

ammonia sulphate, and hydrocarbons, were recalibrated at the Foxboro RD&E

Laboratories after several hundred hours of field operation. The results

of a comparison of the before and after field-test calibrations indicated

no change in linearity and a mean meter factor (K-factor) within ±0.1 percent of the factor stamped on the meter data label. Two calibration data

sets, one taken before and one taken after field use, are shown in Figure

8. Note, the agreement between the two calibration data sets is within the

estimated random uncertainty for the data.

556
9. Conclusions

In order to achieve confidence in the specifications for a flowmeter,

the number of units tested should represent a valid statistical sample.

Using a statistical approach in the analysis of data correlates numerous

data points and portrays the results in terms familiar to the user. It is

expected that others will consider using statistical procedures as outlined

in ISO Standards so that flowmeters may be compared on some common basis.

Based on the data obtained from the 167 flowmeters tested under reference laboratory conditions, these vortex shedding type flowmeters consistently

provide an accuracy of ±0.5 percent over a 10 to 1 flow rate range. This

accuracy is in percent of actual flow rate reading.

Application experience shows that no performance degradation occurred

after considerable in-line use.

10. References

1. Lamb, Sir Horace, "Hydrodynamics", Dover Publication, Sixth Edition.

2. The Foxboro Company, PUB 416, "E83 Series Vortex Flowmeter".

3. International Standard ISO/2715, "Liquid Hydrocarbons - Volumetric

Measurement of Turbine Meter Systems".

4. International Standard ISO/DIS 5168, "Measurement of Fluid Flow - Estimation of Uncertainty of a Flow Rate Measurement".

5. Spencer, E. A., and Hayward, A. T. J., "The Accurate Calibration of

Flowmeters with Water", Trans, of the Society of Instrument Technology,

Volume 9.

6. Sprenkle, R. W. , and Courtright, N. S., "Straightening Vanes for Flow

Measurement", ASME Paper No. 57-A-76.

7. Shafer, M. R. , and Ruegg, F. W. , "Liquid Flowmeter Calibration

Techniques", ASME Paper No. 52-A-70.

8. Meyer, C. A., et. al. , "Thermodynamic and Transport Properties of

Steam", A.S.M.E., 1967.

9. Filban, T. J. Jr., Shafer, M. R. Jr., "Flow Measurement Standardization",

ISA Transactions 1964, New York.

10. "Proceedings of the 1962 Standards Laboratory Conference", NBS

Miscellaneous Publication 248, Issued August 16, 1963.

557
TABLE 1. PARAMETERS FOR LOW VELOCITY LIMIT

Meter

Size

Viscosity

Centistokes

Minimum Flow Rate

Ft./Sec.

2" (50 mm) "CS

< 1.6 1A/G[

v cs > 1.6 .62 , csif

3" (75 mm) v cs < 2.2 1/n/Gl

u cs >2.2 0.45 v M if cs i/Vg[

4" (100 mm) "cs

< 3.0 i/Vg[

'cs

>3.0 0.34 i> if cs 1/x/G L

where G. = Specific Gravity at line conditions.

558
TABLE 2. COMPLETE DATA SET FOR ALL FLOWMETERS CALIBRATED

2" (50 MM)

LINEAR RANGE

1-10 FT/SEC (.3-3 M/SEC) 1-20 FT/SEC

(.3 - 6.1 M/S)

MEAN MEAN

NO. K- FACTOR LINEARITY K-FACTOR LINEARITY NO.

LINEAR RANGE

1-10 FT/SEC

(.3 - 3 M/SEC) 1-20 FT/SEC.3 - 6.1 M/S)

MEAN MEAN K-FACTOR LINEARITY K-FACTOR LINEARITY

LINEAR RANGE

1-10 FT/SEC

(.3 - 3 M/SEC)

1-20 FT/SEC

(.3 - 6.1 M/S)

MEAN MEAN

NO. K-FACTOR LINEARITY K-FACTOR LINEARITY

1 23 807 - JO Co OU/ -

3fl

. JO j i 24 117 ± . 1 o 24 048 ±.47 61 24 040 ± 30 24 024 ± 37

2 24 . 293 - 47 24 293 .47 32 24 108 + 1

6

24 060 ±.36 62 24 094 + 24 24 034 ± 49

3# 24 . 1 90 76 24 119 + . 05 33 24 205 ± . CJ 24 205 ±.29 63 24 1 79 ± 29 24 179 ± 29

4 24.239 12 24 239 .12 34 23 949 *i . 11I J 23 873 ±.44 64 24 208 ± 17 24 1 64 35

5 24^373 + 65 24 373 !65 35 24 034 ±.14 23 961 ±.44 65 24 249 37 24 249 + 37

g 24. 1 29 40 24 129 .40 36 24 030 X. 1 1 23 982 ±.31 66 24 120 ± 12 24 091 + 24

7 24.223 50 24 223 . 50 37 24 195 ± . JO 24 195 ±.35 67 24 193 ± 36 24 193 + 36 g 24. 182 34 24 182 . 34 38 24 284 + 28 24 276 ±.32 68 24 050 + 32 24 050 + 32

9 24.117 13 24 086 . 26 39 24 033 ±

.

24 033 ±.49 69 24 126 + 11 24 062 + 38 10 24J20 + 19 24 080 + !36 40 24 270 ±.52 24 270 ±. 52 70 24 132 1

4

24 131 1Al*t

11 24.059 21 24 036 ± .30 41 24.020 ±.20 24 074 ±.78 71 24 128 57 24 125 + 58

12 23.974 16 23 935 + .32 42 24 066 ±.30 24 066 ±.30 72 24 287 61 24 287 61 13* 23.997 89 23 954 ±1 .07 43 24 054 ±.37 23 965 ±.74 73 24 039 35 24 015 + 44 14 24.076 + 21 24 008 .49 44 24 202 ±.23 24 193 ±.26 74 24 060 + 29 24 035 39 15 23.968 34 23 941 + .45 45 24 268 ±.45 24 268 ±.45 75 24 121 + 40 24 121 + 40

16 24.138 25 24 100 + .41 46 24 129 ±.26 24 080 ±.47 76 24 090 + 29 24 052 45

17 24.132 + 35 24 088 + .54 47 24 016 ±.35 23 978 ±.51 77 24 087 + 34 24 044 51 18 24.111 21 24 111 + .21 48 24 168 ±.20 24 153 ±.26 78 24 171 56 24 167 56 19 24.095 + 19 24 049 .37 49 24 131 ±.41 24.131 ±.41 79 24 079 61 24 058 69

20 24.039 ± 24 23 980 + .49 50 24 149 ±.50 24.149 ±.50 80 24 243 57 24 243 57

21 24.017 + 27 24 017 .27 51 23 995 + .37 23 995 ±.37 81 24 190 45 24 190 45

22 24.086 + 14 24.048 .30 52 24 187 ±.28 24 187 ±.28 82 23 985 14 23 959 25 23 24.279 45 24 279 + .45 53 24 041 ±.39 24 030 ±.43 83 24 172 50 24 151 58 24 24.218 ± 14 24 180 .30 54 24 108 ±.68 24 108 ±.68 84 24 186 + 19 24 159 + 30

25 24.095 24 24 063 .36 55 24 148 ±.24 24 151 ±.25 85 24.222 44 24 222 44

26 24.157 36 24 149 ± .40 56 24 073 ±.18 24 052 ±.27 86 24 154 + 54 24 145 57

27 24.147 42 24 147 + .42 57 24 252 ±.36 24 257 ±.38 87 24 237 + 31 23 237 31 28 23.997 ± 49 23 997 + .49 58 24 112 ±.18 24 073 ±.35 88 24 123 29 24 064 + 54 29 24.129 + 32 24 115 ± .37 59 24 095 ±.17 24 095 ±.17 89 24 206 27 24 158 47 30 24.242 t 29 24.185 + .53 60 24 134 ±.33 24 111 ±.31 90 24 179 + 37 24 179 37

3" (80 MM)

LINEAR RANGE 1-10 FT/SEC 1-20 FT/SEC

(.3 - 3 M/S) (.3 - 6.1 M/S)

MEAN MEAN

NO. K-FACTOR LINEARITY K-FACTOR LINEARITY NO.

LINEAR RANGE

1-10 FT/SEC 1-20 FT/SEC

(.3 - 3 M/S) (.3 - 6.1 M/S)

MEAN MEAN

K-FACTOR LINEARITY K-FACTOR LINEARITY

4" (100 MM)

LINEAR RANGE

1-10 FT/SEC 1-20 FT/SEC

(.3 - 3 M/S) (.3 - 6.1 M/S)

MEAN MEAN

NO. K-FACTOR LINEARITY K-FACTOR LINEARITY

1 8.709 + 45 8 709 ± 45

2 8.676 ± 63 8 676 63

3 8.674 + 51 8 674 + 51 4 8.683 ± 37 8 684 ± 38

5 8.688 + 50 8 688 t 50

6 8.690 + 66 8 690 + 66

7 8.703 + 38 8 703 ± 38

8 8.686 + 51 8 686 + 51 9 8.725 41 8 725 ± 41 10 3.713 14 8 701 + 28

11 8.702 49 8 702 ± 49

12 8.713 + 39 8 713 ± 39 13 8.688 + 44 8 688 ± 44

14 8.698 + 50 8 698 ± 50 15 8.705 ± 36 8 705 36

16 8.670 50 8 670 ± 50

17 8.695 38 8 695 38 18 8.685 ± 41 8 685 ± 41 19 8.697 ± 47 8 697 ± 47

20 8.678 ± 56 8 678 1 56

21 8.700 ± 32 8 700 + 32

22 8.705 ± 50 8 705 + 50 23* 8.663 ± 79 8 663 ± 79

24 8.664 ± 56 8 664 56 25 8.700 + 45 8 700 + 45

26 8.693 ± 40 8 693 + 40

27 8.696 + 49 8 696 ±.49

28 8.685 + 44 8 685 ±.44

29 8.677 49 8 677 ±.49

30 8.706 44 8 706 ±.44

31 8.703 + 52 8 703 ±.52

32 8.711 29 8 703 ±.37

33 8.705 ± 30 8 699 ±.37

34 8.695 28 8 689 ±.36

35 8.726 + 32 8 726 ±.32

36 8.696 59 8 696 ±.59

37 8.673 51 8 673 ±.51

38 8.702 + 47 8 702 + .47 39 8.690 + 35 8 690 ±.35

40 8.707 + 34 8 706 ±.35

41 8.695 + 41 8 695 ±.41

42 8.713 + 27 8 713 ±.27

43 8.682 ± 27 8.678 ±.31 44 8.720 34 8 720 ±.34

45 8.675 ± 36 8 675 ±.36

46 8.691 51 8 691 ±.51

47 8.730 + 27 8 730 ±.27

48 8.640 + 60 8 640 ±.60

49 8.698 ± 55 8 698 + .55 50 8.717 + 37 8 723 + .43

51 8.689 + 53 8 689 ±.53

1 3 964 + 13 3 952 ±.43

2 3 957 + 38 3 950 ±.54

3 3 964 27 3 950 ±.62

4 3 966 + 37 3 956 ±.65

5 3 949 + 12 3 936 ±.45

6 3 947 + 34 3 933 + .71

7 3 952 14 3 938 ±.49

8 3 955 + 35 3 942 ±.69

9 3 960 + 21 3 949 ±.49

10 3 945 + 32 3 928 + .75

11 3 953 + 43 3 943 + .69 12 3 958 + 14 3 946 ±.43

13 3 945 + 48 3 931 ±.83

14 3 950 + 26 3 938 ±.58

15 3 950 + 15 3 939 + .43

16 3 958 + 17 3 950 ±.38

17 3 954 + 31 3 938 ±.72

18 3 952 + 31 3 942 ±.58

19 3 955 + 39 3 938 ±.81 20 3 953 + 31 3 939 ±.64

21 3 956 ± 26 3 945 ±.53

22 3 958 ± 24 3 947 ±.51

23 3 952 + 22 3 938 ±.56

24 3 959 + 32 3 945 ±.65

25 3 957 + 27 3 946 ±.56

26 3 955 + 37 3 944 ±.67

559
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570
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS

,

Gaithersburg, MD, February ' 23-25 , 1977. .(Issued October 1977)

TEMPERATURE FIELD MEASUREMENTS IN TURBULENT THERMALS

Mohamed Gad-el-Hak

Flow Industries, Incorporated

Kent, Washington 98031

Laboratory studies of buoyant vortex bubbles and thermals

in an unstratified atmosphere are presented. Thermals are

generated by filling a soap bubble with a combustible mixture

and igniting it with an electrical spark. These are compared

to the thermals produced by igniting a similar mixture inside

a cylindrical box with a sharp-edged orifice at its top. Detailed temperature field measurements are obtained using an

array of hot-wire probes operating at low overheat . The temperature signals are digitized and different statistical quantities are obtained using an ensemble-conditional averaging

technique. It is found that initial conditions do have a

strong effect on the development and growth of a thermal,

even for gross parameters such as the "entrainment coefficient."

Key Words: Buoyant thermals; entrainment coefficient; fireballs; turbulent thermals; vortex bubbles

.

1 , Introduction

The study of instantaneous and continuous sources of buoyancy 1 (thermals and plumes, respectively), is of great practical importance

in various fields. In 1941, G. I. Taylor, in an unpublished report,

studied the early stages of formation of a thermal which would be produced by a very intense (atomic) explosion. He later published his

findings [l] 2 regarding the formation of a blast wave and compared his

results with photographic records of the first atomic explosion. 3

1 A fluid possessing a density difference with respect to its surroundings, whether as a result of differences in temperature, molecular

weight (for gases) , or concentration of a solute (liquids)

.

2 Figures in brackets refer to literature references at the end of this

paper,

3New Mexico, 1945.

571
Schmidt [2] considered what happens to the convection currents rising

from heated bodies, at a distance above their source. He discussed

the dynamics of turbulent plumes by supposing that the distribution of

temperature and velocity can be found by balancing the horizontal turbulent transfer of heat and momentum against the vertical convective

transfer. A simpler transfer assumption was made by Taylor [3], who

related the inflow into a convective plume to its characteristic

velocity. More theoretical and experimental studies were made for

a body of fluid rising (or falling) through a uniform ambient [4-6],

or through a stratified ambient with any vertical density distribution [7].

The motion of isolated buoyant thermals was also studied with a specific practical application in mind, such as the formation of cumulus

clouds [8-10], the development of fireball in lighting [11], or the

intermittent release of smoke from chimneys as a means of increasing

the height attained [12],

In a series of studies [13-15], Wang, et al. tried to relate the

turbulence intensity within the thermal to the entrainment parameter =. Escudier and Maxworthy [16] presented an analysis for the motion of a

turbulent thermal in an unstratified environment, based upon the

entrainment hypothesis introduced by Taylor [7]. Their analysis is

valid for any density difference between the thermal and its surroundings since they considered the influence of the "virtual mass" [17] of

the unsteadily moving fluid.

Different investigators have used different techniques to generate

identical thermals in laboratory studies. For example Morton, et al.

[7], carried out their experiment in a stable stratified salt solution

in which discrete clouds were released suddenly by removing the cover

from the top of a small reservoir, which contained a known volume of

light fluid. Fohl [18] burst helium filled soap bubbles at atmospheric

pressure. Lin, et al. [14] produced relatively small but strongly

heated thermal bubbles by pulsed arc discharges in otherwise undisturbed

air. Haigh and Mantrom [19, 20], developed a system to remotely form

and burst helium-filled soap bubbles in a high pressure tank filled with

air. Shlien and Thompson [21] injected heat into a liquid by operating

a conductivity probe at high power.

From these and other experiments one can deduce, among other

things, a value for the entrainment coefficient a . It is found that <* does not have a universal value, and changes over the range 0.01 - 0.35.

Also called entrainment coefficient: the constant of proportionality

in the mass conservation equation [16].

572 !
As Escudier and Maxworthy [16] have pointed out, it appears that = might be a function of the initial density difference, and also of

the detailed nature of the initial conditions under which a given

thermal is formed 5. Fohl's [18] experiments (A El- initial

density /ambient density - 0.85) gave a value « - 0.08 for the best

organized thermals, and <* - 0.17 for the least organized ones.

Experiments on less organized thermals [8] gave values of « in the

range 0.2 - 0.35 (A - -0.15). Maxworthy [private communications]

obtained <* - 0.01 by giving a thermal an initial circulation.

The present study was motivated by these inconsistencies in

previous measurements and a desire to understand the role played by

initial conditions in forming a well organized thermal. As such it

is only a preliminary effort which has, like so many, raised as many

questions as it has answered. Thermals are generated by two new and

distinctly different methods. In the first, a soap bubble is filled

with a lean mixture of oxygen and propane and ignited with a spark.

In this case, the thermal initially assumes the form of a smooth

sphere. In the second, a cylindrical box with sharp-edged orifice

at its top is filled with a similar mixture and then ignited. In

this case, vorticity is not only produced by buoyancy effects, but

also generated by viscous effects at the sharp-edged orifice; hence,

different initial conditions are expected in the two cases. In

both cases a structure like a vortex ring is observed to form at a

later stage, particularly when a rich mixture is used and combustion

continues as the thermal rises and mixes with ambient oxygen.

Detailed temperature field measurements are obtained using an

array of hot wire probes operating at low overheat ratio. The temperature signals are digitized, and different statistical quantities

are obtained using an ensemble-conditional averaging technique.

2 . Experimental Equipment and Procedure

i. Generation of Turbulent Thermals

Preliminary calculations of the conditions to be expected in

thermals produced in air, under various circumstances, showed that a most encouraging approach would be to fill a soap bubble with a com-'

bustible mixture and ignite it with a spark. Since the buoyancy of

the initial mixture in air is amall, a large stable soap bubble can be

produced initially while large buoyancy forces results after ignition.

In the laboratory, Reynolds numbers of the order 1014 - 10 5 can be

attained by this method at atmospheric pressure, thus more closely

simulating large scale thermals in the atmosphere.

Hopefully, 1 is a constant for any given thermal. However, Dr..

J.S. Turner (private communication) has suggested that « might be a

running variable dependent upon the local density difference.

573
The soap bubble generator, figure 1(a), consists of a glass-blower's

torch for mixing oxygen and propane, attached to a rotating funnel

(diameter = 3.6 cm) for picking up a soap film (when in the downward

position) , and producing a stable soap bubble (when in the upward position) . A special soap bubble solution was developed to produce large

(10 cm diameter), long lived bubbles. It consists of 600 cc, commercially available, Jack dishwashing soap solution5

, 300 cc glycerol and

0.1 cc strong ammonia solution. A known flow rate of oxygen and propane is fed to the torch, from their respective tanks which are equipped

with pressure regulators and needle valves. The mixture Is lean (20%

excess oxygen) , and the theoretical energy released from an exothermic

reaction inside a 10 cm diameter bubble is about 10^ Joule,

Extreme care has to be taken to generate identical thermals eachtime. It is necessary to fill each soap bubble to the same desired

diameter, with the same combustible mixture ratio. From an error

analysis, visual observations using high speed photography, and examination of instantaneous temperature profiles, it is estimated that,

in a series of experiments on any one day, the thermals are initially

generated with a repeatability ± 5%. 7 However, the repeatability from

day to day is within ± 10%, presumably due to changes in ambient

conditions

.

Thermals are also produced by filling the cylindrical box shown

in, Figure 1(b), with the same volume of oxygen and propane used to fill

a 10 cm diameter soap bubble. The (heavy) mixture enters the bottom of

the box radially outwards to minimize or prevent escape. The box has a

10 cm diameter sharp-edged orifice on top, large enough to prevent a

jet-like ejection of the combustion products after igniting the

mixture. As the combustion products expand out of the box they roll

up into a body of moving fluid which initially takes the form of an

oblate spheroid [22], with considerable vorticity generated by

viscous forces at the sharp edge.

Thermals are generally generated at the rate of two per minute.

This would allow enough temporal separation to prevent interaction

between two consecutive thermals. In the meantime, a large number of

thermals could be produced before any appreciable drift in the ambient

conditions would occur. To prevent external influences from interfering

with the thermals (drafts in the room, etc.), they are generated inside

a 120 x 120 cm plexiglass box 300 cm in height, with a fine screen on

top to provide an exit for the rising gases. Near the ceiling, a

typical thermal diameter is less than 80 cm or 35% of the cross-sectional

area of the box.

Proctor & Gamble Corporation.

Range of variation of initial diameter and A/F ratios: hence, initial

energy contained in a thermal.

574
ii. Flow Visualization

During the early stages of formation of a thermal

} the temperature

is high enough to cause strong visible radiation, which enables direct

observation. A high-speed 16 mm movie camera (Fastax, category I,

type WF3 8

), capable of attaining speeds as high as 8000 frames per

second, is used to observe the initial 300 milliseconds of thermal formation

and development. This high camera speed necessitated using high ASA

rated film specially perforated on both edges to prevent tearing. At

a later stage, the temperature inside a thermal is considerably lower

due to energy loss by radiation and entrainment of colder ambient air,

and, hence, it loses all its luminosity, with the result that conventional

photography cannot be used. Shadowgraph movie films are taken at 64

frames per second, using a 500-watt mercury short arc lamp to project a

shadowgraph image on screen. Because of the small density differences

and low sensitivity of the shadowgraph method, no satisfactory pictures

were obtained in these preliminary experiments.

Other flow visualization techniques are possible, such as holographic interf erometry [19, 20], light scattering from small helium

filled soap bubbles which are neutrally buoyant, or from dust particles,

etc

.

iii. Temperature Field Measurements

An array of four hot wire probes is used to obtain detailed information of the temperature field structure inside the turbulent therinals

.

Each probe is a straight wire mounted on jewelers' broaches (0.3 mm

diameter) encased in epoxy resin, with 5 mm stainless steel tube for

the main shaft. The sensitive part is 1.27 microns in diameter and 1 mm

long, platinum - (10%) rhodium etched from Wollaston type after the

silver coating has been soldered to the tips of the jewelers' broaches.

A four channel constant current anemometer supplies about 1 mA current to

each probe to maintain an overheat ratio of 0.8%. At this low overheat,

the probe is essentially sensitive only to temperature fluctuations, and

it can be shown that, under typical operating conditions, the sensitivity

to temperature is about 100 times the sensitivity to velocity or concentration. Probe temperature (hence, resistance) follows closely changes

in gas temperature, this unbalances the Wheatston bridge and the difference

voltage is amplified in two stages by a factor of 6000. The first stage

amplifier also serves as a low-pass filter to remove undesired high

frequency noise above 3 kHz . The output voltage is proportional to the

gas temperature above ambient.

The spatial resolution of a probe is of the order of the length of

the sensitive part (1 mm) , while the temporal resolution is governed by

the diameter of the wire, overheat ratio and heat transfer coefficient [23].

3 M Company.

575
Direct sine-wave calibration gave a frequency response of about 1 kHz

to the "3 db down point", which is satisfactory for our purposes.

The temperature sensitivity is determined for each probe by direct

calibration with a thermocouple in a heated oven. The response is

found to be linear over the temperature range of interest (20 - 50 C).

The signal from the four channel anemometer is a,c. coupled and

FM-recorded on a 3 M company wide band recording tape using a four

channel Hewlett-Packard Instrumentation tape recorder, series 3960, at

a recording speed of 3 ips. At this speed the frequency response of

the recorder is flat up to 1 kHz, and the signal-to-noise ratio is

48 RMS/RMS (db). The analog signal is then digitized at a sampling

rate of 4000 milliseconds per four words, and processed on a digital computer

The hardware which performed the analog-to-digital conversions is a 12 bit

5 volt full conversion [24], providing a resolution of one part in 4096,

or a digital signal-to-noise ratio of about 72 db . Digitized data are

stored on a 9-track digital magnetic tape for processing by FORTRAN

programs.

The four resistance thermometers are located at Z = 70, 124, 175

and 245 cm, above the initial position of a thermal center (Z = 0).

The array is moved horizontally to measure the temperature fluctuations

at six different locations across the thermal: X = 0 , 6 , 13 , 25 , 32

and 38 cm.

3 . Formation of the Buoyant Thermals

Combustion inside a soap bubble has been used before in flame propagation research [25]. For the large diameter bubbles considered the

internal pressure hardly changes as the diameter increases, hence

approximately constant pressure combustion can be attained. For our air/

fuel ratio and fuel types, the flame speed is about 350 cm/sec, so it

takes about 14 milliseconds for the flame front to cross the region of fuel

mixture. However, as the spherical combustion front advances, the burned

gas being much hotter than the initial reactants occupies a larger volume.

As a result, both the combustion front, the unburned reactants and the

soap bubble interface are pushed outwards. In fact the combination of

flame speed and expansion due to heating is so great that a weak spherical

shock wave is formed. At some state during this process the soap bubble

breaks probably before the flame front reaches it. When all of the combustible mixture has been consumed the diameter of the hot "fire ball"

is approximately 23 cm. This has been deduced from photographic records,

and also from thermodynamic calculations for the reacting mixture. At

this state the temperature is estimated to be 2760 C ± 10%, and the

density of the combustion products is 1.2 x 10_Lf gm/cm 3

. We arbitrarily

choose this state to be the origin of time, since observations show that

the combustion process is finished before the hot gas sphere starts to rise.

576
The important parameter "initial density difference" A = 1 - p /p , where p is the (average) density of the combustion products at°t = 0,

and p^ is the ambient density, is then 0.9 ± 2%.

Figure 2 shows a one second exposure picture immediately following

the explosion of a soap bubble. The gas temperature is high enough to

cause strong visible radiation. From such a picture, one might gain a

qualitative idea about the large-scale structure responsible for

entrainment, although as Lin, et al., [14] has pointed out, an inference

of the temperature field structure from the luminous profile is difficult

due to the nonuniform nature of the convective mixing process and the

strong dependence of air emissivity on temperature. The increase in

size with height is evident, and one might even attempt to compute very

crudely an entrainment coefficient from such a picture, keeping in

mind the limitations just mentioned.

A movie film is available for the early stages of formation of a

thermal generated from the explosion inside a soap bubble. A camera

speed of 3000 frames per second is used. Initially a smooth spherical

fireball is observed, and a mushroom - like gas with vorticity generated

by buoyancy effects is followed after about 60 milliseconds . The rotational

motion causes the entrainment of colder ambient air with the gradual

loss of luminosity particularly at the outer edges, and, hence, the

thermal appears smaller than it actually is. The thermal accelerates

upward to a maximum speed, then decelerates and eventually stops. The

Reynolds number based on this maximum upward velocity and an "equivalent"

diameter is calculated from the temperature field measurements to be

about 3 x 10h

.

A second film taken at the same speed is also available for the

early stages of formation of a thermal generated using the sharpedged orifice. The viscous forces at the sharp edge generate vorticity,

and as the combustion products expand out of the box, they roll up into

a body which initially takes the form of an oblate spheroid. As in the

previous case, the thermal entrains colder air from outside, and its

size increases as it moves upward. Although approximately the same

amount of energy is fed into thermals generated by the two methods, it

is not expected that even gross parameters, such as the entrainment

coefficient would be the same for the two cases.

4 . Ensemble - Conditional Averaging

A typical signal from a resistance thermometer during the passage

of a thermal is shown in figure 3. The probe is located 70 cm directly

above the origin (Z = 0) . The signal is obtained by playing back the

analog tape into a Hewlett-Packard X-Y recorder model 7004B*

The X-Y recorder has very limited frequency response which filters

out the high frequency fluctuations.

577
The signal may be considered as representing (approximately^ 0

) an

instantaneous temperature profile along a vertical cut in the center

of the thermal. As in previous experiments [14], a sharp temperature

interface at the top of the thermal is evident by the sudden rise in

temperature as the thermal first touches the probe; also, a wake

formation is suggested by the gradual decay near the end of the signal.

To extract useful statistical information from such a transient

signal is a very difficult task. Time and space averages do not have

any great physical significance, and only an ensemble average [26]

would enable us to study the temperature field structure. This means

an average taken over a "large" number of experiments that have the

same initial conditions. In order to complete our task, we have to

define the beginning of an event (or ensemble). Fortunately, in the

problem at hand, the beginning of an event is very well defined by the

sudden rise in temperature, hence a condition for the start of an

event can easily be found.

If i indicates the event number, t the time measured from the

beginning of that event, n total number of events, and T.(t) is the

temperature (above ambient) at time t of the it*1 event, izhen the

ensemble average temperature is:

1 n

T (t) = - I T. (t)

n

i-1

1

n

T.(t) =f(t),+ T! (t) , Z T.' E 0

1

Average

^

Fluctuation

^

i=l

l

The average temperature is, of course, a function of time. The rootmean- square temperature fluctuations is given by:

Vt* 2 (t) =fil (T.(t) - T(t)) 2

i=l

= [- E T.(t) 2 - T

2

(t)]^,

n

i=l

1

also a function of time. And so on for other statistical quantities

10 Since the thermal' s characteristics vary slightly during the time

of transient.

578
The spectrum is rather more difficult to define for an ensemble

of transient signals. For the much simpler case of a stationary

random function, the spectrum can be obtained by Fourier transform,

the two-point correlation function (mean-lagged product}; or by calculating the Fourier coefficients of the (time) series, then the

spectrum at any frequency f is a

2 + b2

, where a(f) + b(f) are the

complex Fourier coefficients. For our transient signal, we divide the

signal from each thermal into one second intervals, calculate the

Fourier coefficients for each interval, and average the resulting

spectra from corresponding time intervals over the whole ensemble.

The resulting spectra is then a function of both time and frequency

[S(f, t)], with a low cut-off frequency inversely proportional to

the time interval (1 sec) . To avoid aliasing in spectrum measurements, the sampling frequency should be at least twice the highest

frequency of physical significance present in the data (the Nyquist

folding frequency) , and appropriate filtering is used when converting

the analog data to digital. By definition, T

1 = f S(f , t)df , and

this can be used for checking the consistency of caiculations

.

The "integral scale" L is a measure of the longest connection, or

correlation distance, between the temperature at two points of the

temperature field. L can be computed by extrapolating the spectrum

to zero frequency using the relation [26]

L(t) = (U/4 T

7^) S (o, t),

where U is the average upward velocity at time t, and T

z is the mean

square temperature fluctuations at the same time.

5 . Results

The time history of the ensemble averaged temperature T(t) for 262

thermals generated using the orifice method, at the four reference

heights directly above the orifice center, is shown in figure 4. t = o indicates the arrival of a thermal at the nearest probe. The arrival

time at the other three probes relative to this origin of time varies

from thermal to another, and an arithmetic average over the whole ensemble

for this time is shown on the abscissa. We note the strikingly smooth

profiles, as compared to the (instantaneous) signal from one event

(figure 3) . This is a consequence of the loss of phase information in

the ensemble average, and can be used to test the convergence of the

averaging process. The averaging was also performed using 20 events only,

and the resulting profiles are qualitatively similar, an indication of a

The fluctuating temperature field may be assumed to be composed of

fluctuations corresponding to different frequencies in a continuous

frequency range. A spectral analysis of the temperature flucuations

will show how the contributions are distributed over these frequencies.

579
good repeatability in initial conditions. As expected, a thermal

cools as it moves upward; the temperature is highest at its top

(about 17 °C above ambient at Z = 70 cm), and approaches ambient

conditions gradually, suggesting the existence of a thermal wake.

A similar set of curves is shown in figure 5 for 169 thermals

generated using the soap bubble method. The temperature profiles

have a similar form to the previous ones, except for the appearance

of a second peak at Z = 70 and 124 cm. This might indicate that, at

this relatively early stage of development, the mass entrainment process does not penetrate all the way into the core of a thermal, hence

the "hot spot" which appears even after averaging over 169 different

thermals. This might also indicate less efficient mixing for this

kind of thermal, consistent with the lower vorticity levels as compared to thermals generated using the orifice method.

Figure 6 shows ensemble average temperature profile at different

positions across 50 thermals generated using the orifice method.

The probe is kept at constant altitude Z = 124 cm, but its horizontal

position is changed as indicated. The "arrival time" (relative to

the nearest probe, Z = 70 cm) as well as the peak temperature are

slightly different for the different positions across the thermal.

The differences are within the variations expected from an ensemble

to another. The signal tail at x = o has the lowest temperature,

perhaps an indication of greater amount of cold air entrainment at

this position. Figure 7 is a similar one for 40 thermals generated

using the soap bubble method. The probe height is the same as before,

and the horizontal positions are x = 0, 6 and 13 cm. Again, a second

peak appears in the average temperature profiles for this kind of

thermal

.

Figure 8 shows root-mean-square temperature profile [ tor

262 thermals generated using the orifice method, as computed using the

ensemble-conditional averaging technique, at x = 0 and Z = 70, 124,

175 and 245 cm. As before, t = 0 indicates the arrival of a thermal

at the nearest probe. We note that the turbulence intensity is higher

at Z = 124 cm than at Z = 70 cm, an indication of continuing production

of new turbulence energy between these two heights. The maximum rms

value is about 7.5°C, almost 60% of the corresponding mean value! One

can estimate the "noise leval" from the rms value at t = 0; in this

case it is about 0.4°G or 5.3% of the maximum rms value. The profiles

bear the same general characteristics as the average temperature profiles.

A similar set of profiles is shown in figure 9 for 169 thermals

generated using the soap bubble method. The maximum rms value is about

8.5°C, almost 70% of the corresponding mean value.

580
The spectrum S(f, t) for different cases is computed using the

fast-Fourier-transform routine. Figure 10 shows a semi-log plot of

S(f, t) versus f, for four time intervals: At = 0-1, 1-2, 2-3 and 3-4

sec. The thermals are generated using the orifice method, and the

probe height is 70 cm directly above the orifice center. Figure 11

is a similar one for thermal generated using the soap bubble method.

The area under each curve (on a linear plot) should equal the corresponding mean square temperature.

The integral scale is computed from the formula

L(t) = (U/4T^) S(o,t),

where S(o,t) is obtained by extrapolating the spectrum to zero frequency

(using a linear plot); T

1 1 is computed from the rms temperature profiles

at the intermediate time for each interval.'12 Table 1 shows the integral

scale L in cm at Z = 70 cm directly above center for both kinds of

thermals, at different time intervals At. Table 2 shows the integral

scale for both kinds of thermals at various heights but only for

At = 2-3 sec. Thermals generated using the soap bubble method tend to

have larger integral scales, perhaps an indication of the lesser degree

of organization as compared to the thermals generated using the orifice

method. Integral scale computations should be viewed with caution, due

to the high degree of arbitrariness in choosing the time intervals, and

in extrapolating the spectrum to zero frequency.

At (Sec) 0-1 1-2 2-3 3-4

Orifice method 8.5 3.3 3.6 4.5

Soap bubble method 31.8 10.7 8.0 5.7

Table 1 Integral Scale L cm; Z = 70 cm.

Z cm 70 124 175 245

Orifice method 3.6 7.6 3.7 3.1

Soap bubble method 8.0 8.5 2.6 2.4

Table 2 Integral Scale L cm ; At = 2-3

U will be computed later in this section

.

581
More information on the dynamics and structure of the thermals. can

be extracted from the temperature records. For example, an average

velocity for a rising thermal can be estimated by noting the time it

takes to travel between several probes directly above each other, 13 and

computing the local slope dZ(t)/dt. It should be noted that this would

represent the average upward velocity of the highest point on the

thermal interface, and that this is not necessarily equal for all

points inside the thermal. Velocities calculated in this way are

shown in figure 12 for both types of thermals. Evidently the data

shown represent the deceleration phase of the thermal. Near the

source, the orifice thermals are faster by about 50%, however both

types reach the same speed as they approach the ceiling, perhaps an

indication of the resistance due to the wire screen on top of the

plexiglass box.

By finding the best fit to the present data using the analytical

model presented by Escudier and Maxworthy [16] , one can estimate a

rough value for the entrainment coefficient. However, it should be

noted that this does not prove the validity of the models, nor the

accuracy of the present measurements. For the orifice thermals,

<* = 0.06 ± 10% and for the soap bubble thermals, « = 0.1 ± 10%. This

agrees qualitatively with the photographic records. An orifice thermal

has strong initial vorticity, and may develop a core (ring) with fast

rotation, which in turn may have a stabilizing effect on the turbulence

field; this would limit the amount of air entrained - - - hence, the

smaller entrainment coefficient. Detailed data on the turbulent

velocity field are needed to verify this point, and hopefully to understand the dependence of <= on the initial conditions quantitatively.

6 . Concluding Remarks

Detailed temperature field measurements in thermals generated using

two distinctly different methods are presented in this paper. First, by

igniting a combustible mixture inside a soap bubble; second, by igniting a similar mixture inside a box with a sharp-edged orifice at its

top. The second kind is initially more organized with strong circulation resulting from the roll-up at the sharp-edged orifice. Initial

conditions are shown to have a strong effect on the development of a

thermal, even for gross parameters such as the entrainment coefficient.

It is shown that « is smaller for the more organized kind of thermal.

A thermal produced more or less "cleanly" 4

as with the soap bubble

method, moves slower initially, as compared to the initially organized

one

.

Again, this is repeated over a large number of realizations, and the

concept of an "average thermal" is invoked.

For example, a perfectly smooth non-turbulent fluid sphere, with zero

initial impulse.

582
Uniform ambient conditions are used throughout the present work.

An obvious continuation of the present experiment would be the use

of stratified surroundings; either linearly stratified (to stimulate

motion in the stratosphere, for example), or with a discontinuity of

density (e. g. , simulation of the tropopause) . Thermals moving in

an atmosphere which has been stirred, by moving grids, so that they

move in a field of almost isotropic turbulence, would be of great

interest to Geophysical studies. Other types of atmospheric structures

can also be considered.

Detailed measurements of the turbulent velocity field are obviously

needed. A laser-Doppler velocimeter with a tracking-amplifier is

needed to measure instantaneous velocity profiles at different positions

since hot wires would be very difficult to use because of the high

temperature and concentration fluctuations present.

This work was supported by the National Science Foundation, under

Grant GK 38147X, to the University of Southern California. The author

is immensely grateful to Professor T. Maxworthy, the Principal Investigator for suggesting the problem, for his guidance in carrying out the

investigations and for providing many fruitful discussions.

References

1. G. I. Taylor, Proc. Roy. Soc. (London), A201, 159 and 175 (1950).

2. W. Schmidt, Z. angew. Math. Mech. } 21, 265 (1941).

3. G. I. Taylor, U. S. Atomic Energy Commission, MDDC 919, LADC 276

(1945).

4. C. S. Yih, Proc. 1st Bat. Congr. Appl. Mech. } 941 (1951).

5. H. Rouse, C.S. Yih and H. W. Humphreys, Tellus3 4, 201 (1952).

6. G. K. Batchelor, Quart. J. R. Met. Soc 3 80, 339 (1954).

7. B. R. Morton, G.I. Taylor and J.S. Morton, Proc. Roy. Soc. (London)

A234, 1 (1956).

8. R. S. Scorer, J. Fluid Mech. , 2, 583 (1957).

9. J. Levine, J. Atmos . Sci. } 16, 653 (1959).

10-.. J. S. Turner, Annual Review of Fluid Mech. 3 1, 29 (1969).

11. Y. N. Zhivlyuk and S. L. Mandel ' shtam, Zh. Eksp. Teor. Fiz. 3 40,483

(1969).

583
12. J. S. Turner, J. Meoh. Eng. Science, 2, 97 (1960).

13. C. P. Wang, Phys. Fluids, 14, 1643 (1971).

14. S. C. Lin, L. Tsang and C. P. Wang, Phys. Fluids, 15, 2118 ((1972).

15. c. P. Wang. Phys. Fluids, 16, 744 (1973).

16. M. P. Escudier and T. Maxworthy, J. Fluid Meoh., 61, 541 (1973).

17. L. M. Milne-Thomson, Theoretical Hydrodynamics, Macmillan, p. 237

(1967).

18. T. Fohl, J. Appl. Phys., 38, 4097 (1968).

19. W. W. Haigh and D.D. Mantrom, TRW Report, .DNA 2981 Z (1973).

20. W. W. Haigh and D.D. Mantrom, TRW Report, DNA 3139 Z (1973).

21 D.J. Shlien and D. W. Thompson, Some fundamental buoyant convection

experiments, Part I & II, submitted to J. Fluid Mech. (1975).

22. T. Maxworthy, J. Fluid Mech. , 51, 15 (1972).

23. J. C. Wyngaard, J. Sci. Instrum., 1, 1105 (1968).

24. C. W. Van Atta, Annual Review of Fluid Mech. , 6, 75 (1974).

25. B. Lewis and G. Von Elbe, Combustion flames and explosions of

gases, Acad. Press, p. 200 (1961).

26 J. 0. Hinze, Turbulence, McGraw-Hill, p. 4 (1975).

584
(a)

Figure 1. Thermal generators, (a) Soap bubble method (b) Orifice method.

585
Figure 2. A one second exposure, showing the convolution of a thermal

that resulted from an explosion of a soap bubble.

586
- o

o

CO - in - O

CD ,G

4-> • cu Q o o

CO I

aj IIN

}-i cu

4-1 cuBo

o

e li u

cu •

4->

O

cuo 4-1 CU cd 6

4J

CO 0) •H o

CO •H

0) •H

cu

o

4-1 • • 6 CU o

>-l

O

14-1 V4a. iH

CO cu c x:

bO 4-1 •H

CD

iH

CO CO o cu H CO a- CO H a

CO

cu

S-i

00

•H

(3)1

587
588
t SEC.

Figure 5. Ensemble average temperature: Soap bubble method; x = 0.

z = 70; , z = 124; z = 175; z = 245 cm.

589

t SEC.

Figure 7. Ensemble average temperature: Soap bubble method; z = 124.

x = 0; , x = 6; . . . . , x = 13 cm.

591
592
593
594
595
80 100 120 140 160 180 200

Z(cm)

Figure 12. Average upward velocity; , Orifuce method; .-, Soap

bubble method.

596
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

FLOW MEASUREMENT UP-DATE

Robert B. Suhoke

Disa Electronics

779 Susquehanna Avenue

Franklin Lakes, N. J. 07417

1. INTRODUCTION

The intention of this paper is to provide insight into basically

two flow measurement techniques. Consideration is given to the latest

innovations in both the thermal and optical methods and the sources of

possible error. Many of these error contributions can be reduced or

eliminated by various techniques which will be explored and evaluated.

2. THERMAL METHODS

Thermal devices, more commonly referred to as hot-wire or film

anemometers, have been in existence in various forms prior to this century

and presently they remain employed in an extremely wide range of applications, the most predominant of course is flow measurement, Figure (1).

In 1914 L. V. King brought forth a solution for the heat transfer from

an infinite cylinder in an incompressible flow written as:

Nu = A' + B' Re^ (1)

This has survived in one form or another and is often used today to

explain the basic related physics. Much of the early work and some of

the initial apparatus developments occurred at the National Bureau of

Standards [1].

Equation (1) can be expanded by writing:

,Q . = A' + B' ( pUd ) 2 (2)

IK (T-To)

A b

y

{ ' )

Q, the heat loss, can be taken as equal to the electrical power delivered to the sensor and can be rewritten:

V

2 = A'RLK (T-To) = B' LKR (T-To) (3)

If the fluid temperature remains constant equation (3) becomes:

E

2 = A + BU^ or E = /A + BUM (4)

597
This response capability and small spacial probe size along with the

continuous signal output are no doubt the most important reasons why this

measurement technique was brought about and also why it is extensively

used today.

If a close inspection of the circuit diagram is made one can readily

see that if the bridge is to maintain balance and the probe is one leg of

the bridge, and the decade or operating resistor is the balancing leg then

the following will occur: The resistance of the probe sensor material will

vary with ambient temperature changes in the flow channel while the resistance of the decade resistance or operating resistor leg remains constant.

The system is calibrated at one given temperature (20°C) therefore the

calibration is no longer an accurate presentation.

To circumvent this a film or wire coil with the same identical a

(temperature coefficient of resistivity) can be made to replace the fixed

leg of the bridge with the appropriate resistance (typically 60-80% above

ambient for gases and 5-10% for liquids) and also placed into the flow

environment. This allows the system to maintain a constant resistance ratio

over the temperature range encountered. However, if the temperature is

fluctuating at a frequency above approximately 2 Hertz this method is not

compensating with fidelity due to the mass of the compensator.

For flows with slowly varying temperature this technique is ideal.

However, for the high frequency case the bridge must be configured somewhat

differently and the compensating leg replaced with a sensor similar to the

velocity sensor with regard to geometry and materials. This method offers

a relatively small mass to contend with and permits accurate velocity measurements irregardless of temperature fluctuation and fluid media.

These techniques may not be adaptable to all thermal-type devices, in

which cases manual adjustment or correlation techniques must be employed.

Also, simultaneous monitoring of temperature in combination with a family

of calibration curves at a range of temperatures can be used to correct the

data.

The next discussion point is the temperature distribution along the

sensor itself. Knowledge of the detailed temperature distribution is not

a requirement in most probe applications. The distribution is glossed over

by the integrated mean temperature or resistance [2].

Much emphasis has been given to calibration technique and therefore the calibration method must also be explored and there are many. For

gases most arrangements rely upon a pressure drop to determine the velocity

using venturi sections, nozzles, pi tot tubes, etc. If the device is not wel

defined one may be introducing inaccuracies into the experiment via the cali

bration obtained.

For liquids the method employed is more dependent upon the velocity

range. Some typical systems most often used are tow tank, time/volume or

weight collection, and standing tank with free jet exit nozzle, etc.

598
This leads directly to the first potential source of error. The value

of the exponent n differs from sensor to sensor and also with velocity, Figure

along with the values of both A and B. It therefore becomes essential to

calibrate each sensor/system individually and exercise periodic checks [2].

Although there has been extensive analysis on the subject of heat

transfer applied to hot wires and films it has resisted all efforts to produce an accurate universal expression to describe it and to reiterate the

only real method for interpretation of the results of thermal anemometry is

direct calibration. A low turbulence flow of precisely known velocity is

acceptable. One criteria is that the sensing probe must have the same

orientation during calibration that which it will be mounted with regard to

the velocity vector in the actual measurement. Typical directional sensitivity plots as shown in Figure (3) indicate the effect of yaw and pitch [3,4].

The probe geometry provides varied results [2]. For example, the prong

spacing vs. sensor length for cylindrical types imparts noticeable changes.

Figure (4). Proper probe design and precise calibration will reduce this

contribution [4].

The temperature of the fluid must remain constant for the duration of

the calibration measurement so that it will maintain accuracy. In the

actual experiment this requirement may not always be satisfied, therefore,

a method for compensation must be used. This can be accomplished via various

techniques, however, before this can be intelligently discussed, a description of a typical electronic anemometer arrangement is required.

Hot-wire and hot-film anemometers are normally operated in the constant

temperature (CTA) mode as shown in Figure (5). The resistance of the probe

and, therefore, its temperature is maintained constant. The output bridge

voltage is related to the heat transfer from the probe and this in turn is

related to the fluid parameter under consideration (usually the velocity).

The bridge is maintained in balance by a voltage from the servo-amplifier.

Any change (aR) in the resistance of the probe resistance due to a change

in the heat transfer will cause an unbalance in the bridge and simultaneously

introduce an error voltage at the input to the servo-amplifier. This error

voltage is highly amplified and fed back into the bridge to maintain balance

via adjusted bridge voltage and sensor current. The probe temperature is

thereby kept essentially constant and the thermal inertia of the probe is

minimized. Due to the very high gain in the amplifier and the small mass

of the sensor the system is capable of responding to very rapid fluctuations

in velocity.

The present art of constant temperature anemometry is based on the

design of a very stable servo-system with a very high closed loop gain and

a well-balanced differential amplifier with a flat characteristic from DC

to high frequencies. With the use of solid-state and integrated circuits

these principles can and have been realized and extremely high feedback

loop gains have been accomplished with stability thus allowing not only

low noise but also the ability to correct for the frequency response of

all types of probes including films.

599
These calibration schemes are static and an assumption must be made

that the dynamic response is the same. Direct dynamic [5] schemes can be

performed in a flow in which sinusoidal velocity variations are superimposed

on a constant mean velocity.

Sensor contamination via the deposition of impurities present in the

fluid can dramatically alter its heat transfer properties and subsequently

the calibration. Cleaning and/or recal ibration is required with the periodicty dependant upon the specific case. Additionally, in liquids dissolved

gases can form bubbles on the sensor surface hence modifying the heat transfer and also the calibration [6]. The bubbles must be physically removed.

To reduce this error contribution the sensor can be operated just slightly

above the ambient temperature of the fluid and, if possible, precautions

should be taken to reduce cascade effects and also implement deaeration

processes in the case of supersaturated liquids.

Electronic drift in the past was a substantial contribution to measurement error but the latest technology in component design has reduced this

problem by several magnitudes. Of course periodic stability checks enhance

the virtue of the data obtained.

From a typical calibration as shown in Figure (2), it can be noted from

the shape of the curve that the voltage resolution and thereby the velocity

resolution can vary from volts to just a few millivolts over the range of,

for example, 0-100 meter/sec. A high resolution voltmeter is then necessary

to monitor the voltage for the velocity determination.

One solution is to provide a linearization circuit which matches the

transfer function for a given probe velocity combination [7]. This can be

accomplished by diode approximations, logrithmic and polynomial curve filtering and velocity controlled variable exponent techniques.

The benefits are twofold: higher accuracy is possible over the entire

range and in the high turbulence case the non-linear distortion is eliminated.

However, each additional electronic device included in the overall data producing system provides an additional drift potential which is additive.

For thermal anemometry it can be concluded that although there is an

extremely wide range of differences of opinion in the extensive literature

published to date, with regard to every facet, accurate measurements are

obtainable with state of the art sensors and electronics. The overall

accuracy result is in the hands of the end-user.

3. OPTICAL METHODS

Optical devices such as laser doppler anemometers or velocimeters are

relatively new to the flow measurement field. In 1964 [23] it was demonstrated that coherent light sources could be used for the measurement of

fluid velocities by observing the doppler shift in the frequency of light

scattered from small particles moving with the fluid, Figure (G) . In the

600
past few years the technique has expanded its capabilities immensely. Application demands have also moved with the same rapidity.

The laws of physics that apply can be expressed as follows: When two

collimated beams of light intersect, they create a fringe pattern. A particle passing through this pattern causes a shift in the incident radiation.

It can be shown that doppler frequency shift and particle velocity are related by:

f

d

=

2 Sin h 0

U (5)

or:

U

=

2 Sin 0

f

d

(6)

A laser doppler anemometer system is described in the block diagram

of Figure (7). Typically most systems will follow this format or offer

some small deviation. Each block will be discussed independantly with a brief explanation of its function and error contribution.

Radiation Source - The laser is monochromatic (single frequency) consisting of plane waves and the signal is both spatially and temporally coherent. Spatial coherence may be described by stating that all light waves

in a cross-section of the beam are in phase with each other. This is

accomplished in the laser cavity by suppressing the noncoherent modes of

oscillation and placing a small aperture in the light path. Temporal coherence is present when the beam can interfere with itself over a considerable difference in path length. The light intensity follows a Gaussian

distribution, Figure (8).

I = Io exp - % ~ I = Ve2 for x = 25 (7)

corresponding to a beam diameter of 4 standard deviations. By integration

of the intensity over the laser beam with a diameter of 4a it can be demonstrated that 86.5% of the total emitted light is within the beam diameter.

Since the laser wavelength \ is a formidable part of the physical law

of the doppler anemometer we must be concerned with multi-mode operation

which is a primary cause of reduced effective coherence length which then

places a requirement on the optical system with regard to equal path lengths.

Path length differences can lead to a reduction in signal amplitude.

In high power lasers it is very easy to operate the laser in a mode

other than TEM00 (which is desired). The modes result in intensity profiles other than the Gaussian distribution and adjustment of the parameters

of the laser cavity must be made. Also, laser oscillators normally operate

at several optical frequencies simultaneously unless special single frequency techniques are used. When the multiple optical frequencies are combined on a square law detector such as a photomul tipl ier, the output contains

601
all possible difference frequencies between the optical frequencies. They

may fall close to the doppler frequency making it impossible to differentiate

one from the other. To limit this effect one can utilize short lasers which

do not exhibit this effect or in the case of long lasers an etalon can be

introduced into the cavity. It then selects one longitudinal mode thus

eliminating the mode beating effect.

Transmitting Optics - The optical system transforms the input laser

beam into an appropriate configuration for generating a doppler signal.

This is normally accomplished with a beamsplitter (or bi -prism), mirrors

and piano convex, a lens with a given focal length. There are three basic

modes from which all other configurations are derived. They are: a) differential, b) reference beam, c) dual beam.

Criteria for measuring accuracy in the design of transmitting optics

are that they be void of spherical and chromatic aberrations, have latitude

for precise alignment adjustment [12]. In the differential mode, without

alignment errors, the crossing of the beams takes place at their respective

beam waists and the interference planes are approximately parallel with

equal spacing. If the two beams intersect on the optical axis where they

are not plane waves but contain a finite radius of curvature the fringe

pattern will have an increasing spacing away from the transmitting lens.

If particles with equal velocities move through the measuring volume perpendicular to the optical axis the doppler frequency generated will be dependent upon exactly where the particle physically passed through the measuring volume. If the two separated beams are parallel but do not encounter

the lens perpendicularly the fringes are parallel but the separation increases

perpendicular to the optical axis.

The Flow - The measuring volume is described as an ellipsoid of revolution of the two intersecting laser beams. Its dimensions are dependent

upon:

a) Laser beam diameter - inversely proportional

b) Scattering angle 9 - inversely proportional

c) Electronic level acceptance

When light falls upon a solid particle it will be scattered in every

direction. The spatial scattering intensity distribution, i.e., the percentage of light going in certain directions in space will depend partly

on the properties of the light itself (incident wavelength) and partly on

the scattering particle (size, shape, refractive index). The intensity distribution for monchromatic light expressed as:

I = Io A

2 K (n, x

z + yz + z

l

when scattered from a single spherical particle with a diameter d, having

a refractive index n relative to the surroundings.

602
The scattering function varies with particle diameter, the wavelength

of the incident light and the refractive index of the particle. For given

values of these parameters, the scattering function can be determined and

the complete scattering picture mapped. The intensity of light radiated

backward is very much lower than the intensity scattered forward.

In real cases, type and size of scattering particles will most often

be restricted by the flow. For example, in very hot flows (a burning gas),

only particles with a high melting point can be used. Furthermore, the

particle must not be so large that its inertia prevents it from closely

following turbulent variations in the flow, nor must it be so small that the

amount of light scattered from the particles becomes too weak for detection.

The efficiency of the scattering process will be affected as the particle size changes from geometric to Mie to Raleigh scattering.

The interference fringe pattern in the measuring volume has a spacing

given by:

dfr = j (q\

2 sin 0/2

K * ]

As a particle passed through the fringes of the measuring volume, light

will scatter from the bright fringes at a rate

a d

If the fringes are aligned in the x-y plane and a particle with a velocity in the x direction passes through the fringes, the light reflected

will have a frequency given by:

f

d

=

Ux

2 sin S' 2

(10)

This frequency as given by equation (10) above bears a striking resemblance to that generated by doppler consideration.

The next consideration is the number of fringes in the measuring volume.

This is essential for optimization with regard to signal quality, with regard to particle size, and also for the requirements of signal processing.

The number of fringes N^

r for a given optical system is given by:

8 fn tan 9/2

K

N fr (11)

Transfer Function vs. Index of Refraction - If the difference in index

of refraction of the wall material is neglected and, considering water (the

most commonly studied fluid with the exception of air), we can apply Snell's

603
Law to the situation indicated in Figure (9) and find that:

U = f

d = f

d, (12)

2 sin 9/2 2 sin 0,/2

The point of this result is that the transfer function remains unchanged when the laser beam passes from one medium to another. This is

because index of refraction and wavelength form a ratio in the transfer

function which remains constant, even though both change.

The offset in position of measuring volume within the flow can be calculated. Figure (10) indicates the effects on beams as they pass through

different materials and thus the effect on the location of the measuring point.

The expressions for w and y may be derived as follows:

(i) From Snell's Law of Refraction -

nw

sin G

w

= n p

sin °p

= n

a sin 9

a

(n

a

= 1 ' 00) (l3 >

so 0W , 9

p

are I

i sin 0 a

i sin 0 e. a — a /-v . — a

= sin — , 0^ = sin —

since L^A = _> x

=

s_ (f . a)

y = x - p tan 9

p = ^ (f - a) - p tan 0

p

(14)

X (f - a) - p tan 0

w = I = £1 ' w

9. (15)

tan 01( tan 01( u °' w w

(ii) From the above equation for w, we can get

a = f 1 - 2(p tan 0

p

+ w tan 0W

)

where f = focal length of lens

s = separation distance of two beams

(iii) From above equation we can derive:

lc \ tan 0

w w

604
If a is fixed and p

= p

Q

I x, then w = w

Q

± y

tan 9 (18)

and y

= tinO x w

It can be seen that the particles that are used for scattering purposes

play a major part with regard to the accuracy of the measurement and that

although an LDA is used to measure fluid velocities, the real measurement is

the velocity of the scattering particles.

a) The largest particles contribute mostly to the light intensity so

the velocities measured are weighted toward the largest particles in the

distribution.

b) Particle sizes greater than 0.1 micron are required for LDA with the

upper limit set at approximately 100 microns.

There are a number of effects that contribute to the relative motion

with regard to the particle and the fluid, Figure (ll). If a particle's

density is different from the fluid medium, the particle velocity will not

respond to the instantaneous velocity changes mainly because of inertia [19].

In air flows the particle density is very often much greater than that

of the air which makes the effect more pronounced. An ideal situation is

obtained when the density ratios are closely matched. Another effect of a density difference is the force of gravity inducing the particles to settle

or drift up dependant upon densities greater or less than that of the fluid.

Also, if a particle has rotation while moving with the fluid a force will be

exerted on the particle in a direction which is perpendicular to the mean

velocity vector and the axis of rotation. Another lifting effect can be

found near the boundary where the velocity gradient is high.

Broadening of the doppler signal can take place if there is a strong

velocity gradient across the measuring volume, velocity [10] fluctuations

within the volume. Also finite transit time - random arrivals and departures

of particles in and out of the volume can cause frequency and phase fluctuations in the doppler signal therefore presenting a finite width to the

doppler spectrum. Signals from individual scattering particles last only

for the time required to traverse the scattering volume. The frequency uncertainty is dependent on the scattering volume dimensions which are often

control lable.

Receiver Optics - The measuring volume is brought into focus by a receiving lens, truncated by a fixed or adjustable field stop and then focused

on a pinhole aperture. Finally, the light permitted to escape through the

pinhole becomes slightly defocused so as to illuminate a large area of the

photo cathode of photomultiplier. This basic geometry is used for all modes

of operation including confocal backscatter.

605
Pinhole aperture size must be varied for optimization of signal-tonoise ratio. It is determined by:

4 X f

TT d

L

(19)

Signal Conversion - Signal conversion is effected by a photo detector;

either a photomul tipl ier or photo diode. Each device simply changes light

energy into electrical energy.

The principle for a typical PM are as follows: Radiant energy enters

the evacuated enclosure through a "window" which has a semi transparent

photocathode deposited upon its inner surface. The photocathode emits photoelectrons by the process of photoemission , i.e., by the interaction of the

incident radiant energy with electrons in the photocathode material. Photoelectrons from all parts of the photocathode are accelerated by an electric

field so as to strike a small area on the first dynode. Secondary electrons

resulting from the process of secondary emission (i.e., from the impact of

the photoelectrons on the first dynode) are accelerated toward the second

dynolde by an electric field between dynodes No. 1 and No. 2 and impinge on

the second dynode. The impact of the secondary electrons on dynode No. 2

results in the release of more secondary electrons which are then accelerated

toward dynode No. 3. This process is repeated until the electrons leaving

the last dynode are collected by the anode and leave the photomul tipl ier as

the output signal

.

The only possible degradation to the system would be additional noise

and limited frequency response.

Signal Processing - The processing technique is a large contributor to

the determination of the overall performance of an LDA system, particularly

with regard to the magnitude and type of errors in the measurement. The

first entry in the line of signal processing methods is the conventional

spectrum analyzer with inherent measuring errors such as the skewness and

broadening of the spectrum. A filter bank has basically the same constraints

but improvement is obtained in that only the frequency range of interest is

swept.

Another system which uses averaging is the photon correlation technique.

This system construsts the time averaged autocorrelation frunction of the

signal from the signal converter and becomes viable when the measurement

offers only veryweak scattered light.

Time averaging methods are limited to long time history velocity measurements.

For real-time data the frequency tracker based on a phase or frequency

locked loop can be considered. This method provides information relative

to the flow fluctuations or short time history. It requires a continuous

606
or near continuous doppler signal to remain in lock. Since most signals

are not entirely continuous due to phase reversal and periods when there

are no particles in the measuring volume a tracker must be designed with

a drop-out detector or hold circuit.

A counter- type processor is an alternative device for measurements where

large drop-out periods are encountered. It is a measurement of the time of

flight of a particle through a given number of fringes in the optical fringe

or differential mode of operation.

The incoming signal which the electronic portion of the system must

process has a given quality described ty the signal-to-noise ratio, ambiguity or broadening, and bias phenomena.

The acceptance level can be made adjustable by threshold levels and

filtering techniques reducing the effect of noise and ambiguity by reducing

the probe volume size. Window adjustments and validation by fringe count

comparisons combined with amplitude level criteria serve to improve the

overall accuracy.

4. CONCLUSION

The laser doppler anemometer on the surface appears to be the ideal

method for flow measurement. It is inherently 1 inear , requires no cal ibrati on

(with the exception of standard electronics calibration checks), and does not

provide any form of interference. However, it does provide a measurement of

particle velocity which, with care, must then be related to the fluid velocity.

Hot-wire and film anemometry technique have been improved to the point

where it can be considered a complimentary method when compared with the

laser doppler anemometer.

Presently the LDA is well established as a useful measuring tool. It

has already been subjected to a wide range of successful applications and a variety of flow problems. With future improvements with regard to operation

and technique the LDA will undoubtedly become an important part of many additional measurement applications. We still require correction procedures for

error and possibly the integration of them into the system would be an asset.

A laser doppler anemometer justifiably is not a "point and measure" device.

It does require sound judgment by the end-user.

NOMENCLATURE

Nu = Non-dimensional heat transfer coefficient

A = Constant determined by calibration

B = Constant determined by calibration

R

e

= pUd

v

p = Density

U = Velocity

607
d = Wire diameter

y = Viscosity

Q = Heat loss

1 = Wire length

k = Thermal conductivity of fluid

T = Wire temperature

To = Fluid or ambient temperature

V = Voltage

R = Resistance

f . = Doppler shifted frequency

A = Laser wavelength

9 = Scattering angle of intersection

I = Light intensity

d = Distance between fringes

REFERENCES

[1] Schubauer, G. B., PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON HOTWIRE ANEMOMETRY, March 1967, ed. by W. L. Melnik and J. R. Weske

(AFOSR No. 68-1492, July 1968)

[2] Sandborn, RESISTANCE TEMPERATURE TRANSDUCERS, Metrology Press, Ft.

Collins, Colorado, 1972

[3] Champagne, F. H., TURBULENCE MEASUREMENTS WITH INCLINED HOT WIRES,

December 1965, Boeing Scientific Research Labs, Report #103

[4] Jorgensen, F. E. , DIRECTIONAL SENSITIVITY OF WIRE & FIBER FILM PROBES,

Disa Information #11

[5] Bechert, D., DYNAMIC CALIBRATION OF A HOT-WIRE ANEMOMETER USING A

PULSATING NOZZLE FLOW, Euromech 63, (August 1975)

[6] Rasmussen, C. G., THE AIR BUBBLE PROBLEM IN WATER-FLOW HOT-WIRE

ANEMOMETRY, Disa Information #5

[7] Comte-Bellot, G., ANNUAL REVIEW OF FLUID MECHANICS, Vol. 8, pp. 209-

231 (1976)

[8] Nagib, H. M. , Pluister, J. W. , and Tan-Atichat, J., THE INTERPRETATION

OF THE OUTPUT OF HOT-FILM ANEMOMETERS AND A SCHEME OF DYNAMIC COMPENSATION FOR WATER TEMPERATURE VARIATION, Proceedings of the Third Symposium

on Turbulence in Liquids, University of Missouri at Rolla, (September

1973)

608
Kovasznay, C. S. C, SHOULD WE STILL USE HOT WIRES?, Proceedings of

the International Symposium on Hot-Wire Anemometry, W. L. Melnik and

J. R. Weske, ed. (March 1967)

George, W. K. , LIMITATIONS TO MEASURING ACCURACY INHERENT IN THE LASER

DOPPLER SIGNAL, Proceedings at LDA Symposium, Copenhagen (1975), p. 20,

The Accuracy of Flow Measurements by Laser Doppler Methods

Owen, J. M. and Rogers, R. H., VELOCITY BIASING IN LASER DOPPLER

ANEMOMETERS, p. 89, Proceedings of LDA Symposium, Copenhagen (1975)

Hanson, S., VISUALIZATION OF ALIGNMENT ERRORS AND HETERODYNING CONSTRAINTS

IN LASER DOPPLER VELOCIMETERS, p. 176, Proceedings of LDA Symposium (1975)

Melling, A. and Whitelaw, J. H., PROCEEDINGS OF THE THIRD BIENNIAL

SYMPOSIUM ON TURBULENCE IN LIQUIDS, pp. 115-135

McLaughlin, D. K. and Tiederman, W. G. , STATISTICAL BIASING IN INDIVIDUAL

REALIZATION LASER ANEMOMETRY, Workshop on Theory and Application of the

LDA held at Oklahoma State University (June 11-13, 1973)

Stevenson, W. H. and Thompson, H. D., THE USE OF THE LASER DOPPLER

VELOCIMETER FOR FLOW MEASUREMENTS, Proceedings of a workshop co-sponsored

by U. S. Naval Army Missile Command and Project Squid, Purdue University

(March 9-10, 1972)

Stevenson, W. H. and Thompson, H. D. , PROCEEDINGS OF THE SECOND INTERNATIONAL WORKSHOP ON LASER VELOCIMETRY, Purdue University (March 27-29,

1974)

Kreid, D. K. , ERROR ESTIMATES FOR LASER DOPPLER VELOCIMETER MEASUREMENTS

IN NON-UNIFORM FLOW, Proceedings of the Second International Workshop

on Laser Velocimetry, p. 398-427, Purdue University (March 27-29, 1974)

Love, T. J., A SIMPLIFIED SCHEME FOR ESTIMATE OF LIGHT SCATTERED BY A

SINGLE PARTICLE IN THE DESIGN OF DETECTOR GEOMETRY FOR LASER ANEMOMETER

APPLICATIONS, Laser Anemometer Workshop, Oklahoma State University,

(June 11-13, 1973)

Durrani, T. S. and Greated, C. A., LASER SYSTEMS IN FLOW MEASUREMENT,

Plenum Press, N. Y. & London (1977)

Bradshaw, P., AN INTRODUCTION TO TURBULENCE AND ITS MEASUREMENT,

Pergamon Press (1971)

Kristensen, H. S., HOT-WIRE MEASUREMENTS IN TURBULENT FLOWS, Disa

Information Department, Disa Electronics (1973)

Tennekes, H. and Lumley, J. L., A FIRST COURSE IN TURBULENCE, M.I.T.

Press (1972)

609
[23] Yeh, Y. and Cummins, H. Z. , LOCALIZED FLUID FLOW MEASUREMENTS WITH A

HE-NE LASER SPECTROMETER, Applied Physics Letters, Vol. 4, No. 10,

pp. 176-178 (1964)

[24] Yanta, W. J. and Smith, R. A., MEASUREMENTS OF TURBULENCE TRANSPORT

PROPERTIES WITH A LASER DOPPLER VELOCIMETER, AIAA Paper, pp 73-169,

AIAA 11th Aerospace Sciences Meeting, Washington, D. C. (January 10-

12, 1973)

[25] Whitelaw, J. H. and Melling, A. M. , MEASUREMENTS IN TURBULENT WATER

FLOWS BY LASER ANEMOMETRY , Proceedinas of the Third Symposium on

Turbulence in Liquids, University of Missouri at Rolla, (September 1973)

610
FLOW PROBE

SYSTEM

BRIDGE SERVO

AMP

SIGNAL

PROCESS

READOUT

COSTROL

RESISTOR

Figure 1

^ BASIC CTA THEORY

o

t

VELOCITY

Figure 2 TYPICAL CALIBRATION CURVE

611

I 1 1 1 1 1 V

-

()) r— .

_—

I I I 1 1 1 120 -90 -60 120 120 -90 -60 -30 30 60 90 120

Directional characteristics of experimental probes

with different prong lengths / and prong spacings s (with

a constant sensory wire length of 1 mm).

The curves are related to the following probe and flow

parameters

:

Curve

Configuration of Hot-wire Probe 0.0

Velocity l/m/s

Linearizer output

voltage for 0 = 0" in volts

Scale mV/DIV

(a) 1, 9 11.3 3.28 100

(b) 1, 9 40.1 9.65 500

(c) 2, 6.5 11.1 2.58 100

(d) 2, 6.5 40.6 10.42 500

(e) 3, 8.8 10.1 2.78 100

(0 33 8.8 40.7 8.85 500

(g) 4, 7.6 9.9 3.10 100

<w 4, 7.6 40.4 9.30 500

(i) turntable 10.1 2.54 100

(j) turntable 40.8 10.45 500

Figure 4. DIRECTIONAL CHARACTERISTICS OF

613

PROBES
614
OIw

W&HU

S3HW

h1

Cm

CmOP

&!

O 3 H W Eh Q < H H B D H

CO

X

CD

o

-p

c

u

•H cu> CO -p •H

-MC

U

«3 II

W

0) (U u

li •H C 0)

II

a

CDM

cr> •H

Cm

615
LASER OPTICS FLOW OPTICS SIGNAL

CONVER- PROCESSING

RSADCVT

SION

Figure ?. LDA BLOCK DIAGRAM

I

BEAM DIAMETER

Figure 8. GAUSIAN BEAM

616
CD

CD

617
618
619

National Bureau of Standards Special Publication ASA, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (issued October 1977)

NEAR WALL VELOCITY MEASUREMENTS FOR WALL SHEAR

INFERENCE IN TURBULENT FLOWS

F. J. Pierce

Professor of Mechanical Engineering

Virginia Polytechnic Institute

Blacksburg, Virginia

D. S. Gold, Engineer

E. I. Dupont

Waynesboro, Virginia

The existence of logarithmic near wall similarity for twodimensional turbulent flows permits the inference of local wall

shear stress from ordinary velocity profile data. In cases of

minimal logarithmic similarity, it would be helpful to use the

velocity measurements closer to the wall, in the 'very' near wall

region. Regrettably, this data is all too often inconsistent,

deviating considerably from the proposed similarity laws, and

thus invalidating its use for wall shear inference. In an attempt

to explain such inconsistent behavior, velocity profiles were

systematically measured with four different probes under six

different flow conditions. Additionally, classical displacement

corrections were considered as was the effect of the choice of

similarity laws and 'universal' law of the wall constants.

While small, consistent differences were identified with

different probes and different flow conditions, none of the

probes or flow variations studied were able to explain the

frequently encountered kind of inconsistency between measurements and proposed similarity laws in this very near wall flow.

INTRODUCTION

Evaluation of the local wall shear stress in a two-dimensional turbulent

boundary layer or channel flow is important in estimating drag forces, pressure losses, and local heat transfer rates. Local wall shear stress can be

evaluated by direct force measurements, but this method requires special

instrumentation and is generally difficult. The existence of universal,

near wall similarity allows for the indirect measurement of local wall shear

stress with such devices as Preston tubes, Stanton tubes, rakes, fences, and

heat meters. Yet an alternative method to infer local wall shear stress is

to use ordinary near wall velocity data points such as are obtained in velocity profiles. This paper focuses on this last method.

Historically, in 195A Clauser [l] 1 first proposed using near wall similarity for inference of local wall shear stress. His method uses several

near wall velocity points with a subjective estimate of a best fit with

parametric skin friction or shear velocity lines. In 1959 Bradshaw [2]

proposed an alternative method using fewer data points and somewhat more

objective. Most recently, in 1965, Schraub and Kline [3] proposed another

^Figures in brackets indicate the literature references at the end of this

paper.

621
variation which can be developed to give a more precise and even a statistical inference of the local wall shear stress.

All these indirect methods make, use of the universal similarity described

by the so called 'inner' or 'logarithmic' law, or 'law of the wall' written

as

+ 1 +

u = — In y + c (1)

Since this law does not correlate the velocity data right down to the wall

through the usually designated buffer region and viscous sublayer, data

points in these regions must be excluded in local wall shear stress inference

methods using velocity profile data. The" inclusion of a sublayer formula

.(and even a buffer region formula) gives an 'extended' law of the wall

formulation made up of two (or three) formulas as

u

+

= y

+

(2)

u+

= r- In y

+

+ c (1) k

Alternatively, Spalding [4] and Kleinstein [5] have proposed the 'single

formula' law of the wall which continuously covers near wall velocity data

down through the viscous wall region. This relationship treats u as the

independent variable with

y

+

= u+

+ exp(-kc) [exp(ku

+

) - 1 - (ku

+

) - -j (ku

+

) ^ - -g- (ku

+

)^] (3)

+ 4

A fourth order term, -(ku ) /4!, can also be included above but its effect

is. relatively small and confined mainly to the so called buffer region.

Equation 3 agrees well with the previous expressions and avoids the difficulty of manipulating two (or three) equations for each profile.

In the following, it is convenient to refer to the data correlated by

the logarithmic law, Eq. 1, as the near wall data, and that yet closer to

the wall as the very near wall data. This very near wall data would presumably correlate with the viscous sublayer relationship, Eq. 2, (and a buffer

layer equation if one choses to use one) and the Spalding formula, Eq. 3,

for small y . The division between the near wall and very near wall

data is somewhat arbitrary as shown in Fig. 1.

In 1973, Pierce and Zimmerman [6] demonstrated how one could adopt

the methods of Clauser or Schraub and Kline* for local wall shear prediction

to include all the near wall data through the buffer region and viscous

sublayer. The inclusion of velocity data points nearer to the wall than

included by Eq. 1 is of interest in flows with minimal logarithmic

similarity as occurs in cases with severe pressure gradients or where

sufficient flow time for the development of the logarithmic region is

unavailable. I n addition, speculating on the extension of such indirect

methods to the case of three-dimensional flows, Pierce and Zimmerman

observed that the usual pressure driven three-dimensional turbulent boundary

layer has a minimum of logarithmic-] ike similarity for use in the possible

inference of local wall shear stress for this more complex kind of flow.

622
Thus, the behavior of very near wall data becomes of stronger and more

necessary interest.

The universality of a logarithmic near wall behavior of two-dimensional

turbulent boundary layer and channel flows is reasonably well established

(with the exception of extreme pressure gradients and flows with insufficient

development distance). On the other hand, typical velocity data for twodimensional turbulent flows nearer to the wall and in the so called buffer

and viscous sublayer regions (the very near wall region) is noted for its

inconsistency. While much of the velocity profile data for fully developed

flows in pipes and channels does follow the viscous sublayer law and the

corresponding portion of the Spalding single formula law, a very large number

of boundary layer flows give velocity data points at significantly higher

values in this very near wall region. It is often not so much a case of data

being erratic in this very near wall region, as a case of the data seemingly

wanting to follow a regular pattern, but well above that predicted by either

Eq. 1 or the single formula law of the wall. The inconsistent behavior

of this very near wall data is described in the reports of Coles [7] and Coles

and Hirst [8] where over 400 profiles are considered in establishing law of

the wall constants. Coles suggested that the discrepancies were not the

fault of the formula, but assumed they were the result of experimental errors,

and he chose to ignore the very near wall data points because of this inconsistent behavior.

Thus, while the techniques are available for the inference of local wall

shear stress using the very near wall velocity profile data, the lack of well

established and universal similarity for this very near wall data make suspect

any inferred wall shear values using these techniques. This experiment attempt

to provide some insight as to the behavior of very near wall velocity data

in a low speed, incompressible, two-dimensional turbulent boundary layer in

air by systematically changing the velocity measuring probe or the flow

conditions. Consideration was also given to changes in the law of the wall

constants, to systematic probe position errors, and to so called displacement

corrections

.

In the first series of experiments, velocity profiles were measured with

1. a gooseneck boundary layer probe (0.020-in. (0.5-mm) OD)

2. a small standard claw probe (0.020-in. (0.5-mm) OD)

3. a large standard claw probe (0.028-in. (0.7-mm) OD)

4. a standard, straight hot wire probe (0.0002-in. (0.005-mm) wire).

In a second series of experiments, profiles were measured for

5. a near zero pressure gradient

6. a mildly favorable pressure gradient

7. a mildly adverse pressure gradient

8. a slightly converging flow

9. a slightly diverging flow.

These last two cases were run in an attempt to determine if slight convergence

or divergence in the flow would explain the inconsistent very near wall

behavior. All of these flow conditions were run with a boundary layer trip

well upstream of the test station. A final flow condition tested was with

10. a sharp leading edge for the floor of the channel.

623
This last case was to determine the effect of the boundary layer trip on

the very near wall velocity measurements. All of the measurements were

made at a fixed unit Reynolds number for the tunnel so that flow conditions

were nominally constant. The pressure gradient flow cases and the convergingdiverging flows had different local unit Reynolds numbers because of the area

variations required to create these conditions. In all, thirty-nine velocity

profiles were measured with four different probes and at six different

nominal flow conditions.

EXPERIMENT AND APPARATUS

A schematic diagram of the apparatus is shown in Fig. 2. Air was drawn

through 1.5-in. (3.8-cm) fiberglas filters into a plywood settling chamber,

49x54x50-in. (1 . 24x1 . 37x1 . 27-m) . A louver damper regulated the flow velocity

from 20 to 120-ft/sec (6.6 to 39.4-m/sec). A ten-horsepower, 60-hertz

ILG Ventilating Company Size 300 centrifugal fan blew air into the test channel. A plywood diffuser connected the fan discharge to a rectangular

45x45x60-in. (1 . lxl . lxl . 5-m) plywood plenum containing a bundle of 1.5-in.

(3.8-cm) diameter cardboard mailing tubes. Screens diminished the fan

fluctuations and insured a moderate turbulence level in the test section air

stream. A 4-ft (1.2-m) long plywood section followed by a sheet metal nozzle

with a nine-to-one contraction ratio reduced the flow area to the 10xl4-in.

(25 . 4x35 . 6-cm) plexiglas walled tunnel cross section. A 1/4-in. (6.4-mm)

gap between the nozzle and the tunnel filled with foam rubber minimized

vibration transmission to the test channel.

Early turbulent transition was forced by 1/8-in. (3.2-mm) diameter rods

across the four sides of the test channel inlet. The length of the twodimensional test channel was 134-in. (3.4-m), and all velocity profiles were

measured at a test station 84-in. (2.1-m) downstream of the test channel

inlet. The rectangular test section served as the entrance section to a threedimensional impinging jet geometry. Velocity profiles reported here were

measured 50-in. (1.27-m) upstream of the jet entrance, and no three-dimensional

effects were detected at this distance upstream. Four static pressure taps,

1/32-in. (0.8-mm) diameter, were placed in the tunnel roof at 2-in. (5.1-cm)

intervals in the transverse direction with additional static pressure taps

placed 2-3/4 in. (7-cm) upstream and downstream of the test station.

Small positive and negative pressure gradients were created by using

a smoothly faired wooden wedge approximately 22-in. (56-cm) long having a shallow angle of 7 degrees. The pressure gradient was measured with three

static pressure taps placed in the wedge, and spaced at 3-in. (7. 6-cm)

intervals in the streamwise direction. The wedge was attached to the tunnel

roof so that it could easily be reversed providing the .area variation for

either rising or falling pressure. A pair of similar wedges were placed along

the tunnel side walls to provide the small convergence or divergence in the

flow on the floor. In this case it was not possible to separate the pressure

gradient effect and the convergence (or divergence) in the flow. Inlet

conditions in the test channel were altered by placing a flat plate with a sharp (45°) leading edge on the floor of the tunnel. When installed, the

leading edge extended approximately 2-in. (5.1-cm) into the inlet flow nozzle,

and all boundary layer trips were removed.

624
The vertical positioning of the various probes was obtained with a traversing mechanism. A dial indicator measured changes in distance from

the tunnel floor to within + 0.0005-in. (0.013-mm). A horizontal-vertical

cathetometer was used to insure accurate vertical placement of the probe

relative to the tunnel floor with the aid of a graduated metal gage block.

After the probe was positioned correctly, the reading of the dial indicator

was adjusted to correspond to the known distance above the tunnel floor.

The estimated tolerance of the probe positioning procedure was + 0.001- in.

(0.025-mm).

The mean velocity profiles were measured by three different stagnation

probes: (1) United Sensor, Model USC-E-101 gooseneck probe (.020-in. (0.5-mm

OD) with an offset radius of nominally one inch; (2) United Sensor, Model CA

120 claw probe (.020-in. (0.05-mm) OD) ; and, (3) United Sensor, Model CA-120-

24-F-CD claw probe (.028-in. (0.7-mm) OD) . The gooseneck probe was visually

aligned with the tunnel centerline as this could be done easily within the

+ 15° cited in [9] as critical for yaw errors less than + 1% of the dynamic

head. The claw probes were nulled for alignment, using the two outer orifices

as is the usual procedure for such probes.

Addit ionally, a DISA straight hot wire probe type 55A22 (0.0002— in.

(0.005- mm) wire), was also used for velocity measurements. This system was

made up of an annemometer, a linearizer, a voltage divider, a VFC and an

electronic counter. The hot wire was calibrated against a pitot-static probe

in the tunnel free stream.

To insure similar tunnel flow conditions the tunnel unit Reynolds number

as measured at ^ fixed location gear the tunnel exit, was held at the nominal

value of 5.8x10 per ft (1.9x10 per m) . All pressure readings were made

with micromanometers . Stagnation pressures were read at one minute intervals

to allow for response time. Hot wire readings were averages of five readings

each of which was averaged over ten seconds by the counter.

RESULTS

The 39 runs at six different flow conditions are coded in a four

digit sequence as follows:

Tunnel geometry

lxxx constant area with trip wires

2xxx falling pressure (accelerating flow) with

3xxx rising pressure (decelerating flow) with

Axxx constant area with sharp leading edge

5xxx diverging floor flow with trip wires

6xxx converging floor flow with trip wires

Probe designation

xlxx gooseneck boundary layer CO. 020-in. (0.5-mm) OD)

x2xx standard claw probe (0. 020-in. (0.5-mm) OD)

x3xx standard claw probe (0. 028-in. (0.7-mm) OD)

x4xx standard, straight hot wire probe (0.0002-in. (0.005-mm) wire)

trip wires

trip wires

625
The last two digits designate repeated profiles under any given probe/

flow conditions.

Space limitations do not allow a detailed discussion of individual

profiles or data reduction options. The following discussion is intended

to summarize and generalize the findings and interpretations. A detailed

discussion of all aspects of the experiment and its results is contained

in reference [10]. Table 1 summarizes the 39 runs made. The several

repeated profiles in series 1100, 1200, and 1300 assured experimental

technique and repeatability, and gave a good indication of the kind of

experimental scatter to be expected with a given probe.

Before measured data can be expressed in similarity coordinates,

the value of the shear velocity, or the wall shear stress, must be determined

either by an indirect method based on near wall similarity or by direct force

measurement. In this investigation the wall shear stress was inferred by

the technique presented by Pierce and Zimmerman [6] which uses the method

of Schraub and Kline [3] to infer a value of the shear velocity from each

data point in the velocity profile. Since the shear velocity is a constant

value for a given profile, the predictions from the individual data points

were averaged to determine a unique value for the shear velocity. The data

used in this prediction was limited to the range of data in the logarithmic

region. Values of y greater than 300 were excluded due to the presence

of the wake region, and values less than 50 were excluded as in [7] and [8]

for this is nominally the very near wall region (see Fig. 1) where inconsistent behavior is noted and to be examined here. The average value of the

shear velocity was normally for six data points per profile. The cubic

Spalding single formula, Eq. +

3, \j7as used to infer individual shear velocities and for comparison in u , y plots.

Both the law of the wall and the Spalding single formula equation

require two constants which must be evaluated experimentally. These constants

are the same for both expressions, and they are generally accepted as being

universally valid, yet there exists some substantial disagreement concerning

the precise numerical values for them.

Table 2 summarizes a collection of these constants and Fig. 3 shows the

effec£ on Eq. 1. These same constants appear in Eq. ^ with the same effect

for y > 50 and a similar spreading effect for 50 > y > 0 as shown in Fig. 4

,

The variation of these constants does affect the value of shear velocity

calculated for a given pr_ofil_e and the 'goodness' of fit to the logarithmic

region when plotted in u , y coordinates. This variation does not appear

to account for the erratic behavior of very near wall data. The Coles'

values are judged to be based on the most exhaustive study of a very large

collection of data. The Patel constants were used initially in this study

because they are more recent and because they gave nearly identical results

as suggested in Fig. 3 and 4. It is noteworthy that the Smith and Walker

constants [11], sharply different from the above, are one of the few sets

obtained from velocity and direct wall shear stress measurements.

T_able 3 shows the range of physical wal_l distance, y, mean u/u , mean u and y , and standard deviation of u/u and u at corresponding y for the 20

626
profiles in the 1100, 1200, and 1300 series. The sample standard deviations in

Table 3 indicate that the uncertainty involved with the velocity measurements

nearest the wall for each of the probes was generally greater than the

uncertainty for the remaining measurements. This type behavior is not surprising for the first data points due to their_ close proximity to the wall. For

all three probes, the standard deviation of u (excluding the data point nearest the wall) was well behaved through the logarithmic region of the profile.

The largest value of the standard deviation in this region is 0.07 and

this value corresponds to an approximate uncertainty of + 0.3 ft/sec (0.09 m/sec)

.for the velocity measurements in the boundary layer and compares well with the

expected uncertainty of the velocity based on a micromanometer uncertainty of

+ 0.005 in. (0.13 mm) of water, or approximately + 0.3 ft/sec. (0.09 m/sec).

Experimental repeatability is also shown in Figs. 5 and 6 for the 1100 series

runs. These figures show typical scatter for subsequent multiple run series.

Probe Effects

Figures 7 and 8 show the typical effects ot the four probes used. In

general, in the near wall region, the hot wire recorded highest velocities,

followed by the large OD claw, the small OD claw, and the gooseneck (offset)

boundary layer probe. The slightly higher near wall velocities measured

with the large claw and wire predicted higher shear velocities, with the net

effect of bringing the u , y plots t into closer agreement among the probes

(higher local u divided by higher u tends to mask the physical velocity

differences) . An initial reaction is to identify the higher velocities

of the large claw probe with so called displacement effects, but the even

higher hot wire values question this conclusion and suggest probe stem

interference effects. Heat loss to the wall would not be a likely explanation

for the low overheat ratio and relatively large distances (for the hot wire)

involved. These figures indicate that the hot wire probe has closer agreement

with the claw probes than with the gooseneck probe, which suggests that the

gooseneck geometry is a factor in the discernable differences in these near

wall velocity measurements. Other factors considered on the readings of the

stagnation type probes are discussed below.

Stagnation pressure is measured by an orifice at the stagnation point

of a body. The presence of a probe will unquestionably disturb the flow to

some extent, which can introduce systematic errors into the velocity measurements. Dean [9] notes that in the usual range of investigations, the total

pressure probe is insensitive to Mach and Reynolds number effects and considerable misalignment. Errors resulting from viscous effects, normal velocity

gradients, near wall effects, or stream turbulence could be significant in

boundary layer velocity measurements. Various investigations cited by Dean

indicate that the stagnation pressure is free of viscous effects for low

velocity flows down to a Reynolds number of 30 based on the radius of the

pressure orifice. For a probe with an inside diameter of 0.010-in. (0.25-mm),

the critical Reynolds number corresponds to a velocity of 12-ft/sec (3.6-m/sec).

Since flow velocities below 50-ft/sec. (15.2-m/sec) were never measured here,

this effect does not appear to be significant.

When a stagnation probe is placed in a normal velocity gradient, there

exists a gradient in stagnation pressure across the face of the probe orifice.

The probe will not integrate this pressure gradient to give an indicated

627
pressure representative of the velocity at the geometric center of the orifice.

Young and Maas [12] express this effect of the velocity gradient as a displacement of the 'effective center' of the probe from the geometric center

toward the region of higher velocities by an amount equal to 0.18 times the

external diameter of the probe. If this displacement correction was applied

to the probes used in this experiment, the effect would be to lower the

velocities nearest the wall, typically less than 2 per cent. Displacement

corrections have also been discussed by Preston [13], Livesley [14], MacMillian

[15] and Davies [16]. These authors discuss different factors affecting the

measurements, and present varying numerical values for the displacement

corrections. In fact, Davies suggest no correction be made for round probes

in the diameter range of 0.031 to 0.48-inches (0.79 to 12.2-mm). Turbulence

corrections suggested by Dean [9] for the normal Reynolds stress effect corrected the measured stagnation pressures by less than 1.2%.

The combined 'corrections' above were typically 3% at the wall, diminishing

through the boundary layer. Such corrections were tried and while they tended

to improve the appearance of the data, no such corrections were used in the

results presented since 1) such corrections did not generally bring the measured

data into 'agreement' with predicted similarity as Eq. 3; 2) such corrections

could not be properly applied to the hot wire measurements which, though slightly

higher, were in general agreement with the stagnation probe measurements; and

3) in his extensive study of such data, Coles [7] suggested the uncertainty

of such corrections warranted their omission.

The assumption of a fixed error in probe vertical position would be the

same as applying a displacement correction. S_ince_ such a correction did not

generally retrofit the data to the expected u , y form, it is assumed that

such errors were not likely present.

While day to day variations in ambient pressure were nominally compensated for in setting the tunnel U/v parameter to a constant value, there was

some unavoidable variance in this parameter. To overcome this effect three

sets of comparisons were made between the two claw probes and each claw probe

and the gooseneck probe, each comparison at one time under essentially identical tunnel conditions to avoid any U/v variances. The 1200, 1300 and 1400

series average behaviors were confirmed with the highest near wall velocities

recorded by the large claw probe and the lowest by the gooseneck. Differences

as large as 4% occurred between the two claw probes; of 6% between the

large claw and the gooseneck; and of 4% between the small claw and the gooseneck. All probes agreed to less than 1% in the outer region of the boundary

layer

.

Flow Field Effects

All of the earlier results on the effects of different probes were

for flow in a constant area channel of essentially zero pressure gradient.

The effects of the flow field were considered in the following.

The effects due to mild negative and positive pressure gradients on

the velocity profile were considered by placing the wooden wedge on the

test tunnel roof as a converging or diverging section. The 22-in. (56-cm) wedge

628
provided a converging (or diverging) area variation over 16-in. (41-cm) by

a 7° angle. Measurements were made at the center of this 16-in. (41~cm)

^ Length. The resulting pressure gradients were approximately -0.0025 lb/in. /

Ln. (-6.79 Pa/cm) and 0.0023 lb/in. '/in. (6.24 Pa/cm), respectively. Comparisons of profiles taken by the stagnation probes in the different pressure

gradients are shown in Fig. 9.

Qualitatively, the relative differences in the profiles due to changes

Ln static pressure behave as expected. The wake region for each probe was

Largest for the profile in the positive pressure gradient. Conversely, the

negative pressure gradient produced the smallest wake region. Near the wall,

there seems to be slight differences in the behavior of the velocity profiles

due to variations in the pressure gradient, but these differences are consistent with the various probes in the constant area configuration. The

pressure gradients do not appear to significantly alter the results in the

lear wall region but there is a tendency for the rising pressure field to

Lower the very near wall data points in the similarity coordinates, though

lot sufficiently. The question of the relatively short length of these pressure gradient flows was considered. It is recognized that the near wall flow

las a much shorter memory than the wake flow, and the fact that Fig. 8 shows

the wake responding to the effect of the local pressure gradient gives support

:o the assumption that the near wall flow did have sufficient flow time to

respond as well.

Patel [17] predicts departures from the extended law of the wall due to

pressure gradients with a pressure gradient parameter, a. Calculated values

}f approximately 0.004 and -0.004 were much too small to suggest significant

departures from the extended law of the wall. Hence, the essentially consistent behavior of these profiles near the wall was expected. In these runs the

tunnel parameter U/v was held constant but the test section area variations

to generate the local pressure gradients gave local U/v values slightly higher

than in the constant area flows.

The question of possible flow disturbance near the wall due to the

presence of the upstream boundary layer trip wire was considered. A flat

plate with a. sharp leading edge was installed as the tunnel floor, and all

boundary layer trips were removed to allow natural transition from laminar

to turbulent flow. These two tunnel geometries are compared in Fig. 10. As

shown, only small differences in the velocity profiles occur near the wall,

rhe smaller wake for the sharp leading edge can be explained by the concept of

an asymptotically developed wake function. Because the trip wires create an

earlier transition to turbulent flow, the wake function has a longer distance

to develop. Conversely, the sharp leading edge allows natural transition;

ience turbulent flow develops farther downstream. Disregarding the changes

in the wake region, the presence of the boundary layer trips has no discernible

affect on the shape of the velocity profile in the similarity coordinates.

Finally, the effects of slight convergence or divergence at the test

station were considered. A slight convergence and divergence was created

(with accompanying unavoidable pressure gradients whose effects had already

been considered) by placing smoothly faired wooden wedges of 7° on the tunnel

629
side walls. No graphical results are presented, but using the goos

probe (as in the other flow field comparisons) no near wall changes

be attributed to the convergence or divergence of the floor flow.

eneck

could

Effects of Formulas and Constants

In all of the earlier discussion, comparisons were made using the thirdorder Spalding equation and the constants suggested by Patel. The specific

choice of formula and constants was a matter of convenience; however the

consistent choice of the formula and constants was necessary to avoid ambiguous results created by varying selection of formulas and constants.

The effect on the prediction of the shear velocity due to the choice of

the formula and constants is considered briefly here. Three formulas were

compared; the Spalding third-order equation, Spalding fourth-order equation,

and the two-formula law of the wall which is a combination of the viscous

sublayer and the logarithmic region expressions. This version omits an

expression for the transition or buffer region and tends to maximize differences with the other two versions. The constants suggested by Smith and

Walker, Coles, and Patel were combined with each formula, resulting in nine

combinations for predicting the shear velocity for any given velocity profile.

The nine predictions of the' shear velocities for several profiles were compared

to show relative differences among the nine methods. ,

Velocity profiles were selected from various tunnel geometries, then

the shear velocity for each profile was inferred for the nine methods. An

average shear velocity was calculated for each run for the nine methods and

differences relative to this average were calculated. A sample standard

deviation was also calculated for each run. The combination of the Smith and

Walker constants and the two-formula law of the wall always predicted the

lowest value for the shear velocity. Values for the relative differences of

the shear velocities are shown in Table 4, and comparisons of the formulas and

constants were shown in Fig. 4 earlier.

Results in Table 4 indicate the relative differences for the various

methods remain nearly constant for all profiles. When the method of wall shear

stress inference from velocity profiles is applied to flows with a shear

velocity in the range considered here, there will exist a systematic difference

in the predicted value of the shear velocity due to the selection of the

formula and constants. The question of which method is most accurate cannot

be answered without direct measurement of the wall shear stress.

The following is judged worthy of consideration. All data was reduced

using the combination of the Spalding third-order equation and the Patel

constants. The Spalding formula is clearly in good agreement with the two-

(or three) formula extended law of the wall, and the more recent Patel

constants are in very close agreement with and nearly identical to the more

heavily researched Coles constants. Not withstanding th^s, it is noted that

in all the similarity plots, the agreement in the 50 < y < 300 range is not

usually impressive. It can easily be shown that the agreement between these

data and the theoretical curve varies with the selection of the formula and

constants. For profiles in this report, best agreement resulted with the

630
two-formula law of the wall and the Smith and Walker constants. Typical

profiles using this mo"del are shown in Fig. 11. Comparisons between this

figure and previous ones show improved agreement throughout the curve,

particularly near the wall. The Smith and Walker work was considered by

Coles but the effect of this one study, among so many others, was small

in the definition of the Coles constants, k and c. It is noted that the

Smith and Walker constants are possibly the only ones defined by direct

force wall shear measurements for the determination of the nondimensionalizing

shear velocity used in the similarity plots. Nearly all other studies determine this quantity indirectly.

CONCLUSIONS

The consistent behavior of the velocity measurements for each of the

three stagnation probes indicated good experimental repeatability. Overlays of the velocity profiles for the probes illustrated the consistent

results, and the standard deviations for the velocity measurements indicated

low experimental scatter associated with the results. Similar consistency

was noted for the hot wire probe as well.

Results from the comparisons of the four velocity probes indicated that

velocity measurements in the boundary layer were affected differently by

the presence of each of the probes. At a given nominal position in the near

wall region, the highest velocities were recorded by the hot wire, next

by the large claw, followed by the small claw, and lowest by the offset

boundary layer probe. Good agreement for the velocity measurements in the

free stream flow by the three probes inferred that the velocity discrepancies

noted in the boundary layer were due, at least in part, to normal velocity

gradients. Typical boundary layer displacement corrections did not bring

the data into agreement with the near wall similarity law assumed and the

highest velocities of the hot wire, for which there should be no displacement

correction, suggested that such a correction was not appropriate. This is

also supported by noting that different velocity measurements were reported

for probes of equal tip diameter but of different geometry. It appears that

the geometry af the probe (and the lower stem) in a shear gradient, does affect

the probe response as typified by the large straight claw and straight hot

wire giving similar high readings relative to the offset (gooseneck) boundary

layer probe. None of these small systematic differences identified with each

probe was of the order needed to bring the very near wall data into 'good'

agreement with the assumed similarity law.

Flow field effects are summarized as follows2 The presence of mild

pressure gradients, approximately + 0.0025 lb/in. /in. (6.79 Pa/cm), did not

significantly affect the near wall data when plotted in similarity coordinates. There was noted a tendency for the rising pressure field to shift

the very near wall data downward in the similarity figures. This was noted

in different degrees for the three stagnation pressure probes. This shift

while consistent, was not large enough to insure a 'good' fit with the similarity law assumed. No significant differences were noted in very near wall

data when the boundary layer trips at tunnel entrance were removed and replaced

by a sharp leading edge. Profiles were measured by two probes and the results

631
were consistent with those in the original geometry with boundary layer

trips. No significant differences in very near wall data were noted with

small convergence or divergence on the test floor and with the original

constant area geometry. None of the flow field variations were of the

order need to bring the very near wall data into 'good' agreement with the

assumed similarity law.

For a given velocity profile, the specific choice of the similarity

formulas and constants had significant effect on both the prediction of the

shear velocity, and the differences between the velocity measurements and

the similarity law chosen. Several profi-les were compared using nine combinations of formulas and constants, and variations in the value for the

inferred shear velocity of up to 3.7 per cent occurred. These differences

can be attributed in large part to the near wall data not following the

assumed similarity law in some cases as well as in others. No choice of

similarity law or constants altered the behavior of the very near wall data

as generalized for this experiment in Fig. 1. For all the profiles' measured

in this report, best agreement between the measured velocities and the

similarity formula was achieved with the Smith and Walker constants and the

two-formula law of the wall.

The results of the study indicate that small consistent changes in the

very near wall velocity data can be identified with different measuring

probes and different sizes and geometries of these probes, and small

changes did exist for some of the singly different flow conditions. However,

there is little doubt that none of the systematic variations made accounted

for or produced the kind of inconsistency in very near wall velocity measurements that characterize a wide range of the well accepted data. In this

sense, then, this work must report a negative result in that while we can

state specifically what single variations in flow conditions and/or velocity

probes did not account for this very near wall behavior, it cannot be stated

positively what conditions must be met to insure agreement with the very

near wall similarity formulas. Thus, in flows where a minimum of near wall

similarity exists in the classic logarithmic region, one cannot yet use the

very near wall velocity data with confidence even though techniques for the

use of these data are available.

632
References

1. Clauser, F. H., "Turbulent Boundary Layer in Adverse Pressure Gradient,"

Journal of the Aeronautical Sciences , Vol. 21, February 1954.

2. Bradshaw, P., "A Simplified Method for Determining Turbulent Skin

Friction from Velocity Profiles," Journal of the Aerospace Sciences , Vol. 26, December 1959. '

"

3. Schraub, F. A., and S. J. Kline, "A Study of the Structure of the

Turbulent Boundary Layer With and Without Longitudinal Pressure

Gradient," Report MD-12, Thermosciences . Division , Mechanical Engineering,

Stanford University, 1965.

4. Spalding, D. B., "A Single Formula for the Law of the Wall," Journal

of Applied Mechanics , Trans. ASME , Vol. 83, No. 3, 1961.

5. Kleinstein, G., "Generalized Law of the Wall and Eddy-Viscosity Model

for Wall Boundary Layers," AIAA Journal , Vol. 5, No. 8, 1967.

6. Pierce, F. J., B. B. Zimmerman, "Wall Shear Stress Inference From

Two- and Three-Dimensional Turbulent Boundary Layer Velocity

Profiles," Journal of Fluids Engineering , Trans . ASME , Vol. 95,

1973.

7. Coles, D. E., The Turbulent Boundary Layer in a Compressible Fluid , USAF Project, Rand Corp., Report R-403-PR, 1962.

8. Coles, D. E., and E. A. Hirst, Computation of Turbulent Boundary Layer , 1968, AFOSR-IFP-Stanf ord Conference, Vol. 11, (Proceedings), Dept.

of Mech. Engr. , Stanford University, Calif., 1968.

9. Dean, R. C, Jr., Aerodynamics Measurements , Gas Turbine Laboratory,

Massachusetts Institute of Technology, Eagle Enterprises, 1958.

10. Gold, D. S., "Near-Wall Velocity Measurements in Two-Dimensional

Turbulent Boundary Layers," M. S. Thesis, Virginia Polytechnic

Institute and State University, Blacksburg, Va. , 1974.

11. Smith, D., and J. Walker, "Skin-Friction Measurements in Incompressible

Flow," NASA RT R-26, 1959.

12. Young, A. D., and J. N. Maas, "The Behavior of a Pitot Tube in a Transverse Pressure Gradient," ARC R & M No. 1770, 1936.

13. Preston, J. H., "The Determination of Turbulent Skin-Friction by

Means of Pitot Tubes," Journal of the Royal Aeronautical Society , Vol. 58, 1954.

14. Livesley, J. L. , "The Behavior of Trasverse Cylindrical and Forward

Facing Total Pressure Probes in Transverse Total Pressure Gradients,"

Journal of Aeronautical Sciences , Vol. 23, 1956.

633
15. MacMillan, F . , "Experiments on Pitot Tubes in Shear Flow," ARC R & M

No. 3028, 1956.

16. Davies, P. 0. A. L . , "The Behavior of a Pitot Tube in Transverse

Shear," Journal of Fluid Mechanics , Vol. 3, 1958.

Table 1. Summary of Flow/Probe Configurations and Number of

Runs

Flow/Probe Runs Flow/Probe Runs

llxx 6 31xx 2

12xx 7 32xx 2

13xx 7 33xx 1

14xx 3 41xx 1

21xx 2 43xx 1

22xx 1 51xx 2

23xx 2 61xx 2

Table 2, Law of the Wall Constants

Investigator k c

Coles 0.41 5.0

Patel 0.42 5.45

Smith & Walker 0.46 7.15

Nikuradse 0.42 5.8

Clauser 0.41 4.4

Spalding 0.40 5.5

Laufer 0.40 7.2

Town send 0.41 5.85

National Physical 0.47 5.9

Labora tory

634
TahLe 3

Experimental Scatter for Stagnation Probes

Run Series: 1100

Mean Sample Standard Deviation

Y (in.)

+

u

+

y u/U

+

u u/U

.013

. UlJ

.017

.020

13.84

141 A . HAUu

14.28

14.54

24.58

i-O 9 ft

. JOTR

32.17

37.87

.5585

. 3D /U

.5762

.5865

.08

.08

.07

.07

.0047

.0051

.0037

.0050

.025

.030

.040

.050

14.93

15.24

15. 72

16.17

47.33

56.80

75. 72

94.65

.6022

.6147

.6341

.6522

.04

.04

.05

.06

.0035

.0032

.0030

.0042

.100

.150

. 200

.300

17.62

18.56

19.24

20. 35

189.30

283.93

378. 57

567.90

. 7105

.7483

. 7758

.8207

.03

.02

.05

.07

.0034

.0035

.0036

.0054

Run Series: 1200

Mean Sample Standard Deviation

Y (in.)

+

u

+

y

u/U

+

u u/U

.013

.017

.020

14.14

14.50

14.75

25.11

33. 39

39.27

.5910

.6061

.6165

.23

.14

.10

.08

.0074

.0056

.0045

.0038

.025

.030

.040

.050

15.04

15. 36

15. 74

16.16

49.09

58. 93

78.59

98.21

.6283

.6420

.6601

.6757

.06

.04

.03

.04

.0041

.0026

.0019

.0015

.075

.100

.150

.200

16.88

17.46

18.25

18.93

147. 31

196.41

294.60

342.84

. 7059

.7300

.7629

.7913

.03

.03

.05

.06

.0025

.0034

.0037

.0037

1 in. = 2.54 cm

635
Table 3 (continued)

Run Series: 1300

Y (in.)

Mean

+

u

+

y u/U

Sample Standard Deviation

u u/U

. 015 14. 48 30.09 . 6163 .15 .0077

. 017 14 . 75 34 . 11 .6275 .11 .0066

.020 14.97 40. 13 . 6370 .09 .0055

.025 15. 25 50.16 .6491 .07 .0048

030 15. 52 60. 19 .6606 .04 .0048

.040 15.92 80. 23 . 6676 .03 .0039

. 050 16.23 100. 29 . 6908 .03 .0037

.075 16.87 150.44 .7178 .04 .0042

.100 17. 37 200.58 .7394 .05 .0051

.150 18.11 300.87 .7705 .05 .0043

.200 18.71 401.17 .7961 .06 .0038

.300 19.56 601. 78 .8325 .09 .0037

1 in. = 2.54 cm

636
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8. TEST CHANNEL

8

TEST STATION

Fig. 2 Schematic diagram of apparatus

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648
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels ana Closed Conduits held at NBS,

Jaithersburg, Ml), February 23-25, 1977. (Issued October 1977)

ON REDUCTION OF ERRORS ARISING IN HOT-WIRE ANEMOMETRY

OF THIN TURBULENT SHEAR LAYERS

J. GAVIGLIO and J. P. DUSSAUGE

Institut de Mecanique Statistique de la Turbulence

12, avenue du General Leclerc - 13003 MARSEILLE

1. INTRODUCTION

In supersonic flows, turbulent fluctuations can be classified ( 1 ) into vorticity, entropy and acoustic "modes". The first represents the

vortical part of the fluctuating velocity field, which will be called

"turbulent velocity field", or "turbulence field"; the second comes from

turbulent heat transfers, involving non-isentropic temperature fluctuations;

the latter expresses local pressure fluctuations, which in the case of

waves radiated by the turbulent flow, is associated with irrotational and

isentropic motions. Measurements of the level of theses modes are performed advantageously by using a constant-current type hot-wire anemometer

( 2 ). Only this type of instrument will be discussed in this paper. It

is well known that, due to the imperfections of the anemometer, (3,4,5 ) the intensity of modes are often underestimated. In some cases this can

be attributed to the low value of the impedance of the circuit feeding

the hot-wire or to the nonlinear response of the associated amplifier;

then the defects can be easily reduced or corrected.

Other sources of errors, which can be important, come from the upper bandwidth limit .This is particularly true for measurements made at

supersonic speeds. An important source of errors is the attenuation of

higher frequencies in the amplifier; a "truncation frequency" fc of

the uncompensated amplifier can be defined: for a sine wave signal, it

corresponds to an attenuation of 50 % of the energy . The influence of

the frequency response varies when the spectral distribution of the measured random signal depends on the temperature of the sensor. Additionally, important errors can also been induced by effect of the thermal

lag of the hot-wire, which must be compensated by a network that at high

frequencies gives only an approximate compensation, thus reducing the

actual bandwidth .The two latter effects are coupled as described below.

A correction is proposed which, in its form, differs from that given by

Laderman and Demetriades ( 6 ) . The errors depend both upon the characteristics of the amplifier, of the wire, but also on the flow characteristics. As it has been shown by Kistler (7 ), for a turbulent shear

layer of thickness 6 with a velocity in the outer flow, the energy

spectra largely extend over the characteristic frequency u<x>/& which

can exceed 10 s hz in supersonic flows of moderate MACH numbe^Moo < 5. A method is proposed to correct for the errors, and to check the validity

of the corrections.

2. METHOD OF CORRECTION FOR ERRORS _INDUCED_BY_THE_C^

Because of the thermal lag of the wire, a sine wave signal of frequency n is reduced and phase shifted following the complex "ideal"

law ; where u = 2jtn is the angular frequency and —

649
the "time constant" of the wire. For most compensation circuits, of which

Kovasznay gives some examples ( 8 )

, it has been verified that the transfer

function can be written in the general form or "theoretical" form:

where g0 and 9oo are the gain of the amplifier for relatively low frequencies and for the higher respectively. Phase corrections must be applied

in the case of double correlation function measurements performed with

wires of differing or non-equalized time constants (9).

Here will be considered only the errors on the standard deviation

of the signal which, after compensation, undergoes a residual attenuation.

For a sine wave, the modulus of the transfer function of the compensating

network, alone reads:

Fig. 1 - TRANSFER FUNCTION OF THE

COMPENSATION NETWORK.

Fig. 1 shows an experimental verification of this law. The measured value compares favourably to the "theoretical values" computed from formula

( 1 ) . The angular frequency u'0 j_ s that for which the theoritical value

of |*^r|/g 0 is 1/^/2 times the "ideal value". In the present case, — = 0.4 ms corresponds to ~ 200 khz and — = 0.8 ms

"o

K

2 it uo corresponds to ^100 khz.

This leads to the following correction:

let fm(n) and Fc (n) be the power spectral density of the measured

signal and of the corrected signal e' such as r

00^ , , . f

00,- 1 \ A

they are related through the relation : ^2 p

(

n ) _ ^

p ( n ) [1 +(-^f l^tn)^ 1

Hence by integration : e^.2

•m

if 9o

><x> 0 J

\9oo/ U2 /%2 F( n)dn = 1+4n2/Jo\

2 N

2 -Xr- (2)

0 \9oo/ u2

where N is an "equivalent frequency "defined ( 10) as n

2 = /^n2 F(n) dn

650
Introducing N helps to compute the corrections because its measurements

does not require a complete spectral analysis. Indeed, N can be deduced

in a simple manner from only the radius of curvature at the top of the

auto-correlation curve, because the latter is the same as that of the

sine wave of a frequency which can be determined as indicated on

fig. 2.

0 5

"

N

Fig

.

2 - DETERMINATION OF N FROM

AUTO - CORRELATION CURVES

N can also be obtained by

using an appropriate passive

filter network that produces

the time de rivative of the

s ignal / de

'\2 s ince

\dtim N2 J (dey0t)

2m

The correction related to the

compensating network imperfections can be nearly exact

when the signal energy lies

in a frequency band much lower

than the upper limiting frequency fc .For example, in

the case of Kistler's measurements ( 7 ) this condition

seems to be practically verified when fc is higher

than four or five times Uco/S

N is characteristic of the dissipation range and, in an equilibrium

boundary layer, increases when u^/g increases. In such conditions, the

analyzed shear layer will be called a "thick" shear layer. The definition

depends upon the characteristics of the flow and 6 , and on the

amplifier through the limiting frequency fc . It corresponds to

uoo/6f

c « 1 » a condition which is easily satisfied in the case

of subsonic flows. By contrast, when uoo/6fc is not negligible, the layer

is called a "thin" layer. The higher the non-dimensional ratio, the thinner the layer. At supersonic speeds, this frequently occurs, because in

most cases, fc must be limited, to about two hundred kiloHertz for example > in order to avoid parasitic effects of a prohibitive background amplifier

thermal noise, radio interference, etc....

Hence a compromise is looked for to choose fc high enough to

measure the main part of the signal energy, and low enough to avoid parasitic effects.

As for the corrections , they must be significant, easy to perform,

and in addition their efficiency has to be checked. One can admit that

each correction applied to a measured power spectral density is significant enough provided it does not much exceed approximately 100 percent. If

several corrections are applied together, the rule is valid for the total

correction

.

The measured spectrum contains the errors due to noise, to the compensation circuit, and to the truncation in frequency. The first step in

the correction procedure is to substract the noise from the measured spectrum. The second step is to correct for the errors introduced by the

651
"i 1 1 1 r "i 1 r

compensation circuit, which are valid for frequencies that are not much

greater than . Fig* 3 shows an example; it corresponds to the expe2tt rimental device indicated in

§.3.1. The curve A represents

the signal energy, corrected

from noise. The curve B is deduced from A by applying the

proposed correction for the

compensation circuit distorsion. This is practically accurate enough for the whole

bandwidth 0 to 210 khz since

-1- =Q57 ras.

One could attempt to cor- rect the measured spectra

for the effects of truncation

for high frequencies, especially beyond the truncation

limit fc .

*

i

1- 240 320

nKHz

400

Fig. 3 - POWER SPECTRA (BOUNDARY LAYER) The total correction,

being large, leads to significant distorsion, as shown by curve C. So only corrections related to

noise and to compensation are retained. But the method is only valid under another condition , namely: fc must be choosen high enough, if

compared to N .

Otherwise, both the measured energy and the measured equivalent frequency would be reduced, and the proposed correction beeing decreased,

would be insignificant. The example given in fig. 3, for which fc- 210 khz,

and N = 100 khz as deduced from auto-correlation measurements, seems to

be a nearly critical one, for fc is not very far from N. Nevertheless,

the efficiency of the method has been checked, as shown in §.3, and the

method remains still valid.

1 Formula (2 ) also needs verification, the time constant — is

0.57 ms . , the correction determined from the spectra is 46 %; that

involving N reaches 53 %.

It may be noticed that the application of the correction method to

a "thin" shear layer, as defined above, does not make it possible to measure the dissipation rate, since dissipation involves frequencies higher

than fc . Would the correction be possible, another limitation would arise because of the lack of spatial resolution of the wire.

A verification of the validity of the application method of the proposed correction is specified below.

3 . EXPERIMENTAL CHECK OF THE EFFICIENCY OF THE METHOD

Experimental results obtained by hot-wire anemometry are used to check

the efficiency of the method through comparisons with results obtained from

652
pressure measurements . Such comparisons have been done in a previous research, in the case of incompressible flows (9). Consider the ratio

PU

; where P is the local density, u' the velocity fluctuation and To the friction at the wall. According to an hypothesis of Morkovin (11), which has been verified by many authors -see for instance

Maise and Mc Donald (12) - the ratio is supposed not to be strongly de-

. pendant on MACH number. p and T

0 are deduced from pressure and temperature

measurements. In the present case, J72 is measured with a tungsten-pla

tinum hot-wire, the diameter of which is 3.8 microns. Ref . ( 13 )

.

Fig. 4 - CHECKING OF CORRECTED RESULTS

Fig. 4 compares the corrected values of Pu

' 2 /

T

0 , measured in a

very "thin" turbulent boundary layer to results made in more favourable

cases by other authors and recapitulated in ref. 14. The layer under examination in the present case develops on the surface of a circular cylinder placed in a supersonic flow, with its axis aligned with the flow

direction; the MACH number is 2.3, the thickness of the layer is 4mm.

It has been verified that the approximation of thin shear layer is valid

for the determination of the mean velocity field and of the wall friction

The momentum thickness Reynolds number ^g** is 1000, the friction

coefficient is 2.88 x 10-3

. The present corrected results agree with

others, although the corrections are large (in one case, they reach about

70 %) .

Fig. 5 shows another comparison of velocity fluctuations between the

present measurements and the results of ref. (7) and (15). As concerns

the MACH number influence, the results obtained at I.M.S.T. are consistent with the results of Kistler.

In fig. 6, uncorrected and corrected values of the ratio

measured at I.M.S.T., and compared to uncorrected values given by other

authors (1,7,15,16) in flows of thickness 8 much larger than in the

experiments performed at I.M.S.T. All the results are plotted together

with Klebanoff's measurements, obtained in a "thick" boundary layer,

i.e., free from bandwidth limitation and compensation errors.

653
The representation emphasizes the differences due to the parameter

uoo/6fr , since the MACH number influence is weak, as underlined by Morkovin (11); it indicates the general trend.

2 0

el

=> 16

1.2

08

04

i i i i i i i i—i—i r

oo

Fig. 5 - MEASUREMENTS CHECKING

MACH NUMBER INFLUENCE.

Comparisons are made for

different MACH numbers, and for

distances to the wall of

y/« = 1/8 and V4 •

A more typical parameter

would involve the influence of

the time constant J_ but

its values are not published in

the available literature, so

that its influence cannot be

rigourously determined. Uncorrected values of , /t0

largely increase with increasing

uoo/6fc

This means that

whatever Mjq.

pu is

often underestimated. When the correction is applied - and this is the

case for the measurements performed at I.M.S.T. in an unfavourable case - they strongly reduce the differences between the case of the "thin" supersonic shear layer and that of the "thick" subsonic layer used at a

reference. The residual differences are attributable to both the residual error related to the compromise accepted in the determination of the

bandwidth (§.2), and to the MACH number effect.

15

10

05

1

y/6 =0125

O / V/^ Ocorrected

1 5

10 -

y/5 =0 250

0 5

00 05 1.0 00

6fc

•frcorrected

05

6fc

1.0

Ha Urn m/sec5 mmfc KHz

U 67 7008 29.2 130(est.)

j o 3.56 656.8 26 7 130 (est) KISTLER

1 72 473 5 17 8 130 (est.) ) • 1 75 473 157 50 KOVASZNAY

+ 1 76 474 12.5 50 MORKOVIN

X 0 15.25 76 2 70 KLEBANOFF

O 23 545 2 4 0 210 I.M.S.T.

Fig. 6 - INFLUENCE OF THE NON-DIMENSIONAL FREQUENCY.

4. EXAMPLES OF MORE DETAILED ANALYSIS

Compensation errors vary with probe overheat. The errors reduce the

654
10r

corrected • uncorrected

J I

I I I I 0 2 0.4 r -£. 0.6 G

0.4

r _ F. 06

G

Fig. 7 - FLUCTUATION DIAGRAM

BOUNDARY LAYER

y/5 - 0,125

Fig. 8 - FLUCTUATION DIAGRAM

BOUNDARY LAYER

y/6 = 0,25

level and distort the shape of the fluctuation diagram* hence obscuring the physical

meaning in terms of modes and correlation

coefficients. This is illustrated by some

typical examples given in fig. 7 to 9 for

the case of the turbulent boundary layer

described in 8.3.1, and in fig. 10 for a

wake*.* All the experiments are performed at

MACH number 2.3. It is recalled that the

abcissa r = F/G i s the ratio of the hot-wire

sentitivities , respectively to mass-flow

and to local stagnation temperature. The

ordinate is obtained from

Ge

the r.m.s. value of the voltage e. The correction applies only to \f&2 . Following

Kovasznay (1) the curve e ( r

\ is an hyperbola. *

This is verified through direct measurements

if the correction

\9oo/ uo

10

corrected

• uncorrected

0.2 0.4 is negligible as compared to 1. Conversely,

this is not the case of direct measurements

when the error is large, whence a change Fig,

in the curvature of et ( r )

0.6

FLUCTUATION DIAGRAM.

SEPARATED BOUNDARY

LAYER, y/6 =0,88

In some limiting cases, the errors could

transform the hyperbolic curve into a straight line, which characterizes either the pure entropy mode, or the acoustic mode: this is nearly

the case for fig. 7. Applying the correction restores a convenient cur

vature except for high values of r, and suitably increases the level.

* The fluctuation diagram method has been extended to subsonic flows

with heat transfer by E . Verollet (17).

**See Table 2.

655
Some indications can be

given on the residual errors re- lated to the correction method.

Let us consider the formula

9o

goo

is a constant which depends only on the apparatus.

In unfavourable cases

\2

\9oo/ "5

is about one. A rather pessimistic estimation of the possible

errors in the determination of

N' and J

u0

1 gives the

••••••

corrected

• uncorrected

01 02

Fig. 10 - FLUCTUATION DIAGRAM

CENTERLINE OF A WAKE

values 20 % an 10 % ; the resulting error on the expression

contained under the square- root

symbol is then about 15 % and the relative error on

0 3 f_ 0.4 r= G

Ve^ about 8 %

Therefore, even large corrections can be applied with some confidence, provided N

2 and J_ are carefully measured.

TABLE 1 BOUNDARY LAYER

Vu* VJ2 0//o u*6'

y u % e VP

6

uncorrected corrected uncorrected corrected uncorrected corrected

0.125 5.65 9.46 5.06 8.94 -0.81 -0.88

0.250 4.63 6.88 5.59 8.13 -0.70 -0.77

0.500 4.17 5.4 5 6.53 9.04 -0.78 -0.85

0.750 2.54 3.02 6.11 8.06 - 0 83 - 0.89

1.00 0.31 0.44 1.62 2.35 - 0.40 -0.80

TABLE 2 REFERENCE FIGURE 10

u Vf2

o/o e

u' 0'VF2

uncorrected corrected uncorrected corrected uncorrected corrected

0.65 0.91 0.90 1.21 -0.51 -0.70

Numerical examples showing the importance of the compensation correction are given on tables 1 and 2, in terms of the vorticity mode,

the entropy mode, and correlation coefficient.

656
5. CONCLUSIONS

Errors arising in hot-wire measurements performed in thin turbulent

shear layers are analyzed. It is shown how these errors increase with

increasing the outer MACH number of the flow and decreasing the layer

thickness. The analysis indicates that the errors could be reduced by

enlarging the bandwidth of the amplifier and by reducing the time constant

of the wire. A simple correction method is proposed to correct for these

errors, it leads to a compromise for the choice of the bandwidth, and of

the characteristics of the compensation circuit. The efficiency of the

method is checked by comparing corrected results obtained in an unfavourable case with results deduced from mean pressure and temperature measurements. Moreover, the corrected results agree with direct measurements

made in more favourable cases.

The analysis indicate how to find optimal conditions required to peerform suitable measurements in supersonic turbulent layers. For a fixed

MACH number, the correction can be lowered by thickenning the turbulent

flow, for example by using wall roughness in the case of a boundary layer.

Reducing the Reynolds number, provided the flow remains fully turbulent,

also thicken? the layer but this effect is moderate; on the other hand,

it increases the time constant. Nevertheless, it diminishes the mechanical

vibrations, strain gauge effects, deformations and risks of breakage of

the wire, so that in some cases, the wire diameter can then be reduced.

This in turn reduces the time constant value and consequently the corrections and the residual errors.

February 2d, 1977

I.M.S.T. - 12 Avenue General Leclerc - 13003 MARSEILLE

FRANCE

and

O.N.E.R.A. - 29 Avenue de la Division Leclerc

92 CHATILLON SOUS BAGNEUX - FRANCE

657
REFERENCES

1. KOVASZNAY L.S.G. - Turbulence in supersonic flow J. Aero. Sc.,

20, 10, 1953.

2. KOVASZNAY L.S.G. - Should we still use hot wires? Advances in hot-wire anemometry, A F 0 S R N° 68 - 1942,1968.

3. CORRSIN S. - Turbulence: Experimental methods. Handbuch der Physic

Encyclopedia of Physics, Springer Verlag 1963-

4. BRADSHAW P. - An introdution to turbulence and its measurent .Aero

.

Dept, Imp. Coll. of Sc. and Techn . , Pergamon Press 1971.

5. COMTE BELLOT G. - Hot-wire anemometry, Annual Review of Fluid Mechanics 8,1976.

6. LADERMAN A.J., DEM2TRIADES A. - Mean and fluctuating flow measurements in the hypersonic boundary layer over a cooled wall; Journal of

Fluid Mech. 63,1, 1974.

7. A.L. KISTLER - Fluctuation measurements in a supersonic turbulent

boundary layer, The Physics of Fluids, 2,3, 1959.

8. KOVASZNAY L.S.G. - Development of turbulence measuring equipment.

N.A.C.A. Rpt. 1209, 1954.

9. GAVIGLIO J. - Sur quelques problemes de mesures de turbulence effectu6es a l'aide de l'anemometre a fils chauds parcourus par un courant

d' intensity constante. These doct. d 'Etat , Marseille 1958 P.S.T. Minist.

Air N° 385.

10. MARTINOT LAGARDE A. - Introduction au spectre de la turbulence,

N.T. G.R.A. 55, Paris, 1946.

11. MORKOVIN M.V. - Effects of high acceleration on a turbulent supersonic shear layer 1957 Heat Transfert and Fluid Mechanics Institute,

U.C.L.A. 1955.

12. MAISE G., Mc DONALD - Mixing length and kinematic eddy viscosity in

a compressible boundary layer, AIAA Journal 6, 73, 1968.

13. GAVIGLIO J., DUSSAUGE J. P., DEBIEVE J.F., FAVRE k. - Behavior of a

turbulent flow, strongly out of equilibrium at supersonic speed;

I.U.T.A.M. symposium on structure of turbulence and drag reduction,

Washington, D.C., 1977.

14. JOHNSON D.A., ROSE W.C. - Laser velocimeter and hot-wire anemometer

comparison in a supersonic boundary layer. A. I. A.A. Journal, 13,4, 1975.

15. KLEBANOFF P.S. - Characteristics of turbulence in a boundary layer

with zero pressure gradient - N.A.C.A. T.N. 3178, 1954.

16. MORKOVIN M.V. - Effects of high acceleration on a turbulent supersonic shear layer - 1957 Heat Transfert and Fluid Mechanics Institute,

U.C.L.A. 1955.

17. VEROLLET E. - Contribution aux mgthodes de mesures de turbulence de

vitesse et de temperature par l'an6mometre a fil chaud . These 3eme

cycle d 'A6rodynamique , Fac . des Sc. Marseille 1962.

658
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS

,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

PROBE AND METHOD FOR SIMULTANEOUS MEASUREMENTS OF "TRUE"

INSTANTANEOUS TEMPERATURE AND THREE VELOCITY COMPONENTS IN TURBULENT FLOW.

Gracio Fabris

Argonne National Laboratory

Need has always existed in the measurement of turbulent

flows to obtain correct instantaneous values of temperature

and three components of velocity at a particular point. Many

proposed lengthy approximate correction methods, that attempt

to account for "nonlinear" effects (cross contamination between different quantities) in hot-wire measurements, cannot

be considered satisfactory.

The availability of powerful digital computers for

theoretical and experimental studies has placed pressures on

experimentalists to develop better probes and methods. This

paper attempts to answer these pressures by describing the

development of a special four wire probe and a method of processing the obtained signals. The use of four 0.000025 inch

sensors makes the probe practically interference free. The

processing method is based on the simultaneous solution of

four complete nonlinear response equations for the sensors

yielding in principle exact instantaneous values of velocity

components and temperature. Additional features of the processing method include: instantaneous full correction for

tunnel free stream velocity and temperature fluctuations,

first order correction for DC drifts of the signals during

data acquisition, subtraction of all 60 Hz related noise,

correction for streamwise displacement of sensors based

on instantaneous streamwise velocity.

1. Introduction

For well over a quarter of a century, hot-wire anemometry has been and reains the most significant experimental technique in single phase fluid

echanics. It is used mostly for the measurements of instantaneous temperature

r streamwise component of velocity.

Higher levels of turbulence, namely non-streamwise components of velocity

luctuations, influence readings of a single hot-wire placed perpendicular to

he mean flow. Such readings have to be corrected for the influence of two

ther velocity components. See Klatt [1], Spencer [2] and Rodi [3].

An inclined single wire can be placed at different angles at a given point

f turbulent flow, and levels of fluctuations u

2", v7 and vr and even six

eynolds stresses as done by Hoffmeister [4] and by Mojola [5] may be determined

figures in brackets indicate the literature references at the end of this paper.

659
by taking at least nine measurements with the wire placed at different angles

with respect to the main stream direction.

Papers that treat response of single hot-wire in three dimensional

turbulence are numerous. One by Champagne, et al. [6] is often referred to.

Others cited are those by Friehe and Schwartz [7], by Collis and Williams [8],

Davies and Fisher [9], by Davis and Davies [10] and by Andrews, et al. [11].

Artt and Brown [12] operated a single hot wire at two different overheats and obtained approximate average streamwise velocity and temperature.

However, a single wire cannot give instantaneous information about more

than one component of velocity; and even that one is contaminated by the

influence of other velocity components and possibly temperature.

By placing several hot-wires or hot-film sensors close to each other, it

is possible to extract more information. "X-wire" was used repeatedly by

many researchers to measure simultaneously u and v components of velocity as

well as Reynolds stress.

The response of a wire in non-isothermal flow was considered by Corrsin

[13], Rose [14], Araya and Plate [15] and others. Chevrey and Tutu [16]

used two wires and an extensive analog scheme to measure simultaneously

approximate temperature and streamwise components of velocity. Ali [17]

has improved the Chevrey-Tutu 's analog processing of two-wire signals.

Sakao [18] used two hot-wires operated at two different temperatures to

measure streamwise velocity in flow accompanied by temperature fluctuations.

Mimaud-Lacoste [19] used constant current wire at low overheat and constant

temperature wire at high overheat, similar to Chevrey and Tutu [16]. However, he used an analytical scheme for taking into account contamination

by velocity on "temperature signal" and temperature contamination on

"velocity signals."

Way and Libby [20,21] used a two sensor probe to measure streamwise

velocity and concentration of a helium jet ejected into the air. By the

addition of one more sensor Stanford and Libby [22] were able to measure

the lateral component of velocity also. Corrsin and Kistler [23] developed

a probe for the measurement of streamwise vorticity component. A similar

probe was used by Coles and Van Atta [24] to measure mean velocity vector

and six Reynolds stresses in swirling flow.

Spencer [2] used a three wire probe designed by him and made by ThermoSystems Inc. He used digital processing of signals to obtain three instantaneous velocity components. However, these components were only approximate since complete response equations for sensors were not used. Computed

time averaged velocity correlations were later corrected for the influence

of the third velocity component on the sensors.

Lakshaminaraya and Poncet [25] placed a two sensor probe and a one

660
sensor probe placed closely together to measure three dimensional values.

Simplified response equations were used and solved digitally.

Due to the tremendous advancement of computational techniques, predictive methods for turbulent flows are becoming more and more sophisticated

trying to introduce more complicated "closure" equations hopefully based on

the physics of turbulent flow. See Bradshaw [26], Hanjalic and Launder [27]

and Morel [28], The use of digital techniques in the processing of signals in

turbulent flows is becoming more common nowadays, promising to bring significantly more insight into the nature of turbulent flow, and to close the

gap that is developing between computational power and experimental facts

available to prediction methodology.

In order to keep pace with the fortunate availability of digital computational power for experimental techniques, it is necessary to improve

experimental probes and ways of processing their output signals. The

development of probes and methods capable of yielding "true" instantaneous

three velocity components and temperature values at one point is long overdue.

It is certain that much more vital information about the structure of turbulent

flow could be obtained by the simultaneous measurement of as many quantities as

possible (Fabris [29]).

Tutu and Chevrey [30] have stated that to solve response equations for

sensors linearly for second order correlations, it would be necessary to have a seven sensor probe to get correct instantaneous values of u and v. However, we

will show that the number of sensors could be smaller when full nonlinear equations are solved simultaneously. Flow reversal is not considered since it

cannot be measured due to prong interference.

The probe described in this paper was used by the author for conditional

sampling in heated single turbulent wake and interacting heated-unheated wakes

flow. Although that flow is not the object of this paper, occasional reference

to it will be made insofar as it relates to the calibration of the probe and the

method of processing of data.

2. Construction of the Probe

The probe as designed and made by the author at IIT is shown in Figure 1.

For wire supports jeweler's broaches with a diameter at the tip of about 0.012

inches are used. The tips are bent inward in order to facilitate the soldering

of the sensing wires. All four sensing wires consist of Wollaston-processed

platinum-10% rhodium filaments. These are 0.000025 inches in diameter and are

enclosed in a silver jacket 0.003 inches in diameter.

The distance between the wire support tips, measured in the plane x is

constant, 7/32 inches, while the bare sensing lengths of the wires are 0.080

inches. Since the tip distance is two to three times larger than for standard

commercial single wires, the interference of the probe tips with the flow at

the sensing spot is minimal. Our diagnostic checks indicated interference of

less than one percent. This finding is in agreement with that of ComteBellot, et al. [31]. The center of the sensing spot is about one inch upstream

661
of the root of the broaches. According to Dahm and Rasmussen [32] the 5/16

inch nose piece which held the broaches should have a negligible influence on

the measurements. The sensing spot is six and a half inches upstream of the

vertical stem of the probe support which has an airfoil like shape, in order

to cut down on flow induced vibrations of the probe. The nose part of the

probe has two hinges (indicated at lower left of Figure 1) and could therefore

be rotated around two axes. Since the probe tip can be rotated around a third

axis, parallel to the broaches, the sensing wires can assume any desired angle

with respect to the flow direction. The sensors numbered one and two in Figure

1 are perpendicular to each other, forming a classical X-wire probe in the x-y

plane. The shortest distance between them is approximately 0.03 inches (.01 is

technically achievable). Sensor number three makes angles of approximately 45°

with the x and z axes. Due to an error in assembling (interchange of supporting prongs), this sensor is 0.064 inches upstream of sensors one and two

although it was designed to be only 0.020 inches upstream. The corresponding

lag time is taken into account in the computer data processing. Sensor number

four is parallel to the z-axis and is located 0.028 inches upstream of the c crossing of sensors one and two (see the side view in Figure 1)

.

If the above-mentioned error in fabrication had not occurred, the sensing

lengths could have been shorter and all sensors could have been placed within

a cube 0.04 inches per side.

Sensors 1, 2, and 3 are operated in constant temperature mode at high

overheats while sensor 4 is operated in constant current mode at very low

overheat

.

In order for a four wire probe to yield reliable results, it is necessary

that each of the quantities to be measured (u, v, w, 6) has a significant

influence on the output signal of at least one of the sensors. As will be

seen later, sensors 1 and 2 are primarily sensitive to u and v components of

velocity, sensor 3 to u and w and sensor 4 to temperature 0.

3. Velocity Sensing

The velocities in the wake were sensed primarily by three inclined wires

and the velocity in the free stream by a wire normal to the flow. All these

wires were platinum—10% rhodium 0.000025 inches in diameter. Constant

temperature DISA anemometers Model 55D01 were used with wires one and two at

an overheat of 300°C and sensor number three at 150°C. DISA linearizers Model

55D10 and DISA filters Model 55D25 were used for all three channels.

Output signals of the anemometers raised to an exponents of 2.7 (experimentally determined) became linear functions of velocity. (Digital linearizati

would be advantageous in terms of data processing.) These linearized outputs

were passed through low-pass filters set at 2000 Hz. This number was chosen

based on the highest frequency of interest in the wake investigation. Kolmogor

frequencies are higher than this but their contributions to the turbulent chara

teristics other than high frequency spectra are insignificant. However, even

when short enough sensors are used to measure Kolmogoroff scales without

662
excessive length corrections (La Rue [33]), the spectral levels at these high

frequencies usually fall below the electronic noise in the signal. Low-pass

filtering avoids aliasing when power spectra are computed.

The output of the anemometry units often drifted for as long as two days

when new wires were mounted. The cold wire resistance would drift and sometimes undergo even a step-wise change. Presumably these changes were due to the

relaxing of internal stresses in the wires or due to oxidization as explained by

Hassan and Dent [34]. All wires were, therefore, left to overheat for over 30

hours until the above-mentioned drift disappeared, before the experiments were

performed

.

4. Temperature Sensing

To measure temperature, the fourth sensor in the four-wire probe was

principally used. The temperature in the free stream was also monitored. In

both cases platinum-10% rhodium wires with diameters of 0.000025 inches were

utilized. Resistances of these two wires were always matched to within ten

percent. The cable leads from both wires, connected in the same "broken bridge"

shown in Figure 2. A paper by Borchardt and Holland [35] explains features of

the "broken bridge." A current of about 0.5 mA was passed through each wire.

The function of this bridge was to subtract the temperature signal in the free

stream from that in the wake and to amplify this difference approximately 8000

times. In this way any drift of the tunnel temperature was automatically cancelled at the bridge output. The bridge is significantly simpler than the

circuits used by Ochs [36] and LaRue [33]. This is probably the reason for

the lower noise level achieved in this study.

Grounding was extremely important for the temperature measurements. Most

of the noise in the temperature signal consisted of the 60 Hz line frequency,

its higher harmonics and some white noise. The stratagem of connecting the

two wires in the same bridge resulted in the cancellation of most of the periodic noise. Proper grounding further decreased that part of the noise.

The output from the broken bridge and the amplifier was a linear function

of temperature in the temperature range used in this study (the wake flow was

overheated for only several degrees Celsius) , a fact which made the processing

easier. To determine its sensitivity to the temperature in the flow, it was

necessary to determine the temperature resistivity coefficient. For one wire

the change in the output signal from the "broken bridge" and amplifier unit

was measured as a function of the change in the air temperature which was

monitored by a precision mercury thermometer. During this process the temperature in the tunnel was varied by 5°C while the tunnel was operated at the

standard speed of 21.2 ft/sec. From the initial resistance and the total amplification factor of the circuitry we obtained a = AR^/R3oAQ = 0.001675 per degree

Celsius. This value falls squarely in the range reported by the wire manufacturer

Sigmund and Cohn, namely from 0.0016 to 0.0017.

663
The sensitivity of the temperature measuring circuitry with both wires in

place was determined by artificially decreasing a known wire resistance

by known decrements AR^. This was achieved simply by connecting a known

resistor of high value (usually lMft) in parallel with the wires. From the

known temperature resistivity coefficient one easily determines what effective

change in the air temperature is represented by AR^/R^* From measurements of

changes in the output voltage we found the sensitivity to be 6.98 V/°C.

In actual experiment, the wake temperature sensor had a resistance of

1358ft, while free stream temperature s< of the bridge part of the broken bridge wasRQ = 1358ft, while free stream temperature sensor R^ = 1444ft. The resistance

(r3+V

2

<Jt>

R.b R

1 (1)

(R

3

+V (14 R">

The voltage drop across the bridge part was

\

E = 15

rTTr (2) VR

0

The output from the broken bridge was

R

A

" if \ (1+aAT)

e

—W E '

since

R

l

R

3

(4)

0

we have R„

e = -r-rl E (5)

* R

The output of the second unit was

R

6 . C6)

e

2 =

"e Rj

664
Other resistances were R_ = 5kft, R, = 25kft, R = 50kfi potentiometer,

R

5 = 500ft, R

5 = 200kft. Taking AT = 1°C , one obtains for this case, sensitivity

to temperature

S = e,'2 =6.97 V/°C,

AT=1°C

which agrees very well with the experimentally determined value of 6.98 V/°C.

The time constant of the wire was measured by means of the square-wave

test applying a current of 0.5 mA. Results given in Figure 3 indicate that the

cut off frequency at 21.2 feet per second is 4500 Hz. This made compensation

of temperature signals unnecessary. No significant decrease in this frequency,

such as reported by La Rue [33] was observed even after several days of running.

5. Calibration of the Probe

As mentioned previously, sensor number four in Figure 1 was used primarily

for temperature measurements while sensors one, two and three were used primarily for velocity measurements. No electronic interference between different

sensor signals due to long cables running together through the probe supports

was ever observed. Angular calibration tests for all three velocity sensors

were performed. Linearized voltage outputs as functions of the yaw angle for

sensors number one and two are displayed in Figure 4. It is apparent that the

data can be successfully expressed by a cosine curve between the ±30° yaw angles,

The operating overheat of sensors one and two was 300°C, while sensor three

was overheated to 150°C. When sensor three was not energized, calibration data

for sensors one and two in Figure 4 moved upward by less than one percent. This

mild temperature interference among previously used sensors is shown as dashed

lines in Figure 4. These earlier velocity sensors were made of tungsten wire

0.00015 inches in diameter with a sensing length of 0.04 inches. Clearly, the

thermal wake of sensor number three had significant adverse influence on signals

from sensors one and two. Decreasing the overheat of sensor three in an attempt

to restore the cosine law for sensors one and two did not solve the problem.

Ultimately the offending tungsten sensor (number three) was replaced by a six

times thinner wire made of platinum—10% rhodium. The cure, however, turned out

to be short lived. During the etching of sensors number three and four, nitric

acid vapors evidently caused unnoticeable damage which impaired the strength of

the tungsten sensors one and two regardless of how carefully the etching process

was performed. Later, usually after two or three hours of running, these two

sensors would burn out. Finally the problem was solved by using Pt-10% Rh wires

for all sensors, as described previously, with the satisfactory calibrations

shown in Figure 4.

Since the development of interference-free multiple-wire probes w±£h_ good

665
spatial resolution remains an art which is essential to investigations of

turbulence structure, it is desirable to relate briefly the experiences of

Spencer [2]. Spencer's sensor number three was downstream of sensors one and

two. Also he reported that his experimental arrangement made the angular calibration of sensor three difficult. He reported a decrease in the linearized

output of the third sensor of seven percent when his two upstream sensors were

energized. He found no adverse effect on linearization, but he could not report

on agreement or disagreement with the cosine law. Clearly the interference

effects are rather subtle.

During our general yaw calibrations of sensor number three the outputs of

sensors one and two, were monitored but disclosed only normal behavior up to

±30° yaw from the nominal position. Beyond these angles the silver jackets of

sensors three and four apparently started to interfere with the flow sensed by

wires one and two.

Calibrations preceding the final data taking and taping include the determination of the exact angles of the wires in the wind tunnel. This determination

is subject to additional geometrical constraints associated with the utilization

of the traversing mechanism. The head of the traversing mechanism was rotated

in the free stream five degrees in the vertical plane for the determination of

angles 3^ and 62 and two degrees in the horizontal plane for 33. The formula

2l AO cos A3^

1

based on the verified cosine law, was then used to compute the angles 3l, 32> and

33. Here E-j^ and E2^ are measured linearized outputs of the corresponding channels

before and after A3£ rotation. The sensitivity to errors in the determination of

33 can be illustrated by noting that a one degree change in 33 leads to a change of

— - n approximately ten percent in the inferred w

z value.

Because of the possibility of the impairment of accuracy in the determination

of the angles due to the physical limitations on the motion of traversing mechanism

the following additional procedures were used. Very careful measurements of u',

v' , and w' at the centerline of the cold wake were carried out with calibrated

single-wire and X-wire probes which were not hampered by the constraints of the

traversing mechanism. These measured values were used as "true" references for

the measurement of the same quantities at the same position with the four-wire

probe. These reference values were used to supplement the information from

equation (7) for iterative determinations of "best" 3-j_ values for the different

runs with the aid of a computer data reduction program.

Angles 3^, 32 > and 33, determined by the iterative process through comparison

with the reference values, were always within less than one degree of the values

obtained using equation (7).

666
6. The Data Processing Equipment

For the acquisition and digitizing of data mini-computer PDP-11/10 was used

with auxiliary equipment including an analog-to-digital converter. The computer

has sixteen channels, four of which are digitized simultaneously and the other

twelve with minimal delay time. Figure 5 presents the block diagram of the complete data acquisition system as used by Fabris [29]. Other researchers may use

different acquisition systems according to availability.

The outputs of the linearizers were adjusted to read approximately 10.5 volts

for the probes in the free stream. The filters (auxiliary units) used with the

velocity channels permitted amplification and DC offset. Thus the linearized

signals were given a maximum amplification of approximately 3.5 and were then

offset for -30 volts D.C.

Using an adjustable potentiometer in the "broken bridge" the temperature

signal was set to approximately -3 volts when the temperature in the free stream

was measured. The filter used with this signal restricted the output to a range

from -6 to +6 volts.

Not more than 20 percent of the allowable range of the analog-to-digital converter (-10 to +10 volts) was used (of course, researchers should tend to use

most of the allowable range). However, the quantizing errors were small so that

the maximum errors incurred in computing instantaneous velocities and temperatures

were less than 0.0015 feet per second and 0.00035°C, respectively. These errors

in instantaneous values can be positive or negative so that, in the computed

averaged quantities, they are substantially cancelled out.

7. The Data Acquisition Program

The data acquisition program digitized five analog signals. The four signals

coming from the four-wire probe (three velocity signals and the temperature

difference between the wake and the free stream) were digitized simultaneously

(the system did not allow for simultaneous digitization of more than four signals).

The free stream velocity signal, which has a much lower frequency content, was

digitized with a time delay of 0.115 ms. with respect to the first four signals.

Figure 6 displays the scheme of data acquisition. The digitized discrete values

were stored as sixteen-bit binary integer numbers on a nine-track magnetic tape.

Actually, only the last 12 bits were used as data. The first four bits were

used as complements since it was easier to handle 16-bit numbers.

8. The Wires Response Equations

Even though linearizers were used in the actual acquisition of data for

the sake of simplicity and generality, raw output signals from the anemometry

units will be treated in this section.

There exist many papers proposing different response equations for the

constant temperature hot wires. Most generally accepted are those by King [37]

and by Collis and Williams [8] for the response of hot wire to the normal component

667
of velocity and to ambient temperature. There are a number of works published

later proposing somewhat different equations like those by Bruun [38] and by

Siddall and Davies [39]. The relationship proposed by Mimaud-Lacoste [19] is

algebraically simple and therefore convenient for digital processing.

There are also a number of papers dealing with the response of hot-wire to

flow under different angles with respect to the wire. Champagne, Fleicher and

Wehrmann [6] introduced the correction factor to account for deviation from the

"cosine" law due to finite wire ratio 1/d. The paper by Friehe and Swartz [7]

deals with the same matter, proposing a different correction scheme. In our

case, since wires of the ratio 1/d > 600 were used, "perfect" agreement with

the cosine curve had been expected. This was confirmed by the yaw calibration.

Thus, for the wires used, outputs of the anemometry units become a straight

forward function of the velocity perpendicular to a wire and of the temperature

of the fluid. According to Morkovin [40] the effect of density fluctuations is

negligible for low speed flows.

For a constant temperature anemometry unit

E0* <A+B(U

n

)

1/n

)(l - Tw-Tref > < 8 >

or

E

0

= A(1+ !

(V

1/n

> (1 - Tw-Tref > <9)

It is well known that A and B are functions of temperature only for a particular

wire and a given ambient fluid at a constant pressure. It is best to experimentally determine the functional dependence of A and B on temperature, see

Chevrey and Tutu [16] and substitute these formulae in the above equation. For

relatively small values of 6 a linear approximation may be used. It is generally

accepted that the exponent 1/n is constant, though Eisner and Gundlach [41] proposed it to be a function of velocity. For wires used in this study calibration

yielded n = 2.7. This was somewhat surprising at the outset. However, since

the Reynolds numbers for the wire we used were smaller than those for the

generally used 0.00015 inch tungsten wire, the above value for n does agree with

the value inferred from Figure 2.9 of Sandborn's monograph [42].

U is the component of velocity perpendicular to a sensor. For sensors

1, 2, and 3 respectively,

U

2 = (U cos 3, + V sin B-,)

2

+ W

2

(10) n^ 1 1

U

2 = (U cos L + V sin B 0 ) 2

+ W

2

(11)

n

2

2 2

668
U

2 = (U cos 6 0 + W sin P„)

2

+ V

2

n„ 3 3

(12)

Sensor four gives the output

E

4 = E4

+ K

4

0 + (/u

2

+V

2 - U

r

) (13)

where Eu is the output of the temperature measuring circuit for the probe in

the free stream at reference temperature T and velocity U . and are proportionality constants expressing output sensitivity to changes of temperature

and of velocity. Linear dependence of constant current anemometry output on

temperature is a well known fact. For relatively small currents the influence

of a change in velocity is only a few percent at most. Accordingly the first

order correction using is justified.

Equations (8), (9), and (13) are really only sample formulae and a

researcher can use different ones according to his preference and the conditions

of his experiment. If less computation and simplified calibration is desired,

simpler formulae should be used; if greater accuracy is desired in experiments

involving extended velocity and temperature ranges, more sophisticated formulas

should be used. The use of lineariness is one possible way of cutting computational costs. In flows with low turbulence levels, equations (10), (11), and (12)

could be simplified by dropping W in (10) and (11) and V in (12) with acceptable

losses in accuracy.

Having voltage outputs from three CTA and one CCA circuits, it is best to

write four corresponding equations with U, V, W and 6 as unknowns, and then to

solve them simultaneously. The Newton-Raphson technique features the fastest

convergence if the initial guess for unknowns is reasonable. Since velocities

and temperature are changing only slightly from one time instant to the next,

it is extremely convenient to take as the initial guess for one time constant

values of U,V, W and 0 that are actual solutions for a previous time constant.

Using this technique, accuracy of numerical solution better than 0.01 percent

has been achieved by Fabris [29] with a single Iteration. If a significantly

higher accuracy is desired, it might prove beneficial to provide an initial

guess of unknowns that would take in account trends in velocities, and temperature

in two previous consecutive instants, thus avoiding an excessive number of

iterations

.

9. Corrections

Digital processing permits a number of corrections to be made that would

be almost impossible to make in analog processing. These corrections contribute

greatly to the accuracy of flow measurements . Such corrections are of importance

in many flows, for example in small deficit wake measurements.

669
9.1. Correction for DC Drifts

In any measurement, there is a finite time lag (often rather long) between the calibration of a probe and the electronics and the actual measurement.

During that time there are inevitably some DC drifts (changes) in voltage outputs, decreasing the accuracy of measurement. The causes of these drifts are in

the electronic instruments as well as in changes in ambient wind tunnel conditions, such as temperature, humidity and free stream velocity. It is virtually

impossible to monitor drifts during the actual measurement, but one can find

the total drift values in a given time interval by taking measurements in the

reference flow before and after data acquisition. One cannot know which of

the parameters has contributed most to the drift, but in the first approximation it can be assumed that the most significant part is or could be included

in proportionality constant A in equation (9) (with the ratio B/A assumed to

remain constant) or in the additive constant El+ in equation (13). Experience

indicates that in practically all cases drifts are a continuous function in

time and for reasonable short time intervals rather monotonic. So, lacking

information on the actual nature of drift, it is justifiable to assume that

drift is linear in time between the reference flow measurements made just before and just after measurements in the flow of interest.

In the case of measurements in the wake flow, or some other free stream

turbulence flow, first reference measurements with the digital acquisition of

data, are made in the undisturbed potential free stream. Then recordings are

taken at desired number of lateral wake profile positions with the last measurements again in the original free stream reference position. During all these

measurements time is noted when data at different wake positions are acquired.

Now, assuming no change in ambient conditions, the computation of the abovementioned constants is performed according to the linear interpolation formula

C.=C. + t. (C. .

1 i,j l, ref. first j i,ref.last - C.i,ref.- firstJ

(1=1,2,3,4,5), (j=l,...,12) (14) I

where i and j indicate the appropriate channel or wake positions.

Of course, the angles of the inclined wires with respect to the main

stream have to be determined prior to the above calculation, so that the velocity

normal to each wire is known for the probe in the free stream reference position.

If one would like to increase accuracy and to correct for more than one constant

per channel, one would have to perform additional reference measurements under

different flow conditions. For example, it would be very convenient if there

were a small still air chamber where the probe could be quickly placed and

readings recorded before and after measurements in the flow to be studied. In

such a way, additional reference values would be provided and interpolative

correction for two constants per channel obtained, such as the constants A and

B in equation (9).

670
9.2. Correction for Streamwise Displacement between Sensors

Inevitably there is some streamwise displacement between each of the

sensors three and four and the (imaginary) crossing of sensors one and two.

The four channels were sampled simultaneously which meant that at a given

time the four wires did not sense the same fluid elements. This effect was

taken into account as explained below.

It is known that in flows with lower turbulence such as the far wake

Taylor's hypothesis is a good approximation to the physical process. This

hypothesis simply states that the turbulent structure is convected past any

point with the local mean velocity U(x,y) so that spatial and time derivatives

are related

u h < > - h (

>

< 15 >

This means that a fluid particle passing the first upstream sensors

changes its temperature and velocity very little before it passes the downstream sensors. To estimate the error when the convection is not taken into

account, we can use the spatial correlation measurements of Grant [43]. Judging by these correlations in a cylinder wake, we conclude that in our case the

fluctuating properties would have changed only about two percent (correlation

coefficient of 0.98) for a maximum wire displacement of 1.6 mm.

In our data reduction program, however, we can compensate for any

displacement by effectively delaying the signals from the upstream wires for

appropriate times using the instantaneous flow velocity in the x direction as

the transport velocity for the signals. The conditions correspond then to the

space-time correlations between two signals of turbulence at two streamwise

locations studied by Favre [44]. Judging by his results when an optimal time

delay would be applied for conditions of our flow, the correlation coefficient

would be 0.997. Such an improvement was considered significant, and therefore

all of our computations and results incorporated the optimum delay for channels

three and four, see Figure 7. Optimum delay was always based on instantaneous

streamwise velocity.

One minor complication arose in connection with the delay times: they

did not correspond to the discrete time values at which our data were given

and therefore interpolations were necessary. Study of Figure 7 should make

the issues and procedures quite clear. The interpolation did degrade our

corrections somewhat, especially when high-frequency components were present.

To assess the degree of degradation, we computed the values of 9' over one

record both for the original data and for the data obtained by interpolation

at the delayed times. The latter was approximately 0.5 percent lower. This

being an undesirable situation, we believe that the net gain in applying the

optimal time delay is important and that the small degradation resulting from

interpolation is negligible except perhaps in obtaining power spectra with high

frequency content.

671
9.3. Corrections for Free Stream Velocity and Temperature Variations

Even though greatest care is taken, some velocity fluctuations remain

in a free stream. Measuring the two point correlation function of the streamwise component of velocity in the free stream of the test section, Fabris [29]

found that a major part of the streamwise velocity fluctuations is simultaneous

at all points (pressure induced fluctuations) with a frequency range 0 to 10

Hz. Slow fluctuations of velocity (less than 1 Hz) had had a peak to peak

amplitude of 0.015 U. Only 85 percent of these fluctuations could be averaged

out using an averaging circuit with a time constant of ten seconds. Although

these slow fluctuations do not influence the analog u' measurements (EMS meter

filters out fluctuations with frequency of less than 1 Hz), they do influence

U measurements. The RMS value of free stream velocity fluctuations measured

by the analog RMS meter was 0.0035 U.

Using the fact of simultaneousness of free stream velocity fluctuations

in the whole test section and the fact that in a small deficit wake only

relatively small changes of streamwise velocity are encountered, one effective

correction scheme was devised. Free stream streamwise velocity was monitored

by a separate constant temperature anemometer probe. This velocity was subtracted by digital processing from the streamwise velocity simultaneously

measured by the four-wire probe. In this manner, the instantaneous velocity

defect in the wake with respect to instantaneous free stream velocity was

obtained with the four-wire probe in the free stream (not close to the free

stream probe). Digitally computed u' was 0.00055 U.

The free stream temperature did not show appreciable fluctuations except

for quite slow variations which were of the order of 0.05°C during a 15 minute

period. Such temperature drifts were compensated for by subtracting signals of

the temperature sensor of the four wire probe from a reference temperature wire

placed in the free stream.

After the above drift signals are eliminated, it is still difficult to

judge the actual free stream temperature fluctuations. They are sufficiently

small for possible false signals from the higher free-stream velocity fluctuations to creep in despite the very low overheat of the temperature wire sensor.

Also, the noise level in the temperature signals is higher than that in the

velocity signals. Be that as it may, 9' in the free stream thus obtained was

0.0014°C, which is considerably less than 8' inferred from a single wire uncompensated measurement.

9.4. Subtraction of the 60-Hz Conditioned Noise

At the outset most of the signal noise was 60-Hz conditioned regardless

of how carefully grounding of the temperature probes and the bridge was effected

This created problems since the temperature signal was used for conditional

discrimination. It forced us to carefully look for a solution. The combination

of the stored information and the computer made it possible, as part of the data

processing, to attempt to purge the periodic parts of this noise from the signal

672
The data acquisition program was written in such a way that all records were

triggered at the same phase of the 60 Hz supply current. Since the sampling

frequency was 4000 Hz, it meant that exactly 200 samples covered three cycles

of the 60-Hz conditioned noise. Using the signals at the first and last

reference recording per wake profile (i.e., free-stream position) each of these

signals was "ensemble averaged" or "educted" in the data reduction program for

200 ordered samples within each interval of three cycles. There were seven

three-cycle intervals used per record (1400 samples) . In total 34 records

were used. This simply meant making 200 separate sums each one composed of

238 summands . In this summation process the regular 60-IIz conditioned noise

cumulated while the random part of the noise and the part of the signals due

to velocity or temperature fluctuations in the flow cancelled out. Then the

averages of these 200 sums were computed for each channel, subtracted from

each of the sums and the result divided by 238, the number of summands.

In this manner three relatively clean cycles of 60-Hz conditioned noise

were obtained for each channel. This repetitive "noise signal" was subtracted

from all the digital data processed in our data reduction program to obtain

what we call "cleaned" signals. Samples of the "educted" 60-Hz conditioned

noise and of the corresponding "cleaned" signals are given in Figure 8 for

channels three and four. The original signal was, of course, the sum of these

two signals. The clear-cut improvement underscores the significance of our

correction process, especially for measurement in low turbulence or in potential

flow.

10. Conclusions

The availability of analog to digital conversion and digital processing

of turbulence signals increases experimental possibilities greatly. The

development of more sophisticated probes and methods of processing of their

signals is necessary in order to more fully utilize the advantage of digital

processing

.

A four-wire probe and method capable of yielding "true" instantaneous

values of temperature and three components of velocity at one point of turbulent

flow has been developed. Due to the use of sensors 0.000025 inches in diameter,

0.012 inch diameter prongs, and with 7/32 inches the shortest distance between

the prongs, the probe is practically interference free. All sensing wires can

be placed within 1 mm3 giving high spatial resolution. Table 1 compares this

probe with the one used by Spencer [2]. The application of the probe and the

method of processing of signals has been illustrated by measurements performed

in small deficit, slightly heated, turbulent wake flow.

The method also includes corrections for DC drifts during measurement, for

streamwise displacement between sensors, for instantaneous variations of the

tunnel's free stream temperature and velocity as well as the subtraction of practically all 60 Hz related noise. Table 2 lists the types of corrections utilized.

673
These techniques resulted in high-accuracy measurement. Turbulence

intensity in free stream was measured to be 0.055 percent of free stream

velocity. Such low turbulence levels usually cannot be measured by CTA;

see Corrsin and Kuo [45]. RMS noise level of processed temperature signal

was determined to be only 0.0014°C. Such a low value, also, cannot be

measured by previously available methods.

It is believed that the probe and the method developed would be of help ii future turbulence research, especially when the technique of conditional samplin

is used.

11. Acknowledgement

The author wishes to express his thankfulness to Drs. M. V. Morkovin

and Y. L. Way, professors at Illinois Institute of Technology who were his

Ph.D. thesis coadvisers. They have followed experimental work on this paper

with keen interest and helped me with constant encouragements. Dr. Way has

written the data acquisition program that digitized analog signals and stored

them on magnetic tape. The research was supported under USAF OSR Grant

No. AFOSR-73-2509.

674
TABLE 1. SINGLE-POINT MULTIWIRE PROBES

Number of Wires

Wire Material

Diameter, inches

(microns)

Measurements

Made by

Wire Interference

Cosine Law for Third Sensor

Computed Instantaneous

Velocities

Computed Instantaneous

Temperature

Determination of Angles

of Sensors

Spencer [2]

3

tungsten

.00015

(3.75)

3 velocity

components

TSI

7%

not reported

approximate

with correction

of results

not done

angular

calibration

Present

Pt-10% Rh

.000025

(.625)

3 velocity

components

and temperature

homemade (IIT)

verified

solutions of

four simultaneous equations

angular calibration and

reference values

TABLE 2. CORRECTIONS

Type of Error

Tunnel Velocity

Variations

Tunnel Temperature

Variations

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Noise

Streamwise Displacement Between Sensors

Way of Correction

digital subtraction of free

stream velocity signal

analog subtraction of free

stream temperature signal

assumed linear in time between first and last reference

measurements

calculated by education of

records, then subtracted

signals delayed using

instantaneous streamwise

velocity

675
12. References

[I] F. Klatt, Disa Information, No. 14, March 197 3.

[2] B. Spencer, Ph.D. Thesis, University of Illinois, 1970.

[3] W. Rodi, Disa Information, No. 17, February 1975.

[4] M. Hof fmeister , Disa Information, No. 13, May 1972.

[5] 0. 0. Mojola, Disa Information, No. 16, July 1974.

[6] F. II. Champagne, C. A. Fleicher, 0. II. Wehrmann, J. Fluid Meoh., Vol. 28,

Part 1, 1967.

[7] C. A. Friehe, W. H. Schwarz, J. of Applied Mechanics, December 1968.

[8] D. C. Collis and II. J. Williams, J. of Fluid Mechanics, Vol. 6, 1959.

[9] P.O.A.L. Davies, M. J. Fisher, Proc. Roy. Soc. A.V. 280, pp. 486-527, 1964.

[10] M. R. Davis, P.O.A.L. Davies, Int. J. of Heat Mass and Mass Transfer,

V. 15 (1972).

[II] G. E. Andrews, D. Bradley, G. F. Hundy, Int. J. of Heat and Mass Transfer,

V. 15 (1972).

[12] D. W. Artt and A. Brown, Sci. Instnon.-, V. 4 (1971).

[13] S. Corrsin, The Review of Scientific Instruments, Vol. 18, No. 7, July 1947

[14] W. G. Rose, J. of Applied Mechanics, September, 1962.

[15] S.P.S. Arya, E. J. Plate, Instruments & Control Systems, March 1969.

[16] R. Chevrey, N. K. Tutu, The Review of Scientific Instruments, Vol. 43,

No. 10, October 1972.

[17] S. F. Ali, Rev. Sci. Instrum., Vol. 40, No. 2, February 1975.

[18] F. Sakao, Scientific Instruments, Vol. 6, No. 9, 1973.

[19] F. A. Mimaud-Lacoste, M. S. Thesis, Pennslyvania State University, 1972.

[20] J. L. Way, P. A. Libby, AIAA Journal, Vol 8, No. 5, May 1970.

[21] J. L. Way, P. A. Libby, AIM Journal, Vol. 9, No. 8, August 1971.

676
[22] R. T. Stanford, P. A. Libby, The Physios of Fluids, Vol. 17, No. 7

(1974)

.

[23] S. Corrsin, A. L. Kistler, MCA Rept 12443 1955.

[24] 0. Coles, C. Van Atta, AIAA Journal, Vol. 4, No. 11, November 1966.

[25] B. Lakshaminaraya , A. Poncet, J. of Fluids Engineering, June 1974.

[26] P. Bradshaw, Aeronautical Journal s July 1972.

[27] K. Hanjalic, B. E. Launder, J. of Fluid Mechanics, V. 52, 1972.

[28] T. Morel, Ph.D. Thesis, Illinois Institute of Technology, Chicago, 1972.

[29] G. Fabris, Ph.D. Thesis, Illinois Institute of Technology, May 1974.

[30] N. K. Tutu, R. Chevrey, 1975. J. Fluid Mech. , V. 71, 785.

[31] G. Comte-Bellot , A. Strohl, E. Alcaraz, J. of Applied Mechanics,

December 1971.

[32] M. Dahm, C. G. Rasmussen, Disa Information, No. 7 , January 1967.

[33] J. C. LaRue, Ph.D. Thesis, University of California, San Diego, 1974.

[34] H. Hassan, J. C. Dent, Brit, of Appl. Phys., Ser. 2, Vol., 1969.

[35] T. G. Borchardt, L. R. Holland, Rev. Sci. Instrum. , V. 40, No. 1,

January 1975.

[36] G. R. Ochs, ESSA Institutes for Environmental Research, IER 47-ITSA-46 (1967).

[37] L. V. King, Phil. Trans. R. Soc, 214A , 1914.

[38] H. H. Bruun, Sci. Instrum., V. 4 (1971).

[39] R. G. Siddall, T. W. Davies, Int. J. of Heat and Mass Transfer, V. 15 (1972).

[40] M. V. Morkovin, AGARDograph 24, NATO, Paris, November 1956.

[41] J. Eisner, W. R. Gundlach, Disa Information, No. 14, March 1973.

[42] V. T. Sandborn, Resistance Temperature Transducers, Metrology Press, (1972).

[43] H. L. Grant, J. Fluid Mechanics, V. 4, 1958.

[44] S. J. Favre, J. of Applied Mechanics, June 1965.

[45] S. Corrsin, A. Y. Kuo, J. Fluid Mechanics, V. 56, Part 3, 1972.

677
678
679
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683
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685

National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

MEASUREMENT OF BOUNDARY LAYER TRANSITION

USING ACOUSTIC TECHNIQUES

Donald C. Sachs, Thomas F. V. Meagher, and Vernon D. Peckham

Kaman Sciences Corporation

P. O. Box 7463

Colorado Springs, Colorado 80933

1 . INTRODUCTION

The acoustical properties of boundary layers on the surface

of bodies moving at hypersonic velocities have not been

characterized fully by detailed measurements. It is known that

boundary layer conditions (i.e., laminar, transitional, or

turbulent) are dependent on a number of factors, including the

Reynolds number of the flow, body orientation with respect to

the flow, body geometry, et al. The essential acoustical

parameters associated with boundary layers in general are well

known to those who have worked in this field; among these

parameters are pressure fluctuations in time which vary greatly

with flow condition, spatial correlation of the fluctuations,

and intermittency during marginal transition conditions (1-6 )*

.

A Boundary Layer Acoustic Monitor (BLAM) has been developed

to take advantage of some of these acoustic properties to

measure transition. In the design of this transducer, consideration has been given to measurand level, dynamic range, directionality, response frequency, packaging design for aerospace

environments, installation requirements, and calibration

techniques. Figures 1 and 2 are photographs of a monitor set;

the set consists of a sensor connected with a cable to an

electronics signal conditioning amplifier.

2. SENSOR DESIGN

The sensor depicted in Figure 1 utilizes an x-cut quartz

crystal of round geometry operating in the thickness extensional

mode between faces; its thickness is .63 cm and diameter is

2.54 cm. The crystal is mounted in a thin aluminum shell and

* Numbers in parentheses indicate the literature references at

the end of paper.

687
is connected in such a way as to cause the external face to be

at electrical ground potential. Isolation from system ground

has been provided by thin epoxy-f iberglass laminate material on

the external face which is placed in contact with the structure

to be monitored.

Internally, the sensor also contains a very high input

impedance pre-amplif ier which interfaces to a cable transferring

the signal to the signal conditioner amplifier; the coaxial

cable also serves to provide d.c. power to the sensor.

In application, the sensor front surface is placed in

direct acoustic contact with the rear surface of the wall over

which the flow moves. A bonding epoxy has been used to provide

both mechanical strength and to ensure good continuity for the

acoustical waves to enter the sensor. The flange on the sensor

which can be observed in Figure 1 is used for attachment in

applications where the surface bonding material may be fluid.

The frequency response of the sensor extends from approximately 10 kHz up to over 500 kHz with resonance peaks occurring

at intervals depending on individual system installations. In

Figure 3 is shown a partial response spectrum of the 2.54 cm

sensor installed on carbon-phenolic material 1.0 cm thick. A

uniform surface peak pressure of 35 N/cm^ (.005 psi) was

applied to obtain the data shown.

3. ELECTRONICS SIGNAL CONDITIONER DESIGN

A functional block diagram of the signal conditioner is

shown in Figure 4. The signal from the sensor is directed into

an amplifier which has a non-linear feedback characteristic.

After amplification, the signal is amplitude detected and

further amplified to produce an output which ranges from 0 to

5 volts. The input-to-output characteristic of this amplifier

is given in Figure 5. It can be noted that for very low input

voltages the gain is several thousand whereas for the highest

input signal, overall voltage gain is less than 1/2. Filtering

is also accomplished in the signal path, both at the input to

select the desired acoustical frequencies from the boundary

layer and at the output to limit bandwidth as may be demanded

by the application.

The circuit includes a voltage regulator and will accomodat

input voltages from 24 to 32 vdc. Current input to the monitor

set is 30 milliamperes maximum.

688
4. SPATIAL RESPONSE CHARACTERISTICS

When mounted on relatively thin-wall cylinders or on flat

sheet material, the sensor is sensitive principally to waves

which originate on the opposite surface within a sensor diameter

distance. A measurement has been taken of the spatial

selectivity of one installation; the resulting data are plotted

in Figure 6 for one response frequency peak. The directionality

is approximately equal to one gage diameter at the conditions

specified in Figure 6.

5. FLIGHT TEST RESULTS

The sensor has been successfully flown on several reentry

vehicles which were launched on ICBM trajectories. The sensor

was attached to the inside of the heatshield surface as shown

on Figure 7. Perturbations to the flow field due to the

presence of the sensor are avoided by the back face mounting.

The flight monitors were placed near heating rate transducers so that a correlation of experimental results could be

obtained. As turbulent flow begins and pressure fluctuations

occur, the heat flow into the ablator increases. For the flight

tests of interest, this heat flow was monitored by General

Electric Corporation AT gages as depicted on Figure 8. The AT

gage produces a signal proportional to the temperature difference

between the forward and rear thermocouple junctions. During a

rapid change in the heat flow into the heatshield, the thermocouples produce a signal proportional to the time dependent

heating rate. The output of the AT gage should correlate with

the BLAM response at the high altitude at which transition

begins. Typical comparisons between the two types of transducers

are shown in Figure 9. The BLAM data have been linearized such

that the plotted analog trace is linearly proportional to the

noise amplitude on the heatshield surface. These overplots

show excellent agreement between the two transducer types during

the onset (1697.3 seconds) of transition between laminar to

turbulent flow. In addition, the BLAM sensor output indicates

other significant boundary layer qualities. During the transition period (Figure 9, 1697.3 to 1698 seconds), the BLAM output

indicates a peak in the amplitude of the fluctuating frequency

components. It is also noted that the AT gage exhibits a

similar characteristic during approximately the same time. This

effect has been identified by several wind tunnel investigators

as an occurrence of transition (7-9) # In each, the researchers

have identified similar increases in either (or both) the

fluctuating pressure or the heating rate during the time of

transition.

689
Another significant finding in the data of Figure 9 is

the presence of pulses in the BLAM output prior to the onset

of transition. Identified as high altitude turbulent bursts

occurring between 1693.5 and 1697.3 seconds, it is believed

these are the first published records of this phenomenon from

flight vehicles. Acquisition of these records was made

possible by the wide dynamic range provided by the logarithmic

amplifier. An as-recorded data plot from the flight test is

presented in Figure 10; these data illustrate the emphasis on

low amplitude signals if this plot is compared with the linear

data in Figure 9.

6. WIND TUNNEL TEST RESULTS

As a part of the gage development work on the BLAM

sensor, a series of wind tunnel tests were performed at the

Naval Surface Weapons Center Tunnel No. 8. The test model

used on these tests is shown in Figures 11 and 12; both BLAM

and AT sensors were mounted, side-by-side, at six locations

on the model, 3 stations on each of two meridians, as shown in

Figure 12.

Representative wind tunnel test results are shown on

Figures 13 and 14, which include data from the AT sensor and

the BLAM. The reason that the indication of boundary layer

transition on this BLAM record is not as pronounced as on the

flight test results is because the noise level in the wind

tunnel was very high. Therefore, the BLAM was required to

measure a change in acoustic level (due to transition) which

was superimposed upon a very intense tunnel noise level. In

both cases shown here, the BLAM and AT data yield transition

times which are comparable; the small differences are not

considered significant.

It is evident that the BLAM sensor as applied to wind

tunnel testing requires some additional development. Further

work is contemplated in an effort to improve the quality of

the wind tunnel data obtained.

7. NEW DEVELOPMENTS

A new sensor, the Acoustic-Pressure Transducer (APT) , has

been designed and built. This sensor is designed to measure,

simultaneously, wall static pressure vs. time and acoustic

noise pressure vs. time on hypersonic reentry vehicles. Body

forces are exerted by slowly-varying static pressures whereas

the presence (and history) of transition can best be determined

by acoustic noise measurements.

690
The APT accomplishes this measurement by using a plug

which penetrates the vehicle's heatshield and thereby transmits

the pressure forces to the sensor diaphragm. The separate

acoustic monitor is contained in the center of the pressure

plug. Development tests on the APT are in progress and include

tests in a 5-megawatt arc heater facility producing Mach 3

flows and surface heating rates of 300-1000 BTU/ft^-sec.

8. CONCLUSION

A sensor has been developed which detects the presence

of turbulent flow by means of sensing components of fluctuating

pressure. Since the sensor is mounted on the inside of a wall

or shield 'over which the boundary layer flows, it does not

perturb the flow. Laboratory tests have been conducted to

establish the directionality of the system. The measurement

technique has been successfully demonstrated on several reentry vehicle flights in which onset of turbulence was measured

during hypersonic flow. Flight data verification was established

by comparing the sensor with thermal monitors and correlating

the acoustic data with flight dynamics data. This data evaluation has verified the measurement of high altitude turbulent

bursts which demonstrates that the BLAM gage has a greater

sensitivity than previous technology.

Wind tunnel tests using the BLAM gage reveal that tunnel

noise partially masks the determination of transition. More

work is required for this application. Some new developments

are being pursued using the BLAM principle.

9 . REFERENCES

1. Willmarth, William W. , "Wall Pressure Fluctuations in a

Turbulent Boundary Layer," NACA Technical Note 4139,

Washington, D. C, March 1958.

2. Kistler, A. L. and Chen, W. S., "The Fluctuating Pressure

Field in a Supersonic Turbulent Boundary Layer," Journal

oh fluid Mechanic*, Vol. 16, Part 1, May 1963, pp. 41-66.

3. Serafini, John S., "Wall Pressure Fluctuations and PressureVelocity Correlations in a Turbulent Boundary Layer,"

NASA TR R-165, Washington, D. C, December 1963.

4. Speaker, W. V. and Ailman, C. M. , "Spectra and Space-Time

Correlations of the Fluctuating Pressures at a Wall

Beneath a Supersonic Turbulent Boundary Layer Perturbed

by Steps and Shock Waves," NASA CR-486, Washington, D. C.

,

May 1966.

691
5. Harvey, W. D., Bushnell, Dennis M. , and Beckwith, Ivan E.,

"Fluctuating Properties of Turbulent Boundary Layers for

Mach Numbers Up to 9," NASA TN D-5496, Washington, D. C.

,

October 1969.

6. Raman, K. R. , "A Study of Surface Pressure Fluctuations in

Hypersonic Turbulent Boundary Layers," NASA CR-2 386,

Washington, D. C, February 1974 .

7. Owen, F. K. , et al, "Comparison of Wind Tunnel Transition

and Frustum Disturbance Measurements," AIAA Journal., Vol.

13, No. 3, March 1975, p. 266.

8. Demetriades, A., "Hydrodynamic Stability and Transition to

Turbulence in the Hypersonic Boundary Layer Over a Sharp

Cone," Aeronutronic Ford Publication U-6139, Interim

Progress Report, October 1975-March 1975, 15 April 1975.

9. Martellucci, A. and Neff, R. W. , "Influence of Asymmetric

Transition on Reentry Vehicle Characteristics," Jou.n.nat

o fa Spaczctiafit, Volume 8, No. 1, May 1971, p. 476.

692
FIGURE 1 BLAM SENSOR

FIGURE 2 BLAM ELECTRONICS

693
o

(d/d) 39VHOA 1DO 1VNOIS 3GV9

694
695
696
697
HEATSHIELD

ELECTRICAL SIGNAL OUTPUT

FIGURE 7 BLAM SENSOR INSTALLATION

FLOW FIELD

HEATSHIELD

0 6 THERMOCOUPLE OUTPUT

FIGURE 8

GE At GAGE

( SCHEMATIC REPRESENTATION )

698

700
FIGURE 11 WIND TUNNEL TEST MODEL,

At AND BLAM SENSORS

701
702
FIGURE 13 WIND TUNNEL MODEL TRANSITION RESULTS,

At AND BLAM SENSORS, RUN NO. 2

703
704
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

MEASUREMENT OF RECIRCULATING FLOW BEHIND A CYLINDER

WITH SPRAY COOLING

R. S. Rudland

Westinghouse Electric Corporation

Bettis Atomic Power Laboratory

West Mifflin, Pennsylvania 15122

A hot-film anemometer was used to measure the

recirculating flow behind a heated cylinder which was

cooled with spray water. The anemometer was electricall

insulated from the water by a thin quartz film which

was heated by the anemometer to help keep it dry. To

measure air velocity in an air stream containing water

droplets requires a sturdy anemometer which can withstand the droplet impact without breaking. The anemomust also be able to measure the air velocity in less

than a millisecond in the presence of water droplets.

The hot-film anemometer was selected because it is a

sturdy, fast response instrument which detects changes

in heat transfer related to changes in fluid velocity.

Since the heat transfer to water and to air are quite

different, it is necessary to keep the anemometer dry

when measuring air velocity. When the anemometer was

calibrated it was found that the anemometer could dry

itself in about a millisecond. This meant that the

anemometer could measure air velocities with as many

as a thousand drops a second hitting the anemometer.

Also, the calibration revealed that the calibration

curve shifted upward in proportion to the amount of

spray present due to the heat loss at the probe support

Once the anemometer was calibrated it was used

to measure air flow patterns behind a cylinder. These

measurements helped evaluate the change in vortex

patterns due to the spray. The test results indicated

that the vortex shedding pattern was noticeably

changed by the spray. The shedding frequency increased

about 20% when the spray was present and the recirculating flow over the trailing surface was also increased

This improvement in flow over the trailing surface is

expected to improve the heat transfer from the cylinder

noticeably.

Key Words: Anemometer; Wake flow; Cylinder; Frequency;

Vortex street; Spray; Two component flow; Hot film

anemometer; Recirculating flow.

705
Introduction

In the study of compact heat exchangers, one promising

approach has been found in the use of spray water- in-air to

increase the heat transfer rate. Tests on single cylinders

have shown that the heat transfer rate can be increased as

much as thirty times that of air alone CO. As a step towards

extending the single tube results to the more general case

with multiple rows of tubes, the trailing (wake) flow behind

the cylinder was examined in detail since the interaction

of the trailing flow behind the cylinder with succeeding

rows of tubes is important in the overall heat transfer

properties of the heat exchanger. A measuring technique was

developed to measure the air velocity in the wake when spray

water was present. The anemometer selected for these measurements was a sturdy, fast response, cylindrical, hot-film

anemometer described by Thermo Systems Inc. C2]. The sturdyness of this anemometer was necessary to withstand impacts

from the spray water and the fast response was needed to

be able to detect the rapidly changing flow behind the cylinder

Anemometer Description

The hot-film anemometer shown in Figure 1 was selected

for measurement of spray water and air flow in the wake of a

cylinder where large scale turbulence is present. This anemometer is constructed of a tough glass fiber supported between

two probes and plated with a thin platinum film which has

electrical properties similar to that of a platinum hot-wire

anemometer. When the thin film of platinum is coated with a

thin film of auartz the sensor becomes electrically isolated

from the conducting fluid but is still sensitive to changes

in fluid velocity. The basis for selection of this anemometer

depends on the following test conditions:

1 . Large scale turbulence was present in the flow at

frequencies up to 7000 cycles per second.

2. Spray water droplets of about 200 microns in diameter

were present in the water at velocities up to 25 meters

per second (80 feet/sec.).

3. Air velocity measurements were needed to determine the

heat transfer properties over the trailing surface of

the cylinder.

The advantages of the hot-film anemometer over other

types of anemometers can be summarized as follows:

1 . The hot-film anemometer is small enough to respond

rapidly to changes in velocity even with spray

present

.

2. The anemometer is sturdy enough to withstand impacts

from large, high velocity, water droplets without

damage to the sensor.

3. The anemometer can dry itself off in approximately

one millisecond after becoming wet.. This allows

accurate velocity measurements of air for droplet

1 Numbers in brackets refer to references in the bibliography.

706
impacts up to 1000 times per second.

This instrument measures the current required to hold

the resistance constant on the sensor. This is proportional

to the square root of the power going to the sensor f3j.

This power is converted to heat in the sensor resistance

and is transferred to the fluid. Heat transferred from the

sensor to the fluid is proportional to the square root of

velocity nlus a zero velocity heat load. This can be written

as ; 2

Q = I R

Q (Power to the sensor)

Q = Q0

+ C

Q fV (Heat loss o< velocity)

.\ V = (I 2

- l|) 2/l* x C,

(1)

where; Q is the power to the sensor

QQ is the power at zero flow

C

Q

is a constant determined experimentally

C

1 is a calibration constant

RQ is the sensor resistance at reference temperature

I is the current to the sensor at zero velocity

I is the sensor current at velocity V

V is the measured velocity

This derivation assumes that the temperature of the fluid

does not change from the calibration to the time of measurement

since C

Q

and QQ depend on the difference in temperature between

the sensor and the fluid. If there is a question about the

temperature remaining constant, a compensating sensor can be

added to the probe with a control circuit to hold the temperature

difference at a constant value. The anemometer sensing element

can also be used to measure the fluid temperature by turning

off the power to the sensor and measuring the sensor resistance

at zero power. The electronic circuit for the anemometer is

shown in schematic form in Figure 2. It is seen that the sensor

is part of a Whetstone bridge having an operational amplifier

across the bridge to provide a feedback signal which adjusts

the power to the sensor thereby balancing the bridge. By setting

the gain on the bridge amplifier as high as possible without

producing oscillations' in' the output, the frquency response of

the system can be made to respond to frequencies as high as

20,000 cycles per second.

Calibration of the Anemometer

When using hot-film anemometers, each application requires

provisions in the test for a calibration In this case the

anemometer was calibrated in a wind tunnel by first measuring

the air velocity with a NPL approved modified Prandtl pitotstatic probe connected to a micromanometer and then measuring

the same flow with the hot-film anemometer. Studies performed

707
on this wind tunnel (See Figure 3) have indicated that the

spray water does not change the air velocity This

allows the spray to be turned on at each setting of velocity

to calibrate the anemometer for changing spray flow rate.

The results of this calibration are shown in Figure 4 where

a typical oscilliscope display is shown to illustrate how the

air velocity was measured when spray was present. The air

velocity corresponds to the lowest level of the voltage-level

(which corresponds to the sensor current) on the oscilliscope

display since this indicates that the sensor has dried off

after being hit by a water droplet. This sensor is connected

to a high power circuit which can produce large surges in

current in response to sudden changes in sensor temperature

which shortens the drying time of the sensor. It takes about

one millisecond for the sensor to dry itself off after an

impact which' means that the sensor can make useful, measurements

up to one thousand impacts per second. It is also seen in

Figure 4 that the curve shifts upward as the spray flow rate

increases. This is due to the heat loss from the supports

which are cooled by the water but are not able to dry off as

fast as the sensor element. This heat loss can be accounted for

as an extra heat load which is dependent on water

rather than velocity. Taking this into account in

produces the following eauation for velocity:

accounted

flow rate

Equation 1

V = C,

? P

(I - I w ) " I 0

I.

(2)

where; I is the increment of current needed to offset W 1 the heat loss to the supports as a function

of water flow rate

Co is a calibration constant

From Figure 4 it is seen that current I is directly proportional to the mass flow rate of the spray. This is replotted in

Figure 5 to show the linear behavior of the calibration curve.

In this figure the heat loss due to water is:

w

x mw

where; C-^ is the calibration constant

mw

is the mass flow rate of water per unit cross

sectional area

Test Description

The measurement of flow past a cylinder with spray water

was performed in a closed loop wind tunnel shown in Figure 3.

The test section was made of plexiglass with a .305 meter by

.305 meter flow area (12 in. sq.). The test cylinder was 7.62

cm. in diadeter (3 in.) and could be heated with electric

heaters. Spray water was introduced through a Delavan SQ-10

708
sauare spray nozzle. The mean droplet size varied with the

water flow rate from about 100 microns at low flows to about

300 microns at high flows. High speed photographs have shown

that the droplets move at the air velocity by the time they

reacli the cylinder. Similar studies have shown that the air

velocity is not altered by the introduction of the spray

into the air £ 1] . Visual observations of the cylinder with

an air-water spray flowing past it have revealed

Q that the flow

sepe rated from the cylinder over a range from 92 to 108°

measured from the forward stagnation point. According to

Schlichting [5] a seperation point near 70° is associated

with laminar flow while a seperation point near 100° is

associated with turbulent flow. Laminar seperation has lower

pressures over the trailing surface while turbulent, seperation

has higher pressures. Hodgson [l] measured The pressure around

the cylinder and found that the flow was laminar up to 16 meter

per second (50 ft/sec) and turbulent above that with air flow.

Measurements of specific pressure gave values near -2.0 for

laminar flow and -1.3 for turbulent flow where specific

pressure is defined as:

c

p

= < p - V/< ie/o > (3)

where; P is the pressure over the trailing surface

P is the static pressure upstream of the cylinder ^ is the density of air

V

0 is the velocity of air upstream of the cylinder

Rudland £6] measured the pressure in the wake close to the

cylinder and found that the specific pressure varied from -1.8

to -3.0 for air but stayed constant when water spray was present.

This suggests that the spray produces turbulent flow which

moves the seperation point back to 100 and raises the back

pressure in the wake. The hot- film anemometer measured sinusoidal

flow patterns in the wake region which corresponded to the

von-Karmen vortex streets which shed periodically from the

back of the cylinder. If we define Strouhal number as:

St = V/(f x d) (4)

where; f is the shedding frequency

d is the cylinder diameter

then a value of .21 was determined for air flow which was

lowered to .18 when spray was added. This reduction in Strouhal

number corresponds to an increase in shedding frequency of

nearly 20%. This increase in frequency is caused by the change

from laminar to turbulent flow which pushes the vortices closer

together thereby Increasing the rate of shedding. Karris C?J

described a similar effect which showed how the frequency goes

up when the vortices are forced closer together behind a

cylinder.

709
Resul ts

Using the hot-film anemometer, the air velocity as well

as the temperature and number of droplets hitting the probe

was measured at various elevation behind the cylinder. These

measurements were made in conjunction with measurements of the

mass flow rate of spray. Turbulence measurements of the air

were Included in these measurements as well as vortex shedding

frequencies. The turbulence measurements and vortex shedding

measurements were used to help understand the nature of the

flow in conjunction with the pressure measurements. Having

established that the spray caused the flow to become turbulent,

it is anticipated that the wake flow will be more active which

will cause the heat transfer over the trailing surface to

increase. Mixing of the spray with the air behind the cylinder

is expected to be more intense for turbulent flow than for

laminar flow. Comparisons of laminar air flow and turbulent

spray flow at the same velocity are plotted in Figure 6 to

illustrate that turbulent mixing is more active than laminar

mixing. It can be seen that the velocity profile for turbulent

flow becomes uniform in only a few diameters downstream while

the laminar flow takes longer. Figure 7 attempts to show how

the spray is mixed in the wake by the large scale vortex motion

and small scale turbulence. Within five diameters downstream

the spray is very well mixed. This is faster than would be

expected to occur in a turbulent flow without the vortex

shedd ing.

Conclusions

Use of the hot-film anemometer to measure air flow in an

air-water mixed flow has demonstrated that this anemometer

is a sturdy instrument which is capable of being used for a

wide variety of flow measurement applications. A calibration

of this instrument in the spray flow revealed that the sensor

was suitable for mixed flow applications with only minor

adjustments to the governing equations. This instrument was

able to measure the flow pattern behind a cylinder with water

present thereby demonstrating that the wake flow provided

good mixing of the spray due to the turbulent seperation

caused by the water on the cylinder. Future efforts to study

tube bundles should concentrate on the mixing pattern of the

air and water behind the cylinders in the tube bundle.

Bibliography

1. Hodgson, J. W. ,R.T .Saterbak, and J .E.Sunderland , "An Experimental

Investigation of Heat Transfer from a Spray Cooled Isothermal

Cylinder" , AIChE-ASME Heat Transfer Conference, Philadelphia, Pa.

,

August 1

1 -1 4,1968.

710
2. Thermo Systems Inc., "Hot Film and Hot Wire AnemometryTheory and Application" Bulletin TB5.

3. Flow Corporation, "Series 900 Application Notes", Bulletin

901 .

4. Disa Information, "Measurement and Analys is" , No . 10, October

1970.

5. Schllchting, h. , Boundary Layer Theory , McGraw Hill, 6th Ed,

1968.

6. Rudland,R,S. , "Convective Heat and Mass Transfer from a

Horizontol Cylinder to an Air-Water Spray in Cross Flow",

PhD Thesis , Georgia Institute of Technology , Atlanta , Ga

.

September, 1 968.

7. Marris , A .W. , "A Review on Vortex Streets, Periodic Wakes, and

Induced Vibration Phenomena" , Transactions of the ASME, Journal

of Basic Engineering, June , 1 964.

711
GOLD PLATED SUPPORTS

QUARTZ COATED

PLATINUM FILM

Figure 1 Schematic of Hot-Film Anemometer

712
OUTPUT

VOLTAGE

Figure 2 Electronic Arrangement for Anemometer Operaiti

713
AIR WET & DRY BULB

THERMOCOUPLES

PLENUM CHAMBER

^HE

TO POWERSTATS

Figure 3 Wind Tunnel Test Facility

714

716
9 Y

V

leter/ sec

6 )r

0

0 25 50

' D BEHIND THE CYLINDER

AIR

SPRAY

75 1 00 i 25

DISTANCE PERPEND I CUT 4R TO THE FLOW cm,

V

tn/ sec

9

0

0

6

-

/sec 3 „

3D BEHIND THE CYLINDER

AIR

50

cm

75

SPRAY

1 00 125

0

0 25 50

cm

75 100 125

Figure 6 Velocity Profile in Wake Behind the Cylinder

717
0* 1 1 1 1 1 0 25 50 75 100 125

cm

DISTANCE FROM CENTERLINE PERPENDICULAR TO FLOW

25 50 75 100 125

cm

30
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

A NEW TYPE OF VELOCITY PROBE

William B. Brower, Jr. and Alan Servoz

Rensselaer Polytechnic Institute

Troy, N.Y. 12181

A trip-wire velocity probe has been designed and tested

which employs a sphere as the mechanism for producing a pressure difference. To render this pressure difference independent of Reynolds number a trip-wire is placed on the upstream

side of the sphere, which trips the boundary layer to turbulent

flowo The resulting design has greater sensitivity than the

Pitot-static tube, and can fit through smaller openings than a

comparable Pitot-static tube. The dimensions of a typical probe

are given, as are the results of a series of wind-tunnel tests

at "low" Reynolds numbers.

Key Words: Calibration; Pitot-static tube; transition; tripwire probe; turbulent boundary layer; sphere flow; Reynolds

number.

1„ Introduction

Along with the need for monitoring stack-gas flows for purposes of pollution control, the need for accurate knowledge of stack-gas velocity distribution has increased. The conventional instrument for making gas- flow velocity measurements is the Pitot-static tube in conjunction with a manometer

to pick up the difference between the probe stagnation and static pressures

which, according to Bernoulli's equation, is equal to the dynamic pressure,

i.e. p°-p = %/3Ij2 = q c The velocity, of course, is proportional to h^, where

h is the manometer reading.

For the stated purpose, a Pitot-static probe has a few difficulties.

In the first place access ports to stacks are the order of 4 inches in diameter. The length of the port duct may be the order of 8-12 inches. Thus

if the outside diameter of a Pitot-static tube were D=0.5 in., the length

of the tube from tip to stem would be the order of 7-9 inches, making it

impossible to insert the probe straight into the hole, or even to insert it

by cocking it. On a large-diameter stack where the length of the probe

support-arm might be up to 20 feet, a probe which cannot fit straight into

the port would be an especial inconvenience.

In addition, in a "dirty" flow, particles suspended in the stack gas

have a tendency to impinge upon and perhaps enter either the stagnationpressure tap or the static-pressure tap, or both. Since in a typical probe

these holes may be the order of 0.1D there is a real danger that the capture

of a few large particles may result in the clogging of one or more taps,

thereby producing erroneous readings. A probe which utilizes large-diameter

pressure taps would be relatively insensitive to accumulations of particles.

Moreover, it could be routinely cleaned.

719
A final problem with the Pitot-static tube is that at low free-stream

speeds its sensitivity (i.e. the pressure difference Ap) is low, resulting

in small manometer deflections. For example, at standard atmospheric pressure and a stack temperature of 300°F, a flow velocity of U=20 ft/sec will

produce a manometer deflection of h=0.062 in. H2O. Field measurements of

such low pressures are more prone to error than in a laboratory. Thus it

would be useful to have available a probe which generates a larger pressure

drop for a given flow speed than is furnished by a Pitot-static tube.

One ordinarily expects that in a stack the turbulence level of the main

flow would be high, due to its previous history involving combustion, heat

transfer, etc. Since knowledge of the actual turbulence level is not usually

available, it is desirable to utilize a probe which produces readings which

are independent of the actual turbulence level - that is, its reading at a

given flow speed should be the same whether the flow is laminar or turbulent.

A Pitot-static tube possesses this quality and, ideally, so should any substitute.

The object of the current investigation is to design and test a new

type of probe which meets the following specifications:

1) It should be constructed so that it can be inserted through a 4- inch

diameter hole and be readily aligned with the flow direction.

2) It should be insensitive to capture of particles and should have relatively large- diameter pressure taps to allow for easy cleaning.

3) It should produce a pressure reading which is independent of the state

of free-stream turbulence.

4) It should produce a pressure drop significantly greater than that

provided by a Pitot-static tube for a given flow speed.

5) It should have accuracies of the same order as the Pitot-static tube,

where a possible error of 0.57o is typical.

It is further noted that a probe may have other requirements such as

the ability to allow tapping off a gas sample, or to verify flow direction,

or to withstand high temperatures. Although the current study is not directed at these objectives, we believe the resulting design can be modified to

accommodate them.

2. Preliminary Design Considerations

In order to achieve a pressure-difference ap, larger than realized

with a Pitot-static tube, one is quickly led to the use of a sphere, for

the following reasons:

1) As is well-known, the theoretical, potential-flow, surface-velocity

distribution on a sphere is given by us =(3/2)Usin0. Thus the maximum

pressure drop below stagnation occurs at 0 = 90°:

AP ]^90°

=

%/°Us]^90°

= h'

720
If a practical device could be designed to achieve this pressure drop,

its sensitivity would be 2.25 times that of the Pitot-static tube.

2) Since the flow around a sphere is essentially axi-syiranetric the effect

of probe misalignment can be minimized by "averaging" the staticpressure values from several taps at the equatorial station.

3) Furthermore, effects of free-stream turbulence are diminished since, as

the flow accelerates over the front surface, the local turbulence intensity actually decreases, and reaches a minimum near ^ = 90°.

4) Finally, since the sphere is supported by a sting from the rear, interference effects can be kept small if the sting diameter is significantly

less than that of the sphere.

The most comprehensive data available on sphere flow appear in a recent

paper by Achenbach [1].^ We summarize below some of his principal findings :^

1) As Eiffel discovered, and Prandtl gave the explanation therefore, the

flow over a sphere can be divided into several regimes. 3 As shown in

Figure 1, the dependence of the drag coefficient on the Reynolds number

Re provides an excellent delineator. The regimes are:

- Subcritical, or laminar boundary layer, Re < 2.5x10"*.

- Transcritical, or transition to turbulence, 2 . 5x10^ < Re < 4x10^

.

- Supercritical, or turbulent boundary layer, Re > 4x10"*.

2) Transition occurs at Re z 3.5x10^, although other experimenters find that

this value will vary over a small range, depending on the state of the

free-stream turbulence.

3) On a smooth sphere, transition from laminar-to-turbulent boundary layer

is first observed at values of «$ t = 90° to 100°, starting at Re~3.5xl05

. As the Reynolds number is increased the transition point moves continuously upstream until ^ t = 60° at Re = 5x10^, the highest value for which

this measurement was made. See Figure 2.

4) In the subcritical regime laminar separation occurs at $g = 82°. As

shown in Figure 3, as the Reynolds number is increased through transition, the separation point moves sharply downstream, stabilizing in the

vicinity of <J> S = 120° for supercritical flow.

1

Figures in brackets indicate the literature references at the end of this

paper.

2Appreciation is expressed to Dr. E. Achenbach for permission to reproduce

four of his figures which appear in this paper as Figures 1 through 4.

3Achenbach distinguishes a total of four by subdividing the transcritical

regime into two. In addition, in this paper we have interchanged Achenbach'

s

use of transcritical and supercritical in keeping with the conventional uses

of the terms.

721
5) At transition there is also a drastic shift in the pressure-coefficient distribution as shown in Figure 4. It is this change which

is primarily responsible for the drop in C in supercritical flow.

Figure 4 gives plots of Cp for two different Reynolds numbers in the

supercritical regime which are nearly coincident in the range - O±0 <C 105°. The minimum reading of Cp = -1.15 to -1.20 occurs

just upstream of the equatorial station of = 90°. This corresponds

to a value of *p/q = 2.15 to 2.20 versus the envisioned upper limit

of *p/qj^=goo

= 2.25. Obviously, for a turbulent boundary layer, the

maximum pressure-drop is greater than for the laminar case. Furthermore, the pressure distribution for turbulent boundary layer appears

to be relatively insensitive to the value of Re„

3. The Trip-Wire Probe

Taking into account the preceding it was decided to use a sphere of

I. 25 in. in diameter. This would give a fairly large body in which to fit

ducting, allow for a sting of "reasonable" length, yet keep within the 4- in.

over-all requirement.

However, in standard air, a 1.25 in. sphere at Re = 10^ corresponds

to a flow speed of 160 ft/ sec, which is higher than we ordinarily expect

in typical stack measurements. That is, in most cases a sphere of this size

would be operating in the lower range of subcritical flows where we expect

laminar separation and a pressure distribution which is Reynolds-numberdependent.

To get around this anticipated difficulty it was decided to investigate

the possibility of using a trip-wire to force transition to turbulent boundary layer. This technique, conceived by Prandtl, was shown by Wieselberger [2].

to have the desired effect. Schlichting [3], p. 40, reproduces Wieselberger 1 s photographs, clearly demonstrating that installation of a trip-wire on the

nose of the sphere induces transition to turbulence, as is shown by the delay ii separation compared to the same flow without a trip-wire. Wieselberger placed

the ring trip-wire at the station & = 82°. The diameter of the wire was

chosen to be equal to the theoretical laminar-boundary- layer thickness for

the experimental flow speed.

The laminar-boundary- layer thickness can be calculated from [3], Table

II. 2, p. 227. For a sphere of D = 1.25 in. the boundary- layer thickness is

plotted as a function of U for various values of in Figure 5, for air at

standard atmospheric conditions.

4. Experimental Procedure

Measurements were made on two models. The first consisted of a 1.25 -in.

diameter plexiglass sphere supported from a 0.75- in. diameter sting 6.25- in.

long, to reduce support interference but large enough to pass all the required

pressure tubes. In addition to the total-pressure tap on the £ two sets of

6 taps were located in spiral patterns at angles of = 15°, 30°, 45°, 60°, 75°,

and 90° to allow for verification of flow symmetry. A United Sensor Corporation type-PA Pitot-static probe was used for calibration. Micromanometers

were used to measure pressure differences at all times.
Pressure-distribution measurements were made over a range of Reynolds

numbers in the RPI indraft tunnel which has a diameter of 12.4 in. The

model was then successively modified by installation of several trip-wires

of varying diameter at the ^ = 82.5 station and additional runs were made.

Based on these results a final model of the trip-wire probe was designed which is shown in Figure 6. A brass sphere was used, 1.25- in. in

diameter, supported from a 0.5- in. diameter sting 2.00 in. long, giving a

longitudinal length (which is the transverse dimension for probe insertion

purposes) of 3.25 in. All pressure taps are 0.125- in. in diameter allowing

for easy clean-out. The four static-pressure taps are spaced at 90° intervals and at 45° from the supporting arm to reduce interference effects. The

four taps are joined internally to allow "averaging" of the static pressure.

Because of a troublesome flow instability in the indraft tunnel which

could not be completely eliminated, measurements on the final trip-wire

probe were made in the RPI 4x6- foot- test-section wind tunnel and calibrated

as before.

5. Results

Figure 7 shows the pressure distribution over the sphere front face

without the presence of a trip1 wire. Since the asymmetry was not severe

the data shown are the average of those of the two pressure taps for each

value of tf. The pressure distribution is as expected, remaining close to

the inviscid theory up to ^^50°, then reaching a minimum near = 75o where

the magnitude of the minimum depends on Re.

A 0.020-in. diameter trip-wire was then placed in a groove at fi = 82.5°.

A micrometer measurement showed that the effective diameter was actually

0.015 in. This corresponds to the boundary- layer thickness on a 1.25- in.

diameter sphere at U = 102 ft/sec. On this configuration the trip-wire

alters the pressure distribution substantially, as shown in Figure 8. In

fact, the pressure distribution becomes almost flat over the range 60°< ^<90°,

with the magnitude depending on the Reynolds number. At speeds below 102

ft/ sec, the trip-wire is completely immersed in the boundary- layer and its

effectiveness is reduced.

In order to reduce Reynolds-number dependence a second set of runs was

made with a 0.026 in. -diameter trip-wire (effective diameter 0.020 in.).

Figure 9 shows the results. Less Re-dependence is obtained but the pressure

variation near 75°^ 0<9O° is distorted by the presence of the trip-wire.

To minimize effects of local pressure-distortion, the trip-wire location in the final probe was moved forward to & = 75°. Results for this

model, incorporating data for several runs which are shown in Figure 10, are

gratifying. An almost Re- independent variation of the pressure coefficient

was obtained; i.e.

C = -0.375 + 0.02, 2xl04 ^ Re * 10

5

, P/^90°

where most deviations are, in fact, much smaller. The corresponding flow

speed range is 31 - U - 162 ft/sec.

723
This value of Cp, converted to a pressure difference^, gives Ap=1.375q

which represents an increase in the sensitivity of almost 40% over the Pitotstatic tube, although it is well below the theoretical maximum ap=2.25q.

4 Below Re = 2x10 the test-data scatter increases erratically. Although

some of this may be attributable to the difficulty of getting reliable readings, the more likely cause is that at Re = 2.7x10^ the boundary layer thickness is the same as that of the effective trip-wire diameter. At the lowest

values of the test Reynolds number, the trip-wire is completely immersed in

the boundary layer and we speculate that the transition from laminar- toturbulent boundary layer becomes unstable over a small range of Reynolds number.

It is apparent that the Reynolds number above which turbulent-boundarylayer is maintained, and the value of the probe calibration constant, are both

functions of the trip-wire thickness -- more precisely of the ratio of the

trip-wire effective diameter to the sphere diameter. The dramatic effect of

the change in both the transition Re and the calibration constant are demonstrated by Figure 11. This test employed the final probe model with a 0.020

in. trip-wire (0.015 in. effective) at the 0 = 75° station. In this configuration transition occurs at Ress5.5xl0^ such that in the fully turbulent

regime Cp = -0.86 or, equivalently , ap/q = 1.86.

This latter value is much closer to the optimum value of 2.25, but the

lower limit of the useful velocity range (for constant calibration factor)

is drastically increased. Depending on the application it should be possible

to modify both the sphere diameter and the trip-wire effective thickness for

optimal characteristics. Thus it would be useful to have available results

of a systematic experimental study of the effect of trip-wire thickness on

these two parameters.

6. References

[1] Achenbach, E., Experiments on Flow Past Spheres At Very High

Reynolds Numbers. J. Fluid Mechanics , 54, pt. 3, 656 (1975).

[2] Wieselberger , C. , Der Luft widerstand von Kugeln. AFMS, 5_, 140 (1914).

[3] Schlichting, H. , Boundary Layer Theory, 6th ed, McGraw-Hill Book

Co., (1968).

[4] McCaffrey, B.J. and Hekestad, G. , A Robust Bidirectional LowVelocity Probe for Flame and Fire Application. Brief Communications, Combustion and Flame , 26, 125 (1976).

4-The reader's attention is directed to another new probe design [4] which

is intended for the use in fire and flame studies. Experimental data are

given for a range of velocities an order of magnitude lower than presented

herein. In the other design it is essential to employ the calibration

curve which is highly dependent on Re.

724

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FIGURE 4 . PRESSURE-COEFFICIENT DISTRIBUTION FOR A SMOOTH SPHERE AT

VARIOUS REYNOLDS NUMBER; FROM [1]

.

728

STATIC PRESSURETOTAL PRESSURE

TRIP WIRE PROBE

.020 EFFECTIVE

4 STATIC

-PRESSURE

HOLES,. 125 DIA

-90° APART

-I.25DPLEXIGLASS

PLUG

.125 DIA

FINAL PROBE MODEL DIMENSIONS ( INCHES)

FIGURE 6. THE TRIP-WIRE VELOCITY PROBE.

3/32 OD

730
8 h

0 L

Potential Theory

rAchenbach

VRe = l.62 x I0

5

-4

C

p

, MODEL NO. I WITHOUT TRIP WIRE

C vs <f> ON MODEL NO. 1 WITHOUT TRIP-WIRE

P ~

731
.8

.6 -

Theory

Experiment

Re x 10' 4

3.37

V 4.17

O 4.90

A 5.50

> 5.98

.4

.2

a

o

- .2

-.4

-.6

Cp

, MODEL NO. I 0.015 IN. EFF TRIP-WIRE

DIA. AT (p = 82.5°

\

-.8 \

\

-1.0

FIGURE 8

\

C vs 4> ON MODEL NO.

TRIP-WIRE.

1, 0.020 IN. (0.015 IN. EFFECTIVE)

732
1.0

.8

.6

Theory

Experiment

Re x

10"

3.80

V 4.97

O 5.56

A 6.40

> 7.09

.4

.2

aO

-.2

-.4

C

p

, MODEL NO

-.6

0.020 IN. EFF. TRIPWIRE DIA. AT <f> =82.5° \

\

-.8

\

\

\

-1.0

FIGURE 9.

\

C

p

VS ON MODEL NO. 1, 0.026 IN. (0.020 IN. EFFECTIVE) TRIP-WIRE.

733
734
735

National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

THE INFLUENCE OF TURBULENCE ON STATIC AND TOTAL PRESSURE PROBES

V. E. Scottron

Institute of Water Resources

University of Connecticut

Storrs, Connecticut 06268

In the course of studying boundary layer flows over a rough

boundary in an adverse pressure gradient in a wind tunnel, measurements of mean and turbulent velocities were taken using a hotwire anemometer. Comparative velocity measurements were taken

with static and impact probes attached toa micromanometer . Attempts

have been made to determine the influence of the turbulence components on the readings obtained by these probes. Also comparisons have been made with the results of similar studies made by

other investigators, such as Toomre, Bradshaw and de Haan.

The probes used in these tests were 1/16 and 1/8 inch diameter

separated probes. Combined probes could not be used near the wall

due to the local pressure disturbances caused by the roughness

.

The boundary layer thicknesses were large, of the order of 10 to 12

inches so that it was possible to obtain a wide variation of turbulence levels by positioning of the probes. Pressure differences

were referenced to a fixed static probe outside the boundary layer

in a very low turbulence region.

Pressure indications were sufficiently large that it was possible

to obtain reasonable verification of the theoretical estimates

obtained by Toomre.

Key Words: Pitot tubes, static pressure probe, impact pressure probe,

turbulence, turbulent boundary layers, velocity measurement.

1. Introduction

Investigation into the effects of turbulence on the behavior of static

and total pressure probes was started as a part of a major study on boundary layer flows over a rough wall in an adverse pressure gradient [1].

Recent studies [2] on the detailed behavior of flow in open-channel

junctions and side-channel spillways have continued this interest in

instrumentation problems. The experimental objectives always require the

measurement of mean velocities within a reasonable degree of accuracy, often

in the presence of very intense, large-scale turbulence.

737
Clearly, the conditions are far from ideal for measurement of either

mean velocities or turbulence intensities. In order to establish even a

first-order correction for the effect of high level turbulence, it is

first necessary to have available an approximation of the turbulence fo~

at least two components. Hinze [3] presents a very discouraging summary

of the problems involved in using the hot-wire anemometer for velocity

measurements under such conditions. Becker and Brown [4] indicate a good

reliability of total pressure up to about

w

2 = u^/U2" =0.2

Let us return to the experiment which initiated the studies on static

and total pressure probes. An attempt was made to determine the role of

wall roughness in the development of the boundary layer in a strongly

adverse pressure gradient approaching separation [1] . Local turbulence

levels turned out to be extremely high throughout much of the boundary

layer. In addition to the eddies generated by the wall roughnesses, the

square screen mesh, which was used to create the roughness, also produced

sizeable pressure disturbances. Since the free-stream turbulence levels

remained quite low at 0.3% or less, both hot-wires and pressure probes

could be used effectively outside of the boundary layer. Within the boundary

layer, it was necessary to use static pressure probes that were separated

from the total pressure probe because of the variation of the static pressure near the rough wall. This wall -generated pressure fluctuation also

prevented the use of wall taps in determining static pressure. Static

pressure distributions along the flow path were checked by means of surface

taps located outside of the rough wall boundary layer in the plane smooth

wall which formed the floor of the wind tunnel and also by static probes

in the central free stream region.

A number of schemes were tried to produce reasonable agreement between

hot-wire and pressure probe readings. A method which combined the suggestions of Hinze [5], Toomre [6] and Siao [7] was adopted since it seemed to

produce the closest agreement. At that time, the behavior of the static

pressure probes was assumed to follow the first-order corrections given by

Toomre [6] and Strasberg [8] . Subsequent experimental results which seem

to verify these corrections are reported in this paper.

2. Equipment and Instrumentation

a. THE WIND TUNNEL

The wind tunnel test section is approximately 2 feet wide and 4 feet

high with flexible side walls 15 feet long. One wall was kept plane and

covered with square mesh screen of 0.500 inch spacing and 0.105 inch diameter wire. The opposite wall was smooth and positioned to control the longitudinal velocity and pressure distribution. It was thus possible to

738
obtain extremely thick boundary layers with free stream velocities approximating 70 feet/second. Variations in static pressure across the boundary

layer were thus large enough to be measured in this situation.

b. PI TOT TUBES AND STATIC PROBES

Three pitot tubes were used to make the velocity measurements: All

had separate impact and static elements. The small pitot tube had a geometrical construction that permitted measurements near the wall. The

impact element was square-nosed hypodermic tubing, 0.025 in. outside diameter and 0.016 in. inside diameter, shaped so that it could be placed tangent to the wall. The static element was 1/16-in. -diameter tubing with

four holes of 0.016 inch spaced at 90- degree intervals around the tube at

a distance of approximately 10 diameters from the leading edge. These

holes were in the same plane normal to the flow direction as the opening

of the impact element. The static element was located 1/2 inch farther

out in the boundary layer and 1/2 inch below the impact element during the

measurements. This geometry ensured that, for all pitot tube positions,

the static element would not be affected by the strong local static pressure variations caused by the rough wall. These pressure disturbances did

not appear to extend over 0.3 inches into the boundary layer. Careful

calibration of this pitot tube under low turbulence conditions in the free

stream showed no appreciable error in comparison with large diameter tubes.

Where the boundary layer was over 7 inches thick, another pitot tube

was used to traverse the boundary layer from about 4 inches from the wall

out to the free stream. This pitot tube overlapped the range of the

smaller tube for a distance of 3 inches and permitted a comparison of data

obtained in this region. Both impact and static tubes were 1/16 inch

in diameter. The static tube was identical to the static tube of the smaller

pitot tube and was located 1 inch out from the impact tube. The tip of

the impact tube had an internal diameter of 0.052 inches.

A pitot tube similar to the 1/16- inch probe, but having 1/8- inchdiameter impact and static tubes, was used as a free stream reference and,

when it would not disturb the flow at a measuring station, for monitoring

the steadiness of the flow. This pitot tube was fixed in position for a

given set of measurements. The standard reference velocity for the wind

tunnel was obtained by calibrating the pressure difference between a fixed

impact tube at the entrance to the tunnel contraction and a static (smooth

wall) tap at the beginning of the test section against the pressure differences across the 1/8- inch pitot tube at fixed locations in the free stream.

c. HOT WIRES

The hot-wire probes were standard Flow Corporation 0.00015-inchdiameter copper-plated tungsten wire having an active length of about 1 mm.

These were set with the wire vertical and parallel to the wall at a

739
longitudinal location identical to that of the pressure probes. The hotwire anemometer was a constant temperature type of instrument which provided a linear relation between mean velocity and d-c amperage measurements.

d. PRESSURE MEASUREMENTS

A sensitive micromanometer, [9] which could be read to the nearest

0.0002 inch, was used to measure pressures at the lower velocities. This

gave excellent results in regions of low turbulence but proved overly

sensitive and difficult to read in regions of high turbulence. Most of

the pressure readings were taken on precision inclined manometers which had

slope settings from 1:10 up to 1:4. Reproducibility of readings proved

quite satisfactory with these manometers. The manometer fluid for all the

units was Dow Corning Silicone 200 (specific gravity of 0.817), which has

properties highly suitable for this use.

e. MEAN VELOCITY MEASUREMENTS

During the tests extremely high levels of turbulence intensity were

encountered close to the wall.' Here the rms values of u were from 40 to

50 percent of the local mean velocity. This gave rise to sizeable errors

in the measurement of both mean velocity and turbulent intensity. Figure 1

illustrates a typical comparison of hot wire and pitot tube uncorrected

mean velocity readings. It was apparent right from the start that the

correction of instrument readings would constitute one of the key problems

in these tests.

3. Hot Wire Anemometer

The measurement of mean velocities and longitudinal turbulence intensities where the intensities are low is a fairly straightforward matter.

A small low- turbulence wind-tunnel was used for calibration of hot wires

and pressure probes with consistently reproducible results. All measurements of u and u were based on such low- turbulence calibrations. It is

also possible to use carefully matched anemometer circuits and hot wire elements to determine the cross -components of turbulence v and w as well as

the Reynolds Stress and a variety of correlations where the turbulence

levels are low.

Unfortunately, as turbulence levels increase to values of u^/TJ

exceeding 0.10, it is necessary to apply a variety of corrections to measured values of U and u . In addition, data collected on the matched

linearized anomometer circuits become completely unacceptable due to lack

of reproducibility. Since v2 and w2- enter the computation of the turbulence

corrections and they can not be measured reliably, it becomes necessary to

estimate these. The evaluation of higher correlations within a high

740
intensity turbulent shear flow becomes an impossibility. Another factor

of great significance is the inability of the hot wire to distinguish between + and - on an instantaneous basis.

In an earlier paper [1] , it was shown that by ignoring the effect of

higher correlations and assuming a Gaussian distribution within the turbulence in order to develop a correction for local velocity reversal [7],

the following corrections could be applied to the hot wire readings

:

U

1 1 v

' 1

2

jpr + ...

U [erf (n) + e~

1 //Fn]

w

£3(n,v/u)

fi(n)

(1)

1 - n

2 (iv/u) 2

/ fi(n) (2)

where

:

n = U//2H2

"

U = corrected mean velocity

U

w

= measured mean velocity

and .for the intensity:

u

u

w

/ 1 - 2n'l{fi(n)} z T] £2 (n)

(3)

combining Equations 2 and 3, we get:

' x £3 (n,v/u) f2 (n) L

(4)

w

U / fi Cn) f rj y

Once the corrected value of u/U is known, it is possible to obtain correct

values of TJ/U^ from equation (2)

.

% U

l

U

w

flCn)

741
U U £3 (n,v/u) U

0r = = ^ = ^F (n,v/u) (6)

Ui Uj fi(n) U!

It should be noted here that Ui , the free-stream velocity exists in a lowturbulence region and was used as a reference calibration value at each

test station. Ui is therefore presumably free from error, at least, free

of those errors which have just been discussed, and may be moved into and

out of equations as a true constant.

The ratio_ of u/Uj involves only the single correction factor faCn)

to modify u^/Ui , but the local intensity ratio of u/U is of more significance in evaluating the corrections for mean velocity. Typical values

of the mean velocity factor, R , are shown in Table 1 for two stations in

the boundary layer.

4. Static Pressure Probes

Before attempting to evaluate the influence of turbulence on the

measurements sensed by static pressure probes, it is necessary to determine the way in which the pressure varies across the boundary layer.

The equation which applies in this case for the y component normal to

the wall will be:

Buy 'dv T _ 1 ap

3x 3y p 3y (7)

where uv = -x/p

on integration from y to 6 , this becomes

:

a.

where P

q = free stream static reference pressure.

The ratio of the integral term is small compared to v

2"

, about +0.10

for the tests described here. A good approximation for the static pressure is therefore pv2 below the free stream pressure on a line normal to

the wall.

742
b. EXPERIMENTAL PROCEDURE

In order to estimate the corrections for the static probes, two

standard static probes as described in Section 2b were used. One of

these was 1/16 inch diameter and the other 1/8 inch diameter. One of

these would be placed outside of the boundary layer for reference and

the other traversed essentially normal to the wall. The micromanometer

described in Section 2d was used to read the differences in pressure

between two probes. If no corrections were needed, the difference should

correspond to v2". As has been noted previously, however, it was necessary to estimate values of v

2" and w

2" so that results are presented in

terms of these estimates in comparison to measured pressure differences.

c. ANALYSIS AND OTHER EXPERIMENTS

In 1936, Goldstein [10] and Fage [11] concluded from both theory

and experiment that:

P

m

= P + Cp(v^" + w*) (9)

= P + CpiF (10)

where C = constant, 0<C<l/3

Toomre [6] later demonstrated that this relationship was correct for random eddies that were smaller than the probe, but that if the probe were

considerably smaller than the typical eddy size, the probe would sense a

yawed flow and a reduction in pressure.

For the large eddy case, Toomre calculated:

P^ = P - Apu^/2 (11)

where A is a constant having a limiting value of unity.

Hinze [5] estimated A>l/2

A variety of experimental values have been obtained. Strasberg [8] obtained

A=-l, but did not attempt to verify the algebraic sign. Siddon [12]

obtained +0.6<A<+1.0 depending on the flow conditions. DeHaan [13] showed

similar values by oscillating a static pressure probe in yaw under controlled turbulence conditions. Bradshaw [14] on the other hand, found

values of A=0 for tests run in a free jet.

743
d. RESULTS

For convenience, all pressure measurements were reduced to nondimensional form by dividing by pUt^. The pressure differences then

became proportional to v

7/U 1 2 or u

2 /!!} 2 If the value of A=l in the Toomre

equation (11), then: n

Since actual values of v2" and w2 are not known, these have been estimated

from other boundary layer data, particularly that of Schubauer and Klebanoff [15] where there were certain similarities in the boundary l ayer

behavior. The estimate was based on the assumption that values of v2 /u2

and w^/u2- would be the same for corresponding values of y/6 as the

flows approached separation.

Three sets of curves have been plotted using these data:

Figure 2. Station 9, showing the traverses for both the 1/16 inch

and 1/8 inch diameter probes versus estimated corrections where

A=l and A=0.

Figure 3. Station 13, using 1/16 inch diameter probe only.

Figure 4. Station 13, using 1/8 inch diameter probe only.

Two facts are immediately clear on examining these curves. The first

is that the estimates are poor. The second is that the correction favors

the upper estimate or that A=l is the more acceptable value. It is thus

concluded that the Toomre analysis gives acceptable results.

The square-nosed impact probe is subject to a variety of corrections

such as those due to its own Reynolds Number, wall proximity, compressibility, etc. These may be eliminated by proper size of probe, flow

speed and position so that only the question of the influence of turbulent flow characteristics need be considered. A carefully made squarenosed pitot tube will have a coefficient approximating unity. Assuming

a coefficient of unity, the effect of turbulence may then be represented by

5. Total Pressure Probes

0> J = p + ipu2 l +

^ tot^meas 2

K u

2" + (l-B)u^

U

2

(13)

744
as given by Hinze [3] . The value of B may be based on an approximate fit

to the directional calibration of the impact tube, or it may be evaluated

by fitting corrected hot-wire data. In general, the effect of the transverse components of turbulence yields values of B greater than unity and

possibly higher than the 1.5 which was estimated in these experiments.

Siao [7] considers the effect of instantaneous velocity reversals

(U+u<o) on the pitot tube. His conclusion is that this is extremely small

even for values of u^/U2 = 0.40, where the correction is about 1%.

The key problem then would seem to be that of evaluating B within a

reasonable degree of accuracy.

Part of the difficulty for the experimental case cited is that the

impact tube and the static probe are not located at the same distance

from the wall. As a consequence, the corrections for the static probe

and impact probe must be applied separately when a differential pressure

reading is used to evaluate the mean velocity. The form of equation

becomes

:

(P„ - P) = pU + Apu^/2 + pv^ - pv^ (14) 2

* t

7 meas

1 + Hi + (l-B)u^

u

2

where subscript s is at location of static probe and other values are taken

at impact probe location. Then since the_desired correction is to be used

to modify U /U*i to the form U/Ui and (P

t

~P) = pU2 /2, the "pitot" function

for mean velocity corrections will have them

form:

m

3 =/5elV and (15)

where U1 is the free-stream velocity. A=l and B=1.5 have been substituted.

Values of this function are given in Table 1 for Stations 9 and 11.

Figure 5 shows a plot of the corrected values of the mean velocity for

Station 11 to indicate the comparison between hot-wire and pressure probe

measurements

.

745
6. Discussion

Subsequent to the development of the corrections indicated, Hinze [3]

on pages 109 and 110 develops a relatively complex correction for the longitudinal turbulence intensity as measured by a constant temperature

anemometer using a linearizing circuit. The interesting effect which this

produces is a reduction from the measured intensity. The correcting function due to the instantaneous reversals of velocity as developed in

Section 3 shows an increase from the measured intensity. There is thus

a tendency for these two effects to cancel each other. Unfortunately,

the terms in the "amplifier" correction proposed by Hinze are not readily

evaluated in a shear flow, so it is not known whether the intensity, u/U,

is larger or smaller than that shown by the measured value.

The mean velocity correction for hot-wire measurements is quite small

as may be seen in Table 1. is thus not particularly sensitive to turbulence intensity variation from the measured values. Even so, it is

probable that the hot-wire mean velocities are somewhat overcorrected.

A careful look at the results shown in Table 1 suggests that the

pitot tube data are also somewhat overcorrected. Study of equations (14)

and (16) seems to leave only the adjustable constant B available for

changing the corrections. To reduce the correction requires an increase

in B from the estimated value of 1.5. Fortunately, the necessary increase

does not appear to be very great, otherwise there would be disagreement

with the published figures of 1.2 and 1.5 obtained by Hinze, although he

also indicates that higher values of B are possible.

For people working primarily in hydraulic flows there continues to

be a need to obtain fairly reliable data on turbulence intensities since

these enter into the calculation of the probe corrections. Becker and

Brown [4] have indicated some success in making these measurements and it

is to be hoped that this activity will be pursued.

7. Acknowledgments

The author gratefully acknowledges the assistance which he has

received from the Naval Ship Research and Development Center, Washington, D. C. 20007 in conducting this research. The assistance of

Mr. John L. Power and Mr. Edwin P. Rood is especially acknowledged.

746
8. References

Scottron, V.E., Turbulent Boundary Layer Characteristics over a Rough

Surface in an Adverse Pressure Gradient, Naval Ship Research and

Development Center Report, 2659, (1967).

Lin, J.D. , Scottron, V.E., Soong, H.K., Friction Effects on Spatially

Varied Open Channel Flows with Increasing Discharge, Am. Soc. of Civil

Engrs., Waterways Division, (Aug. 1976).

Hinze, J.D., Turbulence, 2nd Ed., McGraw-Hill Book Co. (1975).

Becker, H.A. and Brown, A.P.G., Response of Pitot Probes in Turbulent

Streams, J. Fluid Mech. , 62_, 85 (1974).

Hinze, J. P., Turbulence, McGraw-Hill Book Co. (1959).

Toomre, A., The Effect of Turbulence on Static Pressure Measurements,

Aero. Research Council, England, F.M. 2972 (June 1960).

Siao, T-T. , Correction for Mean- Velocity and Turbulence Measurements

for High Turbulence Levels, Scientia Sinica, Vol. VIII, No. 12,

p. 1558 (1959).

Strasberg, M. , Measurements of the Fluctuating Static and Total-Head

Pressures in a Turbulent Wake, David Taylor Model Basin Report 1779,

(Dec. 1963).

Smith, A.M.O., and Murphy, J.S., Micromanometer for Measuring Boundary

Layer Profiles, Rev. of Scientific Instruments, 2^3, 8 (Aug. 1955).

Goldstein, S. , A Note on the Measurement of Total-Head and Static

Pressure in a Turbulent Stream, Proc. Roy. Society, London, A Vol.

CLV, p. 570 (1936).

Fage, A. , On the Static Pressure in a Fully Developed Turbulent Flow,

Proc. Roy. Society, London, A Vol. CLV, p. 576 (1936).

Siddon, Th.E., On the Response of Pressure Measuring Instrumentation

in Unsteady Flow, Inst. Aero. Studies, Univ. Toronto, UTIAS Rep.

No. 136 (1969).

DeHaan, R.E., Design of a Probe Microphone, App. Sci. Res., 2_2, 306

(1970).

Bradshaw, P. and Goodman, D.G., The Effect of Turbulence on StaticPressure Tubes, Aero. Res. Council, London, R. and M. No. 3527 (1966).

Schubauer, G.B., and Klebanoff, P.S., Investigation of Separation of

the Turbulent Boundary Layer, Nat. Adv. Comm. for Aero., Report 1030

(1951).

747
TABLE 1

Comparison of Hot-Wire and Pitot-Tube Corrections

Station 9

Corrected Hot--Wire Pitot--Tube AU/u*!

y u/TT LA/ F

P

T7/TT-,

0

0.130 0.626 0.925 0.151 0.710 0.156 +

0.160 0.573 0.945 0.171 0.750 0.171

0.205 0.565 0.948 0.189 0.779 0.190 +

0.250 0.515 0.958 0.212 0.809 0.210 0 9

0.325 0.503 0.960 0.232 0.829 0.232 O O

0.400 0.484 0.965 0.262 0.854 0.258 - 1.5

0.550 0.416 0.976 0.306 0.883 0.295 3.6

0.700 0.366 0.980 0.352 0.906 0.340 : 3.4

1.000 0.326 0.984 0.416 0.931 0.410 1.4

1.300 0.280 0.987 0.486 0.948 0.488 + 0 4

1.600 0.239 0.990 0.556 0.965 0.561 4.

V 1.900 0.208 0.992 0.615 0.977 0.637 T "\ ft 2.200 0.165 0.994 0.708 0.987 0.708

2.650 0.122 0.997 0.821 0.993 0.785 L L

3. 100 0.085 0.998 0.904 0.997 0.892 JL . J

3.550 0.052 0.999 0.942 0.999 0.951 JL.

1 1 ft 4.000 0.027 1.000 0.984 1.000 0.984 ft ft

Station 11

0.130 0.386 0.982 0.111 0.792 0.113 4- 0.160 0.412 0.978 0.114 0.784 0.107 6 1 0.205 0.441 0.974 0.117 0.781 0.112 4H.J^ 0.250 0.457 0.971 0.123 0.791 0.118 4H.J.1 0.325 0.512 0.957 0.122 0.778 0.119

0.400 0.470 0.968 0.136 0.805 0.129 S 1 0.550 0.474 0.967 0.150 0.817 0.145

0.700 0.540 0.950 0.154 0.801 0.152 -L.J

1.000 0.467 0.965 0.190 0.828 0.180 5.3

1 300 0 495 0 958 0 209 0 829 0 207 1.0

1.600 0.470 0.961 0.236 0.831 0.230 2.5

1.900 0.450 0.964 0.272 0.851 0.270 0.7

2.200 0.446 0.963 0.308 0.869 0.307 0.3

2.650 0.373 0.974 0.384 0.901 0.372 3.1

3.100 0.335 0.978 0.448 0.930 0.446 0.4

3.550 0.286 0.983 0.512 0.946 0.518 + 1.2

4.000 0.247 0.987 0.593 0.960 0.594 + 0.2

4.600 0.195 0.991 0.701 0.979 0.697 0.6

5.100 0.149 0.994 0.798 0.988 0.793 0.6

5.600 0.121 0.996 0.855 0.995 0.855 0.0

748
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753

National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS

,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

DETERMINATION AND ELIMINATION OF ERRORS IN

VELOCITY READINGS AT VENTILATION TUBING INLETS

Robert A. Haney

Mining Enforcement and Safety Administration

Pittsburgh, Pennsylvania

1. Abstract

Accurate air velocity measurements have been obtained

by applying a methods factor to vane anemometer readings at

the inlet of an exhaust tubing installation. Methods factors

were determined by comparing simultaneous 4-inch rotating

vane anemometer readings at the centerline of the tubing

inlet to a Pitot-static tube traverse of the duct. Test

velocities ranged from approximately 600 to 8,600 fpm.

Methods factors were independent of velocity but dependent

on tubing diameter and tubing entrance configurations. For

straight unflanged tubing, the methods factors for 12-, 14-,

16-, 18-, and 20-inch diameter rigid tubing and 24-inch

diameter spiral reinforced tubing were 0.69, 0.68, 0.66,

0.74, 0.75 and 0.72, respectively.

2. Introduction

Underground coal mine ventilation networks consist of a primary

ventilation system and a secondary or face ventilation system. The primary

ventilation system delivers fresh air to the last open crosscut of each

working section and the face ventilation system moves the air from the last

open crosscut to the working faces.

Primary airflow or main mine ventilation is induced by fans ranging

from 4 to 10 feet in diameter. Separate intake and return openings to the

surface are required. Main fans are installed on the surface and generally

exhaust air from the return openings. Multiple intake and return openings

with multiple fans are common in modern coal mines. Fan capacities of

200,000 to 500,000 cfm are common, and the total air volume in a ventilation

system may reach a million cfm. Fans generally operate at 4 to 8 inches of

water gage.

Air entering the mine is directed to the working places through the

use of stoppings or walls built in the crosscuts that separate the intake

and return airways. In this manner, the entire mine entry is utilized as an air duct. Mine entries are typically 3 to 7 feet high and 15 to 20 feet

wide. Because of the great distance the air must travel, leakage or airflow

from intake to return before it reaches the working face is usually high.

Generally less than 50 percent of the air that enters the mine eventually

reaches the last open crosscuts.

755
Statutory provisions of Public Law 91-173, the Federal Coal Mine

Health and Safety Act of 1969 require that:

the minimum quantity of air reaching the last open

crosscut in any pair or set of developing entries and

the last open crosscut in any pair or set of rooms

shall be nine thousand cubic feet a minute, and the

minimum quantity of air reaching the intake end of

a pillar line shall be nine thousand cubic feet a minute. The minimum quantity of air in any coal

mine reaching each working face shall be three

thousand cubic feet a minute.

In addition, Title 30, Code of Federal Regulations, Part 75.301-4

requires that except where blowing face ventilation is used the

minimum mean entry air velocity shall be 60 feet a minute..." In order to

determine compliance with these standards, air velocity and air quantity

measurements must be taken by mine officials and mine inspectors.

Face ventilation which is an extension of the primary ventilation can

be either an exhaust or blow system. However, since good exhaust ventilation

is currently the best means to control air borne dust in the face area,

most coal mines utilize the exhaust method of face ventilation.

Air is carried from the last open crosscut to the face by either a line brattice or an auxiliary fan and tubing system. Line brattice is a jute or plastic material extending from the last open crosscut to the face

and separates the face entry into an intake and return side. As the working

face advances, the face ventilation system also advances. Federal regulations

require the face ventilation system to be maintained not greater than ten

feet from the point of deepest penetration of the face.

In auxiliary fan installations, a fan is placed in the last open

crosscut and is used to induce airflow through tubing that has been extended

into the face area.

While fan and tubing systems can be designed to provide sufficient

airflow in the face area, circumstances may occur which would result in an

insufficient air quantity in the face area. Lumps of coal or debris in the

fan inlet could restrict the fan airflow. Cracks or holes in the tubing

could short circuit air from the face, or the fan and tubing system may be

improperly designed and may not be capable of delivering sufficient air

volume to the working face.

The measurement of air quantities in underground auxiliary ventilation

tubing is necessary to determine the air volume being delivered through the

tubing and to assure that fan and tubing systems are performing properly.

The standard method of air quantity determination employs a Pitot-static

tube traverse of the ventilation duct to determine the average air velocity

through the duct. This technique is time-consuming and the required

instrumentation is cumbersome to handle and transport underground. A

Pitot-static tube traverse and the resulting calculations may take as long

756
as 20 to 30 minutes where as a single vane anemometer reading and calculations

:an be made in less than 2 minutes. While standard rotating vane anemometers

are commonly used to determine air velocities in mine entries, they have

lot been used to determine air velocities at the inlet of auxiliary tubing

Decause tubing entrance configurations and tubing diameters create conditions

that give anemometer readings other than true air velocities.

While ventilation tubing diameter varies with the requirements of

individual mines, the tubing inlet configuration is generally a straight

jnflanged or unbelled opening. It was, therefore, desirable to know what

factor should be applied to a centerline 4-inch rotating vane anemometer

"eading at the inlet of different sized tubing with a straight inlet so that the actual air velocity in the tubing could be determined.

3. Testing Procedure

The testing procedure adopted was one which would allow centerline

anemometer readings to be taken at the duct inlet while Pi tot-static tube

traverse readings are being taken in the duct itself. Approximately 50

feet of tubing was used for each test setup. Airflow during the study was

induced by an axial flow fan. A 16- by 18-mesh screen straightener was

inserted 10 feet downstream of the tubing inlet and perpendicular to the

iirection of airflow. This reduced the turbulence and established a more

jniform velocity profile at the point of the Pitot-static tube traverse,

five diameters downstream from the straightener. An illustration of the

general test setup is shown in figure 1.

During the tests, the tubing was supported approximately 8 inches off

the ground on concrete blocks. The supports were maintained at least 4

feet away from the tubing inlet. No other obstructions or surfaces were

lear the tubing inlet.

Because air velocities at the tubing inlet were often above the range

3f the standard 4-inch 8-vane anemometers, 4-inch 4-vane high speed anemometers

vere used. While running tests with these anemometers, care was taken to

avoid placing the anemometer in an air velocity that was above the range of

the instrument thus preventing damage to the instrument.

Anemometer readings were taken at the centerline of the tubing inlet,

ro avoid damage, the anemometer was moved slowly into the airstream. The

anemometer was supported on a 5/16-inch diameter rod that was 2 feet long,

and, except for starting and stopping the instrument, the operator's hands

/vere out of the airstream. The rod was physically held against the duct so

the inlet plane of the duct approximately bisected the anemometer frame.

This method of positioning the anemometer permitted little or no movement

Df the instrument during the tests and was easily repeated. Since no

simple and compact attachment could be devised to positively centralize the

anemometer in all sizes of the duct it was decided that the axial position

A/ould be estimated by the aid of a scale located on the rod. Effects due

to positioning or variation of the instrument are included in the experimental

error. The actual air velocity in the duct was determined by a 20-point

Pitot-static tube traverse (four readings at right angles at the centroid

of each of five equal area concentric circles). Figure 2 illustrates the

technique adopted at both the inlet of the duct and the Pitot-static tube

traverse location.

757
758
10 ftAirflow

Centerline

anemometer

reading

Tubing

50 ft

20 ft minimum

Straighteners

ELEVATION

Rotating vane anomemeter

0.342 diam

0.226 diam

0. 146 diam

0.082 diam

0.026 diam

Support

SECTION AA

Anemometer reading

SECTION B-B'

Position of Pitot static tube

traverse points

830

FIGURE 2. AIR VELOCITY MEASUREMENTS AT THE TUBING INLET AND INSIDE

THE TUBING.

759
Tubing sizes used in this investigation were 12-, 14-, and 16-inch

polyvinyl chloride (PVC); 18- and 20-inch fiber glass; and 24-inch spiral

reinforced tubing. For each tubing size, three to five velocity levels

were tested. At each velocity level, five groups of readings were taken.

Each group consisted of five 1-minute anemometer readings and a concurrent

Pitot-static tube velocity traverse of the duct. Indicated anemometer

readings were corrected by application of a calibration curve and Pitotstatic tube readings were corrected to ambient air density. In all, approximate

160 tests were made over a velocity range of 600 to 8,600 fpm.

Recognizing that inlet configurations could be critical in establishing

a methods factor, several additional tests were performed to determine the

effect of changes in inlet configuration. For this series of tests, readings

were taken with a 1-1/2-inch wide flange attached to the entrance of a 14-

inch diameter duct. Readings were taken at the inlet with a rotating vane

anemometer and inside the duct with a Pitot-static tube as in the other

tests.

4. Test Results

The methods factor to be applied to field anemometer readings was

obtained by taking the ratio of the average velocity in the duct as determined

from the 20-point Pitot-static tube traverse to the average of the corrected

anemometer readings concurrently taken at the centerline of the duct inlet.

By examination of figure 3, it was found that the methods factor showed

little, if any, dependence on velocity for a given tubing size; however,

the factor did change as the diameter of the tubing changed.

Table 1 gives the average methods factors determined for each size of

tubing for high speed anemometers. The table also shows the range of

velocities and the standard deviation from the average methods factor for

each set of tests. The average methods factor ranged from 0.66 to 0.75 for

the high speed anemometers.

TABLE 1. - Methods factors for centerline anemometer

readings at the inlet to exhaust tubing

Tubing

diameter,

inches

Velocity

range,

ft/mi

n

Average

methods

factor

Standard

deviation Type of tubing

HIGH SPEED 4-•INCH, 4- VANE ANEMOMETER

12

14

16

18

20

24

1,000-4,300

1,000-8,600

1,100-6,900

1,200-5,000

1,000-4,400

600-1,800

0.69

.68

.66

.74

.75

.72

+0.01

+ .02 + .03

+ .03

+.04

+ .07

PVC

PVC

PVC

Fiber glass

Fiber glass

Spiral reinforced

760
1.00

.80

.60

.40

1.00

.80

.60

AO

1.00

.80

g .60

o

<

^ .40

S 1.00

1.00

.80

.60

.40

Avg methods factor, 0.69

Rigid tube diam, 12 in

!

i

1 i 0.68

• 1 "

i

14 in

i i i

i 1

I i 0.66

-

u— 1

!

1

% 1

i 16 in

i

i i i i 0.72

•

•

• • 24 -in diam spiral reinforced tubing

i

i i 2 4 6 8

AIR VELOCITY IN DUCT, 1,000 fpm

10

03/

FIGURE 3. METHODS FACTORS VERSUS AIR VELOCITY FOR VARIOUS DIAMETER

TUBING.

761
The largest standard deviations occurred during the tests where the

velocities in the tubing were the lowest. This corresponds to the velocity

range where Pi tot-static tube readings are the least accurate. At higher

velocities, the largest standard deviation was +0.04, corresponding to +5

percent of the mean. This indicates very little fluctuation in the methods

factor and a high degree of confidence in the average methods factor.

Table 2 gives a compilation of the air quantity that would be present

for various anemometer readings at the inlet of different diameter tubing.

In each case, the methods factor is applied to the corrected anemometer

reading and the air quantity is computed from the formula: air quantity

(cfm) equals corrected anemometer reading (fpm) times methods factor times

area (ft^). This table is compiled to reduce field calculations.

When a 1-1/2-inch flange was attached to the inlet of the 14-inch

tubing, the methods factor for velocities between 4,000 and 6,000 were

determined to be 0.80 with a standard deviation of +0.02, as opposed to the

unflanged inlet system having a methods factor of 0.68 for similar velocities.

This shows that any change in the inlet configuration of the duct system

may change the established methods factors.

5. Conclusions

For routine air measurements in exhaust auxiliary mine ventilation

systems, a methods factor dependent on tubing diameter can be applied to

centerline 4-inch rotating vane anemometer readings at the tubing inlet to

determine the air velocity through the tubing. Accuracy of +10 percent is

easily obtained by this method. If a higher degree of accuracy is desired,

air velocity measurements should be made using a Pitot-static tube traverse.

While the methods factors showed a dependence on tubing diameter, they

showed little, if any, dependence on air velocity.

The factors determined by this investigation and shown in table 1 apply only to readings taken at the inlet of a straight unflanged duct.

These factors should not be used when other inlet configurations exist as

tests have shown that the addition of a 1-1/2-inch wide flange at the inlet

of 14-inch diameter tubing increases the factor from 0.69 to 0.80.

762
TABLE 2. - Air quantity for vane anemometer readings at the inlet of different

diameter tubing (extrapolated to 10,000 fpm)

(Air quantity = corrected anemometer reading X methods factor X area)

Corrected

anemometer

reading,

fpm

Air quantity--cfm

Tubing diameter, inches

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5,200 6,980 8,850 12,550 15,710 21,710

5,310 7,120 9,030 12.810 16,040 22.170

5,420 7,270

J 9,210 I 13,080 I 16,370 22,620

1,000

1,200

1,400

1,600

1,800

2,000

2,200

2,400

2,600

2,800

3,000

3,200

3,400

3,600

3,800

4,000

4,200

4,400

4,600

4,800

5,000

5,200

5,400

5,600

5,800

6,000

6,200

6,400

6,600

6,800

7,000

7,200

7,400

7,600

7,800

8,000

8,200

8,400

8,600

8,800

9,000

9,200

9,400

9,600

9,800

10,000

763

National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

INDIRECT TWO-PHASE FLOW MEASUREMENT:

ANALYSIS AND REDUCTION OF METHODS ERRORS

N.N. Kondic

Industrial Systems Engineering

University of South Florida

Tampa, Florida 33620

- Abstract -

Flow measurement is systems characterized by adverse

features ( high temperature and/or pressure, aggressive

fluids, chemically reacting materials, vibrations, etc.)

often require the application of indirect methods. Although

more complex, due to instrumentation and data processing

involved, such methods sometimes offer an additional advantage, when they are devised to be contactless (i.e.

when pick-up probes and similar flow-field disturbing

elements are eliminated). This family of methods introduces either tracers (chemical, radioactive, colorimetric

,

etc.) within the flow, or wave-transmitting and receiving

devices (sound, ultra-sound, photons of various wavelength).

Tracer concentration and wave-field characteristics (energy,

flux) are functionally dependent on the characteristics of the

original flow-field (velocity, gas fraction, particle concentration, etc.). This functional dependence, i.e. its accuracy

(which depends on the assumptions and approximation in the

mathematical analysis of all phenomena involved) is an important component of the overall method's accuracy . In

addition, statistical fluctuations within the basic flow-field

(turbulent in most practical cases) are generally independent

of statistical fluctuations which are often inherent with the

measurement method employed: fluctuations of tracer density

or of the radioactive decay rate or other wave-source intensity

variations. An appropriate analysis of these sources of errors

which are different from the usually listed errors when directreporting instrumentation is being utilized — can give an

assessment of their magnitudes and indicate approaches to

reduce them, including experimental procedures and data

analysis improvements.

76$
1 . Introduction

In elementary, straightforward measurements,

a strictly defined function correlates the basic measured property

(e.g. temperature) and the registered one (length of mercury

column); in this case the function is linear, expressing proportionality. Fluctuating temperature, use of thermocouples or pyrometers

etc. introduce the need for a phenomenological-mathematical

analysis to obtain the correlation between the basic and the measured

property (magnitude).

In turbulent two-phase flows, which are inherently

fluctuating, the phases' concentration and/or temperature represent

important measurement goals in various disciplines of applied

sciences, especially in thermal (power) engineering, the chemical

industry and bio-medical applications. The measurement task is

much more involved when it is necessary to meet the requirement

of using exclusively external (contactless ) devices to determine

the properties of a turbulent multiphase system. Such experimental

approaches exclude insertion of any sensors ("pick-up") into the

fluid, to prevent the possibility of a chemical or flow-desturbing

interaction between the inserted device and the fluid. Also, in

numerous systems, any addition of tracers is strictly forbidden.

The measurement problems already encountered, caused by these

restrictions, become extremely complex when the measurement

objectives are the local values of properties, i.e. their spatial

distribution within the system, which can be in the shape of a 2-

or 3-dimensional field.

This report deals with two-phase flow concentration

(defined conventionally as the mass- or volume ratio of the denser

phase or component to the total mass or volume) as the measured

property, but the general considerations can be applied to others

(e.g. temperature). A comparative analysis as well as experience

proves that with an increased complexity of measurement methods

the errors are augmented in two ways; new causes of errors appear

and the quantitative effect of old and new errors increase.

766
2. Literature survey

Since the time when radiation-attenuation usage for

determination of the average void fraction along a beam started, the

geometry related source of errors has been noticed and assessed,

first in a simplified way, /

J\/ . This source of errors, pertaining to

the two-phase system pattern (i.e. arrangement of phases) was later

statistically treated, analytically in /2/ and analytically-experimentally

in /3/ and /4/ . Nearly in the same time, a different approach to

resolve the same problem analyzed the effects of shape, size and

relative position of bubbles (voids) along the radiation beam. This

was reported in /5/, /6/ and /7/. The results emerging from Ref's

/2/ through /I/ help enhance the accuracy of line-average void fraction

measurements and they point out to the researcher how to design and

better tuilize an experimental facility and the data it renders.

As the next step, two advanced, more recent methods,

able to measure indirectly local values in any system where a 2- or

3-dimensional concentration field exists, are reported in /8/, /9/ and

/10/. These methods employ gamma (or X-ray) sources and detectors

(standard commercial equipment), all of them located externally, i.e.

at the outer side of boundaries which enclose a 2-phase system. Three

unique characteristics of electro-megnetic radiation are utilized; (a) its

exponential attenuation along the propagation path, (b) initiating of secondary

radiation "sources" along the primary beam due to scattering, and (c)

the dependence of the scattered photons' energy and radiation absorption coefficient on the scattering angle. Fluctuations inherent with radioactive

(and some other) sources of penetrating radiation are treated in

while statistical fluctuations of turbulent flows are extensively dealt with

in /12/ and /13/. The dynamics of multiphase systems and those with

flowing suspensions are subjects of /14/ and /15/, while for useful

probabilistic criteria and statistical formulae /16/was used.

3. Components of indirect methods' errors

Mathematical derivations of functions which correlate

registered signals with concentration values are based on true, i.e.

representative values of magnitudes involved (pertaining to steady state),

such as radiation source intensity, fluid velocity, concentration, detector

efficiency etc. For sake of brevity, this report will not elaborate on the

so-called standard sources of errors (individual, instrumental, systematic,

external — such as mechanical vibrations, supply voltage or pressure

variations —etc.) and will focus on the specific family of methods' errors.

The following analysis will be performed in regard to the most complex

of the methods listed, described in /10/, and a special emphasis will be

put on the influence of random fluctuations of various origin and character.

The only assumption is that these random phenomena can be expressed

in terms of statistical probability functions. This assumption is well

supported by /11/ and /12/. The application of the analysis which follows

to simpler methods involving similar phenomena in the measured and

measuring system is straightforward.

767
Users of many indirect measurement methods, which

are applied to systems with time-fluctuating properties should be

cautioned that simple (linear) time-averaging of registered signals

within an interval of time "larger than the system's characteristic time"

is generally far from a cure-all of the fluctuation-caused effects. This

remark is true also in respect to systems without fluctuations in the

wave-source of the measuring device, which can be closely achieved

when light or (ultra-) sound is used. Only in very special cases can

simple time-averaging properly compensate for the distortions due to

random phenomena occuring during the measurement period. The

first reason which supports this warning statement lies in the existence

of a multitude of available averaging functions (linear, square, reciprocal,

log etc.), thus, the best one has to be selected, if possible. The second

reason, which can be considered as the dominant one, emerges from the

closer analysis to follow. It pertains to a general situation represented

by an example, illustrated by Fig 1 and explained by a condensed description of several phenomena occuring and thus enabling the method from

/10/ to be successfully implemented on two-phase (even multiphase)

systems. These phenomena are:

A. The source emits radiation in a random fashion, with which

a probability function P

s can be associated. For some nonradioactive sources Ps is a uniform function in time, equal

to 1 when normalized.

B. The photons emitted by the source traverse an average

linear density (integral of density versus length) of atoms

interacting with the oncoming radiation (photons) in the twophase system. This integration is performed along ZS | from

the inner system wall at the source side up to the beamintersection point (subscript ip), defined as the location where

the longitudinal axes of the source-collimator (z) and detectorcollimator (y) intersect. Those two axes form an angle ranging

between 0° and 180° , as shown in /9/ and /10/. This angle is

90° on F ig . 2

.

The time-fluctuations of the above defined length-average linear

density are described by a probability function, Ps |.

C. Analogous to B . , a probability function P^ pertains to the

average linear density along the path of scattered photons from

the intersection point up to the inner wall of the system at the

detector, i.e. along y-axis distance Y|j.

D. At the beam-intersection point, P^p is the probability of

scattering atoms presence. Normally, a finite volume exists

physically there, and the intersection point is merely the

center of that volume.

768
It should be noted that each of the three probabilities

explained (Pg^j Pid > Pip) * s a ^unction — with a good approximation

a product — of two sub-probabilities: (different in si, id and ip

regions), which is mass-concentration related, i.e. pertains to the

presence of denser phase (according to the convention adopted) in

the respective region. The second probability is Psa (which is practically equal for regions si and id, but generally different from the one

at location ip), describing the chance of the presence of scattering

atoms in the paths of arriving photons in the volumes considered

(microscopically, the atoms density is not uniform, and, on the other

hand, the arriving photon is hitting or missing a moving target). The

three Psa functions are also temperature-dependent, but they differ

noticeably from uniformity (= 1 when normalized) only for weak radiation

sources and/or when extremely narrow beams are utilized, when the

equalizing effects of large numbers of events decrease.

E. The radiation detector efficiency is assumed constant,

resulting in Pde= 1 (when normalized). This is because,

as already mentioned, the instrumental and external sources

of errors (mechanical vibrations, pressure and voltage

fluctuations etc.) are disregarded here.

Taking in consideration the above listed probabilities, the

=ollowing equation can be written. It describes what happens with any

Dhoton (gamma quant) to be generated by a spontaneously emitting radioactive source, which photon moves initially (prior to scattering ) in a

desired direction, which is axis z. The equation, as well as the analysis

outlined, neglects the evaluation of straightforward calculable phenomena

'which can be associated with fully uniform probabilities), such as

radiation attenuation in system walls, scattering in surrounding air and

present objects, as well as in the source - and detector hardware. All

these probabilities are lumped in the term P\u

of the following equation,

sxpressing the total resulting probability for the above defined photon to

reach the detector:

Pto= ( plu) (PS)[RA(PC > Zsi)](Psi>[crip (Z

st)]( P ip)[R/HPc> Yld)J(P ld) (1)

2 rip (Zsi) is the simple time-averaged dirrensionless (relative) concentration

Df the denser phase, i.e. matter at the intersection point. "Simple timeaveraged value" means the one resulting from a direct, linear intergration

in time. Any other average concentration can be (arbitrarily) defined and

jsed, only then, the probability function P ip and others have to be redefined,

Dut all already said remains valid. RA are radiation attenuation functions

^negative exponential), which include the radiation scattering and absorption

coefficients ko and k1 and Zsi . The latter is the distance along z-axis

From the inner wall surface at the radiation source along the initial beam

jp to the beam-intersection point. Yid is analogous to Zsi , but along axis y.

In the detailed mathematical expressions the power of the exponential

attenuation functions (RA) contains also integrals with Zsi and Yid as their

upper limits, as well as the probability Pip (as shown in section 4.3.) Pc

is related to Pir. and explained in section 4. 2.

IP

769
The described complex shape of functions within the

expression for P^Q renders it obvious that it is not possible to perform

any simplified association, e.g. a multiplication of the probability functions

involved. This rules out a simplistic forming of a joint product-probability

function ( in addition, the average product f product of average factors).

The listed probability functions are mathematically different due to their

different physical origin; Ps

is ruled by nuclear processes, next three

P-functions with 2nd subscript ph are consequences of hydrodynamic

phenomena; finally, the corresponding three P-functions with sa as the

2nd subscript depend on molecular mechanisms in fluids and are temperature dependent.

The given equation makes it clear chat none of the timeaveraged detector signals (i.e. using any function for the time-intergration

cannot be equal to the true steady state signal, which is defined as follows:

it would result from the simple time-averaged source intensity (flux),

attenuated by the (simple) time-averaged concentration field, which is the

measurement goal(simple time-averaging is equivalent to the steady state).

The here formulated exclusion of direct averaged signals use is not a deadend negative statement. On the contrary, the task is now clearly formulated.

It is necessary to find (evaluate, derive, assess, etc.) all the probability

functions playing the role (as described) in the detector reading, which

reports the counting of events characterized by probability P^o (see equation).

Once the probabilities involved are described (as analytical functions, graphs

or tabulated data), the representative signal, emerging from measured data

processed by these functions, can be further used. This is done by proper

implementation of the representative signal as explained in the analysis /^0/

of data interpretation and final results derivation, which are the local values

of the concentration field. /10/ also explains the mathematical procedures to

be performed with the values of representative detector readings.

Next chapter elaborates more closely on the analytical

procedures necessary to implement in order to achieve the reduction of

several among the five listed kinds of methods' errors.

4. Analysis to reduce indirect methods' errors.

4 . 1 . General

The contents of this chapter will concentrate on error sources

listed under phenomena B, C, and D, in chapter 3. The corresponding

probability functions needed for the concrete application of the analysis

to follow have been at least partially explored in particular disciplines.

To phenomenon A. corresponds probability Ps , which is the subject of

numerous works dealing with nuclear physics, such as while Pde

(related to phenomenon E.) is either constant or defined by detector

design. Psi, Pid and ^ip are first of all inter-related functions, obeying

the laws of constrained random statistical behavior /15/, /16/. Second,

for many systems in practical application, tubulent fluctuations - which

770
are the ultimate physical cause of these functions, have been successfully

measured and thoroughly analyzed: classical work /12/, further on /13/,

/ 14/ and /15/, as well as a number of volumes of N . A .S . A . reports

(especially between years 1940 and 1970) can serve as a valuable source

of pertinent data.

Concerning the two sub-probabilities, Pph (describing mass

concentration, i.e. mixture density) and Psa (describing atoms density

fluctuations within the phases), the latter one will be considered constant

and equal to one when normalized. This will result in PS [ = (Psi) etc.

In special cases, when Psa ^ 1, which warrants a closer micro-study,

classical textbooks on Kinetic Fluid Theory, Statistical Physics and

Thermodynamics or similar works give sufficient material for evaluating the probability function Psa . The outcome of such a study can be

easily introduced into this report's results.

4. 2. Probabilities Pc and P^p

Before evaluating the integral probabilities Ps| and , attention should be focused on the local probability, Pc , wnich is greatly

affecting Ps | and P[d'

For systems where an analogy between temperature and concentration holds at least qualitatively, the results of turbulent temperature

fluctuation analysis. /13/, could be used, but with due caution, or they

may be properly adapted to two-phase systems . Results pertaining directly

to particulate (or bubble-containing) systems are definitely more desired

for application in this study. Diffusion of discrete particles in homogeneous

turbulence represents a topic in /12/; it seems closer applicable to this

report's goals, despite certain restricting assumptions listed in /12/,

which idealize the system. Also, /12/ deals mostly in terms of the widely

used velocity-defined correlation coefficients (C c) and intensity of turbulence

(Ij-). These parameters are consequences of local properties' fluctuations,

but the time-dependence and the spectral (probability) distribution of these

fluctuations themselves cannot be derived in the reversed direction, i.e.

from Cc and 1^. which parameters are in essence integrated time-averaged

values

.

The analysis and results from /15/ are more suited for the flowing

2-phase system from /10/, which is under closer consideration in chapters

3. and 4. of this report and shown in Fig. 2.

Utilizing the more familiar notations from /12/, in a turbulent

2-phase fluid, with fluid velocities (U^, uQ along three Cartesian axes

( i=1 for x, i=2 for y and i=3 for z) and mass concentrations (C, c), it holds:

U^Ui + u. (2)

C = C + c (3)

771
Eq. (3) holds also for volumetric concentration of the denser phase,

as this convention has been adopted in this report. Being a scalar

property, concentration does not carry the axes' subscript.

The normalized probability function, describing the

fluctuating component of the velocity, u (omitting from now on the

axis' subscript), defining the chance of u to be in the interval u ± du,

is, according to /15/:

P =(1/Y2nO exp (- a/2) (4)

This is the Gaussian probability law, with the exponent:

a = u

2

/ (u')

2

(5)

The denominator in the last equation is the mean-root-square value,

defined on p. 4 of /12/ as:

u' = I U (6)

Using Eq. (6), the exponent a is more conveniently expressed as the

ratio of two relative magnitudes:

a = (u/U) /I

fc (7)

U is the time-averaged, linear mean value of velocity and it is known

for the flow under consideration, while Ij. can be measured /12/, or

estimated based on published data pertaining to similar systems.

It should be noted that, according to /15/, the dimensionless

exponent a depends on five dimensionless parameters: (1) Reynolds

© 5 number, (2) Eroude number (velocity/ (( grav . acceler .)-(duct diam.) )

* ),

(3) quotient of representative particle diameter/duct diameter, (4)

ratio of densities of two phases and (5) dimensionless concentration of

the mixture, denoted as c

p

in Eq . (1).

In order to find the probability P , which is defined similarly

to Pu , but it pertains to concentration fluctuations, a different coefficient,

b, has to be used instead of a. The following Gaussian law is applicable

for a scalar property in free turbulence, according to /12/ , pp. 292, 311 , without a condition of velocity/concentration analogy in the system.

Pc = 0/}r2jT) exp(-b/2) (8)

b= c

2

/ (c')

2

(9)

Pc pertains to any location, or Pc

(z) or P

c(y), because b is position

dependent. In the special case, when z = Zs | , Pc represents in fact the

previously introduced and defined Pip. (c')

2, is the average square concentration fluctuation . ___
A possibility to express c' in terms of known magnitudes

is to utilize in some way F ick's laws of diffusion. This is done in

/12/, p. 311, where the compliance of these laws with the Gaussian

probability for a particle to advance over a certain distance is proven.

The exponent of that Gaussian probability is defined analogously to

a and b, only with Lagrangian distances replacing velocities respectively

concentrations

.

All of this encourages the use of eq's (8) and (9), although

neither /12/ nor /15/ relates c' to some known or numerically available

parameter, analogous to It. This leaves c' as the only unknown magnitude.

In the absence of available experimental data, c' can be measured by an

appropriate data interpretation procedure in two-phase systems (using

specialized anemometers). On the other hand, c' can be expressed

through a ratio which corresponds to 1^ see Eq. (6), and available

values for It can be utilized for the first approaches, i.e. computer runs.

A subsequent calibration (assumption checking) procedure, using an integral

function of Pc , i.e. a special case of Ps [, which covers the whole region

from wall—to-wall of the system, can be easily included in a feedbackiterative process. The aim of such a process would be to verify and/or

ultimately establish the best usable value of c' or (c'/C), the latter being

a kind of "intensity of concentration turbulence''.

The following two sections will explain the previously introduced

notion of constrained, or rather inter-related random behavior of some

properties within the system under consideration.

4.3. Probability Psi

It is obvious that at any instant (time, t) at different locations

along z axis, the values of Pcwill be different, or, a more general functional dependence has to be taken in consideration: PCz= Pcz(z, t, b)

.

As time fluctuations, i.e. its influence will be taken care of by the

integration of detector signals in time, and b is already a function of z

( but not a pronounced one, as will be discussed later), the lengthintegrated probability, Ps [, involves the proper probabilistic use of

Pc from Eq. (8). The problem of application of that equation to an

interval along z-axis emerges from the fact that in the same moment,

at various locations along any axis, the fluctuating components of

concentration, c, assume different, random values, but, with a probability P

c

.

P

s l will be derived in continuation, based on the original

interpretation of the radiation attenuation formula. In this formula,

/10/, the absolute value of the negative exponent with e for the path

Zs | as the interval in question along z-axis, can be expressed either

as a sum or as an integral:

773
si ]

kQ Az (C+c) z + (C + c) z + + (C + c)

•St C (z) dz + c (z) dz ~ Esa + E

s f _ Es (10)

kQ is the linear attenuation coefficient for the initial, primary radiation,

(unscattered , originated by the source).

It has to be stressed that mathematical derivations and results

in works dealing with radiation attenuation methods' application to density/

concentration measurements. — including ref's /"\/ through /4/, /8/, /9/

and /10/, introduce only the first, ideally averaged (i.e. steady state

corresponding) part of the exponent, Esa . The second exponent, Esf , which

is a consequence of fluctuating concentrations, can be calculated as follows.

At any point in time, at various values of z along the interval Zsi > c has

different values. Although they are random, they can range only between

•mi and cmx These extreme values of concentration fluctuations are

calculable for any system under consideration: they correspond to the

limiting cases of C: all gas or all liquid, or liquid and solid etc. Generally,

the limiting values of C ( i.e. of c ) are independent of location, i.e. of

coordinates z or y. According to Eq. (3), c can assume positive and

negative values, and in each point along Z

s ^

, a probability P

c , Eq. (8),

will be associated with any value of c. Therefore. ESf from Eq. (10)

would be more precisely expressed as (with the subscript f for

"fluctuating "):

si

sf = k, ( cf P

c>z

dz (11)

But, the following equation, which is the finite form version of the above

one is more realistic. Such a form is needed in order to correctly interpret the physically existing statistical nature of the phenomena involved:

E = k Az sf o ^|?f pc(v]r k

o

A z c

sf (12)

Az = Z ./N (13) si z

N is the average number of discontinuities (bubbles, particles etc.)

along Z^, which number is directly calculable form the average linear

numerical concentration between z=0 and z=Z s ^.

It should be noted that P

c

is a function of c', through b — see

Eq. (9) — and therefore it depends on z, i.e. on the subscript i, but from

/12/ , p. 521-523, the following is obvious: for all practical purposes, It- changes very little with the distance from the wall (z or y), and since

c'/ c is analogous to I t

, the same can be expected. Therefore, the work

with an average c' (resulting in an average b) along Z^ and Y-^ can be

774
deemed satisfactory accurate.

Each time Eq. (12) is implemented, a set of N random numbers

(generated) defines N values of fluctuating concentrations, c. This should

be done in the following way. The maximal random number in the

group ( R N) will be associated with c mx , and the minimal RN with cmi . In this way a scale is estab lished between the RN's and c's. Any c which

corresponds to a RN> RN will be i nterpreted in Eq. (12) as positive,

while any c corresponding to a RN<RN vill be treated as negative. RN

corresponds to C, and that, average random number emerges from the

explained scaling procedure; an analogous procedure is to be used when

calculating t> and P. from Eq. (8). Finally, based on the steps outlined

and equations listed, one obtains the needed probability, P

"Esf

P

si = e

S

(14)

This equation has to be implemented M times, and from these results a

linear average P

s j is then to be calculated. Such an averaging corresponds

to a uniform probability for each group of random numbers to show up

(or, for each composite event to occur), while the probability function Pc

has taken care of the effects and proper application (such as occurence

chance) for each of the random numbers in the group. M is the number

of "changed situations" along the length Z

s ^ during the total measurement

time, t . M can differ somewhat along z and y axes, but it is calculable

from system parameters, such as fluid velocity, concentration etc. One

can realize that the concentration, which is built into M and N, has to be

initially assumed or assessed and that feedback iterative loops will be

generally included into the final numerical data interpretation, which

procedure is a routine when computers are utilized.

Eq . (14) can be used without joining P

s ^ with P and P^ only

when represents the total length of the system. This would be the case

when the detector is aligned along z-axis, receiving the non-attenuated

portion of the original radiation. Otherwise, when the detector is aligned

with y-axis, receiving the radiation scattered from the "ip" point (where

z and y axes intersect), as is the case in system from /10/, Eq. (14) has

to be used in such a way that the magnitudes it contains have to be evaluated

simultaneously with the ones built into the probabilities P^ and P^p , as

explained in next section.

4. 4. Probability P id

Based on identical considerations of random phenomena involved,

as done in section 4.3., one obtains the following final results:

E

df = k

1 Ay.IT [cfPc

(cf) ] . = k^yc af (15)

Ay = Y.

d/N

y

(16)

775
(17)

k

1 is the linear attenuation coefficient for the scattered (secondary)

radiation. Concerning its application, there are hardly any situations

where Eq. (17) would be used alone, i.e. without Eq's (8) and (14).

The procedure for the joint usage of eq's (8) and (14) and (17) is as

follows:

Two groups of random numbers, one of them containing N2

and the other N random numbers will be generated ( or selected from

tables) and thes^e two groups will be "paired" or associated with each other

also in a random manner; a third, independent random number will be

used to calculate b. Now, for each of these pairs, the following probability

will be calculated:

Psd Psi P

id P

ip

"< E

sf

+ E

df

+ W

e /\27T (18)

Finally, a linear average of PsC| will be calculated, after Eq . (18) was M

time used. If M ^ M ^ M , one can either work with a value of M •= z y (Mz

+ M ) /2 or do as follows: two groups of random numbers can be

paired and used as explained Mm

. times (where Mm

- is the smaller value,

say M2); then (i.e. P^) will be calculated (My - M^) times more

using the remaining groups of random numbers. At the end a proper

averaging, including P|

p

, needed to calculate the such combined F> sc| will be

performed. The simultaneous calculations of components within Psc| represents a certain constraint in the analysis of the composite random

phenomenon, occuring along axes z and y.

Looking at the exponent of Eq. (18),

Esd = Esf + E

df

+ (b/2) = ( ko^z) c

sf + (k 1 AY) c

df + (b/2) (19)

the following could be observed: if c values are randomly distributed about

c=0 (where C=C ). for very large values of M, N and N , both average

values c

s

j, and c will approach zero, which would render Pscj= 1 (because

b —* 0 in that case too), but as long as they differ from 0, the non-zero

positive multipliers in parentheses — see Eq. (19) — keep Escj ^ 0. Also,

three additive terms forming E

scj can have various signs at each of the M

implementations of eq's (18) and (19). Further on, the averaging of P

sc| is done by powers of E

scj, which is different than averaging E

sc| themselves.

Finally, looking deeper into the analysis, it could be anticipated that generally, even for M, and as large as desired, it has to be PSc| ^ 1 . Explanation for this is as follows. The spectral distribution of c, Eq . (8),

based on the philosophy which in /15/ renders Eq. (4) for velocities, assumes

the time-average value, C, as the most probable value in the same time,

which could be a matter for discussion. Obviously, the following holds for

the statistical (weighted) average: Cav>- C . If this would be taken in account

when performing an improved scaling of random numbers with fluctuating

concentrations, c, a shift would appear in final numerical results. In other

776
words, a bias would show up, resulting in a compulsory Esd ^ O ( and

Psd ^ 1 ) for any desired large values (even for infinitely large) of M, Nz

and N . But, even if accepting the spectral situation for concentrations

as given in /15/ for velocities, since generally C - C: ^ - C , a

III N

skewing of the probability spectrum exists due to the asymetry of its

cutt-off points. Therefore, the outlined probabilistic random number

interpretation (which is in no jeopardy because of this explanation) will

again result in the condition Psd ^ O for any duration of measurements.

Concerning the estimate whether Psd is ^1, the following holds:

P

sd ^>1 ifC^Cm and Psd<1 if C<CmJ whereCm=(Cmi + Cmx)/2.

This criterion emerges from a quantitative discussion of the cut-offs in

the Gaussian probability curve.

4. 5. Procedural remarks

Based on the analysis performed, it is evident that for finite,

even very long measurement times, the simple (linear) time-averaged

detector signals should not be directly implemented, i.e. used in equations

derived for ideal steady states. This holds for all systems where

fluctuations of any measurable property occurs with non-uniform probability.

Recording and a general statistical processing (seeking mean values,

deviations etc.) as thorough as possible of the signals should be performed

during various lengths of measuring intervals. This would at least provide

indications of various phenomena occuring in the system under consideration.

Very often, interpretation of signals' behavior in time can directly or

rather indirectly yield information needed in performing measurement

error reduction, such as the one which is the subject of this report.

The analysis outlined in previous sections, especially eq's

(1), (3), (8), (9), (12), (13), (15) through (18) represent all the essentials

necessary for a precise measurements interpretation procedure, which

can take care of those random phenomena which do not possess a selfcompensating feature in time. These phenomena, if not properly taken

in account, can represent a significant contribution to the measurements

errors. This kind of error would show up when direct, simple interpretation

of recorded data is done, when these data are directly caused by nonuniform random phenomena. Errors of this sort can exist for any desired

duration of experiments.

A complex algorithm, which represents the data interpretation/

measurement errors reduction procedure consists of the equations listed

in the previous paragraph, together with the analytical results of the

basic (steady state) phenomena innerent in the system under consideration.

These results, as derived in /8/, /9/ and /10/, pertain to a generalized,

more complex situation, where local values of concentration are measured,

having the entire instrumentation placed externally to the system. Further

on, the algorithm contains the assumptions - checking formulae (for

concentrations etc.), which represent self-correcting feedback inputs built

in corresponding iteration loops. A program corresponding to such an

777
algorithm is applicable to a variety of systems and can be executed

in a straightforward way on commercially available digital computers*.

5. Conclusion

In order to reduce measurement errors, particularly

when employing advanced indirect (contactless) methods needed for

aggressive, or high pressure/temperature/velocity multi-phase turbulent

flows, it is necessary to go beyond standard avenues and procedures of

improving hardware, instrumentation, recording techniques etc. It is

important to take in account properly and as accurately as possible all

the phenomena taking place in the physical macro- and micro-system

under consideration, which is the measured system, as well as those

taking place in the measureing system. This system is to be selected

carefully and attached to the original, existing system with the purpose

to render usable and reliable data, which can be successfully processed to

finally yield the desired results. The necessary correcting functions,

based on a probabilistic analysis of all statistically occuring phenomena

during the measurement are evaluated, their influence demonstrated

and a general accuracy-improving data interpretation procedure presented.

* The assistance of Ms. H. Wilson, Tampa, in the technical preparation

of this report is greatly appreciated.

778
References

1. Hooker, H. H. and Popper, G.F., A Gamma-Ray Attenuation

Method for Void Fraction Determination ... ANL~5766, Nov. 1958.

2. Kondic, N.N. , A Contribution to the Analysis of Real Attenuation

of the Penetrating Radiation Depending on the Elements of the Measured and

Measuring System, Colloque Euromech No. 7 sur la Mecanique des Liquides

Contenant des Bulles, April 23-26, 1968, Grenoble, France.

3. Sudhakar, N., Statistical Improvement in the Void Fraction

Determination with Nuclear Radiation , Thesis, Graduate School, Univers.

of Kentucky, Lexington (Mechan. Eng. College), 1970.

4. Sudhakar, N., Hahn, O. J. and Kondic, N., Channeling

Correction for Void Fraction Measurements, American Nucl. Society Meeting,

Nov. 1972, Washington, D.C.

5. Harms, A .A . , Lo, S. and Hancox, W.T., Measurement of TimeAveraged Voids by Neutron Diagnostics:, J. of Applied Physics, Vol. 42,

No. 10, Sept. 1971 .

6. Harms, A. A., Dynamic Effects in Radiation Diagnosis of

Fluctuating Voids, Nuclear Science and Engineering, 46, 1971 .

7. Harms, A. A. and Laratta, F.A.R., The Dynamic-Bias in

Radiation Interrogation of Two-Phase Flow, Internat. J. Heat & Mass

Transfer, Vol. 16, 1973.

8. Kondic, N. and Hahn, O.J., Theory and Application of the

Simultaneous Parallel and Diverging Radiation Beam Method in Two-Phase

Systems, Paper No. Mt.1.5., International Heat Transfer Conf. , VersaillesParis, France, 1970.

9. Kondic, N.N., Contactless Methods for Measuring Local Values

of Concentration and Temperature in One- or Multiphase Systems, International

Congress CHISA , Sept. 1972, Prague, Czechoslovakia.

10. McAdams, V.D., Kondic, N.N. and Baldwin, M.N., Determination

of Local Density by Gamma-Scattering Using External Means, American Nuclear

Society Meeting, June 1973, Chicago, Illinois.

11. Lapp, R.E. and Andrews, H.L., Nuclear Radiation Physics

(Englewood Cliffs, N.J., Prentice Hall, Inc. 1963).

12. Hinze, J.O, Turbulence (McGraw Hill Book Comp. New York, 1959).

13. Lin, C.C., Statistical Theories of Turbulence (Princeton University

Press, Princeton, N. Jersey, 1961).

779
14. Soo, S.L., Fluid Dynamics of Multiphase Systems (Blaisdel

Publishing Corp . , Waltham, Massachusetts, 1967).

15. Fortier, a. t Mecanque des Suspensions (Masson et Corp. , Paris, France, 1967).

16. Sokolnikoff, l.S. and Sokolnikoff, E.S., Higher Mathematics

for Engineers and Physicists (McGraw —Hill Book Corp. , New York & London 1941).

780
DUCT PORTION OF ANY, LENGTH DEPENDENT SHAPE

1 "4 IRREGULARLY SHAPED OBJECTS

NON-UNIFORM

VELOCITY FIELD VECTOR

PIGURS__1_

GENERAL 3-DIMENSIONAL FLOWING CONCENTRATION FIELD SITUATION

781
APPLICATION TO a CONCRETE bYSTEM (below) and STATISTICAL REPRESENTATION (up)

EXTERNAL </ALL VAKlAbLE POSITION

DETECTOR

m — FLOWING BOILING

T / SYSTEM

VARIABLE POSITION SOURCE

782
National Bureau of Standards Snecial Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

MEASUREMENTS OF DENSITY AND DENSITY GRADIENT

WITH AN OSCILLATING CONDUCTIVITY PROBE

Donald P. Delisi and Robert H. Kirchhoff*

Flow Research Company

A Division of Flow Industries, Inc.

Kent, Washington 98031

Density measurements obtained using single-electrode conductivity probes in a stratified salt solution are reported. A

comparison of vertical density profiles obtained from upward

and downward traversing probes show that measurement errors take

the form of a hysteresis loop. Non-dimensional plots of these

measurements characterize probe performance in terms of the

size of the hysteresis loop as a function of the parameters in

the experiment

.

A series of experiments were performed with vertically oscillating conductivity probes to decrease the hysteresis effect in the

density measurements. Typically, a probe was oscillated at a peakto-peak amplitude of 1 mm at a frequency of 20 Hz. Analysis of

the data yields, for a single dimensionless parameter, a range of

values over which the hysteresis effect is negligible. This parameter is a simple combination of the probe dimensions, gravity,

and the oscillation characteristics. The data indicate that,

above a certain value of the parameter, the hysteresis effect is

negligible regardless of the local density gradient.

Also reported are a theoretical development and results of

additional experiments, in which the oscillating conductivity probe

signal is analyzed to calculate the local density gradient. It is

shown that phase synchronous detection of the probe signal can

result in the direct measurement of the local density gradient.

Experimental data showing satisfactory agreement with the theoretical

results are reported.

Key Words: Conductivity probe; density; density gradient; stratified

flow; oscillating probe; experimental; laboratory; internal wave.

1. Introduction

Conductivity probes measure the electrical conductance between two

sensing elements. If the sensing elements are far from each other and if

one element is much smaller than the other, the probes are called single

electrode conductivity probes, and the measured conductance is essentially

the conductance of the fluid around the smaller element [l].** With one _

Consultant, Associate Professor of Mechanical Engineering, University of

Massachusetts, Amherst, Mass.

**Figures in brackets indicate the literature references at the end of the

paper.

783
sensing element much smaller than the other, the probes measure the conductance in a very small volume of fluid, and the conductivity measurements

become essentially point measurements.

In laboratory experiments investigating stratified fluids in water

tanks and water tunnels, it is common to use salt water as the working fluid.

In this case, varying the salt concentration changes the density of the

water and varies the stratification. Conductivity probes measure the conductance of the saline solution, and, using a prior calibration, we can

obtain the local density of the solution at a point. Errors in measuring

the conductivity of the fluid reflect as errors in determining the density

of the solution. Conductivity probes have been used as a laboratory tool for

the diagnosis of a variety of problems, including studies of internal gravity

waves [2,3], measurements of concentration profiles in reverse osmosis [4J

,

investigations of momentumless wakes [5] , and studies of the properties of

turbulent flows [6j.

In this paper we report density and density gradient measurements that

are obtained with single-electrode conductivity probes in a non-flowing,

stratified salt solution. We characterize the errors associated with measuring

density and density gradient with the macroscopic parameters of the conductivity

probe, as distinguished from the microscopic electrokinetics of the probe.

In section 2 we discuss the operating characteristics of conductivity probes

and the nature of the associated error. The reduction of the probe error by

forced oscillation of the conductivity probe is examined in section 3, and

the technique of oscillating the conductivity probe is extended to measurements of the density gradient in section 4. In section 5 we give a summary

and conclusions.

2. Operating Characteristics of Conductivity Probes

The experiments reported in this paper were performed with cylindrical,

single-electrode conductivity probes of characteristic probe-tip dimension a , operating in a non-flowing, stratified tank of saline solution. A schematic

drawing of a typical probe tip is shown in figure 1. The sensing element

in the probes is platinum wire. The exposed tip of the wire is covered with

a platinum black coating by using a commercial platinizing solution.

In this study we used two probe tip designs. In the first design, the

exposed wire tip is flush with the glass surface at the probe tip. In the

second design, the wire extends 1-1% wire diameters beyond the glass surface.

We found that this second design yields probes with a higher signal-to-noise

ratio than probes of the first design. The characteristic probe-tip dimension a is taken as the arithmetic average of the wire diameter and the

probe- tip body diameter.

Seven different conductivity probes were used in this study. Six of

the probes had glass tips and were similar in design to either the probes of

Gibson and Schwarz [l] or the probes of Mied and Merceret [7] . The tip of

the seventh probe was made of ADAPTIC, a commercial dental restorative

manufactured by Johnson and Johnson. In this study, the characteristic tip

dimension a ranged from 0.31 mm to 3.05 mm, and the diameter of the platinumwire sensing elements ranged from 0.05 mm to 0.81 mm.

Figure 2 is a schematic drawing of the experimental apparatus. The

experiments were conducted in a salt water tank measuring 150 cm long, 89 cm

deep, and 28 cm wide. A typical density-versus-depth profile used in these

experiments is also shown in figure 2. The profile consists of a linearly

784
stratified region at the top of the tank, with a density jump and a constant

density region at the bottom of the tank, below the stratified region. The

density gradient in the top region and the magnitude of the density jump

were varied in these studies. The conductivity probe was attached to a

traverse, which moved the probe vertically through the fluid.

We calibrated the probes by immersing them in salt water solutions of

known density and measuring the output voltage of the conductivity gauge

(Flow Research Model 1104) . From this calibration, we determined the transfer

function e = f(p) , where e is the measured voltage at the output of

the conductivity gauge and p = p(z) is the density of the salt water, where

z is the depth of the probe. For a given range of densities, the transfer

function is linear, and e = kp(z) , where k is a constant. The value of

k varies with the conductivity probe and the conductivity gauge. Typically,

for these experiments, k was approximately 250 volts cm

3 gm , and_the

measured voltage was linear with density between 1.008 and 1.023 gm cm

3

. A single-electrode conductivity probe measures the electrical conductance

of the fluid near the probe tip. Ideally, if the probe moves into a region of

different conductance or, alternately, if fluid of different conductance moves

past the probe tip, the probe measures the conductance of the new fluid. If

the working fluid were inviscid and if the probe worked ideally, the probe

would always measure the conductance of the new fluid. In reality, however,

some old fluid is always carried with the probe, with the result that the

probe reading is in error.

Conductivity probes are often used to measure internal wave motions in

stratified salt solutions [2,3]. In many applications, the conductivity

probes are stationary in laboratory coordinates, and the internal waves

propagate past the probes. In this study, we simulated this situation by

moving a conductivity probe vertically through a tank of stratified salt

water which was at rest in laboratory coordinates.

A comparison of vertical density profiles obtained from upward and

downward traversing probes show that measurement errors take the form of a

hysteresis loop. A typical density profile is shown in figure 3. In this

figure, the dashed line represents the true density profile. Assume a conductivity probe is positioned at depth and is allowed to reach equilibrium

at that depth. Now, we move the probe vertically downward through the fluid

at a constant speed U . At the depth Z2 , we reverse the probe motion

and the probe moves upward through the fluid at the same velocity U . At

the depth , we again reverse the motion of the probe, and the probe

traverses downward through the fluid. The density (inferred from the conductance) profile measured by this probe is shown by the solid line in

figure 3. Initially, the probe measures a density p^ at the depth Z-^ . As the probe traverses vertically downward through the fluid, the density

measured by the probe at a given depth is different from the true density

at that depth. This density difference reflects the fact that some fluid

from higher levels has been dragged to lower levels with the probe. When

the probe reaches the depth Z2 , the motion of the probe is reversed, the

probe now drags fluid from lower levels to higher levels, and, at a given

depth, the probe measures a density that is the true density at a lower

level. At the depth Z-^ , the probe again reverses direction with similar

results. Thus, we see that the measurement error takes the form of a

hysteresis loop in a depth-versus-density profile. Here, we define the

hysteresis loop error Ap^L as the density difference between an upward

and downward traverse.

785
Measured density profiles are shown in figure 4 for several traversing

speeds. In this figure, the true density profile (inferred from careful

static measurements of the density) has a constant gradient with depth, and

the Brunt-Vaisala frequency, defined as N = (- g/p dp/dz)^ is constant,

where g is the acceleration due to gravity. The data in figure 4 show

that the hysteresis loop error decreases as the traversing speed decreases.

This decrease in Ap^L occurs because the traversing time between two levels

is approaching the diffusion time of the fluid. Thus, for an infinitely slow

traverse speed, the fluid carried with the probe from another level will have

an infinite amount of time to diffuse away from the measuring volume of the

probe, and the probe will measure the correct density.

A dimensional analysis of the significant probe parameters yields three

independent, non-dimensional groups:

a Froude number =

a Reynolds number = — , and

a dimensionless number characterizing

the hysteresis loop error

where V is the kinematic viscosity of the fluid. In these experiments,

the Reynolds number was varied between 0.2 and 5.3, and the Froude number was

varied from 1.9 x 10~ 3 to 8.8 x 10 2

. Experimental measurements for four probes of different probe diameter

are shown in figure 5 for a variety of operating conditions. Figure 5 shows

that, for a given probe in a given density gradient, an increase in the

traverse speed produces an increase in Apm • Cross plots of this and other,

more extensive data show that, for a given probe and a fixed traverse speed,

an increase in the local density gradient will increase ^Pm • Also, for

a fixed probe traverse speed and a fixed density gradient, an increase in the

probe diameter will increase Ap^ . These results are summarized in table 1.

The results shown in table 1 indicate that, to reduce Ap^L » we must

make the probe as small as possible and the traverse speed as slow as possible,

and the density gradient should be weak. Thus, decreasing the probe size

not only increases the resolution of the probe, but also decreases the density

measurement error.

An immediate application of these results is that, for a stationary probe

that is measuring internal waves in a given density gradient, high-frequency

wave oscillations (corresponding to a large traverse speed) will have a larger error in the measured amplitude than will low-frequency wave oscillations. We can also use the data shown in figure 5 to estimate Ap^ for

a given probe moving in a given density gradient with a given traverse speed.

We can then use Ap^ to estimate the error in the measured amplitude of

an internal wave of a given frequency of oscillation.

3. Density Measurements With Oscillating Conductivity Probes

Using oscillating conductivity probes, we conducted a series of experiments aimed at reducing the hysteresis loop error. A schematic drawing of

the oscillating probe system is shown in figure 6, and a block diagram of

Ap

HL

g dz

786
the associated electronics is given in figure 7. In this study the probes

were oscillated vertically by using a solenoid, which was driven by a lowfrequency signal generator. The probe and oscillating system were driven

at the resonant frequency to achieve sufficiently large amplitudes. Typical,

maximum peak-to-peak amplitudes were 1 mm at a frequency of 20 Hz. The

vertical motions of the probes were measured with a Linear Variable Differential Transformer (LVDT) . The oscillating system was attached to the

traversing mechanism by thin, stainless-steel strips. A linear potentiometer

was also attached to the traverse for measuring the mean depth of the probe.

Figure 8 shows typical results of density measurements made with the

oscillating probes, for a linear density profile. In the case shown in

this figure, the traverse was run at its maximum speed, and the measurements

shown are for several amplitudes of oscillation A . The data shows that,

for a given traverse speed and a given density gradient, increasing the

oscillation amplitude decreases Ap^ . Oscillating the probe introduces two new parameters into the dimensional

analysis: the amplitude of oscillation A , and the frequency of oscillation

0) . The result is that there are now the following five non-dimensional

groups to be considered:

a Froude number =

1

a Reynolds number (Aoo)a

v

APHL

^

an error parameter = :

tt~ » g dp/dz

a velocity ratio = ^ , and

A

a geometric ratio = —

Note that the Froude number defined here is appropriate for the oscillating

case and is the Froude number defined in section 2 times the velocity ratio.

For these experiments, the velocity ratio is always greater than ten, the

Reynolds number spans the range between 55 and 440, and the frequency of

oscillation of the probe co is always considerably greater than the BruntVaisala frequency N , the ratio having values of 62 j< to/N j< 184.

Density measurements from an extensive set of experiments are shown in

figure 9. This figure plots the error parameter defined above versus the

Froude number squared. Data for seven different probes are shown for a

variety of operating conditions. The data show that the measurements from

all the probes collapse reasonably well onto one curve. The initial effect

of increasing the amplitude of oscillation while a given probe is traversing

a given density gradient is a decrease in Ap^ . If the amplitude of

oscillation is increased, Ap^ decreases, and the measured density approaches

the true density. The data shown in figure 9 are essentially independent

of the velocity ratio Aoo/U . We conjecture that local mixing generated by

the forced oscillation of the probe is responsible for the decrease of Ap^

as the amplitude of oscillation increases. We discuss the effects of this local

mixing on the flow in section 4.

787
The data shown in figure 9 indicate that for all probes there is a

single value of the square of the Froude number (Aco)2/ag « 0.6 above

which the magnitude of the hysteresis loop is negligible. In figure 10

we plot the amplitude of oscillation necessary to decrease ApTMr to zero

versus density gradient. This figure shows that the amplitude of oscillation for Apj^ =0 is independent of the value of the local density

gradient. The data shown in figures 9 and 10 are significant because they

imply that the errors in measuring density can be reduced for a given probe

by a judicious choice of the amplitude and frequency of oscillation and

that these errors will be independent of the density gradient. These results

differ from the non-oscillating probe results shown in table 1, where we

saw that increasing the density gradient increases the hysteresis loop error.

Thus, an experiment performed with oscillating conductivity probes can be

designed a priori for a single value of (Ao)) /ag _> 0.6 , independent of

the local value of the density gradient, and the hysteresis loop error will

effectively be reduced to a negligible value.

4. Density Gradient Measurements With Oscillating Conductivity Probes

By oscillating conductivity probes in the vertical direction, we

can also measure the local density gradient. This technique is an extension

of a similar technique used to measure local velocity gradients in air with

hot-wire probes [8,9].

We expand p(z) in a Taylor series about z D to get

p(z) = p(z

o ) +ff

A . 1 3 P Az +

2 72 Az

2

+

A^

dz'' z ^ 3z^ z o o o

3

Az

J

+

If we assume that the transfer function between the measured voltage at the

output of the conductivity gauge and the density of the salt water is

linear and of the form e = kp(z) (section 2), and if we introduce a smallamplitude harmonic perturbation Az = A sin oot , we may write the transfer

function as

dp(z

Q

) e(t)=k p(z)+A - sin U)t + • o dz

n + 6(A ,nw) (1)

where 6 indicates higher order terms. In eq. (1), we assume that the

amplitude of oscillation A is small compared to the characteristic length

scale of the change in density gradient.

We have performed experiments where phase-synchronous detection is used

to measure the coefficient of the first harmonic in eq. (1). The voltage

signal at the output of the conductivity gauge along with the signal from

the LVDT is fed into a Princeton Applied Research Model 129A lock-in

amplifier. The lock-in amplifier yields the rms amplitude of the coefficient

of sin oat in eq. (1), and a direct measurement of the local density

gradient dp(z )/dz is obtained. In the experiments, the densities

were in the linear range of the conductivity gauge, and the amplitudes of

oscillation were small compared to the thickness of an interface.

Typical density gradient measurements are shown in figure 11 for a density profile that is linear on top, constant on the bottom, and has a

788
density jump centered at z = 70 cm . In this figure, the solid line

indicates the density gradient, which was inferred from careful static

measurements of the density profile. The density gradient measurements

obtained directly from eq. (1) are shown for three amplitudes of oscillation for a single probe. The results show that the measured density

gradient approaches the inferred density gradient as the amplitude of

oscillation increases.

Figure 12 shows density gradient measurements from several experiments

using an oscillating conductivity probe. In this figure we plot the ratio of

the density gradient measured with phase-synchronous detection (eq. 1) to

the density gradient inferred from careful, static measurements of the

density profile versus the ratio of the amplitude of probe oscillation to

the characteristic probe-tip dimension. Two sets of data are plotted in

figure 12. We obtained the stationary measurements by positioning the

probe at a given depth and oscillating the probe with different amplitudes

of oscillation. For these measurements, the mean depth of the probe was

constant with time. We obtained the moving measurements in figure 12 by

oscillating the conductivity probe as it slowly traversed vertically through

the fluid. Thus, the mean depth of the probes was slowly changing with

time during these measurements.

The measurements in figure 12 show that the ratio of the measured

density gradient to the inferred density gradient approaches unity as A/a

approaches approximately 1.5. The moving measurements have a slightly larger

error than the stationary measurements.

The results shown in figures 11 and 12 are encouraging because they

show that local density gradient measurements can be obtained at a point

without either moving the probe or using two probes, which involves double

calibrations.

We examined the effect on the fluid of oscillating the probe to determine

if the mixing generated by the oscillations is significant. To determine

the effect of oscillating the probe, we monitored the stationary density

gradient measurements as a function of time. (The density gradient measurements were monitored since we believed that mixing effects would show up in

measurements of the density gradient more rapidly than in measurements of

the density itself.) The results of the preliminary measurements indicate

that mixing does not affect the measurements of the density gradient until

at least three to five minutes after the oscillation of the probe has started.

We therefore believe that oscillating conductivity probes initially have

very little effect on the structure of the local density field.

5. Summary and Conclusions

This paper illustrates some of the errors in measuring density in nonflowing, stratified salt solutions. The errors take the form of a hysteresis

loop in profiles of density versus height. The error in the hysteresis loop

is a function of the probe, the density gradient, and the speed of traverse,

or, alternately, in the case of a probe fixed in laboratory coordinates,

the frequency and amplitude of internal waves passing by the probe.

The hysteresis loop error can be significantly reduced by oscillating

the probe. We present measurements which show that the hysteresis loop

error can be effectively reduced to a negligible value if the square of

the Froude number is approximately 0.6 or larger. This result is substantiated

for several different probes and is independent of the local value of the

789
density gradient. The result is significant since it allows investigators

to design an experiment with a priori knowledge of the errors that will be

associated with the measurements of density and permits the design of

experiments with reduction of this error.

By properly analyzing the signal from a vertically oscillating conductivity

probe, we can also obtain a direct measurement of the local density gradient.

Our measurements show that the measured density gradient approaches the

inferred density gradient obtained from static measurements of the density

profile as the ratio of the amplitude of the probe oscillation to the characteristic probe tip dimension approaches 1.5. This method offers a unique

technique of directly measuring the local density gradient in stratified

salt-water solutions.

Acknowledgments

The authors would like to express appreciation to the Geophysical Fluid

Dynamics Laboratory/NOAA at Princeton University, where the experiments were

performed. We would also like to thank Princeton Applied Research Corp. for

the use of a lock-in amplifier during the course of these measurements. The

first author would like to express his appreciation to the National Research

Council for the support of an NRC/NOAA Resident Research Associateship

during part of this investigation. Part of the analysis of this data was

supported by Flow Research IR&D funds.

References

[l] Gibson, C. H. and Schwarz, W. H. , Detection of conductivity fluctuations

in a turbulent flow field, J. Fluid Mech. 16 , 357-364 (1963).

[2] Delisi, D. P. and Orlanski, I., On the role of density jumps in the

reflexion and breaking of internal gravity waves, J. Fluid Mech . 69 , 445-464 (1975).

[3] Martin, S., Simmons, W. , and Wunsch, C, The excitation of resonant

triads by single internal waves, J. Fluid Mech. 53 , 17-44 (1972).

[4] Hendricks, T. J. and Williams, F. A., Boundary layer flow problems in

desalination by reverse osmosis, Dept. of the Interior, Office of

Saline Water, Grant No. 14-01-0001-951, Final Report (1970).

[5] Stockhausen, P. J., Clark, C. B., and Kennedy,- J. F., Three dimensional

momentumless wakes in density stratified liquids, MIT Hydrodynamics

Laboratory Report No. 93 (1970).

[6] Gibson, C. H. and Schwarz, W. H., The universal equilibrium spectra of

turbulent velocity and scalar fields, J. Fluid Mech. 16, 365-384 (1963).

[7] Mied, R. P. and Merceret, F. J., The construction of a simple conductivity

probe, Johns Hopkins University Report, Department of Mechanics (1970).

[3] Kirchhoff, R. H. and Voci, E. K. , Direct measurement of the velocity

gradient in a fluid flow, AIAA J. 10, 1119-1120 (1972).

[9] Kirchhoff, R. H. and Burbank, R. A., Response of a hot wire oscillating

in a shear flow, AIAA J. 12, 96-98 (1974).

790
Table I Probe Response Functional Relation

DEP \ INDEPENDENT

VAR. \ VARIABLES

A(? hl\ \

"

1

a \.

\

de/dz \

INC INC FIX FIX

INC FIX INC FIX

INC FIX FIX INC

791
Figure 1 Schematic Drawing of Conductivity Probe Tip

89 cm

Density

150 cm "-j

Figure 2 Schematic of the Experimental Apparatus

792
f

Q2

Density

ure 3 Schematic of a Typical Depth-Versus-Density Profile

for a Traversing Conductivity Probe. The True

Density Profile is shown by the Dashed Line; the

Measured Profile is shown by the Solid Line.

A@hl is the Hysteresis Loop Error.

793
Depth

Density

Figure 4 Measured Density-Versus-Depth Profiles for Two

Traversing Speeds; dgldz = 4.4 x 10"4 gm/cm4

794

Linear

Potentiometer

Traverse

Conductivity

Probe

LVDT Plunger

(Attached to Probe Holder)

Solenoid Plunger

(Attached to

Probe Holder)

Figure 6 Schematic of the Oscillating Probe System

796

Depth

Density

Figure 8. Measured Density Versus Depth Profiles For An

Oscillating Probe; a = 0.305 cm, U = 9.4 cm/min,

dg/dz = 4 x 10-4 gm/cm4

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802
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

NEW TECHNIQUES FOR AUTOMOTIVE FUEL FLOW MEASUREMENTS

Milton Baker

General Motors Proving Ground

Milford, Michigan 48042

1 . Introduction

This paper discusses techniques for making accurate automotive fuel economy

measurements using an in-line flow transducer and an electronic display unit. The

paper reviews the fuel delivery system of a conventionally carbureted vehicle and

describes some of the sources of flow measurement errors this system introduces. Design requirements for automotive fuel flow measurement instrumentation are developed

and techniques are presented for making accurate flow measurements in the presence

of these error conditions.

The descriptive material presented is general in format as each vehicle manufacturer has different design requirements for the fuel delivery system. Testing, however,

has shown this information applicable to vehicles from a number of different vehicle

manufacturers

.

2. Fuel Delivery System - Conventionally Carbureted Vehicle

The fuel delivery system of a conventionally carbureted vehicle shown in Figure 1 consists of three major elements: the fuel tank, the fuel pump, and the carburetor.

FIGURE 1 . SIMPLIFIED FUEL DELIVERY SYSTEM DIAGRAM - CONVENTIONAL CARBURETOR

8a3
The fuel tank functions as the primary fuel reservoir for the vehicle. The fuel

pump draws fuel from the tank and supplies it under pressure to the carburetor for

metering into the engine.

Many vehicles contain fuel pumps with a bypass or vapor return line. On each

output stroke of the pump, fuel is delivered primarily to the carburetor with a portion

returned to the fuel tank. Orifices in the fuel pump outlet line and bypass line determine the flow rate ratio between fuel flow to the carburetor and return flow to the

fuel tank.

The function of the circulating fuel loop between the fuel tank and fuel pump is to assure that cool, liquid fuel is supplied to the carburetor. This eliminates adverse

vehicle performance due to vapor formation in the fuel line.

Fuel from the fuel pump outlet is delivered to a secondary fuel reservoir in the

carburetor called the float bowl . A needle valve and float system maintain a predetermined level in the float bowl to assure adequate fuel delivery to the engine

during transient conditions. When the level in the float bowl falls, the needle valve

opens admitting fuel to the chamber until the predetermined fuel level is again

reached

.

It should be noted that the float bowl reservoir acts as a buffer accumulator between the fuel line and fuel consumed by the engine. During transient operations,

fuel will begin flowing into the engine before the float level drops enough to admit

fuel from the fuel line. Virtually all types of transducers which measure fuel flow into

the float bowl will produce flow data which lags actual consumption during transient

operation

.

3. Potential Sources of Flow Measurement Errors in the Fuel Delivery System

Extensive study of the conventional vehicle fuel delivery system has isolated three

major sources of error -producing flow conditions: reverse fuel flow, pulsating fuel

flow, and fuel vapor.

A. Reverse Fuel Flow

Reverse fuel flow is a condition where fuel flows from the carburetor back to the

fuel pump or tank during normal steady-state or transient driving conditions.

In order to understand the cause of reverse fuel flow, it is necessary to examine

the vehicle's fuel pump shown in Figure 2.

804
IAPHRAM

JTLET CHECK

VALVE INLET VALVE

OUTLET

REVERSE FLOW

PATH

INLET

VAPOR RETURN

FIGURE 2. MECHANICAL FUEL PUMP

The fuel pump is a mechanically driven diaphram device. In operation, as the

rocker arm driven by the engine camshaft moves down, fuel is drawn into the pump

through the inlet valve. A check valve prevents any fuel from being expelled at the

outlet. As the rocker arm moves up, fuel is displaced out of the pump chamber through

the outlet line to the carburetor.

It can be seen that on the positive stroke of the fuel pump, when the outlet check

valve is closed, a common chamber is formed between the outlet line and bypass line.

Fuel from the carburetor at a higher pressure can flow through the outlet orifice to

the fuel tank via the bypass line orifice.

Any element of compliance in the fuel line, such as vapor, exaggerates this

condition. Large relative forward and reverse fuel displacements cause errors in inline flow transducers.

This condition was first observed using high-speed motion picture photography

with a turbine-type in-line flow transducer. Reverse flow produces large errors in

transducers which are unable to determine fuel flow direction. Most transducers used

in fuel consumption measurements cannot distinguish forward and reverse flow. Any

flow, regardless of direction, causes the transducer to indicate fuel consumed. Without flow magnitude and direction sensing, in-line flow transducers have been observed

to indicate as much as 100% higher than actual fuel consumption.

805
Another situation where reverse fuel flow is a serious error contributor is during

long-term tests where the vehicle is turned off and then restarted.

When the vehicle is turned off, the fuel line will eventually drain from the carburetor to the fuel tank through the bypass line or system check valves. This fuel

must be subtracted from the total; otherwise, when the vehicle is restarted, fuel necessary to charge the lines will be counted as fuel consumed. This can produce errors as large as 100-200 cm^ of fuel consumed.

Because of errors contributed by reverse flow during vehicle operation, a design

requirement for any in-line flow transducer is the ability to sense flow magnitude and

direction . In addition, dither conditions where fuel is oscillating in the fuel line

must produce a zero net flow indication.

B. Pulsating Fuel Flow

A second source of measurement error is pulsating fuel flow. The output pressure

waveform from a mechanical fuel pump is shown in Figure 3.

ILU

32

Ol w

=> a: a. o

-J CO M M

D E

u. a. AVERAGE VALUE* 48 kPA

TWICE

ENGINE

TIME (SECONOS)

FIGURE 3 . PRESSURE VS. TIME WAVEFORM FOR AUTOMOTIVE FUEL PUMPS

The superimposed time varying portion of the waveform, together with fuel line

resonances, produces pulsating flow. In addition, the needle valve opens and closes

periodically allowing fuel to surge into the float bowl . As with reverse flow, any

element of line compliance magnifies the effect. These pulsating conditions can

produce a water hammer effect causing the transducer to move in response to pressure

pulsations

.

806
Certain types of transducers, such as the turbine type, when excited by a pressure

pulse continue to rotate due to paddle wheel inertia after fuel has stopped flowing.

This "overcoasting" response to fluctuating pressure conditions in the fuel line can produce large errors in flow measurements.

C . Fuel Vapor

A third error source in automotive in-line fuel flow measurement is from fuel line

vapor. Vapor is usually formed by excessive temperature conditions somewhere in the

fuel line. The Reid Vapor Pressure (RVP) of fuel is an indication of the temperature at

which fuel will vaporize. Different RVP fuels are used by customers in different ambient environment operating conditions to minimize the problem of engine vapor lock.

Volumetric transducers are very susceptible to vapor-induced measurement errors,

due to the volumetric difference between a quantity of fuel in the liquid or vapor

state. If the transducer rotating element is displaced by fuel vapor instead of liquid

fuel, the transducer will indicate much higher flow rates than are actually encountered.

Transducers which operate with differential pressure across an orifice will produce

erroneous outputs when vapor is present in the flow orifices. Vapor collecting within

a transducer may cause the transducer to cease functioning as no fuel is present to make

the transducer rotate.

4. Criteria for Automotive Fuel Measurement Systems

Many types of fuel transducing devices exist today employing a wide range of

physical principles to produce outputs proportional to fuel flow rate.

The choice of a transducing technique is often dictated by practical considerations. The automobile manufacturers, United States Government agencies, and independent testing organizations perform fuel economy measurements on large vehicle

fleets, using short-term, high-resolution tests run by unsophisticated test personnel.

These considerations dictate an easily installed and easily operated device capable of producing high-resolution measurements. Generally in-line flow transducers

tend to fulfill these design requirements.

Other techniques such as gravametric and carbon balance measurements tend to

be much more difficult to install and require sophisticated test personnel. These

techniques are generally not applicable to vehicles operating on road test schedules

and are usually confined to laboratory environments.

The in-line flow transducer element is compatible with testing goals of multiple,

short-term, high-resolution automotive fuel flow measurements.

807
1 . In-Line Flow Transducer Specifications

a . Flow Rate Range

A practical system must be capable of covering the .5 cm^/s-20 cm^/s flow

rate range in order to be able to measure idle fuel flow on subcompact vehicles and wide open throttle conditions on large vehicles.

b. Linearity

The device should produce indicated readings which are within ±1% of

actual readings over the .5 cm3/s-20 cm^/s flow rate range. Society of

Automotive Engineers' specification J1082 calls for cumulative fuel consumption readings to be within .5% of actual values. A device with a ±1%

of reading error versus flow rate curve situated symmetrically around the

zero error line can meet this specification.

c. Resolution

With emphasis on vehicle fuel economy and projections for more fuelefficient vehicles, resolution becomes important. A practical cumulative

fuel measurement resolution is .1 cm^.

The Society of Automotive Engineers' J1082 specification requires 3.785

cm^ resolution (.001 gallons); however, for many test schedules, this res- olution is too course to resolve the .5% of reading accuracy specification.

d . Pressure Drop

For any in-line transducer, pressure drop is an important consideration. Too

large a pressure drop can affect vehicle performance. A specification of

14 kPa maximum pressure drop at 20 cmys has been found to have minimal

effect on vehicle operation.

e. Bidirectionality

A transducer must maintain the same pressure drop and "K" factor (fuel

displacement/revolution) in both directions so that reverse flow may be

measured and accounted for.

f. Safety

Transducers which mount in the passenger compartment without outside

venting, or have glass burettes which could become broken in the passenger

compartment, could pose a safety hazzard. Any electrical wiring should

be explosion-proof.

808
Ease of Installation

As previously mentioned, the ability to mount the transducer quickly on

board the vehicle greatly facilitates testing programs.

A wide variety of commercially available transducers have been evaluated

against these design specifications at General Motors Proving Ground. Devices which perform flow filtering, use auxiliary fuel pumps, pressure regulators and pulsation dampers have been found unacceptable because of

alterations to the vehicle fuel delivery system. Devices which consume

large amounts of electrical power, such as electrically driven pumps, may

also influence fuel economy.

Turbine type flow meters can meet pressure specifications, but are subject

to reverse flow and pressure pulsation errors associated with the dynamics of

the internal paddle wheel.

Differential pressure drop across an orifice devices seldom can meet dynamic

range specifications without multiple orifices and a complicated hysteresis

switching system. The problem of orifice switching in the presence of dynamically changing flow conditions produces errors.

Vane type transducers are sensitive to pressure pulsation and reverse flow

conditions. Multiple chamber reservoir systems where fuel fills one reservoir while the vehicle runs on the other reservoir have high pressure drops

and leakage associated with solenoid switching times.

Testing has shown the positive displacement transducer the best choice.

Positive displacement transducers are affected by reverse flow and vapor;

however, are not subjected to inertia I coasting effects. Only fuel moving

through the transducer will cause the device to rotate. Fuel present at the

outlet will inhibit further rotation.

A positive displacement transducer can be made bidirectional so that fuel

displacement/revolution is the same in either direction.

The important characteristic of the positive displacement device is that

barring vapor and leakage only precise quantities of fuel through the measurement element will cause the device to rotate.

Positive displacement transducers are subject to leakage errors through the

device which are usually prevalent at low flow rates. Vapor causes large

errors in positive displacement systems. No positive displacement transducer is capable of accurate flow measurements without external electronic

hardware to recognize and correct for various error conditions.

809
2 . Electronic Specifications

The previous sections discussed sources of error and the selection of a positive

displacement flow transducer as a best choice. No positive displacement transducer evaluated was capable of eliminating error source contributions.

A strategy was adopted employing a four-piston positive displacement transducer

with an integrated electronics unit to recognize error producing flow conditions

and to correct for them. The concept of an underhood mounting transducer and

manifold assembly and a dashboard mounting electronics signal conditioning and

display unit forms the basis for a General Motors -designed precision fuel measurement system shown in Figure 4. This section describes the design of the electronics unit. These techniques have general application in flow measurement

systems

.

MOOIt M

IHNHHH HHI MHm

FIGURE 4. MODEL 76 PRECISION FUEL METER

5. Techniques For Reducing Contributions From Sources of Error

A. Reverse Flow Errors

A primary error contributor is reverse fuel flow, where fuel is flowing from the

carburetor to the fuel tank during normal vehicle operation. To make accurate flow

measurements with reverse flow present, fuel flow magnitude and direction must be

sensed

.

810
Most all in-line positive displacement flow transducers convert rotational motion

of the transducer element to an electronic signal with optical electronics, hall effect

switches, reed switches, etc.

A way to produce flow magnitude and direction signals is to place two pick-up

devices 45° apart so that a quadrature phase signal is produced. This is shown schematically using an optical technique in Figure 5.

PICK UP A _JLJLJi_n_ji_n_n_n_

_r i_j—l__t

PICK UP B _r

FUEL FLOW

SIGNAL

SIGNAL A

SIGNAL B

FIGURE 5. QUADRATURE SYSTEM

Each edge of the signal A represents a quantity of fuel flowing. Signals A and

B are sent to an electronic circuit which differentiates signal A to produce fuel flow

magnitude and uses signals A and B to decode fuel direction, using the algorithm shown

in Figure 6.

TRANSITION OF A STATE OF B DIRECTION

_r LOW FORWARD

HIGH FORWARD

HIGH REVERSE

LOW REVERSE

SIGNAL A

SIGNAL B

FUEL FLOW

SIGNAL

DIRECTION

J l_l L

jLJi_ji_fLJLJL_Ji_riri_n_n_Ji FFFFFFFFR FFF

FIGURE 6. QUADRATURE ALGORITHM AND ILLUSTRATION

811

199.8

UP/ DOWN

TOTALIZER
The flow magnitude and direction information signals are sent to an up/down fuel

flow counter. Magnitude pulses with forward direction information cause the counter

to increment; magnitude pulses with reverse direction information cause the counter

to decrement.

With this technique, all forward and reverse fuel flow is accounted for. This

technique has been found very effective in reducing reverse flow errors.

B. Msating Fuel Flow Errors

As shown in the quadrature phasing diagram of Figure 6, should the transducer

dither (oscillate forward and backward a short distance) at a pick-up site, forward and

reverse counts are added and subtracted with a zero net flow indication. This technique is effective in eliminating pulsating flow errors.

C. Vapor Induced Errors

A major source of measurement error affecting in-line flow transducers is fuel

vapor. Vapor conditions are primarily the result of excessive temperature conditions.

Vapor induced errors can be controlled in a number of ways. Since vapor is primarily produced by high temperature, the transducer should be located where it will

remain cool

.

As previously mentioned, using a fuel with a lower Reid Vapor Pressure will help

eliminate any temperature problems.

With many installations, however, alternative techniques must be used. Two

effective techniques are vapor elimination and optical vapor detection.

Vapor Elimination

A vapor eliminator at the inlet to the transducer has been effective in eliminating

system vapor. Although this vapor represents fuel lost, it is eliminated prior to the

transducer so that vapor loss is not a source of measurement error.

An effective vapor eliminator is shown in Figure 7.

812
VENT VALVE

FLOAT

FUEL RESERVOIR

3- FUEL INLET TO TRANSDUCER

FIGURE 7. VAPOR ELIMINATOR DETAIL

Vapor which is lighter than liquid fuel rises as liquid fuel moves down toward the

transducer inlet. As more vapor and less fuel enter the chamber, the float falls allowing the vapor to vent to atmosphere. When the fuel becomes almost totally vapor, the

vapor eliminator may become ineffective and vapor will move into the transducer producing measurement errors.

Optical Vapor Detector

To warn the operator that vapor is passing through the transducer, an optical vapor

detector can be incorporated in the transducer manifold.

The optical vapor detector contains a light emitting diode and phototransistor

focused across a clear glass tube in which fuel is flowing.

Normally, the fuel maintains a clear optical path allowing the light emitting

diode to sustain the phototransistor in a saturated state. When a bubble is present,

an optical distortion is produced at the liquid-vapor interface (meniscus) which momentarily upsets the optical path and turns off the phototransistor. Phototransistor turnoff

is connected to an audible warning device indicating the presence of vapor. The unit

is shown schematically in Figure 8.

GLASS TUBE .LIGHT EMITTING DIODE

OPTICAL PATH

PHOTO TRANSISTOR

FIGURE 8. OPTICAL VAPOR DETECTOR -SIDE VIEW

813
Vapor elimination and optical vapor detection have been found effective in

reducing vapor induced errors.

D. Additional Considerations

1 . Conversion to Engineering Units

Each transducer element is configured to produce electronic pulses to indicate the

number of times the transducing element was rotated. Each transducer will have

a slightly different fuel displacement/revolution or "K" factor due to machining

and assembly tolerances.

Precision fuel measurement requires each transducer to be individually calibrated

and its "K" factor used to generate a conversion from transducer rotations to

engineering units (cm^ of fuel).

A technique which has been incorporated in the General Motors Precision Fuel

Meter is to store an 8-bit binary representation of the "K" factor for each transducer in the transducer manifold. This binary word programs the electronics display unit to correctly convert transducer pulses to engineering units. This technique permits transducers to be used interchangeably with electronics display

units.

As an example of how this works, consider a transducer which displaces 10.8 cm^

of fuel per revolution. If there are ten evenly spaced electronic pulses generated

for each transducer revolution, each electronic pulse represents 1 .08 cm3 of fuel.

For this transducer, the number 108 would be stored in the transducer manifold.

The electronics uses the binary number representing 108 to cause exactly 108

high-frequency pulses to be generated for each electronic pulse from the transducer (effectively multiplying the number of input pulses by 108). The highfrequency pulses are divided by 100 so that the first pulse from the transducer

produces 1 pulse output from the divide-by-100 circuit with a residual of 8 left

in the divider.

The first 12 transducer pulses produce 12 output pulses from the divider with a

residual of 96, and the display will read 12. When the next pulse from the transducer is received, 108 pulses are produced by the high-frequency clock and the

display increments by 2 (96 residual plus 108 divided by 100 equals 2.04) and

indicates 14 correcting the display since each transducer pulse represents 1 .08

cm^ of fuel . The electronics will continue to correct throughout the measurement period. Figure 9 shows in detail the quadrature detector integrated with

the engineering unit converter and totalizer.

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2 . Electrical Noise Immunity

Many fuel -measuring devices are connected to the vehicle electrical system and

therefore are subject to a very noisy, poorly regulated power source. Care must

be taken to ensure that data is actual and not the result of transient electrical

noise produced by the vehicle electrical system.

Techniques which increase system noise immunity including isolating power

supplies, high noise margin logic such as CMOS, shielding, transient suppression,

and extensive filtering at high and low frequencies should be incorporated. It is also recommended that test instrumentation be shielded from sources of Radio

Frequency Interference.

3. Data Displays

Three basic display parameters are desirable in an automotive fuel measurement

device: cumulative cm^ of fuel, elapsed test time, and fuel temperature.

Cumulative fuel measurements with elapsed time information can be used for

totalized fuel measurements or flow rate information. Fuel temperature information is required for volumetric temperature corrections. One degree celcius

readout accuracy allows volumetric correction to within . 1%.

In addition, a display of transducer outlet gauge pressure is often desirable to

ensure correct operation of the transducer element. Low outlet pressure (with

respect to atmospheric pressure) indicates incorrect operation of the transducer

element

.

4. Display Technology

A wide range of display technologies are available to designer. Analog meters

for flow rate measurement can generally become damaged in the vibratory automotive environment.

Digital displays for automotive use require high intensity for readability on high

ambient light days and low ambient light levels for nighttime viewing.

Planar gas discharge displays have been found to be intense enough for daytime

viewing and with a dimming circuit acceptable for nighttime use. No other type

of display appears to provide this much dynamic intensity.

6. Calibration And In-Vehicle Accuracy Verification

Two types of testing are required to assure the accuracy of instrumentation used

for precision automotive fuel flow measurements. Laboratory calibration is used for

setting "K" factor and checking the operational accuracy of the device.

816
In-vehicle accuracy verification is used to assure that the device works correctly

in the actual measurement environment (the automotive fuel system). A large number

of devices advertised as fuel economy measurement instruments have never been accuracy tested on an operating vehicle.

A. Laboratory Calibration Techniques

A laboratory calibration facility should be capable of producing accurate, repeatable fuel flow while simulating conditions encountered in the vehicle fuel delivery

system. The calibration facility in Figure 10 meets these design requirements.

FUEL METER UNDER TEST

_J

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MOTOR DRIVEN

UEL RESERVOIR AUTOMOTIVE FUEL

_\

ROTAMETER FLOW

CONTROL

NBS TRACEABLE BURETTE

PRECISION

ELECTRONIC FLOW

FILL

SOLENOID

EVAC. PUMP EVAC. SOLENOID

CUTOFF

FLOW CONTROL

CONSOLE

99.9~|

NBS \

TRACEABLE TIMER

FIGURE 10. PRECISION FUEL METER CALIBRATION FACILITY

A fuel reservoir is used to store calibration fuel. The mechanical fuel pump

driven by an electric motor causes fuel to flow through the fuel meter under test into

a National Bureau of Standards traceable burette system. Calibration fuel should be

of the type the fuel meter is to be used with so that viscosity induced errors show up

during calibration.

In operation, a console starts fuel flowing through the fuel meter into the burette

system. The rotameter is set for an approximate flow rate. The exact flow is determined at the end of the test. The console control will then evacuate fuel to the zero

line on the burette. An electronic shutoff closes the evacuate solenoid precisely when

the zero line is reached.

817
In the run condition, fuel flows through the fuel meter into the burette. When a precise fuel level is reached, the electronics simultaneously shuts off the fuel meter

under test, the burette fill solenoid, and a National Bureau of Standards traceable

timer

.

Three numbers are obtained at the conclusion of the test: cm^ of fuel in the

burette, indicated cm^ from the fuel meter under test, and test time from the precision

timer.

Burette cm^ divided by test time produces test flow rate. Percentage error is computed by comparing burette cm^and indicated cm^ from the fuel meter.

A graph can be plotted expressing percentage error versus flow rate for the fuel

meter under test. Figure 1 1 shows a sample data table and graph.

BURETTE cm3 METER cm3 A cm3 TIME (s) FLOW RATE PERCENT ERROR

1000.0 999.0 -1.0 322.87 3.097 -.1

1000.0 998.0 -2.0 500.0 2.00 -.2

PERCENTAGE ERROR VS FLOW RATE (FUEL METER S/N 67)

PERCENTAGE -j

ERROR -2

-.3

0 I 2 3 4 5 6 CM°/S

FIGURE II. SAMPLE CALIBRATION DATA

B. In-Vehicle Accuracy Testing

Any on-board fuel measurement system must be tested for accuracy on an operating vehicle. A technique has been developed using a small, light, aluminum alternate source fuel tank for in-vehicle testing.

A test system is shown in Figure 12. The alternate source fuel tank is closely

coupled to the fuel pump to minimize non-repeatable line initialization problems.

The fuel tank is connected to the fuel pump with quick disconnect type fittings.

818
FUEL METER

ALTERNATE SOURCE

FUEL TANK

\

FUEL PUMP

/

/

9

SHORT FUEL LINES CARBURETOR

FIGURE 12. IN-VEHICLE TEST INSTALLATION

The tank is weighted prior to connection to the fuel pump. When the test commences, the fuel meter is actuated and the vehicle driven in a dynamometer. Temperature conditions can be varied within the dynamometer cell.

Fuel temperatures should be sampled and logged during vehicle operation.

At the conclusion of the test, the tank is uncoupled from the vehicle and weighted.

Knowing the fuel density accurately for the test conditions, calculated fuel consumption

can be obtained from the following formula:

initial weight — (grams) - final weight (grams) 3 r r i j

2-;—*2 L _ 2 i» L = cm <-> of fuel consumed

density at test conditions

This number can be compared with measured fuel consumption data from the fuel

meter with volumetric corrections made for temperature changes. Using this technique,

a percentage error can be calculated for a fuel meter installed on an operating vehicle.

819
7. Conclusion

The techniques presented in this paper of bidirectional counting, vapor elimination and optical vapor detection, individual transducer calibration and digital

conversion of data to engineering units, electronic noise suppression, precision calibration techniques and the use of a positive displacement fuel transducer have been

found effective in reducing the sources of error on fuel measuring systems.

These techniques have been incorporated in a precision fuel measurement system

designed by General Motors Corporation.

Although the paper focuses on techniques for reducing fuel flow measurement

errors on conventionally carbureted vehicles, many of these techniques are directly

applicable to fuel economy measurements on fuel injected vehicles, diesel engine

vehicles and vehicles with non-standard fuel delivery systems. Further information

on application of these techniques to any of these vehicles may be obtained by contacting the author at General Motors Proving Ground.

820
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS

,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

DIGITAL COMPENSATION TECHNIQUES FOR POSITIVE-DISPLACEMENT AND

TURBINE FLOWMETERS

Roger Jennings

Fluidyne Instrumentation

Oakland, California 94612

INTRODUCTION

Limitations in the availability of fossil fuels, natural gas,

and other energy resources due to physical and geopolitical

factors have, in recent years, increased the price of these

products by as much as a factor of five. During the next 20

years, prices of both petroleum and natural gas are expected

to increase at a rate substantially in excess of, and will

thus contribute greatly to, the rate of inflation. While

conservation of these resources by the fundamental laws of

economics combined with government intervention in the production and consuming segments of the economy will undoubtedly

result in improved conservation practices, virtually all projections show increasing usage of these vital raw materials

through at least the year 2000.

The first step in any conservation program must be the accurate determination of production and consumption quantities.

For conservation programs to be effective, these measurements

must be made with sufficient accuracy and resolution to allow

the determination of the effects of incremental conservation

measures. Further, because of increasing cost of petroleumbased fuels and their petrochemical derivatives, accurate

measurement of product delivery and consumption, whether in

pipelines, tank trucks, rail cars or ships, as well as within energy and raw material consuming processes themselves,

must be made to assure proper billing for these products or

to allocate their costs for accounting purposes.

Transportation vehicles, of course, constitute one of the

major sources of fossil-fuel consumption in all developed

countries. Industry-sponsored and governmentally-imposed

fuel economy improvement programs are designed toward the

goal of resource conservation. Here again, accurate measurement of fuel consumption under both test-stand and in-vehicle

conditions must be obtained. Rationalization of present dynamometer data obtained under simulating driving cycles with

that achieved by normal users of the vehicle must occur if

meaningful fuel economy data for consumer guidance is to be

prepared. For instance, current consumer fuel consumption

data prepared by the Environmental Protection Agency differs

821
substantially from that obtained by in-vehicle measurement

of fuel consumption with professional drivers under simulated

normal-use conditions [1]

.

1

Measurement of consumption of petroleum products and petrochemicals is determined primarily by flow transducers. These

range from simple orifice or venturi devices to highly sophisticated positive-displacement meters. Turbine, gear and

piston-type positive-displacement, and vortex-shedding flowmeters are most often used where accurate flow measurement

under a wide range of operating conditions is required. The

electrical output of both turbine and vortex-shedding flowmeters is inherently digital in nature, while positive-displacement flowmeters are available with both pulse and digital

outputs. The introduction of digital integrated circuits, and

particularly large-scale integration (LSI) techniques has reduced the cost of digital electronic systems to the point where

they are used on virtually an exclusive basis in instruments

for the determination of volumetric flow.

Petroleum products are universally sold on a volumetric

basis (gallons, cubic meters, etc.), however their fuel value

is related to weight (btu/pound, calorie/gram, etc.). The

determination of flow rates in continuous operations or charge

quantities in batch processes in the chemical or petrochemical

industry is also based on weight. For this reason, conversion

of the output of the flow transducer, basically a volumetric

device, must be made to gravimetric or standard volumetric

units (related to a specific reference temperature) to provide meaningful data. Mechanical temperature-compensation

methods for positive-displacement flowmeters (such as ball

and disk integrators or gear-changing devices) and electronic

systems for turbine and vortex-shedding flowmeters have been

developed with widely-varying cost/accuracy relationships.

Compensation for fluids having non-linear specific gravity

change with temperature have been difficult, if not impossible

to achieve at reasonable cost using techniques employed to

date

.

This paper outlines a new technique for both linear and nonlinear specific gravity compensation of both positive-displacement and turbine flowmeters. As a byproduct of methods

developed for this purpose, simplified compensation systems

for changes in turbine meter output frequency with fluids of

varying viscosity as well as compensation for the non-linear

portion of the flow rate-versus-output frequency curve for

turbine transducers used under widely-ranging flow conditions

are now commercially available.

figures in brackets indicate the literature references at the end

of this paper.

822
DIGITAL FLOW TRANSDUCER COMPENSATION TECHNIQUES

The development of the flow transducer compensation technique

described in this paper was brought about by the search for

improved accuracy in the determination of automotive and industrial engine fuel economy. Studies made at the proving

ground of a large U.S. automobile manufacturer [2] indicated

that a precision, four-piston positive-displacement flowmeter

represented the most accurate transducer for in-vehicle fuel

economy tests. These transducers are characterized by slight

variations in K-factor (pulses/gallon) from unit-to-unit as a

result of manufacturing tolerances. To obtain display of fuel

consumption in engineering units (in this case cubic centimeters of fuel consumed) as well as interchangeability of

transducer and display units, a digital compensation method

was developed wherein the transducer assembly itself provided

information to the display electronics identifying the Kfactor of the particular meter connected.

As the resolution required for fuel economy measurement (0.1

or 1 cc) and the K-factor of the meter was very close to the

required resolution, conventional variable-time base division

circuits used to normalize flowmeter outputs were not practical. Further, because reverse flow regularly occurs in the

fuel systems of spark-ignition engines, up-down counting

techniques were required to provide net fuel consumption information. This led to the development of the unique pulse

multiplication/division system which forms the basis of the

compensation techniques described below. Adding test time and

fuel temperature to the display resulted in conformance to

the requirements of an industry- standard road test procedure [3].

As shown in figure 1, a two-phase flow transmitter comprising

an optical disk driven through a magnetic coupling by the flow

transducer interrupts the flow of infra-red energy from a pair

of light-emitting diode (LED) /phototransistor couples located

such that their outputs are in phase quadrature relationship.

The square wave outputs of the two LED/phototransistor pairs

are amplified and applied to the input of a quadrature detector circuit which determines the direction of flow (FOR/

REV) and in addition provides a pulse output multiplied by

a factor of two. In the example shown, the transducer has

a K-factor of 1.07 cc/pulse.

Count pulses from the quadrature detector circuit are applied

to the set input of a flip-flop which allows clock pulses at

a high repetition frequency to be gated to the count input

of an 8-bit down counter which has been previously preset to

the desired K-factor. In this case, the K-factor is derived

from jumpers internal to the transducer assembly which have

been factory-installed to correspond to the K-factor of the

823
824
flowmeter as determined by calibration procedures. When the

counter reaches zero (min or borrow), the flip-flop is reset,

opening the clock gate. The 107 output pulses are input to

a divide-by-100 up/down counter, the output of which is directed to the six-digit display. It can thus be seen that

for every input pulse from the flowmeter, 1.07 counts will

be registered. If the display is calibrated in cubic centimeters, it will appear to count normally for the 13 pulses

from the flowmeter. The fourteenth pulse from the flowmeter

will cause the display to increment by two. If the K-factor

of the meter is less than one cc/pulse, the display will always

increment by one. Systems utilizing the above technique have

met with wide acceptance in precision automotive fuel economy

measurement [3] and several hundred of these devices are now in

use throughout the United States, Europe and Asia.

For industrial applications, K-factor resolution in excess of

the approximate -0.5% achievable with the system shown in

figure 1 is required. In this case, the length of the multiplier and divider chains is simply increased. Further, since

transducers are seldom interchanged in industrial applications,

it is more convenient to use a conventional thumbwheel switch

to set the flowmeter K-factor. Thus binary-coded decimal

(BCD) rather than binary counters are preferred. By suitable

setting of the K-factor thumbwheel switches, output pulses

equal to volumetric flow in any desired engineering units

may be achieved with the degree of resolution limited only

by the number of stages of multiplication and division.

If the system is designed such that the multiplier is always

less than the divider, pulse multiplier/divider circuits may

be cascaded, each performing an individual correction function. If the output of the first correction stage is volumetric units, and the K-factor switches of the successive

stage set to the specific gravity (in lbs/gal, gm/cc, etc.),

gravimetric engineering units can be obtained. Although the

meter K-factor can be set to take into account specific

gravity, it is usually more convenient for the operator to

set both meter factor and specific gravity in meaningful

engineering units.

Linear Specific Gravity Compensation Techniques

In diesel engine applications, for instance, fuel consumption

measurements are made in gravimetric units as fuel efficiency

is expressed as brake specific fuel consumption (BSFC) , lbs/

horsepower-hour or kilogram/kilowatt-hour [4] . As fuel temperature is difficult or impossible to control under normal vehicle operating conditions , measurement of the fuel economy

of diesel-powered vehicles requires specific gravity correction to the appropriate reference temperature (60°F or 28°C)

for accurate results. The compound correction system shown

in figure 2 incorporates this feature.

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Digital specific gravity compensation techniques require an

accurate temperature sensor located immediately up or downstream of the flow rate transducer. The output of the sensor

is amplified and scaled in accordance with the coefficient of

thermal expansion of the fluid. This amplified output is applied to an absolute value circuit which provides a unipolar

output to an 8-bit analog-to-digital converter as well as a

deviation-direction (polarity) signal to the clock control

circuit. The output of the analog-to-digital converter is

used to preset a specific gravity correction counter in a

fashion similar to that for the K-factor correction counter

of figure 1.

For each pulse output by the K-factor multiplier/divider

circuit, a pre-selected number of pulses are output from the

fluid specific gravity multiplier. If the fluid temperature

is above the reference temperature, the number of pulses preset in the specific gravity correction counter is subtracted

from the resulting pulse burst output to the specific gravity

pulse divider circuit. Conversely, if the fluid temperature

is below the reference temperature, the appropriate number

of pulses are added to that from the specific gravity multiplier .

Assuming a specific gravity of 1.000^ this technique can provide specific gravity correction of -25.6%, more than adequate

for most industrial applications. Using a pulse addition and

subtraction technique, rather than direct multiplication/division by temperature data, provides increased resolution and

minimizes the accuracy requirement of the analog-to-digital

converter. This reduces system cost and complexity.

Non-Linear Specific Gravity Compensation

Many fluids such as f luorocarbons , light hydrocarbons, etc.,

exhibit highly non-linear coefficients of thermal expansion.

Prior to the development of the digital correction system

described herein, the only practical technique for non-linear

flow transducer compensation involved the use of multi-segment

analog arbitrary function generators. These devices consist

of an operational amplifier with a number of diodes connected

in its feedback loop which create, through adjustment of an

equal number of potentiometers, a transfer function approximating the specific gravity versus temperature curve of the

fluid. Analog arbitrary function generators are difficult to

adjust and are subject to the well-known vagaries of analog

circuits in general - time and temperature-induced drift,

offset errors, etc.

827
Using the digital specific gravity correction technique,

shown in figure 3, an electrically eraseable and reprogrammable read-only memory (EPROM) organized as 256 words of

8-bits can be inserted between the analog- to-digital converter and the specific gravity correction counter. In

this case, the output of the analog- to-digital converter

provides the address to the EPROM. The corresponding data

pre-programmed from the specific gravity-versus-temperature

curve of the liquid is used to preset the specific gravity

correction counter.

Due to their widespread use in microprocessor-based systems,

256 x 8 EPROMs and their required programming equipment are

available from a number of sources at relatively low cost.

Two 2 56 x 8 EPROMs, as shown in figure 3, one for temperature excursions above and one for those below the reference

temperature represent the equivalent of a 512-segment arbitrary function generator, an obviously impractical device

to construct or calibrate. As the outputs of each EPROM are

open collector and may be bussed, other sets of EPROMs may

be included in the system and automatically or manually

brought into play if a variety of fluids are to be metered

by an individual transducer.

TURBINE FLOW TRANSDUCER COMPENSATION TECHNIQUES

The K-factor and specific gravity compensation techniques

described for positive-displacement flow transducers are

equally applicable to turbine flowmeters. Where bi-directional

flow is expected, turbine flow transducers with dual magnetic

pickups, located such that their outputs are in phase quadrature relationship, may be utilized to supply signals identical

to those of the optical disk transmitter associated with positive-displacement meters. Although divider circuits are often

used for K-factor compensation of turbine flow transducers,

the pulse multiplication/division circuitry described provides

a scaled and compensated output which may be used not only for

totalizing purposes, but also for flow rate indication through

the use of frequency-to-voltage conversion techniques or fixed

time-base counters.

A more interesting extension of the K-factor multiplier/

divider technique allows the usable range of turbine flowmeters to be extended from the normal linear area within a

10:1 ratio of minimum to maximum flow (turn-down ratio).

Figure 4 shows the performance characteristics of a typical

turbine flowmeter in both its linear and non-linear areas.

Non-linearity at lower flow rates is due to viscosity versus

momentum (Reynolds' number) characteristics of the flow as

well as drag effects in the bearings. Although simple ana828
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log or digital offset techniques have been used to approximate non-linearity at low flow rates, these methods cannot

be optimized for the individual characteristics of turbine

flow transducers.

Figure 5 depicts a fully-digital flow linearization technique

which can greatly extend the turn-down ratio of conventional

turbine flow transducers. By multi-point calibration of the

transducer, the K-factor versus flow rate curve can be determined with any degree of resolution necessary. This data

is then programmed into an EPROM which provides the correction data to the meter K- factor multiplier/divider circuit,

in similar fashion to specific gravity correction techniques.

In this case, the address of the EPROM is derived from a

time period measurement of the interval between successive

pulses from the transducer's magnetic pickup. Assuming that

the blades of the transducer are totally symmetrical and

evenly spaced, the time period from pulse-to-pulse will be

proportional to the reciprocal of flow rate. If such symmetry cannot be guaranteed, the input divider and count logic

system can be organized such that the interval required for

one complete revolution of the rotor is used to provide the

time base. Clock pulses are gated into an 8-bit binary

counter/latch combination, the output of which is proportional

to the reciprocal of flow rate and which is used to provide

the address to the EPROM. If the counter overflows, this

signal can be used as an underflow alarm or count inhibit

signal to indicate "no-flow" or a flow condition below that

which may be compensated by the system.

Using the reciprocal of the flow rate to provide the address

to the EPROM simultaneously accomplishes two objectives. At

the point where the flow rate reaches the linear portion of

the curve, the output of the 8-bit binary counter and thus

the EPROM address becomes zero for all higher flow rates.

Thus, appropriately, no correction is applied to the K-factor

multiplier/divider system. In addition, the resolution of

the system is greatest at that point on the K-factor/flow

rate diagram (figure 4) at which curvature is maximum. This

provides a "data compression" function which increases the

effective resolution of the system in that area in which it

is most needed.

As no analog components are included in this system, its

overall accuracy is solely a function of the frequency stability of the correction clock and the resolution of the

EPROM and K-factor setting system. The use of multiplication/

division circuits provides an output which is compatible with

conventional turbine flow transducer instrumentation systems.

This allows the correction device to be easily inserted between the transducer and existing display or process control

equipment at minimum incremental cost.

831
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03

<iQQOimJtfVf)

»8-l>

V-1L) 3 "SS3

Z22 _i_>

QIC

a o<J *_

832
Viscosity Compensation of Turbine Flow Transducers

Although the relationship between K-factor and viscosity is

more accurately expressed as a function of Reynolds number

(R ) , over a relatively limited flow rate range characteristic

ofemany process control applications the K-factor-versusviscosity characteristics of a typical turbine flow transducer will be represented by figure 6. The data shown in

figure 6 is derived from multiple measurements at the expected flow rate with fluids having viscosities selected

to duplicate the range expected in service.

The viscosity compensation technique as shown in figure 7 is

similar to that used for specific gravity compensation. Since

temperature is a very much simpler value to measure than viscosity, the EPROM contains temperature versus K-factor correction values derived from the combination of a temperature/

viscosity curve for the liquid and the K-factor/viscosity

curve for the transducer. As the K-factor set in the basic

multiplier/divider system is the maximum (normally at approximately one centipoise) , the K-factor correction counter

need only add pulses to compensate for the reduced K-factor

resulting from viscous drag.

If substantial changes in the K-factor/viscosity characteristics are expected over the normal flow rate range of the

meter, additional EPROMs can be prepared and selected by

means of a flow rate detection circuit similar to that of

figure 5.

Reynolds ' Number Compensation for Turbine Flow Transducers

A more elegant solution to viscosity compensation of turbine

flow transducers over a wide range of flow and viscosity

conditions takes into account Reynolds' number effects on

turbine transducer K-factor. This technique uses a "universal viscosity curve" [5] developed for a specific flow transducer by multipoint calibration over the expected flow rate

range with fluids of different viscosities. The results of

the calibration procedure are plotted in terms of K-factor

(pulses/gallon) versus Reynolds* number, R . Reynolds'

number represents the ratio between the inirtial and frictional forces of a fluid and thus effectively determines,

along with mechanical design characteristics, the speed of

rotation of the turbine element.

833
834
g

at hj

<9

O

OIO

-JfP5

«2

a.

C-lftJ

3 <Qoo»iuO(r)

<6i£§

835
Numerically, Reynolds' number is expressed as:

R = VD/v (3)

A<? • V = — = — 2 (4

)

As. V A

{1)

R = iQ = c Q (5 ) e TTDvC

v

(5)

And: F

fc = KQ

Thus : R

c t

(6)

e K (7)

where: R = Reynolds' number

(dimensionless

)

V = fluid velocity

D = pipe or flowmeter diameter

v = kinematic viscosity

where

:

where

Q

A

c =

where : F^_ =

K =

flow rate, volume/time

flowmeter crosssectional area

units constant

(including diameter)

turbine flowmeter

frequency, Hz

flowmeter K-factor

Since both c and K are constants under given conditions, the

actual K-factor (pulses/gallon) may be plotted as a function

of Reynolds' number or F /v. Such a plot is shown in figure

8. t

By the Hagan-Poiseuille expression, the viscosity of a fluid

in a laminar flow element may be described by the following

equation

:

= APgD

V 32dLV (8) where AP = pressure drop through

flow element

g

= gravitational acceleration

d = fluid density

L = length of flow

element

D = diameter of flow

element

Substituting Q for V as above and eliminating constants:

^

(9) dQ where: n = units constant

(including length

and diameter)

v = n

836
837
Thus the instantaneous viscosity of the fluid can be determined by measuring the pressure drop through a laminar

flow element (which may consist of nothing more than a length

of pipe of accurately-known dimension) or the flow transducer

itself) , knowing the fluid flow rate and density. In this

case, however, the fluid flow rate, Q, must be the true, corrected flow rate, rather than the flow rate directly indicated by the pulse output frequency of the flow transducer.

The compensation system shown in diagramatic form in figure

9 is designed to determine viscosity and to divide this value

into the pulse output frequency (F ) of the turbine meter.

The resultant value is used as the address for a read-only

memory in which the "universal viscosity curve" for the meter

is stored. Data stored in the EPROM adjusts the pulse output

frequency to its corrected value, F . This corrected value

is multiplied by the turbine pulse output frequency, F , and

then divided by the pressure drop through the flow element

(measured by a differential pressure sensor) to obtain the

memory address.

It will be noted that the Reynolds' number data lags the

measurement interval by one second. This time constant will

ordinarily be acceptable as viscosity changes are a function

of temperature variation, the rate of which will be determined

by the thermal inertia of the flowing product. The time delay

also provides the system stability required by the feedback

loop from the corrected flow rate output through the frequency

divider to the loop-up table address.

One of the interesting features of the compensation system

shown in figure 9 is the ability to perform a relatively

simple calibration procedure on the combination of the turbine

flow transducer and laminar flow element to obtain the "universal viscosity curve" look-up table in the EPROM without

the necessity of calculating Reynolds' number or knowing the

instantaneous viscosity of the fluid. In this case, the span

of the input amplifier to the analog-to-digital converter is

adjusted to provide full-scale output at the maximum expected

pressure drop. This value can be calculated or determined

experimentally from the maximum expected combination of flow

and viscosity.

If a positive-displacement or previously-calibrated turbine

meter is available to determine the true volumetric flow

rate, flow transmitter pulses, suitably scaled, are applied

to the input of the frequency multiplier in lieu of the

self-generated corrected flow rate. Ey the use of a microprocessor or a minicomputer, each time a new look-up table

address is generated by the counter/latch combination, the

instantaneous frequency of the flow transducer can be determined and stored in a random-access memory for subsequent

processing to generate the complete look-up table.

838
<To/ <0<OJj

t(_ CJ O

, IL

~ QO

Ml

(SI

2

830

3:

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3

i

1

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id

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On

IL.II

839
Turbine flow transducer calibration is, however, most often

accomplished with ballistic calibrators which do not provide

rate information. Assuming that the flow rate through the

ballistic calibrator can be maintained at a constant rate

during the test, integration techniques can be used to provide the look-up table data. In this case, an arbitrary but

accurately-known frequency, F^ , is injected into the F

c input

of the frequency multiplier, not shown. The output of the

multiplier/divider is applied to a totalizer actuated by the

position indication switches of the ballistic calibrator.

Similarly, pulses from the flow transducer under test are

accumulated in a second counter. The time for the displacement of a given volume of fluid is simultaneously determined.

The basic equations associated with ballistic calibrators

flow transducers having pulse outputs are as follows:

for

Q = 37

V

t (10) where: Q = flow rate, gpm

V = ballistic calibrator

volume, gallons

t = calibration period,

minutes

K - N

K t

t " ^ (ID where

:

V

N -

meter K-f actor,

pulses/gallon

number of flowmeter

pulses counted

during calibration

60

N

t

rot (12) where: F = flowmeter output

frequency, Hz

The output of the pulse multiplier/divider, Nv , is integrated

over the time of the injection frequency,

held constant:

the test. With F

i'

N = v

F. F.

l t

KAP

F.

l

K 5P d3)

where

:

N =

F.=

l

number of pulses

output from multiplier/

divider

injection frequency,

Hz (a constant)

KAP= frequency divisor

(proportional to AP)

840
Thus the ordinate of the curve is given by:

where : F = corrected output

frequency at flow

rate Q (see text)

And the abcissa is given by (11) above.

The corrected output frequency, F , may be established with

reference to the maximum K-factorcof the meter under test.

This value will ordinarily be obtained at viscosities between

1 and 2 centipoise and flow rates in the mid- or upper range

of the capacity of the meter. F for the particular test is

calculated by the following formSla

:

c =

t (max) V

Q

(15)

(max)

where : F

t (max)

(max)

frequency obtained from

conventional

calibration at

PU1S6S/

flow rate at

maximum K-factor

Alternately, any reasonable arbitrary value may be assigned

to F

t ( max ) and all measurements throughout the curve related

by (15) above.

As the greatest resolution is obtained by the correction-addition method, the data to be stored in the EPROM as a result of

the test is derived from the difference of F

c

and Ft . cause of the inversion of the expression F /v for improved resolution at lower Reynolds' numbers, the reciprocal of the

result obtained in (14) above is used to generate the numeric

value of the EPROM address.

Values intermediate between points determined by the technique

described can be generated by the computer system through

linear interpolation or conventional curve-fitting techniques,

depending upon the number of data points obtained. As the

system requires calibration at a substantial number of flow

points with liquids of several different viscosities, a considerable improvement in efficiency over manual calibration

techniques is achieved.

841
Compensation of Turbine Flow Transducers in Gas Service

In the previous discussions, it has been assumed that the

turbine and positive-displacement flow transducers have been

used with liquids having densities varying only with temperature and not with pressure - that is, incompressible

fluids. When gases are measured with turbine flow transducers, their electrical output must be normalized to standard conditions of both temperature and pressure. This is

done in accordance with the relationships established by

Boyle's Law and Charles' Law, respectively.

Turbine flowmeters measure the flow rate of gases in actual

cubic feet/minute (ACFM) or actual cubic meters/minute

(ACMM) . For data to be meaningful, it must be expressed

in standard cubic feet/minute (SCFM) or standard cubic meters/minute (SCMM) . This is achieved by the following equation : Q x P x T

Q = a a s

s

P x T (16) where (in English units)

:

s a

Q = standard gas flow rate (SCFM)

s

a Q = actual gas flow rate (ACFM)

measured by flow transducer

P = actual gas pressure at

a flowmeter, psia

P = 1 atmosphere, 14.7 psia

T = actual gas temperature,

a °R (°F + 460)

T_ = 520°R (60°F reference

temperature + 46 0°R) s

Q x P x 520 P Thus: Q a a _ 7 n

a

S 14.7 x T y

a T (17)

a a

842
The above equations, of course, require that the gas behave

in "perfect" fashion and that viscosity effects be negligible.

If this is assumed to be the case, the modified multiplication/

division system shown in figure 10 can be used. If not, the

EPROM linearization technique may be used as previously described .

Output pulses from the turbine flow transducer are amplified

and converted to square waves by the input comparator. The

square wave output is applied to an 8-bit pulse multiplier

which provides a burst of pulses for each input pulse numerically equal to the output of an 8-bit analog-to-digital converter representing actual gas pressure (P^) . For simplicity

it is assumed that the least significant bit (LSB) of the

analog-to-digital converter for pressure is equal to 1 psi,

thus the pressure range of the system is 0 to 256 psia.

Pulse bursts from the pressure multiplier are applied to a

12-bit divider for temperature compensation. Again, for

simplicity, we assume that the least significant bit of the

analog-to-digital converter represents 1°F. If an acceptable

temperature range for the system is 52°F (512°R) to 307°F

(767°R) , the offset adjust switch for the 512-bit would be

opened presetting the divider to 512. The output of the

amplifier for the temperature sensor would be adjusted to

zero at 52°F and to the full-scale input voltage of the

analog-to-digital converter at 308°F.

The output of the multiplier/divider chain thus represents

the ratio P

a/Ta of equation (2) above, requiring only that

the pulse train be divided by the K-factor of the meter (in

pulses/ACFM) to obtain one pulse/SCFM.

Again, the output of the multiplier/divider may be a signal

compatible with existing instrumentation or process control

systems minimizing the incremental cost of the compensation

system.

Such a system can be cascaded with the rate-related compensation system of figure 5 to remove linearity errors as a function of flow rate. If the principle source of linearity error

is related to the actual velocity of the turbine rotor, the

rate linearization system can be inserted between the transducer and the gas-law compensation system. If rate-induced

linearity errors are expressed in relation to SCFM, the ratebased correction system would be added after gas-law compensation.

843
844
COMMERCIAL SYSTEM IMPLEMENTATION

The systems described above hsve been implemented commercially using standard CMOS logic for all components other than

analog-to-digital conversion and EPROMs. Converters and

EPROMs used are PMOS with CMOS output compatibility. This

results in high noise immunity (a 12-volt power source is

used) combined with low internal heat dissipation and power

requirement.

Throughout the systems described, 8-bit analog-to-digital

converters and EPROMs have been used. With polarity sensing

techniques for specific gravity correction, 9-bit accuracy

(1 part in 512) can be achieved. Although 10- and 12-bit

converters are available from a number of sources, their

accuracy is substantially in excess of the associated transducer. In the case of specific gravity compensation, the

deviation from the reference temperature is measured and,

at a specific gravity of 1.000, 0.1% compensation resolution

and 0.2% accuracy may be achieved. As analog transducers

become available with greater accuracy, it is expected that

converters of higher resolution and EPROMs of greater word

length will be warranted.

The use of microprocessors, of course, was considered during

the early phases of the development program for the various

compensation systems. Although microprocessors are well

suited for ma thematic operations of the type discussed above,

an excessive number of peripheral components (in excess of

the total number of components used to implement the above

designs) was required to perform an identical function.

Microprocessors appear better suited for more sophisticated

compensation techniques such as inclusion of second order

deviations from the perfect gas laws, effects of gas viscosity

and density on transducer output, etc.

On the other hand, the use of discreet logic allows compensation for metering errors with an accuracy and resolution approximately equivalent to that of the transducer itself (0.25

to 0.5%) which is felt to be adequate. To attempt compensation with resolution beyond the precision of measurement of

the primary transducer element is a violation of the laws

of information theory. Finally, the discrete-component approach to the compensation techniques achieves a high cost/

benefit ratio. This allows a sufficiently rapid recovery of

initial investment to warrant inclusion in the vast majority

of industrial and scientific flow measurement systems.

845
SUMMARY

Linear and non-linear compensation of positive-displacement

and turbine flow transducers for the coefficient of thermal

expansion of the liquid being measured, as well as correction

for Reynolds' number effects on turbine flowmeter accuracy

can be achieved by the digital techniques described. Compound correction systems for turbine meter gas-law compensation may also be implemented using these methods.

Using digital techniques, non-linear compensation can be

obtained through the use of programmable read-only memories

(PROMs). If erasable and reprogrammable PROMs (EPROMs) are

used, the compensation system may be periodically recalibrated

along with the flow transducer and revised compensation lookup tables created at minimum cost. Although some techniques

such as multiplication and division may be accomplished with

analog circuit modules with somewhat less circuit complexity,

digital techniques eliminate the time and temperature-induced

drift associated with analog components.

Evolutionary improvement in the accuracy and dependability of

both positive-displacement and turbine flow transducers combined with accurate compensation techniques for those sources

of error which cannot be conveniently overcome mechanically

will provide the process industries with the instrumentation

systems necessary to meet the conservation challenges of the

1980s.

REFERENCES

1. West, D. T. , et al, "A Technical Report of the 1975

Union 76 Fuel Economy Tests," publication 750670,

Society of Automotive Engineers, Pittsburgh, PA. (1975).

2. Baker, Milton, "New Techniques for Automotive Fuel

Economy Measurement," Flow Measurement Symposium,

National Bureau of Standards, Gaithersburg , MD. (1977).

3. Fuel Economy Procedures Task Force, "Fuel Economy

Measurement - Road Test Procedures - SAE J1082," SAE

RECOMMENDED PRACTICES, Society of Automotive Engineers,

Pittsburgh, PA. (1974).

4. Jennings, Roger, "Fuel Economy Measurement using

Positive-Displacement Flow Rate Transducers,"

Instrument Society of America, 2 2nd International

Instrumentation Symposium, Pittsburgh, PA. (1976)

.

5. Stine, G. Harry, Ed., "Calibration in Liquids, The

Flow Factor," vol. 3, no. 4, Flow Technology,

incorporated, Phoenix, AR. (1975).

846
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

VISCOSITY EFFECTS ON THE TURBINE FLOWMETER

J. M. Ball, Physicist

Flow & Pressure Group

US Army Metrology & Calibration Center

DRSMI-MSP

Redstone Arsenal, AL 35809

ABSTRACT: The so called universal viscosity curve

has been a common medium for the presentation of turbine

flowmeter performance characteristics for some time. This

paper shows that the most common types of turbine flowmeters

do not usually perform according to a single curve when the

viscosity is changed. We also present data which demonstrates

that certain modulated carrier type turbine flowmeters do

respond predictably when the fluid properties change.

Errors produced by the misuse of the universal curve are

demonstrated, and errors in the characteristic value (K

factor or C factor) due to fluid property measurement

errors are described.

Key Words: Accuracy; calibration; characteristic factor

(K or C) ; curve fitting; pickoffs (magnetic and RF)

;

turbine flowmeter; universal curve; viscosity measurement.

1. Introduction

For the past several years there has been discussion and disagreement

among turbine meter users and makers concerning the so called "universal

viscosity curve" (See Figure 1). Most often the questions raised concern

the accuracy with which one can expect to use such a curve. Some recent

studies have indicated that either such universal curves do not exist,

or that they cannot be used to the accuracies desired (less than 1/2%

of reading)

.

There are numerous turbine flowmeters in the US Army system, and

this laboratory has received several requests from customers for universal

curves - most of which could not be supplied due to inadequacies in the

turbine meter's performance. Cases have occurred in laboratory applications where a "universal" curve based upon a single fluid calibration was

being used for multiple fluid applications.

The widespread use (and misuse) of the universal curve for turbine

flowmeters prompted this paper. The test data and results which follow

were obtained in the US Army Standards Laboratory (USASL) , the primary

standards laboratory for the US Army.

847
1

LINEAR SCALE

• i ... . — r - - ^ 0 500 1000 1500 2000 2500

TYPICAL UNIVERSAL VISCOSITY CURVES

Figure 1

848
2. The Turbine Meter

Throughout this paper the term "turbine meter" will mean a propellortype flow transducer which has the turbine mounted with the axis parallel

to the direction of flow. The electrical output is produced by a pick

off coil (inductance, variable reluctance, or modulated carrier (RF))

mounted upon the body of the meter. The meters considered are constructed

of steel. Figure 2 shows this type of turbine meter, which is the most

common design in use today in the US Army system.

3. Description of Calibrators

As a primary liquid flowmeter calibrator the USASL uses a volumetric

displacement device which is basically a large cylinder within which a

piston moves due to pneumatic pressure (See Figure 3) . The moving

piston displaces liquid through the turbine flowmeter being tested. This

primary system uses an optical/electrical encoding system to produce

pulses proportional to the volume displaced during a period determined

by the output frequency of the turbine meter being calibrated.

Using this calibrator (which is temperature and pressure controlled)

the calibration of turbine meters is reduced to counting the number of

encoder counts and the number of turbine meter pulses generated during

a timed interval. All data reduction is performed by computer (Figure

4 shows a typical data list) . By nature the calibrator is unaffected

by fluid density or viscosity.

The USASL also has gravimetric calibrators which determine flowrate

through the weight of fluid displaced during a timed period (See Figure

5) . These machines have a systematic error of approximately twice that

of the volumetric device (.1% volumetric, .2% gravimetric), but are

still suitable for turbine meter study.

4. Description of Method

The data which follows was produced by the USASL calibrators when

testing turbine flowmeters. The viscosity of the flowing fluid was

determined through frequent calibrations of the fluid viscosities

versus temperature and continual monitoring and control of the operating

temperature.

5. Characteristic Factor

For turbine meters the most common method of relating the flowmeter

output frequency to the flowrate is through the "K-factor" (number of

pulses per gallon) . Another form in common use in the Army is the

"C-factor11 (C-factor x frequency = GPM) which is used as a frequency

meter preset value. Functionally, the C-factor looks like the inverse

of the K-factor (See Figure 6)

.

849
STRAIGHTENING

VANES

TYPICAL TURBINE FLOWMETER

Figure 2

niSPl ACEMENJ-SENSING SYSTEM (ENCODER)

liiiiiiiiiiLJeiiiiL

E

PISTON

FLOWMETER

ROD

PISTON

FLUID

VOLUMETRIC DISPLACEMENT CALIBRATOR

Figure 3

850
TOTAL "LOWCAL CYCLES

-FLOWMETER—COUNTER TIME FREQUENCY EL-OWRATE PER C- PULSES READING (SEC) <CPS> <GPM> GALLON

5400. 56100 . 2.69140 2006.3937 10.41306 11560.8128 . 51899465E - 02

-54 QQ. —56100. 2.68890 .- 2-008*2562 -10*42274 —41560.3123 - —.51899465E - 02-

5401. 56057. 2.68480 2011. 6955 10.43624 11565.6333 . 51977831E - 02

-5400. 56132. 2*97870- 1812*8714 —9*41407 — 11554.2222 . 5 1929069E - 02

540U. 56113. 2.97540 1814.8320 9.42132 11553.1345 . 51911492E - 02

5403 . 56108

.

2.97000 -1818. 1818 9.4-3761 11559*16*5 ,51906866c - 02-

5400. 56103. 2.96890 1818. 3555 9.44027 11560.194b . 5 1902240E - 02

-5401. - 56152* 3.33954 —1617.3030 -4.3 99-97- -11552.2453 .51937953E - 02

5401 . 56146. 3.33940 1617. 3564 8.39932 11553.4333 . 5 19324C4E - C2

-54-01. 56137— 3.33500 141-9.490-3- -8.40905 11555.3326 . 51924079E - 02

5401. 56179. 3.71970 1451. 9938 7.54501 11546.6937 .51962927E - 02

-5442. —561 65- 3-7-20-80 1451. 6333 —7—54 Q90— 11551.7103 _. .-51940361E - 02

5402

.

56157. 3.71230 1454.9666 7.55607 11553.3559 . 519329 f.3E - 02

54 0*. • 56216. 4.48100 1205.9338 6.26728 11545.5033 . 519682e4E - 02

5403. 56196. 4.43020 1219. 5338 6.336 89 11547.4751 . 5195941CE - 02

-5402. 56197. - - 4.42580 1224.57-0 3- -6.34330 -11545.1324 . 51969954E - 02

5402. 56183

.

4.420 30 1222. 0890 6.35017 11546,9817 . 51961631E - 02

-540* . 56230. - -5.145 7-0 1050.1973 5*459 05- - 11542.6233 . 51981226E - 02

5*04 . 56225. 5.13410 1052. 57 0 1 5.47090 11543.6552 .51976604E - 02

-5403. 56214* - 5.13220- 1452.-764 9 5*47186 11543.777b . 51976053E - 02

5404. 56248. 5.90820 914.6510 4.75604 11533.9350 . 51997866E - 02

5403 . 56237. 5.90730 -914.6310 4.75584 11539.0564 . 5 1997320E - 02

5*03. 56246. 5.90353 915.2199 4.75966 11537.2100 . 52005641E - 02

-5404. 5-6238..... 5.89990 915.-94 7 7 —4*76189 11540. 985* . 5 1988622E - 02

5404. 56274. 6.73160 802. 78 09 4.176 22 11533.6037 . 52021902E - 02

5403. =6257. 6.73560 802.15 5 7 4.172 48 11534.9541 . 520 158 12E - 02

5403. 5 62 33. 6.72300 803.6591 4.17889 11539.8512 . 519982-.4E - 02

5403. -. 56270. 6.77470 7-97*5261 -4.14936 11532.2892 . 52027832E - 02

5403. 56254. 6.77230 797.8037 4.14965 11535.5692 .52013038F - 02

-5402. 56252. ... _7-*62810 708. 1711 . .. 3.683 96 — —11533. 34*3 -. 52020817E - 02

5402. 56255

.

7.62480 708.4776 3.68575 11533.2292 . 5 2023591E - 02

5402. — 562<*9. 7.63164— 7-07-.-8463 —3*682 06 11534.4594 . 5 20 18042E - 02

5398. 56240

.

9.08590 594. 10 74 3.09223 11527.7630 . 52048259E - 02

-539*. 56219. - 9.09160 — 593.7349 -3.48913 —11532.0691 . 5 2028825E - 02

5397. 56229. 9.08390 594. 12 81 3.09230 11527.8822 .52047721E - 02

-5393. 56227*— 9.07520 __5 94*3180 3.09516 11532.5644 . 52026590E - 02-

5400. 56249. 8.19050 659.3004 3.430 82 11530.1890 . 5 2037308E - 02

-5401. 56257*— -8.19410 _- 659.1328 —3.42980 11530.6843 .52035073E - 02

5402. 56253. 8.20350 658.4994 3.42563 11533.6392 . 52021742E - 02

-5401. 56247. - 8.1910O--659.3822 - __$*.* 30 49- -11532.7343 . 5202582UE - 02

539o. 56217. 10.05640 536.5737 2.79267 11529.2065 .52046257E - 02

-539o. ...... 5 6235. 10.06340.

.

536.2005 - -2*79162 11524.5165 -. 52062922E- 02-

5396

.

56215 . 10.06990 535.8544 2. 7 88 82 11528.6165 . 5 2044406E - C2

5396

.

5 6215. —10.06690 536.0141. -2.78965 11523.6166 . 52044406E - 02

539a. 56208. 10 .52330 512. 6475 2. 66821 11527.9156 . 52047571E - 02

539* . 56192. ... 10.53250 -5-12.1291 -2.665 24 11529.0636 . 52042401E 02

539*. 56201. 10 .52780 512. 3578 2.66636 11527.21*4 . 52050737E 02

-5367. -56136— 13.76860 391*2526 —2.036 79 1152 5.5852 .52056094E 02-

5387. 56125. 13.77970 390. 9374 2. 03475 11527.8441 . 52047893E 02

5387. 56112. —13.76470 - 391.3634 -2.03649 11530.5149 . 52035338E 02

5379 . 56046. 19. 07640 281. 97 14 1.46772 11526.9495 .52051932E 02

5379. 56027. - --19. 07630 — 231.9729 —1.46723 —11530.8535 . 52034286E C2

5379. 56027. 19.08960 281.7765 1.46620 11530 .8536 . 5 20 3*286E 02

-535o. 55726-. . 26.592 50 201.4102 1.04687 11543.5733 .519769fc5E 02 - 5365. 55953. 56.52190 94.9190 .494 58 11515.0234 .52105820E 02

Figure 4

851
SCHEMATIC OF WEIGHT-MEASURING FLOW CALIBRATOR

Figure 5

C or K

A

K

Comparison of C- and K-Factor Curves

Figure 6

852
K

_ counts _ GPM

gallon Hz

6. Universal Curve

In 1961 the relationship of H. M. Hochreiter

Q = A (

, F , E , , V 24 2^2 D

; nD p n D pn D

was used by R. Shafer to describe for one particular meter geometry the

function (f>^.

f = <J>, (f/v)

Q

f = frequency, Q = flowrate, V = kinematic viscosity

Shafer' s data indicated that no single form of the function (J)^ describes the performance of a turbine meter. He also noted that

this form of data presentation (the universal curve) is often used by

meter manufacturers (See Figure 7). L. 0. Olsen's technical note from

NBS in 1974 restated some of these conclusions.

Other researchers have concluded that the universal curve is only

useful at high Reynolds Numbers (note the response of J. Grey to the

Hoscheiter article) . Since f/v is similar to Re (if Q - Af where A is

a constant, then Re - B f/v , where B is constant), high Reynolds Numbers

mean either high frequency or low viscosity operation (See Figure 6)

.

Three researchers, V. R. Withers, F. A. Inkley, and D. A. Chesters

in a paper presented at a flow measurement conference in 1971 found

differences of one percent and more in the turbine meter characteristic

factor in the same fluid at different temperatures (i.e. different

viscosities) (See Figure 8)

.

7. Magnetic Flowmeter Data

Following (Figures 9A, 9B, & 9C) are curves showing the results

obtained from typical multiple fluid calibrations of high quality

variable reluctance or inductance type turbine meters ("magnetic"

turbine meters) . In those figures which show a "universal curve"

sketched in, note the percentage spread. Most manufacturers clain + .5%

or less uncertainty for their instruments, and our results show that

such expectations, while reasonable for a single fluid curve over a small

temperature band, are unrealistic in a universal curve. We have also

observed that only meters larger than 1/2" show good (near 1% overlap)

performance.

853
200 400 600 800 1000 1100

f/v

Figure 7

854
0 «— ' ' H

0 10 20 30 W

Flow Rate, l7s

Performance of One Flowmeter With Different Oils and Temperatures

Figure 8

855
k (normalized) vsj^ meter "b"

Figure 9B

856
100 200 %, 300

TYPICAL DISAGREEMENT RESULTING FROM DIFFERING VISCOSITY FLUIDS

Figure 9C

.540

CxlO2

.520

.5001

MAGNETIC

R.F.

i

T

0 1000 2000

PERFORMANCE COMPARISON, MAGNETIC VS R,F. PICKOFF

Figure 10

f/y 3000

857
Since this meter type is at present by far the most commonly used,

most users should not expect to obtain universal curves from calibration

laboratories, and those people who use a single calibration fluid curve

to predict other fluid performance are quite probably introducing

significant errors into their measurements unknowingly.

8. RF Flowmeter Data

Magnetic drag affects the performance curve as illustrated in

Figure 10. A flowmeter was calibrated in the same fluid under the same

conditions, first as a magnetic meter, and then as a modulated carrier

(RF) meter. This was accomplished by changing pickoffs between calibrations. Note that the curves run together at higher frequencies, but

that the effect of magnetic drag is more pronounced at the lower end of

the range.

It might be expected, based upon the more nearly linear response

of the RF meters at low frequencies that this type of meter would perform

better in multiple fluids, and even that a single (J), might exist for such

meters

.

9. Test Results

Unfortunately, sample turbine meters of the RF type from several

manufacturers were not available in sufficient numbers, and so the

results which follow are based primarily upon the periodic calibration

and recalibration of approximately 100 RF turbine flow transducers

purchased by the US Army for use as transfer standards (all of which

are manufactured by the same company)

.

Illustrated in Figure 11 and the Appendix are typical multiple

fluid C factor curves, and typical single fluid curves for these meters.

Note the random error percentage in the multiple fluid example of + .037%

(99.7% confidence). The random error is a measure of the fit of the

computer generated curve to the real data (both the computer generated

curve and the real data points are shown) . For these 100 meters typical

random errors ranged from about .05% to about .25% of reading.

The curve was generated based upon the assumption that a function

<))_ existed, and, while the exact form of (J)^ might not be determinable,

it was assumed that <J>^ would be well behaved enough to be approximated

by the polynominal series

C = (f/v) = A + B f/v + C (f/v)

2

+ -I- P (f/v)

N_1

Due to the performance of the meters at the "minimum" point, (See

Figure 11 and Appendix), we used two polynominal approximating functions,

one from the start of the curve to the frequency corresponding to the

"minimum", and a second from the "minimum" onward.

858
i TYPICAL COMPUTER GENERATED MULTIPLE FLUID CURVE

FOR TRANSFER TURBINE METERS

c BEST FIT U«S FIFTH CEr,P?E

SIGf.a = .067

RfiNOrm FRBOR - .221

BAWjFflCTUBER BEST PIT UftS NINTH OEGBEE » 702m1 TYPE .bib .6*8 80.0

"COEL NO. SIGnft = .041 B OlfSEL 3.098 .833 80.0 SERIAC NO. 010 AANOfti EBBOR = .187 C 5t>(H> lfc.7M3 .857 80.0

Figure 11

859
Typical orders of the polynominal curve for "best fit" on each side

of the "minimum" for the 1" meter were 8th and 8th respectively, and for

the 1/2" meter 10th and 9th respectively, with a spread through the group

of about + 30%.

The minimum point was found to occur at a Reynolds Number of about

5000 for the 1" and about 4000 for the 1/2" meter. This would add weight

to those theories which have contended that the shape of the performance

curve is due to changes in the flow regime from laminar to transition to

turbulent (See Lee and Karlby)

.

These 100 meters have been found to repeat their original curves to

better than + .1% after being fielded and used for one year; then being

returned to our laboratory (See Figure 12) f

10. Conclusions

Our results show that universal viscosity curves accurate to

better that + .5% can be routinely produced by certain precision RF

meters of the variety available to the general public, and that such

performance generally cannot be expected from magnetic pickoff meters

or from meters of less than 1/2" bore. A meter should always be calibrated in the fluids in which it is to be used. Interpolations from one

fluid to another should not be performed unless calibration data demonstrates that such is possible, and the errors introduced by interpolating

considered (which increases the uncertainty of the measurement)

.

The need for accurate and frequent viscosity measurements is

demonstrated. Especially in the low range, the universal curve is

worthless without an accurate measure of V to divide into the frequency

(note the response to V in Figure 1) . The accuracy required of the

viscosity measurement is illustrated in Figure 13. Figure 13 shows the

likely error introduced by viscosity error, and that the viscosity induced

error in the "high" range (solvents, fuels, etc.) is small except at the

lower frequencies.

Factors which affect the viscosity such as pressure and temperature

must be included in calibration reports, if the universal cuvre is to be

used, because both affect the viscosity.

Even though several sources of error remain which are not considered

here (such as the effect of line pressure on the turbine meter) , there

are turbine meters which do show a single $ and for which a universal

curve or table can be used to routine accuracies of + .5% or less.

11. References

1. Hochreiter, H. M. : "Dimensionless Correlation of Coefficients of

Turbine-Type Flowmeters ,Transactions of the ASME , October, 1958.

860
2. Lee, W. F. Z., and Karlby, H. : "A Study of Viscosity Effect and its

Compensation on Turbine-Type Flowmeters ,

Transactions of the ASME , Journal of Basic Engineering, September, 1960.

3. Olsen, L. 0.: "Introduction to Liquid Flow Metering and Calibration

of Liquid Flowmeters , "N . B. S. Technical Note 831, June, 1974.

4. Shafer, M. R. : "Performance Characteristics of Turbine Flowmeters,"

Transactions of the ASME , Journal of Basic Engineering, Paper No.

61-WA-25, 1961.

5. Withes, V. R. Inkley, F. A., and Chesters, D. A.: "Flow

Characteristics of Turbine Flowmeters, "Proceedings of the International

Conference at Harwell, England, September, 1971.

6. Tan, P. A. K. , and Hutton, S. P.: "Experimental Analytical, and

Tip Clearance Loss Studies in Turbine-Type Flowmeters," OP. CIT.

Figure 12

861
20

-

Vcs

15

10

4— i i i i i i > i 70 90 110 130 150

Temp °F

Viscosity vs Temperature, Typical Oil

.1 1 V 10 CS 100

Typical Error in K Due to a 1% Error in Viscosity Value

Figure 13

862
Appendix

Samples of US Army transfer turbine meter response curves . Figures

Al through A3 are single fluid response curves, and Figures A4 through

A6 are multiple fluid (<f>^) curves.

All of these curves are computer generated plots of real data

points (represented by letters) and computer generated curves (shown

by X's and lines). The illustration below will aid in interpreting

the figures which follow.

These plots are not printed to a uniform scale, but both X and Y

scales vary from figure to fugure.

1st Segment Information

Polynomial Order

Standard Deviation

Random Error

C Factor

Meter Identification

f/

v

2d Segment Information

Polynomial Order

Standard Deviation (%)

Random Error

A MIL-XXX

B MIL-YYY

C MIL-ZZZ

X DUMMY

/

16

3

1

.876

.801

.679

y . o

863
TYPLICAL SINGLE FLUID RESPONSE CURVES

MANUFACTURE*

HOOEL NO. SERIAL NO. 041

BEST FIT WAS NINTH OEGHEE S!6«A s .112 AANDOH ERROR z .369

A S606

I OUWY

l<t. 290 .8*4 tO.O

A 1

864
865
A 3

866
TYPICAL MULTIPLE FLUID RESPONSE CURVES

BFST FIT WAS FIFTH DFGBEE SIGUA = .13<» RfiNDHn FFRPB = .Mt5

867
BEST FIT UftS FIFTH DECREE

C SIGMA = .0*7

C PflNOnn ERROR s .221

A

*AN<jFACTuReR BEST FIT WAS NINTH OEGRFE A 702<«B TYPE .6?6 HCOFL NO. 5ir.HA = .061 6 DIESEL 3.098

SERIAL NO. RANDOM ERROR = .187 C 5606 16.7H3

A 5

868
BF<T FIT WAS FIFTH OFRAFF

SffiMA = .01?

MAMUFAfTUAfft WOFl M*. * SEHI*l MO.

SFST FfT WAS HHTH OFRBFP

sig«a > .o??

ft««oon FR»nn « .06*

3.080

3. 1 TO

3. ISO DTF5FI Fl> "5T 111 M S*06 II .9S0

mi-ro?«i-i .*?t mi.-ro?*-i .6?r

J* * .*»0

)• * 1.01*

.SSI

. 6«*

.7*1

.7*1

SoTs?*

SO. 00

AO. 00

30.

A 6

869

National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersbure, MD, February 23-25, 1977. (Issued October 1977)

TURBINE METERS FOR THE MEASUREMENT

OF GASEOUS HYDROCARBONS

Paul J. LaNasa

Daniel Industries, Inc.

Houston, Texas 77024

Turbine meters for the measurement of gaseous fluids

have been available for many years. However, their

application in the United States to the measurement

of hydrocarbon fuel gases has occurred over the last

fifteen years. The evolution of the turbine meter

for this particular application has resulted in specific design consideration to insure its continued

reliability and performance. In addition to specific design considerations, this particular measurement

application requires the accuracy of the turbine meter

be verified on location, thus necessitating the development of accurate high pressure field testing methods.

Key Words: Turbine meter, gaseous hydrocarbons, fundamentals, fuel gas measurement, field testing, installation, performance characteristics, design considerations.

INTRODUCTION

During the last decade the gas turbine meter has become established

as a very useful instrument for the measurement and control of gas

flow. This paper will present a summary of the principles of

operation, the basic construction and the performance characteristics of the gas turbine meter.

PRINCIPLE OF OPERATION

The gas turbine meter is a velocity measuring device. The theory

of its operation is as follows: The gas enters the meter and is

constricted increasing its velocity. It then passes through a

free turning rotor which is mounted coaxially on the pipe centerline and exits the meter. In passing through the meter the gas imparts an angular velocity to the rotor proportional to the linear

velocity of the gas in the meter. As the gas velocity is directly

proportional to the volume flow rate it follows that the speed of

rotation of the rotor is also directly proportional to the volume

flow rate. Therefore, by accurate measurement of the rotor speed

and the application of a predetermined calibration constant the volume flow rate can be obtained. The necessity of the calibration constant stems from the difference between the theoretical and the actual.

In theory, as the gas passes through the meter it encounters a free

871
running rotor on which to impart its energy. However, in

actuality the rotor has certain retarding forces which impede

its movement. These retarding forces are due mainly to bearing

friction and aerodynamic forces. As flow is increased from

zero through the turbine meter a certain amount of gas is

allowed to pass through the rotor unaccounted until a point is

reached where the gas imparts enough force to overcome the

frictional retarding forces of the rotor bearings. At this

point the rotor begins to turn and the frictional forces in the

bearing becomes negligible. From here on the aerodynamic forces

become the predominate retarding force and control the rotor's

speed. The existence of these retarding forces create a difference between the theoretical rotor speed and the actual rotor

speed. This difference is accounted for by the calibration constant.

BASIC CONSTRUCTION

The essential elements of the gas turbine meter's construction

are shown in Figure 1. As the gas enters the meter it encounters

a flow deflector which constricts it into a smaller annular

passage. This annul ar passage is approximately one-third the

area of the pipe and serves to increase the velocity of the gas

before it passes through the rotor. The resulting increase in

velocity gives more driving force to the rotor thereby improving the accuracy at low flow rates.

Parts List

A Housing

B Cover Plate C Flow Deflector D Inner Housing

E Rotor Hub

F Bearings

G Rotor H Magnet Housing

J Coil Housing

K Cover Plate & Outlet Tube

L Boss

M Preamp Housing

N Preamp

O Pressure Tap

P "O" Ring

Q Swagelok Nut

R Dram Plug

FIG. 1 Cross-sectional View of an Electro-magnetic Gas

Turbine Meter.

872
The flow deflector also serves to lessen the thrust loads on

the rotor bearings by shielding the center of the rotor from

the flowing stream. As the flow continues it passes through

the rotor and exits the meter. The potential accuracy of the

meter is to a great extent determined by the design of the

rotor. The rotor carries a number of blades set at a predetermined angle. The blades are seldom of aerofoil shape,

usually being machined or molded as an integral part of the

hub and may be twisted or untwisted. In most meters the rotors

are made of a present day plastic with high strength and substantially impact resistant. The rotor is supported on ball

bearings which are lubricated by shielding the bearing with the

lubricant incorporated at the time of their manufacture, or by

furnishing supplemental lubrication through wicking or external

supply line. A prime advantage from the standpoint of construction is to have the bearings for the rotor centrally enclosed

in an area which is not in the direct line of flow. This helps

protect the bearings from contamination in the pipeline. In

order to keep the frictional torque low, the bearings are of a small diameter in relation to the meter size; and, since in

some meters they are the only part of the meter in running contact, the reliability and life between overhauls are solely dependent on their design.

The method for accurately measuring the rotor speed is as critical as the rotor and bearings. At this stage in the basic

construction there are two distinct designs for accomplishing

this measurement - mechanical and electromagnetic.

In the mechanical design the rotor is an integral part of a mechanical gear train which relates its rotation to the volume

flow rate as displayed on a clock type index on the exterior of

the meter housing. The extent to which the mechanical design

can accurately measure the speed of the rotor is dependent on

the possible gear ratios available in the gear train driving

the external index. As a result of this system the mechanical

readout meter incurs some retarding forces over and above the

basic bearing and aerodynamic forces. Additional forces that

must be overcome are gear losses, losses due to eddy currents

in the magnetic coupling and any loads imposed by the meter

registers or the correcting devices that might be employed. All

of these forces have the effect of reducing the turbine meter

range at the low flow rates.

In comparison to the mechanical design we have the electromagnetic.

The electromagnetic measurement of the rotor speed is accomplished

in either of two ways: 1) By placing small permanent magnets

within the rotor and electrically counting the passage of these

magnets with a pick-up coil. This is called the induction method.

2) By having a magnet housed inside the pick-up coil and the

rotor blade tips made from, or contain suitable magnetic materials

to stimulate pulses in the coil. This is called the reluctance

method. With the electromagnetic design the meter encounters only

a small additional retarding force due to breaking of the magnetic

873
line of force. In addition, with the electromagnetic design

there is a high frequency digital output available for control

purposes

.

As a final point of construction many of the turbine meters are

designed so that the inner housing containing the measurement

assembly can be removed from the meter without removing the

entire meter housing from the pipeline. On the larger size

meter this offers a distinct advantage.

PERFORMANCE CHARACTERISTICS

The discussion of performance characteristics of gas turbine

meters will be divided into the following sections: rangeability,

meter capacity, effects of gas density, field test methods,

and piping considerations.

RANGEABI LITY

A prime characteristic of the turbine meter is its rang ea bi 1 i ty

.

This is defined as the ratio of the maximum meter capacity to

the minimum capacity for a stated set of operating conditions

and during which the meter retains its specified accuracy.

In comparison to other types of meters, the turbine meter increases its linear rangeabi lity with increases in gas density.

This increase in rangeability results from a decreasing of

minimum velocity required for linear operation. The minimum

velocity required is a function of the gas density, as the

density increases the minimum velocity required is allowed to

decrease. A relationship for approximating the variation of

rangeability with density is developed by examining the minimum

kinetic energy necessary to achieve linear meter performance:

KE

r * 1/2 J) r V

p

V = V x r

As increases V is allowed to decrease maintaining the

energy necessary for linear meter performance.

KE

r

= Minimum Kinetic Energy Required

& jD^ = Gas Density at Respective Conditions

V r & V = Gas Velocity at Respective Conditions

The rangeability of most present day gas turbine meters at

atmospheric pressure is 10 to 1 greater as shown in Table 1.

*Available kinetic energy per unit volume for steady flow of

a f r i cti on 1 es s , incompressible fluid along a streamline.

874
TYPICAL TURBINE METER PERFORMANCE

METER

SIZE

MAX. FLOW

RATE

SCFH

RANGE MIN. FLOW

RATE

SCFH

APPROX. DIFF.

INCHES W.C.

2

4

6

8

12

4,500

18,000

36 ,000

60,000

150,000

10

15

15

20

20

1

1

1

1

1

1 ,200

2,300

3,000

7 ,500

450 2.0

1 . 2

1 . 5

1.8

1.7

METER CAPACITY

The capacity of the turbine meter is determined by many control 1 i ng factors

.

The maximum capacity is determined by such factors as rotor

speed, pressure drop, and gas velocity. The limitation of the

meter capacity due to rotor speed is a relative matter. The

bearings used in the turbine meter have a given life under a given load and at a specific speed. As the speed of the rotor

is varied the speed of the bearings varies. Although the turbine meter is capable of turning at three or four times its

maximum speed without immediate damage, its life can be substantially reduced if this speed is maintained for prolonged

periods.

The pressure drop across the rotor also influences the maximum capacity of the turbine meter. In some applications, such

as distribution systems with line pressures running from 7 to

10 inches of water above atmospheric, the pressure loss caused

by measurement equipment must be at a minimum.

In most cases the pressure loss called out in the manufacturer's

literature is listed for a 0.6 specific gravity.

In order to convert the pressure loss for a different gas the

following relationship can be utilized:

APmax =APmax

(x) (0.6)

Qmax

Qmax (0.6)= Maximum Volume Flow Rate of (.6) Gravity Gas

Qmax (x) = Maximum Volume Flow Rate of (x) Gravity Gas

Pf(.6) = Line Pressure of (.6) Gravity Gas

G = Specific Gravity of Gas

875
A further limiting factor resulting from pressure loss is a variable thrust load on the rotor shaft and bearings. This

thrust component is intensified with rising pressure loss

resulting from increases in line pressure or specific gravity. Therefore, holding the pressure loss to a minimum increases the life span of the meter.

The gas velocity becomes a controlling factor due to the

aerodynamic characteristics of the rotor blades and also the

need to avoid the possibility of obtaining sonic velocity within the meter.

The minimum capacity of the turbine meter is limited by meter

accuracy. This minimum flow meter accuracy is determined by

gas density, bearing friction and the aerodynamic characteristics of the rotor.

The bearings in a turbine meter are selected for their ability

to carry a load while introducing a minimum amount of friction.

Thus, while increasing the minimum capacity of the turbine

meter by reducing friction the maximum is limited by reduced

load capacity.

EFFECTS OF DENSITY

The gas density can have three principle effects on the performance of the gas turbine meter. These are:

1) Increase rangeability

2) Vary pressure differential

3) Alter calibration

As previously stated the gas density can increase the rangeability of the turbine meter by increasing the kinetic energy

available "for driving the rotor.

In gas flow the pressure differential across a restriction

increases as the density increases. Hence, the loss through

the turbine meter intensifies as the density increases. This

intensification can range from 2 inches of water of atmospheric

condition to 200 inches of water at 1440 psig.

Finally, as density increases it can cause a shift to occur in

the turbine meter proof, normally in the positive direction.

The amount of the shift, if it occurs at all, depends upon the

design of the meter and seems to be a function of the rotor

design and meter size.

INSTALLATION

Since the turbine meter is a velocity type meter the pattern of

the velocity upstream of the meter is of basic importance. The

876
meter is particularly sensitive to any spiral ing motion that

may result from upstream piping configurations. The American

Gas Association sponsored intensive testing to establish standards of construction applicable to proper design for the meter

tubes used in orifice metering. The probable effect of piping

configurations, pinched valves, etc., to a degree might be

estimated as to the probably severity of these non-uniform conditions on turbine meters. The streamline character of the

diffusor section ahead of the rotor has a tendency to minimize

some of these adverse effects. The net effect, consequently,

is dependent somewhat on the particular design employed by the

manufacturer. It is consequently impossible to give specific

rules for all makes of turbine meter; it is recommended, rather,

that the recommendation of the manufacturer be employed in

specifying the required piping system.

The rotor of the turbine meter is inherently of light construction and is vulnerable to damage from foreign objects in the

gas stream. Depending upon the degree of cleanliness of the

gas and the degree of caution warranted to safeguard the mechanism, strainers or filters might be installed upstream of the

meter. The rotor and the rotor bearings can also be damaged

from momentary high flow rates encountered when the shut-off

valve is opened too rapidly. To protect against this condition

restricting orifices can be placed downstream of the meter. The

objection to a restriction orifice is, of course, that the pressure loss over the restriction can be objectionable when the

meter is operating at its rated capacity.

There are two principle piping configurations recommended for

turbine meter installations.

The conventional coupling utilizes ten diameters of straight

full pipe upstream with straightening vanes. The downstream

contains five or more full pipe diameters. Test results have

shown that the conventional coupling is suitable for most installations encountered in meter station designs.

The short coupled installation consists of a full size elbow

or tee upstream and downsteam. In addition to being a space

saver, the short coupled configuration can be designed to provide bypass and test connections. If the short coupled configuration is utilized it is a must that the meter be calibrated

in this position, particularly for high pressure service.

FIELD TESTING

There are several methods that can be utilized for field testing

a turbine meter. The choice of which one will be determined

by operating conditions, location of meter, number of meters

involved, preference, experience of personnel, and availability

of equipment. In general, the methods available for field calibrating the turbine meter are the same as those used on other

high volume gas meters, such as critical flow prover or low

pressure provers.

877
Current field test methods include the spin test and transfer

proving

,

SPIN TEST

The spin test consists of spinning the rotor of a gas turbine

meter to a given speed in a draft-free environment and letting

the rotor coast to a stop. The time it takes the rotor to

coast to a stop is the spin down time (Fig. 2) . The spin test

of a gas turbine meter is no more a calibration than a physical

inspection of an orifice plate is a calibration of a plate's

flow coefficient.

0 10 20 30 40 50 60 70 80 90 100

PERCENT FLOW RATE

MAX. FLOW RATE (A.C.F.H.): 18,000

FIG. 2 Changes in proof of 4-inch gas turbine meter due to

variations in spin time.

The spin test at best can be used to infer calibration? that is,

if under similar conditions , there is no less of spin time then

the meter can be expected to have maintained its original proof.

878
In comparing the spin test to the physical inspection of an

orifice plate it can be pointed out that when an orifice plate

is found to be dirty or poor measurement conditions exist, the

plate is cleaned or replaced, the condition is corrected and

the coefficient is then assumed correct because all conditions

are met. Likewise, with the turbine meter, if the spin test

repeats and there is no physical damage to the meter, then its

flow coefficient can be expected to remain unchanged.

TRANSFER PROVING

Periodically it becomes necessary to perform a test in addition

to checking the mechanics of the primary devices in order to

verify accuracy. In doing this the most desirable method is to

compare the device to an accepted and recognized primary standard .

In the United States the primary measurement standard for gas

volume is the cubic foot bottle calibrated by the National

Bureau of Standards. However, use of the calibrated bottles

for production or field testing is highly impractical.

Therefore, it has become necessary to designate more practical

methods for these operations and in doing so establish secondary

proving standards. These proving methods obtain a statement of

accuracy from a primary standard; thus, the original of the

transfer prover.

It is of particular importance that the field test be conducted

under steady state conditions. That is, the turbine meter is

brought up to speed and allowed to run for a period of time and

the pressures and temperatures are allowed to stabilize. During

a test it is necessary to run a mechanical drive meter for at

least two revolutions of the output shaft. This allows the

slowest gears in the train to make several revolutions and balance out gearing irregularities.

Transfer proving consists of meter calibration by means of a transfer or master meter. In transfer proving the master meter

and test meter are piped in series. A selected volume of gas

is simultaneously passed through both meters and their registration is observed. These observations (registration) are

then corrected for any temperature and pressure difference between the two meters.

A percentage error is determined for any flowing conditions by

installing the master meter in the pipeline with the test meter,

or at atmospheric conditions by installing the test meter in

series with the master meter and using a portable blower to

provide through the two meters.

Such devices as the orifice meter, critical flow provers, rotary

meter and turbine meter are used as transfer provers (Fig. 3).

879
FLOWING CONDITIONS

v AIR - 48.7 PSIA & 70°F a AIR — 48.7 PSIA & 90°F

CALIBRATION BY CRITICAL VENTURI

CALIBRATION BY MASTER METER

CALIBRATION BY FIELD ORIFICE

• 1.0 BORE

o

CO 117

CO

I 2 116

§115

Q_

£114 U

0.582 NAT. GAS @ 700 PSIG & 105°F

o^ 1i.j^ RORF Dune

2.125 BORE

4" FLOW CALIB

SENIOR FITTING

a 2.750 BORE

1

T _ ^ o Q 0 o o o cP A *a A*

# or " ^ d ^

A AAA

D Q

1

i i i i i i i i i I I I

±.5%

i i i i i i 6 8 10 12

ACF OR DIAL RATE (MCFH)

14 16 18

FIG. 3 High pressure orifice field calibration of a 4-^inch

turbine meter.

These devices obtain their statement of accuracy either by having

been calibrated by a bell prover which in itself is a transfer

prover calibrated by the cubic foot bottle, or by reference to

tolerances as established by previous thruput tests upon which

appropriate industry standards are written. Each of these methods

establishes a meter's performance to within specified tolerances.

REFERENCES

1. Gebre H. and Smits J. - "A Turbine-Type Gas Flow Meter"

Flow Measurement in Closed Conduits Vol. II 1962

2. Miller R.E. - "Evaluation of Turbine Meter Performance"

American Gas Association Transmission Conference, 1971.

88; 0
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

ON A NEW METHOD OF GAS FLOW MEASUREMENT USING CRYOGENIC TECHNIQUES

D. B. Mann and J. A. Brennan

Cryogenics Division

Institute for Basic Standards, National Bureau of Standards

Boulder, Colorado 80302

Direct comparison of ambient temperature gas flow measurements to mass is made possible by a new continuous closed-loop

measurements method. The direct comparison is made possible by

modification of a proven flow reference system based on masstime.

The complete gas flow reference system has, as yet, not been

demonstrated physically; however, the liquefied gas portion has

been continuously proven over a period of six years and is the

flow standard for the recently developed cryogenic flowmeter

code. Modifications are state-of-the-art additions of heat

exchangers and process control. It is believed that the accuracy

of the liquid system (less than + 0.2%) will be maintained after

modification.

If implemented, the method would be extremely valuable in

improving and redefining many of the present gas flow measurements and standards. Gas and liquid meter coefficients could be

related directly to mass and to each other without the tedious

reliance on state equations and critical pressure and temperature

measurements. The validity of liquid calibration for gas service

could be confirmed on a mass basis. Current codes and recommended

practices could be supported and improved with new, more accurate

empirical data. The method can be extended to mixtures such as

natural gas and would improve the accuracy of these measurements.

It is believed that this modification is a significant and

timely improvement within measurement science which could have

major impact on custody transfer and energy conservation.

Key words: Cryogenic; flow; gas; liquid; mass flow; measurement.

881
1. Introduction

A new and more accurate method of measuring gas flow in terms of mass

is possible using existing, well developed cryogenic techniques. The

method, which could be used to redefine present gas flow measurement codes

and standards, is a natural and logical development from codes and standards measurements of cryogenic liquids such as oxygen, nitrogen, argon and

hydrogen. The method is closed-looped allowing extended periods of observations at set gas pressures, temperatures and flow rates. Gas pressures

above 1000 psi and gas temperatures above ambient temperatures are possible.

The method is suitable for air, oxygen, nitrogen, argon, methane and natural

gas mixtures of methane, ethane, propane, butanes, and nitrogen, and could

be extended to neon, hydrogen, helium and other fluids.

Total uncertainty in mass flow is based on an existing cryogenic flow

reference facility having over six years of operational experience. If

successfully applied to gas flow measurements, gas flow measurements and

standards could be improved by a factor of from five to ten.

Other studies made possible with this new method are:

a) Direct comparison of gas to liquid flow on a mass basis.

b) Intercomparison of gas to water or other fluid flow on a mass

basis.

c) Performance of gas flowmeters operating on low temperature gases.

d) Investigation of Reynolds number variations at constant mass

flow.

The new method will be described in general terms with several operating modes followed by a detailed description of the existing Cryogenic

Flow Facility and modifications necessary to prove the new method.

2. Gas-Mass Flow Reference System

The system is shown in an elementary schematic in Figure 1 and thermodynamically in figure 2. The cyclic process is continuous with only power

to the pump and refrigerant to the subcooler as requirements. Liquefied

gas subcooled under moderate pressures (0.7 MPa) is fed to the inlet of the

pressure pump 1. The pump is of the turbine type to minimize flow pulsations and capable of pressurizing the liquefied gas to above critical

pressures 4 MPa) at 2. This single phase compressed fluid is then fed

to the first pass of the counter flow regenerative type heat exchanger

where it is heated to ambient temperature or above at 3. An electric

heater is installed at this point to stabilize the gas temperatures. The

gas meter test section contains all necessary upstream and downstream flow

conditioning such as pipe length, flow straighteners , the meter and all

other standard meter run equipment. Gas leaving the gas meter test section

will be at a lower pressure (depending on the meter type) and at a different

temperature (depending on test and ambient temperatures) at 4. The gas

882
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883
ENTROPY

Figure 2. Operation of flow measurements system at above critical pressures.
will then be fed to the second pass of the counter flow heat exchanger

where it leaves as a compressed fluid at cryogenic temperatures at 5. The

pressure of the fluid is reduced by a simple expansion through an expansion

valve to moderate pressures 0.7 MPa) and fed to the subcooler at 6. The

subcooler provides a controlled liquid temperature prior to the liquid

meter test section.

The liquid meter test section contains all necessary liquid flow

treatment and the cryogenic flowmeter. This meter can be of the same type

and design as the gas meter or can be a proven cryogenic meter used as a secondary standard.

After metering, the liquid enters the catch and weigh system which are

shown as concentric containers. The weigh tank is supported on a load

string and a load cell. Load cell calibration is maintained with standard

weights referenced to NBS standards of mass.

At periodic intervals the drain valve in the weigh tank is closed and

a quantity of cryogenic fluid is accumulated in the weigh tank 10. The

time required to accumulate a given weight of liquid is measured and the

mass flow rate calculated. The weigh tank drain valve is then opened and

the liquid cryogen is released to the catch tank 11.

Pressures within the catch and weigh tank are maintained above the

fluid saturation pressure by inert gas pressurization to maintain subcooling

and to eliminate flashing after expansion at point 6. The actual pressure

selected will also depend on the pressure ratio available from the pressure

pump.

The schematic of figure 1 is the simplest equipment arrangement and

will allow operation of gas meters above the critical pressure and with low

pressure drop through the gas meter. These conditions can be met with

flowmeters with 100 in. water pressure loss such as orifice meters, venturi

meters, some turbine meters and most non-intrusive type flowmeters.

For operation at pressures below critical pressure, some additional

equipment must be added. Figures 3 and 4 show these modified arrangements.

In figure 3, a low-head high-volume flow circulation pump is used in

place of the pressure pump. A boiler and heat source are added to vaporize

the liquid prior to heating to ambient temperatures and a condenser is

required to reliquefy the gas prior to subcooling. This additional equipment is made necessary because the temperature of condensation of the fluid

from the gas meter test section is equal to or less than the boiling point

temperature of the fluid discharged from the circulation pump. A high

capacity blower could be installed at the outlet of the gas meter test

section to increase the pressure and therefore the saturation temperature,

but this would defeat one of the advantages of the method which is low

power requirements and simplicity.

885
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; ENTROPY

Figure 4. Operation of flow measurements system at less than critical pressures.

887
For the special case of large meter pressure losses, such as choked

nozzle flow, a combination of the two cycles would be necessary. The pump

must be a pressure pump, as in figure 1, to provide the necessary high pressure

at the gas meter inlet; however, a condenser and heater will be necessary

as in figure 3, to provide external heating of the high pressure stream and

condensation of the low pressure stream. No pressure reducing valve would

be required.

3. Liquid Mass Flow Reference System

In the gas mass flow measurement system just described, the actual

mass flow measurement takes place while the gas is in its liquid phase.

For commercial industrial gases such as oxygen, nitrogen, argon, methane

and natural gas mixtures, the liquid phase is in the cryogenic temperature

region. This is a fortunate situation because we can establish the potential

limiting accuracy of the gas mass flow system by referring to an existing

cryogenic liquid mass flow measurement system.

The cryogenic flow measurement reference system was established in

1968 in a joint government-industry program on cryogenic f lowmetering.

Under that program, NBS joined with the Compressed Gas Association and

state regulatory agencies to establish a flow reference system, to evaluate

existing flowmeters used in commercial service, to evaluate new measurement

methods and to establish a national model cryogenic flow measurements code

through the National Conference on Weights and Measures. A schematic of

the facility constructed under that program is shown in figure 5. The

similarity to the previously described gas mass system is obvious. The

basic operating principles of the two systems will be very similar and the

basis for the estimate of uncertainty in mass flow measurement should be

identical

.

The cryogenic flow measurement program was completed in 1976 with the

acceptance of a permanent cryogenic flow measurement code by the Conference

on Weights and Measures. The description of the facility and program are

well documented in the literature (see references). The most pertinent

reference to this discussion of the gas mass flow system is the work of

Dean, et al . (1971). This report is a summary of an 18-month study to

determine the accuracy of the flow reference system, "At this time the

uncertainty of the measurement of totalized mass flow is estimated to be

+0.18%. This figure includes an uncertainty of +0.12% for known sources of

systematic errors plus an uncertainty of +0.06% for random error. The

estimated uncertainty due to the random error is three times the standard

deviation calculated from 23 applications of the calibrated masses over a period of three months." The report provides a complete description and

data on how this accuracy statement was determined and, in addition, provides a description of the process control which allows the reference

system to be kept under statistical control.

Over sixty flowmeters based on five different generic types were included

in the evaluation program. Transfer standards were developed for field

certification of commercial meters as well as being used in inter-laboratory

888
889
comparisons which provided additional validity to the accuracy statement.

Confidence in the ability of this system to provide a mass flow measurement

was established in almost 4000 hours of operational experience. The report

itself was a provisional accuracy statement and during the six years of

operation, more precise measures of systematic error have been made which

should allow the uncertainty statement to be improved significantly.

However, if the accuracy of this system could be maintained while adding a regenerative heat exchanger and gas flowmeter test section, the improvement

in measurements of a gas mass flow reference would be significant. Present

estimates of the latter are between plus or minus one and two percent, therefore, an improvement could be realized of between five and ten over present

methods.

The process fluid used in the facility of figure 5 is nitrogen although

argon has also been used successfully. The system itself could be adapted

to other cryogenic fluids such as air, oxygen, hydrogen, methane, ethane,

propane and liquefied natural gas.

4. Applications

The potential for such a system, if the total uncertainty can be maintained at +0.2% or less, is impressive and would allow the following studies:

o Redefinition of gas flowmeter factors relative to mass flow

directly and continuously. No intermediate calculations or

approximations are required.

o Gas flow pressures and temperatures could be controlled independently of the mass flow reference and would allow wide variations

in experimental conditions. An added benefit, particularly in

the case of nitrogen as the process fluid, would be that the

Reynolds number can be increased by a factor of 4 or 5 by reducing

the temperature and therefore the viscosity of the gas.

o Gas flowmeter performance could be compared directly with existing

codes and standards which are based on volumetric or water calibration predictive calculations. Errors in predictive correlations

could be identified and corrected.

o The working hypothesis that water calibration may be transferred

directly to gas flow can be tested to an accuracy not previously

possible. Errors in this hypothesis can be identified and corrected.

o The effects of upstream and downstream meter flow conditioning

(straight runs and/or flow straighteners ) can be redefined with

gas flow with greater accuracy than previously available.

o Evaluations of potential gas flow transfer standards on a long

term mass flow basis. This would include such devices as the

choked nozzle and other new devices such as the laser Doppler

velocimeter or ultrasonic meters, the success of which would make

gas flow or water flow reference systems increasingly unnecessary.

890
o An evaluation of velocity effects on direct reading densitometers.

This work would be in support of the development of a natural gas

energy meter.

o As a precision reference system, test sections could be used to

investigate the development of boundary layer and turbulence, and

the effects of these phenomena on gas meter size.

Component design would be heavily influenced by the selection of the

fluids to be used. If multiple fluids were to be tested, then components

must be designed for the most severe conditions. This would particularly

be the case in the selection of pressure pump and regenerative heat exchanger. Table 1 is the result of calculations made on two different

applications. The methane/LNG system was based on a flow rate of 16.4

cubic meters per second (50 MMCFD). It is believed that a system of this

size would meet many of the natural gas industry requirements for flow

calibration in meter studies.

The nitrogen example is basically a modification of the existing

cryogenic flow facility to demonstrate the feasibility of the gas flow

measurement reference system. The gas flow rate of 1.2 cubic meters per

second (2750 SCFM) would be of such a capacity as to allow testing of

existing codes and practices and at the same time would not require a large

investment in heat exchange or pressure pump equipment.

Other applications are also possible and a reduction in size of the

facility for small flow should also be feasible. This suggests that a small portable gas measurement mass flow standard could be constructed and

used routinely for field calibration and certification of meters.

5. Summary

Direct comparison of ambient temperature gas flow measurements to mass

is made possible by a new continuous closed loop measurement method. The

direct comparison is made possible by modification of a proven flow reference system based on mass time. The anticipated total uncertainty in mass

flow of gas at operating conditions should not exceed +0.2%. This is an

improvement of a factor of 5 to 10 over existing gas flow standards.

At a time when natural resources and raw materials are decreasing in

quantity and increasing in cost, it is believed that new measurement

methods, such as proposed, are essential to provide the necessary measure of

accuracy and precision for establishing product quantity and value.

891
Table 1. Examples of application of gas mass system.

Gas Side

3

Flow rate (m /s @ 14.73 psia to

Pressure (MPa)

Temperature (K)

Pipe diameter (cm)

Methane/LNG Nitrogen

60°F) 16.4 1.2

5.5 3.4

289-300 289-300

20-25 10-15

Heat Exchanger

Heat transfer load (MJ/s)

Liquid Side

Weigh tank capacity (m-)

Catch tank capacity (m ) Pressure (MPa)

Temperature (K)

Pipe diameter (cm)

Pressure Pump

3

Flow rate (m /s)

Pressure ratio

Power Requirement (kJ/s)

9.27 0.52

3.8

5.7

0.83

100.0

10.0

0.379

0.433

0.69

80.0

7.6

0.027

6.6

395.0

0.0019

5.1

16.04

892
REFERENCES

ISA, Ad Hoc Committee Report of Flow Measurements, Instrument Society of

America, Pittsburgh, PA (1967).

Mann, D. B. , Cryogenic flowmetering research at NBS, Cryogenics ]_]_, 179

(1971).

J. W. Dean, J. A. Brennan and D. B. Mann, Cryogenic flow research facility

of the National Bureau of Standards, Advances in Cryogenic Engineering 14^

(Plenum Press, New York, 1969).

D. B. Mann, J. W. Dean, J. A. Brennan, and C. H. Kneebone, Cryogenic Flow

Research Facility, (Unpublished NBS report to sponsor, Jan. 1970).

J. W. Dean, J. A. Brennan, D. B. Mann and C. H. Kneebone, Cryogenic flow

research facility provisional accuracy statement, Nat. Bur. Stand. (U.S.)

Tech. Note 606 (1971).

J. A. Brennan, J. W. Dean, D. B. Mann and C. H. Kneebone, An evaluation of

cryogenic positive displacement volumetric flowmeters, Nat. Bur. Stand.

(U.S.) Tech. Note 605 (1971).

J. A. Brennan, R. W. Stokes, D. B. Mann and C. H. Kneebone, An evaluation

of several cryogenic turbine flowmeters, Nat. Bur. Stand. (U.S.) Tech.

Note 624 (1972).

J. A. Brennan, R. W. Stokes, C. H. Kneebone and D. B. Mann, An evaluation of

selected angular momentum, vortex shedding and orifice cryogenic flowmeters,

Nat. Bur. Stand. (U.S.) Tech. Note 650 (1974).

National Bureau of Standards, Specifications, tolerances, and other technical

requirements for commercial weighing and measuring devices, Nat. Bur. Stand.

(U.S.) Handbook 44, 4th Ed. w/revisions (1972).

893

National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

AN ANATOMY OF THE INTERNATIONAL STANDARDS

PRODUCING SYSTEM - FLOW MEASUREMENT

L. K. Irwin

Mechanics Division

National Bureau of Standards

Washington, D. C. 20234

The several international organizations that, collectively,

form the "system" to promulgate and maintain the documents and

publications that are explicit or de facto international standards

are described. Included in this review are the International

Organization for Standardization, International Electrotechnical

Commission, International Organization of Legal Metrology,

European Economic Community, European Committee for Standardization, World Metrological Organization, and International Bureau

of Weights and Measures. Also, elements of organizations, that

are not international by design but that generate standards used

internationally, are reviewed. This second group includes the

American Society of Mechanical Engineers, American Society for

Testing and Materials, American Petroleum Institute, and British

Standards Institution.

Summary information is given for the current activities of

most of these organizations and the scope and technical output

of selected technical committees as they affect standards for

flow measurement or the quantitative determination of volume or

mass of fluids. The efforts on coordination and apparent overlap of the work are noted. Some discussion of the existing and

needed relationships between physical measurement standards and

international documentary standards is given.

Key Words: Closed conduit flow; flow measurement; international

standards; open channel flow; petroleum product standards.

1 . Introduction

Flow measurement is usually a means to an end; to determine the quantity of

material passing a point. This determination results from sets of measurements

of parameters such as length, time, temperature, mass, pressure, volume, density,

viscosity, and others. Thus, the complexities of the standardizing documents

and of the procedures for using them are often greater than corresponding

standards for other quantities. The problems of understanding and using standards are compounded when they are international standards since translations

do not accommodate many of the idiomatic differences in language country-tocountry and industry-to-industry.

895
In this country, technical managers, engineers, and purchase agents have

problems when they attempt to utilize standards in their operations or to

respond to contractual requirements that include standards. These arise from

several causes including (a) the corruption of the meanings of "standard,"

(b) the multiplicity in the form and structure of standards, (c) the lack

of ready access to all the required documents, particularly when there is

interdependence between the documents, and (d) the absence of nationwide

quality control for standards.

Except for brief comments on the meanings, form and structure, and quality

control for standards, this paper will discuss a limited aspect of "ready

access" to the international standards relating to fluid flow measurements.

Readers of the English-language standardization and standards periodicals

have been exposed to numerous editorials and feature articles on the 'what',

'why', and 'how' for standards, on rationales to support the several viewpoints

of the editors, and on definitions for standards and standardization. An

extensive two-part series [1,2] 1 is given in the February and March 1977

issues of ASTM^ Standardization News. A related, intellectual discussion by

Verman and Visvesvaraya [3] is given in the first issue.

The following discussions will accept Webster's Dictionary for

standard, n- that which is established by authority, custom or

general consent, as a model or example; criterion;

test,

and will not attempt to establish a new, or correct, or incorrupt meaning.

The study is concerned primarily with documentary standards, either explicitly

entitled or de facto.

The form and structure of standards are beyond the scope of this paper

except to call attention to the great variety in which users can expect to

find the desired information. For example, compare the one-page ISO 5024-

1976 (See Appendix 2, Table 2) with ASME PTC 3.3-1969 (See Appendix 2, Table

7). In one page, the former provides the standard reference conditions for

temperature and pressure as the basis for comparing quantities measured under

other conditions and the latter includes most of ASTM D 1071-55 for information

on how to test gas provers and a variety of flow meters along with more than

fifty pages of other material. The procedures in D 1071-55 are applicable to

many non-fuel gases. But, how can all potential users of this flow measurement

standard know of the multiple applications for these documents?

The proper exercise of quality control for documentary standards is an

elusive goal and deserves more than the passing notice given here. Agreement

on proof of "quality" is not general and, sometimes, not attempted. Some

attributes of quality control would include completeness, specific scopes,

demonstrable uncertainty statements for the necessary physical measurements

and documented calculating algorithms. Others may be equally important.

-j—

Figures in brackets indicate the literature references at the end of this

paper.

2

Complete titles of all organizational acronyms used are given in Appendix 1.

896
Those several organizations and institutions, that promulgate, maintain or

influence international standards, their documentary technical outputs, and the

users of these outputs are treated as a system. The elements of this system

are described as they are perceived to affect flow measurement or the quantitative determination of volume or mass of fluids. The material presented and

discussed may increase "ready access" to available standards by some of the

many users.

2. International Organizations that Promulgate Flow Measurement Standards

Four international organizations have been identified that clearly are producing or issuing documentary standards important to the measurement of fluid

flows. All details concerning the structure of these organizations are necessarily lacking due either to the continuing evolution of their programs of

work or to the author's failure to locate the required documents.

2.1 International Organization for Standardization

The ISO is a voluntary organization 3 comprised of the national standards

bodies of more than 80 countries, with 63 member bodies and 18 correspondent

members at the end of December 1975. The technical work is carried out through

more than 150 Technical Committees (TC) which operate through about 500 subcommittees (SC) and about 1000 working groups (WG) . The secretariats for each

technical committee, subcommittees or working groups are distributed among the

member countries that choose to participate actively in the work (P-members)

and other member bodies are kept informed if registered as observers (0-members)

.

Typically, an international standard evolves from a draft proposal (DP)

of a technical committee P-member or the results of an assignment to a working

group through several stages of comment and revision. When agreement is reached

within the technical committee, the document is sent to the Central Secretariat

for registration as a draft International Standard (DIS) and circulated to all

member bodies for voting. The DIS is sent to the ISO Council for final acceptance if 75 percent of the votes cast are favorable. With Council acceptance,

the document becomes an International Standard subject to review every five

years or earlier when technical changes are agreed to by the members.

The ISO work is available through the approximately 3000 International

Standards currently in use as published or as national standards. The annual

Memento [5] and publications catalog [6] provide connecting data on available

standards and the responsible participating organizations. Two technical

committees, TC 30 and TC 113, have primary assignments to produce flow measurement standards, and technical committees TC 28 and TC 144 are probable sources

for additional standards important to flow measurement. If the titles and

scopes reflect the areas of their activity properly, twelve or more other

technical committees are users of or contributors to flow standards.

Technical Committee 30, Measurement of Fluid Flow in Closed Conduits, has

as its scope:

Standardization of rules and methods for the measurement of fluid

flow in closed conduits including:

(1) Terminology and definitions,

(2) rules for inspection, installation, operation,

International organizations involved in standardization are described briefly

in BSI PD4845 [4]

.

897
(3) construction of instruments and equipment required,

(4) conditions under which measurements are to be made,

(5) rules for collection, evaluation, and interpretation of

measurement data, including errors.

At the beginning of 1977, seven subcommittees and four working groups were

organized as shown in Figure 1 to conduct this program of work. The TC has

produced seven International Standards and one Technical Report; it has ten

documents advanced to DIS or DP status (See Appendix 2, Table 1); and fourteen other items of work in various stages of development and comment. The

wide-spread interest in this program of work is reflected in the fifteen ISO

and IEC liaisons and the five external liaisons with intergovernmental and

international technical organizations.

The scope for Technical Committee 113, Measurement of Liquid Flow in

Open Channels is as follows:

Standardization of rules and methods relating to different

techniques for the measurement of liquid flow with particular

reference to sediment transport in open channels including:

(1) terminology and definitions,

(2) rules for inspection, installation, operation,

(3) instruments and equipment required,

(4) conditions under which measurements are to be made,

(5) rules for collection, evaluation, analysis and

interpretation of measurement data including errors.

In 1976, there were six working groups to carry out the program of work as shown

in Figure 2. By the end of 1976, the TC had produced twelve International

Standards, had eleven documents advanced to DIS status (See Appendix 2, Table

2) and had eighteen other working projects including revisions to three standards. There are five ISO and IEC liaisons and seven external organization

liaisons

.

Technical Committee 144, Air Distribution and Air Diffusion, is relatively

new and had produced one standard on vocabulary by the end of 1976. The scope

reads as follows:

Standardization in the field of air distribution and air

diffusion including performance testing both in the laboratory and on site, dimensional characteristics and terminology.

Specifically excluded will be fans (TC 117 refers), heat

exchangers (TC 116 refers) , filters (TC 142 refers) , cooling

and air conditioning devices (TC 68 refers) , but when these

elements are an integral part of the air terminal device or

high velocity/pressure assembly or low velocity/pressure

assembly, or valve or damper, they are included.

This TC is organized with four subcommittees that have five projects in their

program of work. These are (1) aerodynamic testing and rating of air terminal

units, (2) aerodynamic testing and rating of constant and variable flow rate

assemblies, (2c) aerodynamic testing of single duct units, dampers and valves,

898
(3a) technique of airflow measurements in conduit, and (4) acoustic testing and

rating. There are seven liaisons with other ISO committees and two external

liaisons. The membership consisted of eleven participating and sixteen observer

bodies at the end of 1976.

The other significant and direct ISO involvement in fluid flow measurements

is Technical Committee 28, Petroleum Products with a scope as follows:

Standardization of methods of measurement, sampling and test,

nomenclature, terminology and specifications for petroleum

and petroleum products.

In 1976, there were five subcommittees and agreement to form a sixth as shown in

Figure 3.

The work of this TC is an example of flow measurement being the means to

an end, an aid in determining the quantity of material, A review of the titles

of thirty-eight standards produced through 1976 does not show the words "flow"

or "flowmeter" in any title. However, ten of these documents (See Appendix 2,

Table 3) deal with fluid properties or with procedures for sampling and obtaining

one or more fluid property of the product. The high level of activity in this

TC is reflected in the twenty-six documents designated DIS, seventeen designated

DP and thirty other projects or studies underway at the beginning of 1977. The

titles of fifteen of the DIS or DP documents (See Appendix 2, Table 3) indicate

the continued output of standards important to flow measurement technology. The

terms 4 that occur in the titles of documents listed in Table 3 include viscosity,

kinematic viscosity, temperature measurement, density, relative density, volumetric measurement, standard reference conditions, positive displacement meter,

turbine meter, measurement of quantities, calculation of quantities, tank calibration, container calibration, and measurement of level.

An incomplete list of titles for other ISO technical committees that

have or appear to have good reasons to use flow measurement standards or to

participate in their formulation are given below. Excerpts from the scope

of a few committees are given as quotations.

TC 11 Boilers and pressure vessels "Methods of inspection and testing

such boilers and vessels."

TC 64 Methods of testing fuel-using equipment "Standardization of

methods of testing for performance and efficiency of fuel-using

equipment .

TC 67 Materials and equipment for petroleum and natural gas industries.

TC 70 Internal combustion engines

.

TC 86 Refrigeration.

TC 112 Vacuum technology.

TC 115 Pumps "Standardization of methods for testing pumps on test

stands, in their final installations, on models ..."

TC 116 Space heating appliances.

TC 117 Industrial fans.

TC 131 Fluid power systems and components "Standardization in the

field of fluid power systems and components, comprising

terminology, ... and testing and inspection methods."

In some cases, the full length term has been editorially shortened.

899
TC 161 Control and Safety Devices for Heat Generating Systems.

It is unclear how those technical committees for equipment powered by internal

combustion engines (TC's 22, 23, 110, and 127) serve their flow measurement

needs since no direct liaisons are indicated with TC 30 or TC 28.

2.2 International Electrotechnical Commission

The IEC is affiliated with the International Organization for Standardization

and has an organizational system and operating rules that are similar, in most

respects, to ISO. The Commission consists of more than 40 National Committees,

each representing one country, which are required to be as representative as

possible of all electrical interests in the country concerned. The IEC produces Recommendations and Reports that are approved if not more than 20 percent

of the member committees cast negative votes. It operates with more than 70

technical committees and 100 subcommittees [7] and has produced nearly 600

approved Recommendations and Reports [8,9],

Although the chief outputs of IEC deal with electrotechnical matters, some

areas of the work impinge directly on flow measurement technology -- particularly

the work of TC's 4, 5, and 65. TC 4 Hydraulic Turbines and TC 5 Steam Turbines

have produced four recommendations (See Appendix 2, Table 4) for acceptance

tests of hydraulic or steam turbines. These documents contain substantial

amounts of technical information to assist with making flow measurements suitable

for these applications. Subcommittee B of TC 65 Industrial Process Measurement

and Control is responsible for standardization of pneumatic control devices

including performance testing and has a program of work that includes the use

of flow measurements. These three IEC technical committees have liaisons with

ISO/TC 30.

2.3 International Organization for Legal Metrology

The OIML is an intergovernmental (treaty) organization set up to resolve

the technical and administrative problems of legal metrology. It is particularly concerned with the compatibility of standards of measurement and the legislative and Government regulations which may affect such standards of measurement. See ref. 10 for a concise review of the USA involvement. As of 1976,

there were 43 member states. Standards are developed through technical committees called Pilot Secretariats (PS) and subcommittees called Reporting

Secretariats (RS) . The responsibility for administering the Pilot or Reporting

Secretariats is assigned to member states on a request basis. There are 26

active PS's and about 160 RS's that have produced more than 30 International

Recommendations through 1976. The programs of work of four PS's have produced

documents or have active projects relating to flow measurement. Two of these,

PS 5 Measures of Liquid Volumes and PS 6 Measures of Gas Volumes, are directly

involved in flow measurement standards. Organizational charts are shown in

Figures 4 and 5 and their published standards or drafts in progress are given

in Appendix 2, Table 5. Certain of the International Recommendations produced

or being developed by PS 9 Measure of Densities, and PS 30 Physio-Chemical

Measures are important for flow measurement, especially, those dealing with

humidity, liquid and gas densities, viscosity and other properties of fluids.

Also, PS 7 Measure of Masses, PS 11 Measure of Pressure, PS 12 Measure

of Temperatures and of Calorific Energy, and PS 24 Equipment for Legal Metrology

9.00
Bureaus have produced standards in their respective areas that are important to

flow measurement laboratories and, in certain cases, to field measurements.

The liaisons of PS 5 and PS 6 are mostly with other OIML technical committees

or with ISO/TC 28 and TC 30. There is one joint OIML/PS 5/RS 13 - ISO/TC 28/SC 5

task group that is trying to deal with the problem of eliminating gas during

the measurement of volumes of flowing hydrocarbons.

2,4 European Economic Community

This organization, often called the 'Common Market', has a continuing

interest in standardization for the primary purpose of removing technical barriers

to trade among its nine member states. The EEC standards are issued as directives

under Article 100 of the Treaty of Rome, 1957. The texts of proposed and adopted

directives are published in the EEC Official Journal. In principle, the EEC work

on standardization avoids activities which duplicate those of other organizations.

From a review of a recent article [11] in Trade and Industry, it is unclear how

closely they adhere to this principle, Eleven items in this article that implied

flow measurement were tabulated (See Appendix 2, Table 6). These show that the

EEC has a substantial involvement in promulgating flow measurement standards.

Information obtained by the author to date is insufficient to comment on the

extent to which these Directives are transformations of documents from other

organizations or represent direct outputs of technical committees of EEC.

3. Other International Organizations

3.1 European Committee for Standardization (CEN)

The CEN is a regional, voluntary standardization organization comprising the

national standards bodies of 15 EEC and European Free Trade Association countries.

The technical work is conducted by working groups assigned to the member bodies

with proposals coming from CEN members or international organizations. Priority

is given to subjects proposed by European intergovernmental organizations. By

early 1976, the approximately 60 working groups of CEN had produced 23 European

Standards (EN) and had 59 draft standards in the final stages of preparation

[12] . The amount of flow measurement technology that will be incorporated into

the European Standards is unclear at this time. The subjects or titles of some

of the working groups include metrological equipment, gas and oil pipelines,

fuels , central heating boilers, gas governors, industrial valves and drainage

equipment. These suggest flow measurement standards from CEN in the future.

3.2 World Meteorological Organization (WMO)

The WMO is an agency of the United Nations of which 140 states and territories are members. Its concerns include the total water resources of the world

and especially the meteorological cycles through which water is transported in

varying amounts over this planet. From this interest, WMO adopts "Technical

Regulations" and "Guides" for use by member organizations about how to obtain

useful data on precipitation, water levels, stream flow, stored water and

other hydrological elements required to assess the quality and quantity of

water in the world. The WMO produces and distributes numerous publications

[13] for systems and instruments on data acquisition, including practices,

procedures, and specifications important to water and air flow measurement.

901
3.3 International Bureau of Weights and Measures

The BIPM is the international metrological laboratory operated by the

International Committee of Weights and Measures, This laboratory provides the

means for national measurement standards to be compared with internationally

agreed standards. With proper attention to measurement transfer chains from

national standards to field measurements, the international documentary standards that depend upon measurements of derived quantities such as flow, viscosity,

pressure, etc., will be compatible with each other and consistent within the

interdependent sets of standards.

4. National Organizations Whose Documents Sometimes Serve as

International Flow Measurement Standards

The transformation of national standards into international standards to

effect a specific exchange of goods or services is probably as old as the

existence of recognizable standards. Some special cases of national standards

serving as international standards deserve comment.

4.1 The American Society of Mechanical Engineers and

the American Petroleum Institute

There are at least two American organizations that have produced extensive

technical information and published documents which have served as de facto

standards. The American Society of Mechanical Engineers produces and maintains

the Boiler and Pressure Vessel Codes and the companion Performance Test Codes

(formerly, Power Test Codes), known worldwide, without "standard" occurring

in either the titles or descriptive information about these documents. Several

of the ASME Performance Test Codes (PTC) contain straightforward prescriptions

about the measuring devices and the methods for the flow measurements performed

during acceptance tests of power plant equipment. A partial list of these

codes is given in Appendix 2, Table 7. When abridged flow measurement procedures are cited in these codes, there are numerous references to the book

popularly known as "Fluid Meters" [14] and its supplement on applications [15].

Also, PTC documents make use of ASTM standards and, occasionally, make reference

to the AGA Report No. 3 [16] (also, published as API Publication 2530) for gas

flow measurement technology.

The other American source of volumetric flow measurement standards is the

American Petroleum Institute whose measurement publications [17] have been

used worldwide for quantifying the amounts of petroleum products. These

publications will deal with volume and mass measuring systems, meter proving,

measurement procedures in the field, properties of fluids, calculating procedures and other information. This manual has many of the attributes of

a de facto international standard, i.e., has international acceptance and use.

In fact, the activities of ISO/TC 28 reported above show that a significant

amount of the measurement technology generated by API is being transferred

to International Standards. Pena and Resnick [18] reported on this trend

earlier.

4.2 American Society for Testing and Materials

The largest single source of standards in the United States is the American

Society for Testing and Materials (ASTM) which has as the central element of

902
its scope "the development of standards on characteristics and performance of

materials, products, systems, and services; and the promotion of related knowledge." At least four of its more than 140 technical committees have produced

or have work underway on methods of flow measurement, on specifications for

flow measuring devices or on measurements of properties of fluids. These

committees include:

D-2 on Petroleum Products and Lubricants,

D-3 on Gaseous Fuels,

D-19 on Water, and

D-22 on Methods of Sampling and Analysis of Atmospheres.

Particular ASTM standards on flow measurement can become used internationally

through reference or inclusion in other documents such as the ASME Performance

Test Codes or the API Measurement Manual. To date most of the ASTM fluid flow

standards (see Appendix 2, Table 8) have dealt with water in open channels or

gases in closed conduits.

4.3 British Standards Institution

The recognized body [19] in the United Kingdom for the preparation and

promulgation of national standards is the British Standards Institution (BSI)

.

This organization also represents the United Kingdom in a wide variety of

international standardizing activities. The international character of

certain British Standards (BS) results, in part, from the use of BS documents

by that economic and cultural association of nations often referred to as

the British Commonwealth and to past political connections with these and

other national entities. Complete sets of British Standards are maintained

in 89 countries. There are five or more locations with complete BS collections

in Australia, Canada, India, Malaysia, New Zealand, Nigeria, South Africa and

the United States of America. Documents that deal directly with flow measurement include:

BS 1042: Methods for the measurement of fluid flow in pipes

(three parts)

,

BS 3680: Methods of measurement of liquid flow in open channels

(thirteen parts) , and

BS 4161: Gas meters (six parts).

5. Discussion

The upsurge in numbers and variety of international standards has been reflected by the increasing pressures on several components of the standardization

system. Until recently, the chief stimulus for international standardization

has been the self (private) interest of groups of people and organizations

with common technological information and goals. Now, we observe significant

efforts to serve the public interest in standardization through intergovernmental

organizations. As one result, there are indications of competition to produce

and promulgate standards among the institutions representing the private interest

and the public interest. Also, philosophical distinctions between standards and

regulations [20] and bases for voluntary versus mandatory standards [1,3] are

receiving attention. Additionally, the perceived present or future shortages

of economically important fluids including water and liquid and gaseous hydrocarbons have caused increased activity to develop acceptable, uniform procedures

903
for quantifying and exchanging these commodities.

These pressures to produce more standards also lead to attempts to coordinat

the work. For flow measurement, coordination is usually accomplished by liaisons

between the several technical groups that produce and use the standards and

through the reviews of documents that are recommended for adoption as standards.

The author's observations indicate that many liaisons are not very effective

except when the representative has high competence in the technical area and is

a capable negotiator. Often, the liaison representative's most useful function

is as a reporter. A noteworthy example of apparently effective coordination is

described by Smoot [21] for hydrologic measurements. Coordination through review

of documents tends to concentrate on minimizing damage rather than increasing use

fulness. Documents that do not contradict accepted practices or preempt assignments of responsibility often get perfunctory study by reviewers outside of the

originating committee. Other factors that contribute to limited usefulness of

reviews are that significant changes or expansions of a proposed standard will

almost certainly entail delay in adoption. Also, reviewing is not widely regarded as creative activity. Within the present pluralist social-economic-technical

system, the mechanisms for coordinating the development of flow measurement

standards probably will continue to be weak.

Reviews of the existing international standards for flow measurement and

those that incorporate flow measurements do not show significant overlaps in

technical content. However, examination of the programs of work [22] of several

ISO and OIML committees giving the titles of draft documents and the projects

being studied suggests widespread overlaps of interest and concern for standardization of flow measurement. The clearest overlaps of interest in new standards

are ISO/TC 28 with TC 30 and ISO/TC 28 and TC 30 with OIML PS 5 and PS 6. In

the absence of strong managerial and coordination mechanisms, these potential

overlaps are logical extensions of the organizations (see Figures 1, 3, 4, and

5) and the scopes of these committees. It is unclear whether the technical content of the emerging flow measurement standards from different committees will

be duplicative or contradictory or both. Administrative overlaps appear inevitable. The present flow measurement sections of IEC standards (see Table 4)

are being duplicated piecemeal by new standards with inconsistencies probable

unless close liaisons are maintained. The technical areas of several CEN

working groups are likely to utilize flow measurement procedures that will use

or overlap with activities of ISO and OIML committees.

Readers of the present measurement methods in international standards

will find statements and phrases such as

"... instruments that cannot be calibrated on site shall carry valid

calibration certificates of an official institution.",

"... scales shall be checked using certified weights . . .",

"... shall be straight and remain vertical during use.", and

"... water flow by collection in a tank for a measured time and

weighing is an accurate absolute method."

We recognize that skilled operators with appropriate technical competences

have and continue to use such qualitative information to make measurements to

obtain useful and quantitative data for making decisions. However, the imprecision of these statements provides little guidance for organizations,

operating at different locations or times, to establish efficient measurement

904
chains for assuring comparability of their results. Also, these statements are

nearly useless for resolving differences in results when a standard method is

used at two or more locations or times to evaluate the performance of an item

of equipment or to ascertain the quantity of a shipment of material measured

at locations remote to each other. Most Technical Committee working groups

lack the capability to include the necessary guidelines to assure the integrity

of all measurements used to implement specific standards. Also, it is seldom

within the scopes of their assignments to provide the means for assuring the

consistency of equivalent measurements across political or regional boundaries.

At this time, the use of physical measurement standards referenced to

national metrological institutions that compare national standards with BIPM

is the only recognized system that operates to establish consistent and acceptable measurements internationally. When this system can be coupled with

appropriate statistical tools for testing the quality of the measurements

obtained to implement each flow measurement standard, the entire system of

measurements and data will have the potential for being consistent and comparabl

The motivation for the separate technical committees and working groups to add

criteria for ascertaining the appropriateness of the measurements probably will

have to come from the parent institutions.

6. Conclusions

The international standards producing system has completed, started, or has

under consideration, a wide variety of projects for flow standards. Two organiza

tions, ISO and OIML, are clearly the leaders for producing and promulgating

additional flow measurement and related standards. Some organizations that have

produced flow standards with international status including IEC, API, and ASME

do not appear to have significantly new work on flow measurement standards

underway outside of the ISO and OIML committees.

The need for coordination to avoid duplicate work and contradictions

among the several flow measurement standardizing committees is clear but the

mechanisms for effective coordination are not evident.

Many existing flow measurement standards are flawed if their purpose is

to assure comparability and consistency of data acquired by competent but

different organizations at different times or locations. These standards are

unclear about relationships with nationally maintained physical measurement

standards or how users of the standards can demonstrate the appropriateness

of their measurements and data to overcome this deficiency.

7. References

[1] The What and Why of Standards, Part I, ASTM Standardization News, Feb. 1977,

pp. 24-27.

[2] The People, Process, and Principles of Standards Development, Part II,

ASTM Standardization News, March 1977, pp. 21-25, 60.

[3] Verman, Lai C. and Visvesvaraya, H. C, A systems approach to standardization, ASTM Standardization News, Feb. 1977, pp. 12-23.

[4] Short Guide to International Organizations Concerned with Standards, BSI;

Its Activities and Organization PD4845, British Standards Institution,

London, March 1977. QnK
ISO Memento 1976, International Organization for Standardization, Geneva.

ISO Catalogue 1976, International Organization for Standardization, Geneva.

IEC Handbook, 1975, International Eleetroteohnical Commission, Geneva.

Catalogue of IEC Publications 1976, International Eleotroteehnical

Commission, Geneva

.

IEC Report on Activities for 1974, International Eleotroteehnical Commission,

Geneva

.

United States Membership in the International Organization of Legal

Metrology (OIML) , HUBS LC 1059, May 1975.

Eliminating Technical Barriers to Trade Within the EEC, Trade and Industry,

pp. 228-230, April 23, 1976.

Standards and Legislation in the European Economic Community, BSI News,

pp. 14-16, February 1976.

Catalogue of Publications, Meteorology and Related Fields Such as Hydrology,

Marine Sciences and Human Environment, World Meteorological Organization,

Geneva, April 1975.

Fluid Meters - Their Theory and Application, Sixth Ed., Howard S. Bean,

ed., American Society of Mechanical Engineers, New York, 1971.

Fluid Meters, Part II, Application of Fluid Meters - Especially Differential

Pressure Type, Report of ASME Research Committee on Fluid Meters, American

Society of Mechanical Engineers, New York, 1972.

Orifice Metering of Natural Gas, Gas Measurement Committee Report No. 3,

revised 1969, American Gas Association, Washington.

Manual of Petroleum Measurement Standards, American Petroleum Institute,

Washington (publication of major additions and revisions in 1977 and 1978)

.

Pena, A. A. and Resnick, I., ANSI/ISO codes and standards for hydrocarbon

measurements, Talk at the 49th International School of Hydrocarbon Measurements, Norman, Okla., 1974.

British Standards Yearbook 1977, British Standards Institution, London,

1976.

Ailleret, Pierre, The importance and probable evolution of standardization,

ASTM Standardization News, Feb. 1977, pp. 8-11 (orig. pub. in Revue

G&ne'rale de I'Electricitr^, Sept. 1975).

Smoot, George F., Standardization of hydrologic measurements, Proc. International Seminar on Organization and Operation of Eydrological Services,

Ottawa, Canada, July 15-16, 1976.

Private communications of technical committee secretariats and U. S. Technic

Advisory Groups for ISO technical committees.

906
ISO/TC 30

Measurement of Fluid Flow In Closed Conduits

Sec: AFNOR (France) WG 14

P-members 15 0-members 25 Error Calculation

Steering Group

SC 2 Pressure Differential

Devices

Sec : AFNOR

P-members 11 0-members 5

SC 3 Velocity Area Methods

Sec : AFNOR

P-members 9 0-members 9

SC 4 Tracer Methods

Sec : AFNOR

P-members 7 0-members 9

SC 5 Electromagnetic

Meters

Sec : AFNOR

P-members 7 0-members 8

SC 6 Glossary of Terms

Sec: AFNOR

P-members 5 O-members 8

WG 2 Low Reynolds

Numbers

Sec: BSI (UK)

WG 3 Primary Element

Installation

Sec

:

AFNOR

WG 5 Critical Flow Measurement

Sec: ANSI (USA)

SC 7 Water Meters

Sec : AFNOR

P-members 14 0-members 14

SC 8 Weighing and Volumetric

Methods of Calibrating

Flowmeters

Sec: GOST (USSR)

P-members 7 0-members 4

Figure 1. ISO/TC 30 Measurement of Flow in Closed Conduits

907
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908
ISO/TC 28

Petroleum Products

Sec: ANSI (USA)

P-members 23 O-members 23

SC 1

Terminology

Sec: AFNOR (France)

P-members 20

O-members 24

SC 3

Static Petroleum Measurement

Sec: BSI (UK)

P-members 14

O-members 11

SC 2

Dynamic Petroleum

Measurement

Sec: ANSI (USA)

P-members 15

O-members 14

SC 5

Measurement of Light

Hydrocarbons

Sec: ANSI (USA pro tempore)

P-members 15

O-members 10

SC 4

Classifications and

Specifications

Sec: AFNOR (France)

P-members 17

O-members 10

SC 6

International Cargo Inspection

and Loss Control

Sec: ANSI (USA)

(in process of formation)

Figure 3. ISO/TC 28 Petroleum Products

909
OIML SP5

Measure of Liquid Volumes

Sec: France & W. Germany

Fl.l

Volumetric Measures

in Laboratories

Sec: U.K. Collaborators: 13

F1.4

Bottles Used as Measured

Containers

Sec: France

Coll: 9

F1.6 Water Meters

Sec: U.K. Coll: 20

F1.8 Measure of Hydrocarbon

in Open Air

Reservoirs

Sec: France & Romania

F1.10

Measure of Hydrocarbons

in Tanks and Tank Trucks

Sec: France & Romania

F1.12 Measure of Hydrocarbons

Distributed by

Pipeline

Sec: Czechoslovakia

Coll: 8

F1.1A

Barrels and Casks

Sec: Austria

Coll: 8

F1.3

Medical Syringes

Sec: Austria

Coll: 6

F1.5

Drinking Glasses

Sec: Switzerland

Coll: 7

F1.7 Meters for Liquids

Other Than Water

Sec: W. Germany & France

Coll: 18

F1.9

Measure of Hydrocarbons

in Reservoirs in Liquid

& Gaseous States

Sec : France & Romania

Fl.ll Measure of Hydrocarbons in

Barges and Oil Ships

Sec: France & Romania

Coll: 22

F1.13

Means of Control of the

Distribution by Pipeline

Sec: Czechoslovakia

Coll: 15

Figure 4. OIML PS5 Measure of Liquid Volumes.

910
OIML PS6 Measure of Gas Volumes

Sec: France

RSI

Gas Meters with

Deformable Walls

Sec: Netherlands

Coll: 16

RS3

Continuous

Voludeprimometers

Sec: W. Germany

Coll: 12

RS5

Method and Means

of Calibration

Sec: U.S.A.

Coll: 7

RS2

Gas Meters with

Rotating Pistons

Sec: W. Germany

Coll: 13

RS4 Measure of Gaseous Hydrocarbons Distributed

by Pipeline

Sec: Czechoslovakia

Coll: 17

RS7 Measure and Calculation

of the Factor for Compressibility

of Gas

Sec: France

Coll: 7

RS9

Gas Volume Connectors

Sec : France

Coll : 6

RS11

Calculators in a Measuring Set

Sec: U.S.A.

Coll: 6

RS6

Verification Methods

for Domestic and

Industrial Meters in Use

Sec: U.S.A.

Coll: 10

RS8 Measure of the Flow

and Volume of Surging Gases

Sec: —

Coll: 5

RS10

Flow Rectifiers

Sec: France

Coll: h

RS12 Instruments for

Measuring Gas Flows

Sec: —

Coll: 6

Figure 5. OIML PS6 Measure of Gas Volumes.

911
APPENDIX 1. Organizations Involved in Flow Measurement Standards

The organizations given below are identified as having some direct role

in the system for international flow measurement standards. A brief

description of most of the non-American organizations is given in a

recently revised BSI publication [4 ]

.

AFNOR Association Francaise de Normalisation, Tour Europe,

CEDEX 07, 92080 Paris la Defence, France

AGA American Gas Association, 1515 Wilson Blvd., Arlington,

Virginia 22209

ANSI American National Standards Institute, 1430 Broadway,

New York, New York 10018

API American Petroleum Institute, 2101 L Street, NW, Washington,

D. C. 20037

ASME American Society of Mechanical Engineers, 345 East 47th Street,

New York, New York 10017

ASTM American Society for Testing and Materials, 1916 Race Street,

Philadelphia, Pennsylvania 19103

BIPM International Bureau of Weights and Measures, Pavilion de

Breteuil, F92-Sevres, France

BSI British Standards Institution, 2 Park Street, London,

W1A 2BS, United Kingdom

CEN European Committee for Standardization, 5, Boulevard de

l'Empereur, B-1040 Brussels, Belgium

EEC European Economic Community, Brussels, Belgium

IEC International Electrotechnical Commission, 1 , rue de Varembe,

1211 Geneva 20, Switzerland

ISO International Organization for Standardization, Case postale

56, 1211 Geneva 20, Switzerland

OIML International Organization of Legal Metrology, 11, rue Turgot,

Paris IX, France

WMO World Metrological Organization, CH-1211 Geneva 20, Switzerland

912
APPENDIX 2. Published Standards and Other Documents

Related to Flow Measurement

Table 1. ISO/TC 30 Measurement of Fluid Flow in Closed Conduits

Designation

R 541-1967

781-1968

2186-1973

2975/1-1974

2975/11-1975

•2975/III-1976

TR 3313-1974

3354-1975

Title

Measurement of fluid flow by means of orifice

plates and nozzles

Measurement of fluid flow by means of venturi tubes

Fluid flow in closed conduits - Connections for

pressure signal transmissions between primary and

secondary elements

Measurement of water flow in closed conduits - Tracer methods - Part I: General

Measurement of water flow in closed conduits - Tracer methods - Part II: Constant rate injection

method using non-radioactive tracers

Measurement of water flow in closed conduits - Tracer

methods - Part III: Constant rate injection method

using radioactive tracers.

Measurement of pulsating fluid flow in a pipe by means

of orifice plates, nozzles or venturi tubes, in

particular in the case of sinusoidal or square wave

intermittent periodic-type fluctuations.

Measurement of clean water flow in closed conduits - Velocity-area method using current-meters

Note: The items below are working documents and not available for general

distribution

.

DIS 2975/VI

DIS 2975/VII

DIS 3966

DIS 4006

DIS 4053/1

DIS 4053/IV

DIS 4064/1

DP 4064/11

DIS 5167

DIS 5168

Water flow - Tracer methods - Part VI - Transit time

method without tracer

Water flow - Tracer methods - Part VII - Transit time

method with radioactive tracers

Velocity-area method using pitot tubes

Vocabulary and symbols

Gas flow in closed conduits - Part I - General

Gas flow in closed conduits - Part IV - Transit

time method with radioactive tracers

Cold potable water meters - Part I - Specifications

Cold potable water meters - Part II

Measurement of fluid flow by means of orifice plates,

nozzles and venturi tubes inserted in circular closed

conduits running full

Computation of limit error

913
Table 2. ISO/TC 113 Measurement of Liquid Flow in Open Channels - Published Standards and Documents Being Developed

Designation

555-1973

555/11-1974

748-1973

772-1973

1070-1973

1088-1973

1100-1973

1438-1975

2425-1974

2537-1974

3454- 1975

3455- 1976

Title

Liquid flow measurement in open channels - Dilution

methods for measurement of steady flow - Constant rate

injection method

Liquid flow measurement in open channels - Dilution

methods for measurement of steady flow - Part II: Integration (sudden injection) method

Liquid flow measurement in open channels by velocity

area methods

Liquid flow measurement in open channels - Vocabulary

and symbols

Liquid flow measurement in open channels - Slope-area method

Collection of data for determination of errors in measurement

of liquid flow by velocity area methods

Liquid flow measurement in open channels - Establishment and

operation of a gauging-station and determination of the

stage-discharge relation

Liquid flow measurement in open channels using thin-plate

weirs and venturi flumes

Measurement of flow in tidal channels

Liquid flow measurement in open channels - Cup-type and

propeller-type current meters

Liquid flow measurement in open channels - Sounding and

suspension equipment

Liquid flow measurement in open channels - Calibration of

rotating-element current-meters in straight open tanks

Note: The items below are working documents and are not available for general

distribution.

DRS 0748 Revision ISO 748-1973 - Liquid flow measurement in open

channels - velocity-area methods

DRS 0772 Revision of ISO 772-1973 - Vocabulary and symbols

914
Table 2 (contd.)

Designation Title

DIS 3716 Flow measurement - Suspended sediment load samples

DIS 3846 Free overfall weirs of finite crest width

DIS 3847 End depth method for estimation of flow in rectangular

channels

DIS 4360 Liquid flow measurement in open channels by weirs and

flumes - Triangular profile weirs

DIS 4363 Methods of measurement of suspended sediment in open

channels

DIS 4364 Bed material sampling

DIS 4369 Measurement of liquid flow in open channels by the

moving boat method

DIS 4373 Measurement of liquid flow in open channels - Water

level measuring devices

DIS 4375 Cableway system

915
Table 3. ISO/TC 28 Petroleum Products - Published Standards

and Documents being Developed that Relate to Flow Measurement

Designation

R 91-1970

R 91/Addendum

1-1975

2909-1975

3104-1976

3105-1976

3170-1975

3171-1975

3448-1975

Title

Petroleum measurement tables (2nd Edition)

Petroleum measurement tables based on a reference

temperature of 20°C

Petroleum products - Calculation of viscosity index

from kinematic viscosity

Petroleum products - Transparent and opaque liquids - Determination of kinematic viscosity and calculation

of dynamic viscosity

Glass capillary kinematic viscometers - Specification

and operating instruction

Petroleum products - Liquid hydrocarbons - Manual

sampling

Petroleum products - Liquid hydrocarbons -Automatic

pipeline sampling

Industrial liquid lubricants - ISO Viscosity

classification

3675-1976

5024-1976

Petroleum and liquid petroleum products - Determination of density and relative density

Hydrometer method

Petroleum liquids and gases - Measurement - Standard reference conditions

Note: The items below are working documents and not available for general

distribution.

DIS 2714.2

DIS 2715.2

DIS 3658

DIS 3829

Liquid hydrocarbons - Volumetric measurement by

positive displacement meter systems other than

dispensing pumps

Liquid hydrocarbons - Volumetric measurement by turbine

meter systems

Crude or liquid petroleum products - Determination

of density and relative density - Graduated bicapillary

pyknometer method

Petroleum products - Determination of density and

relative density - Jaulmes pyknometer method

916
Table 3 (contd.)

Designation Title

DIS 3838 Crude and liquid or solid petroleum products - Determination of density and relative density - Capillary stoppered pyknometer method

DIS 3967 Liquid hydrocarbons and petroleum distillates - Determination of density and relative density - Bingham pyknometer method

DIS 3993 Petroleum products - Light hydrocarbons - Determination of density and relative density - Pressure hydrometer method

DIS 4256 Liquefied petroleum gases - Determination of vapour

pressure - LP Gas method

DP 4266 Petroleum and liquid petroleum products - Measurement of temperature and level in

storage tanks - Automatic methods

DP 4267 Petroleum and liquid petroleum products - Calculation of oil quantities

DP 4268 Petroleum and liquid petroleum products - Temperature measurement - Excluding

averaging thermometers

DP 4269 Petroleum and liquid petroleum products - Tank calibration - Liquid measurement methods

DP 4270 Petroleum products - Determination of density

and relative density - Reischauer pyknometer

method

DP 4271 Petroleum products - Determination of density

and relative density - Capillary stoppered

conical pyknometer

DP 4273 Vocabulary of petroleum measurement terms

DP 4511 Petroleum and liquid petroleum products -

>

Measurement of oil quantities and free water - Manual methods

DP 4512 Petroleum and liquid petroleum products - Measurement

equipment - Manual measurement and container calibration

917
Table 4. IEC/TC 4 Hydraulic Turbines and TC 5 Steam Turbines - Published Standards That Relate to Flow Measurement

Publication

Number Title

41(1964) Recommendations for international code for the field

acceptance tests of hydraulic turbines

46(1962) Recommendations for steam turbines, Part 2:

Rules for acceptance tests

193(1965) Recommendations for international code for model

acceptance tests of hydraulic turbines

198(1966) Recommendations for the field acceptance tests

of storage pumps

Table 5. OIML/PS 5 Measures for Liquid Volumes and PS 6

Measures for Gas Volumes - Published Standards and

Other Documents That Relate to Flow Measurement

Recommendation*

IR 5(1970)

IR 6(1976)

IR 27(1973)

IR 31(1973)

IR 32(1973)

IR —(1975)

Draft (1973)**

Draft (1975)**

Draft (1975)**

*Number in parentheses is the year of adoption of last revision or last draft

**Not available for general distribution.

918

Title

Meters for liquids other than water with measuring

chambers

Gas meters - General

Meters for liquids other than water - Complementary

devices

Gas meters with deformable walls

Gas meters with rotary pistons and turbine meters

Water meters

Orifice meters

Measuring systems for liquids other than water - Equipped with metering devices

Measurement of gaseous hydrocarbons distributed by

pipeline
Table 6. EEC Directives Related to Flow Measurements That

are Listed in ref. 11

Reference or

latest draft

71/349/EEC of

10/12/71

71/319/EEC of

7/26/71

COM(75)577

FINAL

71/348/EEC of

10/12/71

71/318/EEC of

7/26/71 Adapted

to technical

progress by

74/331/EEC

of 6/12/74

75/33/EEC of

12/17/74

Status

Directive (OJ 10/25/71)

Directive (OJ 7/26/71)

Commission Proposal

Directive (OJ 10/25/71)

Directive (OJ 9/6/71)

Commission Directive

(OJ 7/12/74)

Title

Calibration of ships, tanks

Meters for liquids other than

water

Meters for liquids other than

water - measuring systems

Meters for liquids other than

water - ancillary equipment

Gas volume meters

Directive (OJ 1/20/75) Cold water meters

Work not yet

started

Hot water meters

Work not yet

started

Heat meters

COM(74)877

FINAL

111/1919/72

Commission proposal

(OJ 9/13/74)

Preliminary draft in

abeyance. Further

work in hand

Head and gas tanks used as

measuring containers

Manometers

Work not yet

started

Differential pressure gas meters

919
Table 7. ASME Performance Test Codes That Include or Require

Standardized Flow Measurement Methods

Designation Title

ASME PTC 3.3-1969

ANSI PTC 3.3-1974

ASME PTC 4.1-1964

ANSI PTC 4.1-1974

ASME PTC 6-1964

ANSI PTC 6-1974

ASME PTC 6 Report-1969

ANSI PTC 6 Report-1974

ASME PTC 6S Report-1970

ANSI PTC 6S Report-1974

ASME PTC 9-1970

ANSI PTC 9-1974

Performance Test Code - Gaseous Fuels

Performance Test Code - Steam Generating

Units

Performance Test Code - Steam Turbines

Performance Test Code Report - Guidance for

Evaluation of Measurement Uncertainty in Performance

Tests of Steam Turbines

Performance Test Code Report - Simplified

Procedures for Routine Performance Tests of

Steam Turbines

Performance Test Code - Displacement

Compressors, Vacuum Pumps and Blowers

•k Partial list given here,

Table 8. ASTM Standards for Flow Measurement

Designation

D 1071-55(1975)

D 1941-67(1975)

D 2034-68(1975)

D 2458-69(1975)

D 3154-72

D 3195-73

D 3464-75

Title

Measurement of Gaseous Fuel Samples

Open Channel Flow Measurement of Industrial Water and

Industrial Waste Water by the Parshall Flume

Open Channel Flow Measurement of Industrial Water and

Industrial Waste Water by Weirs

Flow Measurement of Water by the Venturi Meter Tube

Test for Average Velocity in a Duct (Pitot Tube Method)

Recommended Practice for Rotometer Calibration

Test for Average Velocity in a Duct Using a Thermal

Anemometer

F 317-72 Test for Liquid Flow Rate of Membrane Filters

920
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

OIML AND EEC, THEIR IMPACT ON THE INTERNATIONAL

STANDARDS PRODUCING SYSTEM

D. E. Edgerly

Office of International Standards

National Bureau of Standards

ABSTRACT

Existing relationships of three major international organizations involved in producing standards

are explored. These are the International Organization

of Legal Metrology (OIML) , the International Organization

for Standardization (ISO) , and the International Electrotechnical Commission (IEC) . Emphasis is given to

differing government versus industry needs in the

production and use of standards and examples are provided in the flow measurement field which illustrate

these differing needs. The technical directives program

of the European Economic Community and its impact on

the international standards producing system is also

considered. Discussion is provided on existing and

needed relationships among these organizations to

ensure compatibility of technical requirements and to

prevent duplication of effort.

Key Words: Flow measurement; industry; intergovernmental; international standards; legal metrology;

measurement; trade facilitation.

1. Introduction

Nations seeking to participate in international standards activities quickly learn that the system that has

evolved to produce such standards is diffuse and complex.

Such complexity is in part due to the sheer number of international organizations involved in standards activities and

to the differing needs of government and industry within the

system. There also exists a degree of duplication and

overlap of activities among standards organizations and a

general lack of concern over instituting effective means to

counter such duplication. Further, regional multi-national

organizations, some of which are intergovernmental, are

developing standards in the name of trade facilitation which

impact the international standards producing system. In

some instances these regional efforts become counterproductive

to the international system when technical requirements are

adopted and followed at the regional level which fail to

gain acceptance in the international standards arena.

921
This paper explores existing relationships of three

major international organizations involved in producing

standards. These are the International Organization of

Legal Metrology (OIML) , the International Organization for

Standardization (ISO) , and the International Electrotechnical

Commission (IEC) . The paper also considers the impact on

these organizations of the European Economic Community (EEC)

and its technical directives program designed to facilitate

trade within the Community.

2. Discussion of OIML, ISO, and IEC

The International Organization of Legal Metrology

(OIML) , was founded in 19 55 as an intergovernmental organization to promote uniformity of national legal requirements

for measuring instrumentation and to foster the development

of Metrology Services within its member nations. The principal

task of OIML is to achieve international uniformity in the

definition of and approach to legal measurements. That is,

to define and set into International Recommendations, acceptable criteria that a measuring instrument or system must

meet to be declared "legal for use" by a national authority.

In the United States "legal for use" predominantly applies

to measuring instruments in trade and industry which directly

impact the consuming public. In the flow measurement field

within the United States there is very little regulation

over the measurement end of custody transfer between producers

and transporters of liquids such as natural gas and petroleum.

In many other nations, particularly in Europe, national

authorities have much greater control over flow measurements

throughout the commerce chain from producer to the consumer.

Similarly, the concept of "legal for use" in other nations

includes measuring instrumentation and systems found not

only in trade and industry but also in science and medicine.

Thus, the scope of OIML is very broad and includes all types

of measurement instrumentation whether found in a retail

food store or in a hospital. The definition of acceptable

criteria for a legal measurement primarily involves international agreement on such basic metrological factors as

accuracy and precision and agreement on the degree of errors

that should be permitted in measurement. However, OIML also

establishes recommendations on the verification of instrument

and system design and performance as a means of assuring

that devices and systems are adequate for intended use and

will perform within reasonable error limits established by

national authority.

922
OIML is by reasonable definition an international standards

producing organization. It functions on a technical level

in the same fashion as the International Organization for

Standardization (ISO) and the International Electrotechnical

Commission (IEC), the world's two major nongovernmental

standards bodies. The principal difference between OIML on

the one hand, and ISO and IEC on the other, is the governmental

character of OIML and its outputs which are drafted as model

laws and regulations designed to be adopted and enforced as

law by its member nations. ISO and IEC produce standards

which are voluntary and whose content are slanted towards a

prescribed set of conditions and requirements designed to

assure acceptable quality or performance of products, materials, or processes. A principal task of ISO and IEC is to

facilitate the international exchange of goods and services

through standards which offer some assurance of product

quality. OIML has a similar goal of trade facilitation

which is to achieve international agreement on legal requirements governing acceptable measurement practices in the

exchange of goods and services. The two goals are not in

conflict and can be complimentary, providing there is some

agreement among the standards organizations covering their

intended scope of operation.

There are many technical areas in ISO and IEC involving

flow measurement, for example, that are oriented towards

agreement on acceptable characteristics for flow control and

measurement whether concerning pipeline systems or electronics

involved in flow control. The purpose of such work should

be the development of a good flow measurement technology

base. While their flow measurement standards do cover

inherent system or device errors and methods for testing and

control of such errors, they should be oriented towards a

documentation of inherent errors in various flow equipment,

the purpose being to inform the user of the standard what he

may expect in the way of operating characteristics of a

meter or a flow system. Such standards should not preempt

OIML's task, for example, of recommending error limits for

acceptance and use of these devices or systems as legal in

trade, industry, science, etc. Similarly, the technical

involvement of OIML in flow measurement should be governed

by like conditions. For example, OIML efforts in developing

the conditions and requirements for flow measuring instrumentation to be legal for use should only center on the development of metrological and technical requirements which influence

the measuring capability of an instrument or system and on

recommended means for use by national authorities in verifying

that instruments or systems meet the prescribed requirements

.

923
Metrological requirements are those which relate to measuring

errors and are approached by examining errors occurring in a

measurement system so as to establish error limits which may

not be exceeded in legal measurements. Technical requirements

relate to an examination of those properties of an instrument

which influence measurement errors and those which determine

the practical usefulness of an instrument for legal metrology

purposes. Examples of technical requirements which might be

imposed on a manufacturer of flow measurement equipment by

OIML recommendations are as follows

:

1. requiring that the primary indicating elements and

primary recording elements of a flow measurement system be

readily returnable to a definite zero indication; or,

2. requiring that a retail motor-fuel dispensing system

be constructed such that after a particular delivery cycle

has been completed by movement of the starting lever to any

position that shuts off the device, an effective automatic

interlock will prevent a subsequent delivery from being

started until the indicating elements and recording elements

have been returned to their correct zero positions.

These technical requirements are imposed to ensure

suitability of equipment for use in commerce and to prevent,

as far as practicable, the facilitation of fraudulent measurement practices. The requirements, however, are couched

in performance language and for the most part do not specify

design requirements to meet stated performance needs. OIML

should not become involved in specifying the design of

measuring instrumentation or systems as a means of assuring

adherence to metrological and technical requirements.

Concern with design criteria in OIML primarily results

from experience gained in those national metrology laboratories which conduct pattern approval of measuring instruments

or systems as the first step in verifying that they are

adequate for intended use and legal for trade and industry

within that country. The government experts who conduct

such testing are the same experts who attend technical

meetings of OIML and who bring with them practical experience gained in the laboratory on the performance of various

instruments. In many cases, these experts feel that the

solution to a measuring problem is to require specific

design criteria which will assure acceptable instrument

performance. The difficulty with this thinking is that if

design criteria are written into legal requirements there is

the possibility of creating trade barriers and of stiffling

technological innovation. A recent experience in OIML

illustrates this concern quite clearly.

924
In December 1975, a technical level meeting was held in

London to discuss a first draft OIML International Recommendation entitled "Measuring Systems for Liquids Other than

Water, Equipped with Volumetric Meters." The draft was

written by France and the Federal Republic of Germany, and

intended as a general legal code for various flow measurement

systems including retail motor fuel dispensers; tank truck

metering systems; receiving systems for unloading of ships,

rail tankers and road tankers; liquefied petroleum gas

systems; pipeline systems; and, even milk measuring systems.

For the most part, the draft Recommendation was found

acceptable. The requirements written into the draft covering

the operation of measuring systems prescribe, in performance

terms, generally accepted specifications for the operation

of transfer points; filling of the meter and pipework;

draining; anti-vortex devices; by-passes; and so forth, as

such components affect the measuring elements of the system.

However, in its discussion of air or vapor elimination, the

draft shifted to very specific design requirements. For

example, requirements were contained which specified that

the volume of an air or vapor elimination device be at least

equal to 8% of the product volume delivered in one minute at

maximum flow rate. This requirement could not be met by

United States manufacturers without substantial and costly

design and construction changes to incorporate larger air or

vapor elimination devices within motor fuel or tank truck

dispensing systems. Fortunately, other member nations

joined the United States in objecting to such a design

requirement and the matter was resolved by creating a joint

OIML/ISO Task Group to study the question of air or vapor

entrapment in liquid and to propose technical recommendations

which would be acceptable to both bodies. It should be added

that this joint working group between ISO and OIML is the

first to be established. Hopefully, other common problem

areas between these international organizations will be

approached in a similar manner as it is through this type of

government/industry relationship that technical conflicts

and duplication of effort are minimized.

3. Discussion of EEC

The problems of duplication of effort and technical

conflict are not confined solely to ISO, IEC, or OIML.

There are other international organizations and multinational regional organizations which, though perhaps not

primarily chartered as standards bodies, do produce technical recommendations which impact the standards producing

925
system. These organizations and their interactions with

ISO, IEC, or OIML have already been discussed. However,

some special emphasis should be given to the European Economic Community (EEC) , and the important impact it has on

the international standards producing system. EEC is important because it is a major trading partner of the United

States and it is an important technology contributor to the

international standards producing system. However, it also

competes with the system and in some cases works counter to

the system by preempting actions under consideration within

ISO, IEC, or OIML.

The EEC operates a technical directives program oriented

towards achieving harmonization of laws, regulations and

administrative actions among its nine member nations as

directly affects the operation of the Common Market. The

intergovernmental character of the EEC and the obligation of

its members to adopt Council Directives makes it an important

organization to reckon with. Basically, the EEC Directives

program generates standards for use by its nine members in

facilation of trade within the Community. At the present

time, for example, the EEC is pursuing the development of

technical directives in many subject areas which are common

with technical activities in ISO, IEC, or OIML, including:

motor vehicles; tractors and agricultural machinery; metrology

and measuring instrumentation; electronics; construction

materials; rubber and plastics; and many other areas. In

the flow measurement field, the EEC now has five final

Directives in force covering such areas as petroleum and

natural gas flow meters, water meters, ancillary equipment

used with flow meters, and calibration of ship, rail and

road tanks. There are another five Directives at the draft

level covering general requirements for flow measuring

systems, differential pressure gas meters, and electronic

devices fitted into measuring instruments. Basically, the

approach taken by the EEC in standards generation is to use

international standards when available as the foundation for

its technical directives. However, when international

standards do not exist, or when there are unique regulatory

needs which cannot be satisfied by adopting a given international standard, the EEC will produce and adopt technical

requirements within its directives without going to an

international forum such as is provided through ISO, IEC, or

OIML. This has an important impact on the international

standards producing system because once efforts are underway

internationally to achieve agreement on standards, the

Common Market nations by virtue of preemptory action speak

as a unified bloc of nine ISO, IEC, or OIML members, thereby

exerting considerable influence over the final technical

content of the international standard.

926
Another action by the EEC which is not uncommon and

which also impacts the international standards producing

system is the practice of introducing draft ISO, IEC , or

OIML international standards into its technical directives

program and moving the drafts through the program to final

adoption as EEC Directives before the standard comes into

fruition at the international level. The danger in this

practice is adopting Directives having legal status within

the Community, whose technical content may differ from the

final standard eventually accepted by ISO, IEC, or OIML.

The net effect of such a practice is technical conflicts

which could result in non- tariff trade barriers.

4 . Summary

OIML and the EEC are standards generating organizations

that have important impacts on the international standards

producing system. Though they are intergovernmental bodies

with standards needs differing from those of industry they

nevertheless impact commercial standards through the adoption

of laws and regulations which govern the flow of commerce.

If commerce is to be unrestrained among nations then the

technical requirements written into law by OIML and the EEC

must be compatible with each other and with standards generated

by ISO and IEC. As has been stated, insuring this compatibility

is not as simple as having OIML or EEC or any other governmental

body adopt ISO or IEC standards as the basis for mandatory

regulations covering trade and industry. There are regulatory

decisions involving commercial equity and public health and

safety which are not and should not be within the purview of

voluntary bodies such as ISO or IEC. Thus, the only apparent

solution to government versus industry generation and use of

standards seems to be greater interaction and participation

by the two within the international standards producing

system. At present, nations face somewhat of a resource

burden in having to be vigilant and active within many

international organizations in order to ensure that both

industry and governmental needs are being met and that the

various organizations are not working counterproductively to

national aims. Unfortunately, this situation is not likely

to change for some time to come.

BIBLIOGRAPHY

National Bureau of Standards Handbook 44; Fourth Edition,

"Specifications, Tolerances, and Other Technical

Requirements for Commercial Weighing and Measuring

Devices," Issued December 1976.

Referowski, Z., "Remarks on the Work Topics of OIML

Secretariats," Draft of an OIML Bulletin article,

September 1976.

927

National Bureau of Standards Special "Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

THE INTERFACE BETWEEN INDUSTRIAL,

NATIONAL AND INTERNATIONAL STANDARDS

Wallace N. Seward

American Petroleum Institute

2101 L Street, N. W.

Washington, DC 2 0037

The oil and gas industries, throughout more than 100

years of historical development, have been able to capitalize

on the rationalization of sophisticated document and technology through industry-wide standardization efforts. The essential incentives of the original industrial standardization programs were threefold:

First, to decrease capital costs and long-term maintenance expenses through the interchangeability of parts and

the establishment of uniform operating, procurement, and training procedures.

Second, to ascertain and develop optimum levels of

performance, safety, and reliability without inhibiting technological development.

Third, to promote economic viability and incentive

among supply and service organizations associated with the resource industries.

There are essentially two end uses for proprietary

measurement standards developed by industry. A significant

number were developed by industrial users to aid in the purchase, operation and maintenance of equipment common to various

companies making up the industry. Conversely, as the product

line of a manufacturing industry multiplied, the manufacturers

themselves generated quality or definition standards to describe

common product characteristics to the customer or user level.

One of the more perplexing aspects of the world's industrial standards development process is the huge number of

organizations involved in preparing technical literature. Overall, there are at least 12,000 known sources of industrial standards (or proprietary support data). In the U. S., approximately

360 trade associations and professional suppliers are currently

engaged in on-going standards development.

So, recalling that industrial standardization first

got its impetus in the U.S., and generally throughout the world,

as mass-production replaced craft manufacture, it followed that

companies faced with expanding their operations or markets

929
sought uniform inventory control and were inherently drawn into

the process. Competitively, however, national markets caused

similar products to be produced by different suppliers in a

multiplicity of ways, often because of differing regulatory

expectations. One way or another, conflicting national industrial standards emerged through trade associations and professional societies. Domestically, if the end-product or methodology impacted on the general public, then an industrial standard

was further reviewed for voluntary national adoption as a consensus of technical, legal and economic interests by the public,

labor, government and private enterprise. Ultimately, if the

commodity or service was offered multinationally , it was

usually submitted to a broad review at an international level.

In those cases where the consuming public or national interests

were significantly affected, individual governments themselves

may require and adopt or legislate the use of the standard

after negotiation and modification, thus making it directly

enforceable by law. This act is called regulation by reference

to standards. But, in many countries, this process is significantly modified because the authority to create and adopt

standards is simply vested in the government, even though it

often has an overriding financial stake in export sales of

equipment or value-added taxes on imported hydrocarbons. Thus,

in some nations, the tax on crude oil may easily be 500 percent

greater than the commercial value, so a measurement shortage is

a greater penalty to the state than to a company.

Application of Standards

Direct enforcement is much more difficult internationally, so for commercial measurement of hydrocarbons, it is quite

common to reference voluntarily-developed standards within a

contract negotiated between a specific buyer and seller. But,

even if governments and private concerns are involved, the

voluntary label is misleading because each contract carries with

it the right of equitable enforcement through a mutually agreed

legal protocol or judicial process. With this in mind, such

non-government standards should best be described as a prenegotiated package of technical information, which, when referenced

in contract , allow any affected party recourse to due process.

That such standards are applied time after time without gross

penalty suggests the satisfaction of all parties, even though

they may contain contradictions to domestic regulations. This

attribute is sometimes overlooked when governments alone seek

to promote and unilaterally enforce conflicting national measurement regulations on petroleum commerce. Especially when pattern approval or prototype testing is demanded, responsibility

is not shared; rather, this stance assumes that government is

somehow invariably right while the supplier and user are invariably deficient. However, since hydrocarbons are measured

at least 12 times between wellhead and consumer, it is evident

that cooperative international standardization offers the only

path to rational economic equality.

930
Organizations Engaged in Oil and Gas Measurement Standardization

Recalling the complexities resulting from the evolutionary process of standards development, it seems preferable

to categorize rather than simply list standards organizations

involved in preparing technical material. Since we are primarily concerned with the measurement of hydrocarbon fluids and

fluid properties, it is not possible to be either all-inclusive

or free of technical overlap in describing the organizations

involved. Thus, there are:

I. Domestic Equipment and Manufacturing Interests

a. Instrument Society of America (ISA)

b. Scientific Apparatus Makers Association (SAMA)

c. Electronic Industries Association (EIA)

d. Fluids Controls Institute (FCI)

e. Manufacturers Standardization Society of the

Valve and Fittings Industry (MSS)

f . Oilfield Production Equipment Manufacturers

Association (OPE)

II. User Industry Interests

a. American Gas Association (AGA)

b. American Petroleum Institute (API)

c. Compressed Gas Association (CGA)

d. Manufacturing Chemists Association (MCA)

e. Natural Gas Processors Association (NGPA)

III. Professional Societies

a. American Society of Mechanical Engineers (AS ME)

b. American Society for Testing and Materials (ASTM)

IV. National Standards Management

a. American National Standards Institute (ANSI)

b. National Bureau of Standards (NBS)

c. National Conference on Weights & Measures (NCWM)

931
V. International Standards Development

a. International Organization for Standardization

(ISO)

b. Organization of International Legal Metrology

(OIML)

c. International Bureau of Weights & Measures

(BIPM)

To clarify one point immediately, there are four

organizations included in this list which are not classifiable

as industrial standardizing bodies. These are shown in the latter

two categories for convenience. The NBS , NCWM, and the OIML

engage in standards development to the extent that they draft

model codes for ultimate adoption and enforcement by regulatory

bodies while the BIPM establishes by treaty scientific definitions of units of measure, including the legal interrelationship

of one unit to another. It also houses such necessary articles

as the prototype kilogram and the prototype litre measure on

which virtually all national calibration equipment is based.

As is self-evident, each category represents a unique

interest having as its objective the satisfying of what it perceives to be in the common good of its respective constituency.

Governments respond to "national interests; " industries to

"markets." Personally, I think of a market as a selective

interest with a limited amount of money. A "national interest"

is usually politically ascertained with greater regard to continuation in power than to economic efficiency or limits.

But many of the contradictions and conflicts in the

international arena, including both measurement equity and useful standardization, are created because existing social "systems"

cannot resolve whether best objectives are obtainable through

an educationed commercial marketplace, or traditional regulatory

prescription or intervention in the "national interest."

Thus, a measurement equipment supplier is primarily

interested in meeting his customer's expectations in terms of

accuracy, convenience, and budget. The user industry, the hydrocarbon companies, tend to wish for reliable and provable performance expectations at a defensible cost for each specific

application. Most governments wish to insure that their national

interest will not be harmed, that export markets will be expanded

and that tax revenues are optimized.

Thus, we are faced with which constituency is to be

pleased, so there are variations in enforcement expectations,

performance versus prototype test requirements, and, not least

of all, a paradox in evaluating who is technically most competent

to judge when a reasonable balance of competence has been

achieved

.

932
Although internationally we still lack the ultimate

resolution of this problem, we have made great progress by

isolating and examining its foundation through ISO and OIML.

However, I also believe that in a world that is as sophisticated

and complex as ours, no one interest can exist to the exclusion

of others, including government. I rest my case by observing

that OPEC officially is a treaty organization, not a cartel of

competing companies. Even though its commercial impact cannot be avoided in the immediate future, its political consequences can only be overcome by the combined talents - economic,

technical, and political - of an inter-dependent world.

Even trade and commerce by OPEC nations must be based

on three principles that, when negotiated and agreed, will result in the exchange of a commodity. First, the level of quality

offered must meet the expectations of the purchaser. Second, the

total amount of material to change hands must be specified and

delivered within reasonable and reliable limits. Third, a price

for either the total exchange or per unit basis can only be

concluded after the first two conditions are clearly understood

and acceptable.

The new role of measurement standardization is to provide standing roles and test methods, composed by the best

available technical talent, to evaluate the level of quality

and degree of quantitative accuracy that is acceptable to all

parties engaged in petroleum commerce. With such agreements

in hand, trade can be assured subject only to price agreement,

without hidden manipulation or prolonged and misdirected negotiations or even worse, including threat of war. The contribution of measurement standardization is that it is responsibly

carried out by the teohnical community in advance of market

pressures. Measurement standardization must not become subject

to the hazards of political bargaining. To suggest diplomacy

as the only recourse is to run the risk of irreconcilable failure.

Conclusion

Recent changes in the politics and economics of the

oil industry have placed new strains on the contractual system

which have, to an increasing extent, become supplanted by governmental negotiations. Domestically, the Energy Conservation

Act of 1975 for the first time authorizes our government to

directly purchase and own crude oil.

In the past, the API Committee on Petroleum Measurement was able to assist in resolving technical disputes by

arbitration based on the industry's integrity reflected through

equitable consensus standards. In that 4 5 percent of U.S. oil

is now imported, with one party more frequently a soverign

933
agency, this procedure has diminished in effectiveness. Therefore, technical support from all affected interests is also

mandated by the inherent conflict between OPEC governments,

consumer governments, and commercial interests.

Leadership in ascertaining the limits to accuracy and

precision, technically rather than legislatively, is a serious

need which must be shared. Our mutual involvement in the Organization of International Legal Metrology and the International

Organization for Standardization has highlighted the degree of

competence that may be brought to bear now and in the future.

To maintain measurement integrity, it is essential

that the National Bureau of Standards continue a program in

fluid measurement standardization and related fluid dynamics at

a sufficient level in support of the historic U.S. reputation

in this field. But overall, API supports work with all those

dedicated to developing useful programs that will be most beneficial in meeting the needs of the world.

934
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

THE ADEQUACY OF THE DATA BASES AVAILABLE FOR

PROMULGATING INTERNATIONAL STANDARDS

H. H. Dij stelbergen

N. V. Nederlandse Gasunie

Groningen

The Netherlands

1. Introduction

The number of international standards for measuring flow rate or quantity

is gradually increasing. In the light of experience with existing ones questions rise with respect to the validity of certain figures or tolerances. To

answer the questions raised implicitly in the title, for all fields of standardization is beyond the competence of the author and the rest of the paper will

therefore be limited to two specific fields. From the observations in these

fields some conclusions might be drawn which are more generally valid.

In general international standards are based on national ones which have

been in existence for some time. In some instances, the data bases underlying

these standards have not been published and are lost in forgotten file cabinets.

If they would be found, hardly anybody would be able to find his way in the

chaos of insufficiently specified data. The adequacy of the data basis can,

therefore, be rarely tested directly on the data itself. If, however, the

claims put in the standards show not to hold, it can be concluded indirectly

that the data base must be inadequate. Instead of speaking of adequacy of

the data base one could put the question more gently by asking whether the

right standard is based on the available data. The paper restricts itself to

two standards. The first is not an international standard in the usual sense

but the EEC regulations on gas turbine flowmeters. The second one is the

international standard on flow measurement by means of orifice plates.

2. The EEC Regulations on Turbine Gas Flow Meters

The practice and philosophy of gas metering in a number of EEC countries

is substantially different from the United States. In these countries the

way to measure gas is limited by law to certain approved measuring devices.

This originates from protecting the (domestic) user - the weaker economic

party - by requiring each and every meter to be calibrated in a flow rig under

legal supervision. Furthermore, the meter had to be of an approved type to

warrant a trouble-free and stable performance over its lifetime.

The rules were not limited to domestic gas meters but also larger size

meters were included. One of the most important aspects of the law was to

avoid the possibility of interference by user or supplier. So, much emphasis

was placed on sealing of parts and of course orifice plate metering was

originally not accepted as being too easy to interfere with. In fact in

Germany orifice plate measurement while accepted in principle, was not applied

until very recently for this reason and in the Netherlands it is still not

officially accepted. Type approval of a meter depended not only on the fulfillment of the legal regulations but also on tests carried out by the official

935
bodies and field trials supervised by the same. It took, for example, three years

for approval of the first gas turbine flowmeter in the Netherlands.

In 1971, the EEC countries prepared under the secretariat of Germany and the

Netherlands a rule on gas meters. It was largely based on current practice in

these two countries, amended by the other members. Highlights of metrological

aspects of the rules are:

Specifications for the indicating counters to facilitate the check

of individual meters in a calibration flow-rig,

Limits to error,

Limit to average error over the measuring range,

Calibration at defined points in the measuring range,

Type approval with air of atmospheric pressure,

Type approval by tests on a number of meters (three to seven),

Specified maximum derivative of error curve with respect to flow

rate at approval,

Endurance tests of 1000 hours at maximum throughput at approval, and

Specified maximum change of error during endurance test.

The data on which the rules are based are very diffuse. Let us investigate what

would be needed.

Evidence that the tests are sufficient to warrant good performance

under actual conditions.

Evidence that the performance does not deteriorate over the lifetime of the meter or the time between two calibrations.

As to the first point it is striking that no limits have been put on either

pressure range or temperature of the gas nor on the ambient conditions. Installation conditions have not been taken into consideration. It is obvious that

the evidence for such a large field of conditions and applications does not

exist. The data reported in the literature are limited to the influence of

pressure on the meter [1] . Furthermore, the base consists of the theory that

the slip of the blades in a turbine gas flow meter is relatively small and

remains so independent of conditions. In reference 1, there is a further

theory on the influence of density especially at the lower end of the range.

The check of this theory has been carried out on too small a number of meters

to be statistically significant.

The second point is to a certain extent covered by the endurance test.

However, it does seem limited when considering the field of application which

includes dust-laden gases and gases more aggressive than air at atmospheric

pressure. The fact that every meter has to be tested individually under controlled conditions assures, however, that at least under those conditions the

meter is capable of a guaranteed performance. The extrapolation of this performance is rather daring, especially in view of the dependence of the error

curve on pressure and installation conditions [2,3]. As a conclusion it can

be said that the data base underlying the EEC rules is insufficient. Furthermore, because of the inaccessibility of the data it is impossible to weigh the

degree of extrapolation for a particular application.

3. The ISO Standard on Flow Measurement with Orifice Plates [4]

The philosophy behind the standardization of these devices is significantly

different from the one behind the rule on turbine gas flowmeters. Instead of

T

Figures in brackets indicate the literature references at the end of this

paper.

936
individual calibration of each meter in a calibration flow rig the standard controls closely all geometrical dimensions. This insures a high degree of geometrical similarity with a number of tested installations which served to establish

the equations or tables relating the differential pressure to the flow rate. The

main reason for this inferential method of calibration is of course that, for the

chief applications, either no primary calibration facilities were available or

the cost of using these would be prohibitive.

The fact that no individual calibration on a flow rig is needed puts a very

high value on the geometrical similarity with the original devices. These original devices form in fact the kernel of the data base. In principle these tubes

and orifice plates should therefore have been carefully conserved. The ISO

standard on flow measurement with orifice plates standardizes flange taps, vena

contracta taps and corner taps. It is presently under revision and this will

result in the incorporation of D-D/2 taps whereas the vena contracta taps will

be left out. The data for the D-D/2 taps and the flange taps originate from

the United States and the corner taps from Germany.

The only readily available data base are the U. S. data. The report [5]

issued in 1935 by the joint AGA-ASME committee on orifice flow meters was not

distributed on a large scale, but copies do exist. It gives a comprehensive

account of a multitude of tests which served as a basis for the present standard.

As such it should serve as an example for those involved in standardization.

The coefficient and the tolerance in these were largely derived from tests

on a water calibration rig at the Hydraulic Laboratory of the Ohio State University, carried out under the supervision of Professor S. R. Beitler. The analysis

of the data was made by Dr. E. Buckingham and Mr. H. S. Bean of the National

Bureau of Standards. In a thorough investigation [6], Dowdell and Chen clearly

show that "Since computers were not available , the accuracy figures

given must represent, to a certain degree, the judgement of the people involved

in the analysis." Although the accuracy quoted in ISO R 541 and the underlying

standard, AGA Report No. 3 [7] is 0.5 percent, the study, by employing statistical

methods on all the Columbus data clearly shows that even when the range of

Reynolds, diameter and diameter ratio are limited a standard deviation of 0.5

percent is found. This means that an accuracy figure should rather be 1 percent

instead of 0.5 percent. Apart from an analysis of the Columbus data alone, data

from six other sources from recognized hydraulic laboratories in the U. S. were

analyzed. When all these data were included and the range of Reynolds number,

line size and diameter ratio was limited to the same values as above, the same

order of magnitude for the standard deviation was found. Curve fitting by

regression analysis and eliminating data wherever there is a justification

yields a curve which reduces the standard deviation of the measuring points

with respect to this curve to 0.37 percent.

Other comparisons with different sources give striking results. If for

example, flange tap coefficients are compared with corner tap coefficients

these should be the same for large diameters. Likewise, the coefficients for

flange taps and for D-D/2 taps should be the same for 2 inch pipe. In Figure

1, which is derived from [8], differences of up to 0.5 percent show.

An important problem arises from the fact that the range of diameter

ratios, flow rates and pipe diameters is more limited for the data itself than

the standards derived from these data. Furthermore, the distribution of data

937
points over the whole field is rather uneven. High Reynolds numbers correlate with

large orifice diameters and measuring points reflect the technical limitations of

the flow rig used. The present standards are therefore a rather far extrapolation

on the original data, especially in those areas where the original data are few.

Although in at least one case such an extrapolation was carefully checked [9], this

was certainly not always the case. Another extrapolation is the application of

coefficients derived in water calibration rigs to gas.

Of course, measurements have been made using primary gas standards such as

bell-provers , but it is improbable that the accuracy of these measurements was

sufficient to detect anything else but first order deviations. After all the

Reynolds similarity is a hypothesis which for these simple configurations holds

to a first approximation. When, however, it is used for extrapolation over such

a wide range and in the accuracy brackets of 0.5 percent it should be checked

whether there are no other effects.

As stated earlier on, it is a pity that the original equipment was not preserved

The roughness and roundness of the adjacent pipes are now only qualitatively known

as is the fact with the edge sharpness. It is now quite possible that due to improve

ment of manufacturing techniques there has been a systematic change in the true coefficient of orifice plates.

The source of the installation requirement in the ISO standard is hazier.

Again one of the best documented set of tests appears in the AGA-ASME report [5].

Another basis is the DIN-standard [10] . The last one even gives for some upstream

disturbances not only the increase in tolerance but also the direction and average

magnitude of the shift. Data supporting this have been published by Schro'der [11].

When comparing the installation requirements in AGA Report No. 3 [7] with

the ones of R 541 it shows that the lengths required for the same accuracy are

according to ISO twice the ones needed according to AGA. A recent study of the

data on disturbance tests given in the AGA-ASME report shows that even the strict

ISO requirements are not sufficient to eliminate the influence of upstream conditions. Some results are listed in Figure 2, where for specific tests the

difference between two orifice meter runs in series is listed together with the

undistrubed lengths required by both ISO and AGA. The disturbance upstream one

orifice plate consisted of three angles in two planes, the other being preceded

by a very long length of the tube.

Field experience from two large gas measuring stations in series at the FrenchBelgian border [12], both meticulously instrumented and maintained, indicate that

on the average one of the stations indicates a flow rate 0.4 percent higher than

the other. Both stations are equipped with several lines in parallel and installed

according to ISO R 541. When changing orifice plates the difference between the

two stations can amount to one percent depending on the particular orifice used.

The difference would remain stable over weeks. Interchanging orifices between

the stations indicated that the systematic difference can only be attributed to

the installation conditions.

From these facts, based both on reanalysis of existing data and on field

experiments, the conclusion that the standards claim too high an accuracy and

extrapolate too much on the existing data is unavoidable.

938
4. Possible Improvements

Possible improvements of the standards can only be achieved by better use of

existing data or the generation of new data.

An improvement to the new ISO standard on flow measurement by means of orifice

plates was proposed by Stolz [13]. By making use of the existing equations and

tables for D-D/2 taps, flange taps and corner taps, Stolz managed to mold these

into one simple single equation which ironed out some inconsistencies in the old

standards. It it is admitted that all of the original data are based on serious

measurements, the odds are on the result being closer to the truth than the

original. The proposed equation incorporates measurements in the vicinity of the

plates by Herning, Witte and Schrb'der. The coefficient has the following general

form

CCL^L^) = 0.(0,0) + A(L

1

) - A(L

2

') + B C^) 0 * 75

where

,

and ' indicate the locations of upstream and downstream tap

respectively (normalized with respect to the diameter)

CCL^,!^ 1 ) indicates the discharge coefficient of a meter equipped

with and L^ 1 taps

0^(0,0) indicates the discharge coefficient for corner taps for

Re

D

= co

A(L.) correction for the distance of the upstream tap from the

orifice plate face

ACl^') correction for the distance of the downstream tap from

the orifice plate face

The full equation is written:

C(L

1

,L

2

') = 0.5920 + 0.0376 3 - 0.1543 3 + 0.900 1^ 3 (1 - 6 )

0.0156 L

2

» e 1 ' 2

+ 10-* [5-27 3 + 38.4 6

4 - 20,2 B 8] [ lf

D

] °' 75

Interesting features of the equation are:

as 3 goes to zero the Re term comes to zero too,

for large diameters corner taps and flange taps give the same coefficient,

for pipe diameters of 2", flange taps and D-D/2 taps give the same coefficient,

the Rep term is the same for all tappings,

the discharge coefficient C comes to one single value for 3 equal to zero

regardless of tappings.

Another improvement which is suggested for the new ISO standard is the introduction of straighteners . The required length between orifice and straightener

and between straightener and disturbance is specified on the basis of measurements

carried out by Plunian and Sens [14] which were confirmed by experiments at British

Gas by Jepson. The introduction of a straightener does not decrease the required

straight length but serves to enable the user to put unspecified disturbances,

such as regulators, upstream of the orifice plate. This was hitherto not allowed.

939

1
If, however, it can be shown, for example by Pitot-tube traverses, that at the

location of the orifice plate the flow profile is fully developed, any length

or arrangement is permitted. The changes are being proposed to bring the

standard in line with presently available data.

For the EEC regulations on gas meters, being a legal document, it is much

more difficult to bring about a change. However, in the Netherlands ways have

been opened to calibrate meters individually with gas at operating conditions

within the still valid national legal framework. There is little doubt that

in the long run the data now available will influence the EEC regulations.

A second possibility would be to gather new data. In fact this is the only

possibility to substantially improve the standards. Of course this has been

obvious to many people, but several reasons prevented the collection of new

data. Mainly this is a matter of cost. If new data bases have to be collected,

which would be adequate for presen.t day needs and possibly for tomorrow's, a massive program would have to be carried out covering the whole field of parameters. In order to avoid any bias, it would be necessary to cross-check

between different laboratories and to use equipment from a large number of

sources, operated with liquids as well as gas, This is very important as the

required accuracy is higher today than it was in the thirties and certainly

higher than the apparent accuracy of existing data bases.

One thing that certainly needs exploration is the stability of orifice

plates measurement. There is evidence that in some cases the repeatability

of a measurement is rather bad although over very long periods it appears to

be better [9]. The same phenomenon showed up, for example, in the Refugio

tests in 1954. In none of the cases an explanation of the instability could

be found. In very small orifices a true instability of the discharge coefficient has been reported [15] , and it would be necessary to investigate if

something similar could occur with normal size orifice plates.

Anyhow in order to get reliable standards, calibration facilities capable

of operating close to the actual practical conditions of the measuring equipment are needed. Several calibration laboratories do exist for water and oil

and up to large flowrates. For high pressure gas the number of calibration

facilities is much more limited. To investigate instruments under the conditions prevailing in gas transportation, our company built a high pressure

calibration rig for 144 000 m^/h (5.10 6 SCF/H) [2] and started building one

for 2.5.10 6 m^/h (9.10 7 SCF/H). The first operates at pressures between 8

and 60 bar, the second at pressures between 50 and 60 bar. To check the

absolute accuracy of these installations a comparison is now being made with

an installation at Gaz de France and one at the National Engineering Laboratory

in Glasgow. These last installations are also capable of calibrating high

pressure gas flowmeters although with a more limited capacity. The three

installations are based on totally different principles. The comparison takes

place under the auspicies of the EEC.

Generally there is a large reluctance to accept evidence that standards

are not as they were believed to be. At the Pittsburgh flow conference in

1971 one of the speakers drew attention to instrument manufacturers supplying

specifications to the wishes of their customers without changing their instruments. He coined the word 1 specmanship 1 for this activity.

It is the feeling of the author that in the case of standards a considerable

degree of 'specmanship' is displayed by users. Instead, a realistic approach

would be more commendable and either the standards should be adapted to the

available data or data should be generated to support the required standard.

940
5. References

[I] Eujen; Untersuchungen Uber die Messeigenschaften von Hochdruck gaszahlern,

II Teilbericht, Messungen an Schraubenradzahlern ; Gas- und Wasserface,

105 (1964), p. 1192-1199,

[2] Bellinga; Calibration of turbine flowmeters under operating conditions;

Paper B2, Conference on Fluid Flow in the mid 1970 's, 8-10 April 1975,

East Kilbride, Glasgow.

[3] Peignelin, Pellous; Etude experimentale a l'aide de tuyeres fonctionnant

en regime sonique de la precision du comptage de gaz sous pression;

Communication IGU/C 21-73, presented at the 12th World Gas Conference,

Nice 1973,

[4] Measurement of fluid flow by means of orifice plates and nozzles, ISO

Recommendation, R541.

[5] Report by the joint AGA-ASME orifice coefficient committee to the gas

measurement committee, Natural gas department AGA and the Special

research committee on flow meters of the ASME - 1935.

[6] Dowdell, Chen; A statistical approach to the prediction of discharge

coefficients for concentric orifice plates, Trans. ASME, J. Basic

Engineering, (1970) p. 752-765.

[7] Orifice metering of natural gas, Gas Measurement Committee Report Bo.

3, American Gas Association, Arlington, Va . , 8th printing 1972.

[8] Stolz; An Approach towards a general correlation of discharge coefficients

of orifice plate meters; Paper K-l, Conference on Fluid Flow in the Mid

1970's, 5-10 April 1975, East Kilbride, Glasgow.

[9] Gorter, DeRooy; An investigation in widening the Reynolds number range

for flow measurement in closed conduits by means of orifice plates,

Paper A-l, presented at the Conference on Fluid Flow in the Mid 1970 's,

8-10 April 1975, East Kilbride, Glasgow.

[10] VDI/VDE; Richtlinie, Entwurf VDI 2040 Berechnungsgrundlagen fur die

Durchf lussmessung mit Drosselgerate, Blatt 1, Durchf lusszahlen und

Expansionszahlen genormter Drosselgerate und Abweichungen von den

Normvorschrif ten. Beuth Vertrieb, Berlin, Koln.

[II] Schroder; Notwendige storungsfreie Rohrstrecken fur Dusen und Blenden;

Brennstoff, Wdrme, Kraft, 13 (1961) Nr. 1, January, p. 20-23.

[12] Roman, Lagier, Blie, Ballez; Comptage de grands debits de gaz au moyen de

diaphragmes et de calculatrices num£riques aux postes de Taisnieres et de

Blaregnies; Communication au Congres de I 'Association Technique de Gaz

(1973)

.

[13] Stolz; A general coordinated equation for discharge coefficients of

orifice plate meters, DOC N 75 ISO/TC 30/SC 2 (Sept. 1976).

941
[14] Plunian, Sens; Etude experimentale de redresseurs d'ecoulement dans la

mesure de debit au moyen de diaphragmes ; Communications IGU/C - 22 - 73, presented at the 12th World Gas Conference, Nice 1973.

[15] ARAKI; Flow instabilities in air orifices; Fourth International Fluid

Symposium, April 1975, organized by BHRA at the University of Sheffield,

England

.

[16] Bean; Fluid meters, their theory and application, 6th ed., American

Society of Mechanical Engineers, New York, N. Y., 1971.

942
943
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944
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

EQUITABLE IMPLEMENTATION OF NATIONAL AND INTERNATIONAL ALLOCATION PROGRAMS

(Summary of Remarks to the Panel)

James A. West

Assistant Administrator

International Energy Affairs

Federal Energy Administration

Washington, D.C. 20461

Following the 1973-74 Arab Oil Embargo of the United States and the

Netherlands and a reduction of Arab oil supplies, the United States and 18

other nations formed the International Energy Agency (IEA) . These nations

consume about 85 percent of the world's oil supplies and formed IEA in

order to establish cooperative measures in the event of any future largescale interruptions in petroleum supplies. Its major programs include an

international emergency allocation program, oil market monitoring, producerconsumer relations, and long-term cooperation on energy problems.

The Federal Energy Administration (FEA) was formed to administer the

national regulatory programs in petroleum product allocations and pricing.

FEA has the major role in the U.S. Government's participation in the IEA

international allocation program. Flow measurement standards are not a

major concern in national allocations but are of very considerable concern in the international emergency program (IEP)

.

In the IEP allocation program, the United States and the other 18

nations have agreed to allocate available oil supplies during an emergency

in order to share such supplies equitably among the participating countries.

Emergency measures are activated when there is a seven percent reduction

in oil supplies (based on average yearly consumption) to the group or to

individual countries. The program requires mandatory demand restraint and

maintenance of 70 days, eventually 90 days, of petroleum imports as stocks.

Allocations are based upon computed supply rights and obligations derived

from allowable consumption levels reduced by stock drawdown obligations.

Basically, the allocation is a crude oil program. All stocks and

allocations are based upon crude oil and crude oil equivalents for broad

categories of petroleum products (gasolines, middle distillates, fuel oils

and other products).

945
In general, each country has its own measurement standards and product

definitions or follows API or other petroleum measurement practices.

This raises several problems relative to flow measurements. The

allocations are complicated by use of broad petroleum product groupings and

lack of international standard definitions of these product categories.

This complicates product exchanges and deliveries of desired products in

allocating supplies. Allocations and stocking obligations are skewed

because of duel use of certain fuels, such as residual fuel oils and

naphthas

.

So far, measurement problems have not been addressed in IEA but are

left to national entities for applying standards, settling disputes and

rationalizing transactions. There is a need for adoption of acceptable

measurement standards in IEA.

946
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

OF FORM AND SUBSTANCE FOR EFFECTIVE STANDARDS

Dr E. A. Spencer

Department of Industry

National Engineering Laboratory

East Kilbride

Glasgow, G75 OQU

With the expansion of demand and consequent increase

in world trade, the need for international standardization

has intensified. The various types of such standards

include product specifications, methods of test and codes

of practice: all are relevant to flow measurement. Their

effectiveness can be measured by how well the operator

attains in practice the objectives set out in the standards

and these are reviewed.

Three ISO Draft International Standards, which can

be used for hydrocarbon fluid flow measurement, are taken

as examples of product specifications and codes of practice.

The importance of their interrelationship with national

regulations is examined.

1. Introduction

Standardization of speech and writing makes communication possible and we

accept this form of standardization without question as being eminently

desireable and necessary. Though standards have existed, however, from

earliest times their scope in man-made products was limited until recently.

Indeed their advantages have only become indisputable in the past century

when the diversity of production which followed the industrial revolution

became overwhelming. Major rationalizations then became crucial to provide

simplifications which would result in economies in terms of effort and

materials, and thus meet the world's increasing demands.

In addition to the benefits gained by simplification, standardization

can also give benefits by setting up minimum requirements. These in a sense discipline society, but at the same time, for example by defining

requirements for quality or safety, they are aimed at the protection of the

individual or consumer interests.

Flow measurement can show examples of both these aims of standardization. The standards on pressure difference devices which emerged

nationally about 50 years ago represented a coalescing of local experience

in each country and an acceptance of a few prescriptions in place of each

instrument maker's own pattern. Simplification of this kind is perhaps

best exampled, however, by one of Britain's very first standards in 1901

which reduced the existing 75 different sizes which were in use for tramway

rails to five. Though it is hard to imagine such a process being applied

947
to the whole of flow measurement with its hundreds of different flowmetering systems available today, there can be useful rationalizations as discussed later.

Oil and gas were being supplied to consumers well before the above

dates and agreements were often individually negotiated. Legal regulations

were later introduced for the protection of the consumer covering the

measurement of the quantity of the fluid, its composition and so on and

took on a role of quasi-s tandardization. Pattern approval and verification

of each flowmeter used for sales to the public was supervised by government

representatives. Thus, while national standards were being used extensively

in the design of plant and pipelines, they were virtually excluded from the

measurement side.

On the other hand, bulk measurements at custody transfer points were

also required and here the interface between regulations and standards was

being shifted. Now with the further expansion of demand and the development of international trade and operational groups, the need for common

ground both at the national and international level has intensified. The

pace is, indeed, such that the evolutionary process of earlier times is

having to be replaced by strong guidance from governments and associations

of users and manufacturers.

2. Types of Standards

If the aims of standardization are to promote economies wherever

practicable, to protect the consumer either individually or collectively

and to provide a means of communication and understanding between all

parties, then it is important to establish what sort of standards can be

used to achieve these aims in the flow measurement world.

While a standardized glossary is valuable in promoting understanding

and clarity in the more practical standards, it is often left until they

have been completed. These latter fall broadly into three categories:

product specifications, methods of test and codes of practice.

Simplification must clearly depend on the selection of a few from the

many available and these few must be considered as capable of standing up

successfully on their own. Implementation of this selection must involve

change for both suppliers and users, and calls for considerable cooperation. Thus, standard sizing to permit interchangeabili ty can be a first stage and product standardization can in initiated in this way.

Interestingly this had not taken place in the case of orifice plate fittings, where the ISO standard [1] while specifying the geometry of the

plate leaves considerable latitude in its housing as well as variety in

pressure tappings and coefficients. A "standard orifice plate unit" in the

fullest sense could well benefit many users.

Dimensional specifications with stipulated tolerances provide one line

of approach whether they cover overall or detailed requirements. Product

specifications can also deal with the meeting of performance levels either

on the basis that by meeting the requirements the appropriate performance

will be achieved or that a level of performance is given which it is

9,48
required that the product must be shown to satisfy.

Within the specification standard or separately a different type of

standard can therefore be adopted which lays down an acceptable method of

test. As the name implies, this is a specification of the way in which

a product can be measured and it must be sufficiently explicit that the

values obtained by the method will be reproducible to within the expected

level for any set of conditions which are permitted.

Less rigorous than either of the above is a code of practice. Having

drawn together various procedures which have been established separately

through experience in different areas, this is a standard which distills

from them a composite set of instructions or guidelines. Thus, these

guidelines provide the user with what is considered to be the best available advice to meet the objective of the standard, but they inevitably

allow a fair amount of latitude. The code is lower down in the hierarchy

of standardization, but vitally important in ensuring that a minimum set

of criteria can be used.

It is logical to conclude from the above description of the sorts of

standards which can be written that they all result from a pruning of

existing information which must involve discarding a tremendous amount of

data. Indeed it could be argued that the longer standardization is postponed, the greater will be the amount of wasted effort which will have been

put into the development of information that is no longer needed.

It is certain that there is a propitious moment for the introduction

of a standard. This is the moment which represents the optimum timing

between missing improvements which were in the making, and delaying to

include them. It is probable that nearly always standardization is left

too long. Indeed it must be remembered that a standard can only be effective if it has time to be used properly and as a corollary it must therefore, once it is issued, remain frozen without changes for a reasonably

long period. Committees preparing draft standards are often over-conscious

of this and delay publication until they believe they are as near perfection as they can get in the hope that the standard will last a very long

time. Though it is clear that, if it is known that a standard is to be

amended after only a short period, there will be a disincentive for it to

be adopted in its first form; nevertheless delay in publication can have

serious consequences, just as will failure to revise it subsequently to

take account of technological advances.

It can be asserted that standards in general should not be aimed at

covering too large a field. If they are, they can take an inordinate time

in preparation and then be left unaltered for too long. Instead the aim

should be to conceive a limited series of objectives and deal with each

separately. A steadily broadening coverage will be achieved and each part

will contain the most up-to-date information. Revisions or supplements

which permit additional ways of meeting the limited objective of each part

are then much more easily prepared and accepted.

949
3. Limiting Objectives For Individual Standards

Certainly the timescale and the scope to be covered must be in the

forefront of the drafting committee's first considerations when they tackle

each project. No hard and fast rules can be laid down but a task which is

likely to take more than five years before it is published and in use could

well be said to be too comprehensive in its inception and would be better

split up into a number of stages. For example, it is ambitious to prepare

a standard to cover in depth the design, installation and performance,

operation and maintenance of a particular type of flowmeter manufactured in

variety throughout the world. A preliminary survey could well show that

certain aspects can be cleared more quickly than others, and hence indicate

a more amenable set of stages which can be tackled separately. The ISO

standards on the use of tracer methods of flow measurement [2] have

followed this pattern.

The scope of a standard must define explicitly the objectives which

are aimed at. The standard will then be effective if it has no ambiguities

and the user can achieve the objectives set out with a minimum of uncertainty. Objectives can be simple or complex, narrow or wide, but they

should never be contradictory. The simplest would be where a single route

is laid down to achieve the objective, for instance for accepting or

rejecting carburettor jets. This could be solely on the basis of whether

they gave flow rates under certain specified conditions which when compared

to the flowrate through a fully specified critical flow nozzle package came

within a defined bandwidth. No other way would be permitted.

The objective could still be the same as in the example above but a number of different routes might be permitted. This could arise in an

international standard because different methods used in different countries

are so strongly supported as being of equal merit that they are all adopted.

Inevitably there will then be jets which if tested by one route would

succeed, but would fail by another. If the quality of the production line

would be virtually unaffected in total by such individual differences

there is no real significance in their occurrence. Cross-checking rigorously between such alternative routes is often sparse, however, and so

there must be a danger of incompatibilities occurring. For example, there

could be a systematic bias between the overall mean value of a batch tested

by the different routes or the resulting bandwiths could be different.

This should be recognized and sufficient intercomparison made for some

indication to be given in the standard of its likelihood, for example by

increasing the overall uncertainty estimate for all the routes.

An example of such an incompatibility is in the International Standard

ISO R541 [l ] where the predicted discharge coefficients for an orifice plate

installed in a pipeline of 32 inches or above are different depending on the

arrangement of the pressure tappings used. Though technically specifications for the locations of the flange and corner tapping arrangements

differ, their proximity is such that at this size they can be regarded as

identical. The pressure differences across the tappings are found to be

the same, so that it is clearly wrong that using the two relevant discharge coefficients the calculated flowrates will be different. This clear

anomaly has arisen because the coefficients evolved from different sources

950
of data and were analysed independently of each other. A fresh and comprehensive re-assessment of the various predictions has been made so that

this and similar discrepancies can be resolved in future editions. Without

new data or the almost impossible task of re-analysis of all earlier data,

it must be accepted that the new solution must have an increased uncertainty to take into account such incompatibilities.

Another situation arises where although the objective of the standard

may be quite clear some extrapolation is in reality involved. Thus there

could be applications permitted in the standard for which the information

is only tentative. For example this could be especially true when the,

limits of the operating range of temperatures over which the standard Sf^n

be used are set. It is very unlikely that strict tests will have been

carried out at the extreme conditions. Again the increase in uncertainty

must be acknowledged in the standard.

Summarizing therefore it can ^e said that a standard can only be fully

effective if the objectives have been closely checked for all the conditions and methods which are covered in the standard. Neglect of this

rule will lead to errors of unknown size of which the user is unaware. Its

observance means that if necessary the scope will have been suitably

modified to allow for these special areas.

If it is the principle condition in setting out to write a standard

that the objectives should be clearly understood, it is proper that when

the standard is published these should be brought together to constitute

its first clause and not be scattered through it. There can be justification for expressly stating what is not covered in the standard where such

exclusions might be overlooked and the standard thus misused. Normally,

however, the scope can be expected to prescribe the actual limits within

which it it expected to apply. References can then be given to any overlapping or fringe standards or to any standards which may be required to be

used in order to comply with the one being published.

Since for most users it is likely that an international standard will

not be printed in their own native language the importance of selecting

words and phrases which are well understood is easily appreciated. Yet all

too often the final editing is hurried and points of this kind are overlooked. A lesson could be taken from the EEC Commission where Directives

in their final stages of preparation are subjected to detailed examination

by both legal and linguistic experts.

Understanding is also greatly aided if the presentation in the text

follows a logical sequence, though in a long or complex standard the best

sequence may not be automatically self-evident. The form or framework most

usually adopted is for the equipment to be specified fully before its

performance is considered.

The tests to be used to check its performance, the methods of computation and analysis and the method of presentation of the results can

then follow. While the method of estimation of the overall uncertainty may

4. The Form of The Standard

951
be left to an appendix, there should always be a clause in the main text

requiring the estimated uncertainty to be given as an essential part of

the statement of results. This should apply whether this statement is a single line giving the flowrate or quantity or a full test report.

Appendices or footnotes should be used wherever possible to separate

non-essential material from that required for the operation of the standard.

It is worth recalling that formally such appendices become a mandatory

part of a standard only if they are defined as such in the main text of the

standard. Similarly tables and figures need a direct reference if they are

to be of similar force to the text.

5. The Substance of Standards

For the purposes of this essay a collection of standards are to be

available which have as their aim the correct measurement of the quantity

of a hydrocarbon fluid passing a particular point in a given time. They

may be used by individuals or organizations being supplied with these

fluids; they may be used at custody transfer points between one distributor

and another or at the source; or they may be used for control purposes at

any stage. The government will be concerned with such measurements both

for their own purposes in taxation and wherever legal transactions between

parties involving flow measurements are subject to the enactments by the

legislature.

Many different standards will therefore be needed to provide full

coverage since the range of hydrocarbon fluids is considerable and the

number of possible metering systems for its measurement is large. The

first breakdown can be into liquids and gases; for in general, the metering devices normally used for these will be different. With mixtures of

liquids and gases, separation is necessary if the measurement is to be

reliable, since the methods which are available at present for the measurement of two-phase flows are only very approximate. Indeed no standardization has even been attempted yet.

The question of contamination which generally occurs at an early stage

in the process, is an important one since precautions must be prescribed

and followed if false measurements are to be avoided. Provided the amount

and size, for example, of solid particles being carried in suspension is

low enough, their influence can be taken into account so long as they do

not change or damage the measuring system. Similarly, if a small percentage of water is mixed with the oil it can be allowed for. In all cases

where contaminants may exist it will be imperative that sampling techniques

are laid down which can adequately assess the amount of the extra constituent being passed.

The only ISO standards so far published dealing with flowmeters for

general use in pipelines and closed conduits are R541 [ 1] and R781 [3] , covering the design and use of orifice plates, nozzles and venturi tubes.

These documents, which are product specifications, have been the subject of

revision and are combined in the Draft International Standard DIS 5167 at

present awaiting ratification T4] • Several other proposals for other

metering devices are also at this DIS stage while there are also a number

952
at the drafting stage.

The R541 and R781 standards have been adopted nationally in a number

of countries, and there and elsewhere they are being used for hydrocarbon

measurements. It has to be remembered that these standards were drawn up

for general use in industry and it is left to the user to judge the overall

accuracy he has achieved in his measurement since a number of factors are

not controlled within the conditions laid down in the standard. For

example, there are no specified methods for measuring the density of the

fluid. Also the measurement of the pressure difference is not prescribed

and uncertainties in this could play a significant part in the assessment

of the overall uncertainty.

If then an agreed level of accuracy is to be the objective for

standards concerned with the use of pressure difference devices for hydrocarbon fluid measurements, subsidiary standards are required laying down

how these various additional measurements are to be made. In addition,

since ISO DIS 5167 covers all industrial measurements, the requirements for

these specific gas and oil applications have to be considered and the

necessary extra constraints then added in a supplementary document to

ensure that the objective in the hydrocarbon standard can be achieved under

all the conditions which are likely to be met.

Intercomparison between the ISO standard and the AGA Report No 3 [5] , so long used in the USA for natural gas measurement, has shown up differences too substantial to be disregarded. Among these, the most

important relate to differences in acceptable installation conditions and

their effect on the estimation of the uncertainty to be associated with the

discharge coefficients which are adopted. On the other hand, it must be

recognized that to be effective the standard needs also to be supplemented

to give full coverage to all aspects making up the final measurement.

In oil flow measurement the dominance of the positive displacement

meter has given way especially in the larger pipeline sizes to the turbine

meter, but between them they provide the vast majority of measurements on

which payment is made. International draft standards are available on both

these devices; ISO/DIS 2714 deals with positive displacement meters [6] and

ISO/DIS 2715 with turbine meters . It is perhaps surprising in view of

the importance attached to the use of these meters that publication of

these standards has not occurred earlier. The ISO Committee concerned is

however simultaneously proceeding with the drafting of a large number of

standards covering various aspects of the measurements involved, including

meter proving.

The coverage aimed at in these two draft standards (2714 and 2715) is

very considerable, though it is fair to note that in substance these

standards are essentially codes of practice. While guidance is given of

the manifold problems which can arise during measurement, there are no

details of how to deal with these problems. The user is left to find this

out from other sources.

Both standards are inevitably limited in their treatment since it is

stated at the commencement that no tolerance or accuracy limits are being

953
set, but in following sentence in each, however, it is claimed that the

provisions of the standard should prove adequate to achieve a degree of

measurement accuracy acceptable to any metering requirement. These objectives are obviously contradictory, for the user cannot determine how

rigorously he must meet provisions which have been so written as to allow

for a wide range of different levels of accuracy to be attained. For

example, having stated that turbine meter performance is affected by swirl

and non-uniform velocity profiles, it is recommended quite rightly that

"sufficient" lengths of straight pipe or a combination of straight pipe and

straightening vanes be used to overcome this problem. No definition of

what is "sufficient" is given for any particular layouts and the recommended flow straightener assembly is described as "effectively assisting

in achieving flow conditioning" without expressly stating the level which

it has been found to achieve.

If then these two standards on oil flowmeters are to be regarded as the

first steps towards fully comprehensive international standards how are they

to be followed up. One way must be to set explicit performance criteria and

associate with these more detailed information on what has been found to be

sufficient in design, installation and operational requirements to achieve

this performance. At present any matters covered in national regulations or

private agreements have been excluded because of their legal implications.

Differences between such regulations are inevitable since they will have

been established, in some instances, many years ago in accordance with procedures developed separately in the different countries. If such differences can be reduced to a matter of degree and not of contradiction

then a major restraint to progress will be removed.

The aims of the International Organization for Legal Metrology are to

promote unification in the measurement practices followed by the governments

of member states. This is achieved by publishing Recommendations agreed by

the member states as representing acceptable compromises between their

individual regulations; the members also agree to implement these harmonized

versions. OIML Working Groups are active in the field of hydrocarbon fluid

measurements so that progress towards rationalization is being made. Indeed

the countries within the EEC are also seeking to obtain a common pattern in

this field; this time through the publication of Directives which are to

take the place of the individual country's rules.

It is clearly of considerable importance that there should be very

close liaison between such govermental organizations and the ISO and IEC.

For the immediate future there is bound to be an overlap of interests, and

aspects that may be more appropriate to standardization could well be

included in the model regulations. Ultimately, however, the greatest benefit to industry as a whole will be achieved by the extension of the coverage of the standards; for example, by dealing with specific ranges of

applications at various levels of accuracy. The necessary regulations can

then be framed in such a way that they require the user to conform to

appropriate sections of the international standards, rather than themselves

prescribe the technical provisions to be met.

There is a marked contrast between bulk metering of oil using, for

example, the draft standards on turbine meters with dedicated pipe proving

954
systems and that of natural gas using the detailed specification for

orifice plates. Both can be made more effective for operational use by

extending their scopes to include areas covered by the other.

6. Conclusion

The main aims of standardization can be said to be to promote

economies, protect the consumer and provide the means of understanding

between parties. These have all been very amply demonstrated in flow

measurement by the extensive use of "standard" pressure difference devices

over the past fifty years and by the development of acceptance test methods

Such standards have not been static and they are still being modified and

improved as fresh analyses and evidence become available.

As more and more flowmetering systems are introduced so the advantages

of a standards framework for their intercomparison and operation increase.

The form of the standard can vary to suit the requirement, whether this be

for the simplification of face-to-face dimensions to allow interchangeability, or the specification of performance criteria at codified levels,

or yet again the guidance given in a Code of Practice. Each such standard

can be effective for a period of time if its provisions unambiguously

permit the operator to achieve the objectives laid down in the standard.

The rapid expansion of industrial activity and the increase in international trade has meant that it is no longer worthwhile pursuing solely

national standards as a goal. Instead international agreement must be

sought and this is especially true of the measurement of hydrocarbon fluids

The existence of differing national regulations, however, has been a restraint which will be overcome only when present efforts to harmonize

these are successful. Indeed the importance of collaboration between

organizations such as OIML, ISO and IEC is recognized and closer liaison is

being developed. This will enable more positive international standards to

be promulgated for the general benefit of industry while allowing

governments to incorporate suitable references to mandatory aspects of

these standards in their own ^regulations

.

Acknowledgement

This paper is presented with the permission of the Director, National

Engineering Laboratory, Department of Industry. It is British Crown

copyright.

[1] Measurement of fluid flow by means of orifice plates and nozzles,

ISO/R541-1967 , 1st Ed., (International Organization for

Standardization, Geneva, 1967).

[2] Measurement of water flow in closed conduits. Tracer methods,

ISO Standard 2975 , Parts I-VII, (International Organization for

Standardization, Geneva).

[3] Measurement of fluid flow by means of venturi tubes, ISO/R781-1968 , 1st Ed., (International Organization for Standardization, Geneva,

1968).

955
Measurement of fluid flow by means of orifice plates, nozzles and

venturi tubes, ISO/PIS 5167 , (International Organization for

Standardization, Geneva, 1976).

Orifice metering of natural gas, AGA Report No 3 , (American Gas

Association, Arlington Va, 1969).

Liquid hydrocarbons - volumetric measurement by positive displacement

meter systems other than dispensing pumps, ISO/PIS 2714 , (International

Organization for Standardization, Geneva, 1976).

Liquid hydrocarbon - volumetric measurement by venturi meters,

ISO/PIS 2715 , (International Organization for Standardization, Geneva,

1976).

956
National Bureau of Standards Special Publication 484, Proceedings of the

Symposium on Flow in Open Channels and Closed Conduits held at NBS

,

Gaithersburg, MD, February 23-25, 1977. (Issued October 1977)

COMMENTS ON: ROLE OF INTERNATIONAL STANDARDS IN MEASURING

AND ALLOCATING HYDROCARBONS - A PROGRAM FOR

SOLUTION OF OUR PRESENT PROBLEMS

Frederick H. Abernathy

Harvard University

Cambridge, Mass. 02138

The four members of the panel concentrated their discussion on

different aspects of the hydrocarbon measurement problem, which are

associated with the international trade in hydrocarbons. There are

a number of features of the present problem that makes the situation

qualitatively different from that which existed in the past. Increasingly

the buyers and sellers of hydrocarbon are units of government rather

than individual corporations. The total mass or volume of hydrocarbons

in international trade is rising and likely to continue to rise over

the next decade. The amount of hydrocarbons primarily trans-shipped

through nations is also rising. Lastly the value of a unit of hydrocarbons has risen by at least a factor of four in so short a period of

time that it can be thought of as a discontinuous change.

In the past when the buyers and sellers of hydrocarbons were

individual corporations, the method of settlement of measurement

dispute was through negotiation of a satisfactory price. National

prestige and techniques of measurements were not necessarily involved,

or at the forefront of the discussion. Now as the unit price of hydrocarbons has risen, monetary value associated with discrepancy in

measurements has also risen. The attention devoted to discrepancy in

measurements of these large volumes and flow rates naturally increases.

In addition, one has the possibility of different measurement techniques

and standards used by each nation in a hydrocarbon transaction. Each

party to the transaction is generally satisfied with its technique and

standards, and when measurements of pipe line flow across national

borders disagree, or when measurements of mass of oil in a tanker

disagree from on-loading to off-loading, then one has a technical

problem complicated by international political considerations. The

question then is really how does one resolve all of these conflicting

points of view and interest. An obvious answer is that each of us do

our task a little bit better and a little more carefully. We should

decrease the uncertainty in our measurements by more carefully defining

procedures and increasing the accuracy of our measurements. This is

easily said and not very easily done, and might in the long run not

even resolve the problem. The differences between many standards cannot

be resolved by increasing the data base alone unless one changes the

range of validity of various standards and/or incorporates additional

957
variables. What should be done? The need for more precise measurements

exists - many of the problems have been identified, but can we agree on

how best to resolve these difficulties?

Let me advance a particular point of view, namely that increased

testing, calibration, and measurement will not alone solve the problem

without simultaneously expanding our understanding of the various fluid

metering processes. Let me give just two examples:

(1) Because the bulk coefficient of expansion of petroleum depends

on its chemical composition in addition to the state variables,

no amount of data taking or curve fitting without awareness of

this property will remove this dependence of the coefficient

of expansion on composition.

(2) Axial swirl apparently affects turbine meter measurements in

pipe flow even when they are installed under conditions which

meet some current standards.

A much longer list of examples could be compiled. From my point

of view, it is only necessary to agree that such a list could now be

made of parameters whose importance is not recognized in present

standards. If one accepts the premise that such a list could currently

be devised, and with additional research could probably be expanded,

then one is naturally led to the conclusion that we need to expand our

basic understanding of flow metering processes. While one might always

wish to expand our basic understanding, the question can be raised, is

now a relatively more important time than the immediate past, and if so

are our chances of success greater than they have been in the recent

past? I believe the answer to both questions is yes.

We have a greater need for more fundamental understanding now,

because the uncertainties in measurements currently involve very

substantial sums, and because increased understanding appears, to me,

in the long run to be the only way to avoid complex political or

judicial solutions of what are in fact technical problems. The

likelihood of achieving increased understanding of the fluid dynamics

of flow metering problems is, in my opinion, excellent, if we find the

strength and courage to move vigorously on the problem. I believe

this to be true primarily for two reasons. We have reached a state

where we are able to numerically calculate solutions to pipe metering

flows and open channel flow from first principles provided we independently know the wall shear stress variation and the turbulent eddy

diffusivity. Because such codes exist, or can be developed, it is

now possible to explore fairly inexpensively the importance of variations in initial conditions, the effects of variation of viscosity on

temperature, etc. on a theoretical basis and check these results against

special experiments designed to test the calculations. The second

factor that makes advances in understanding likely is the improvements

in instrumentation. It is not only that spatial resolution and time

response of velocity and pressure probes have been improved, but also

that non-intrusive velocity probes are now available for the first time,

958
In addition, the introduction of the mini-computer to the laboratory

is in the process of changing our entire view of what it is possible to

measure and analyze. As a result, for example, it seems likely that we

will be able to routinely acquire spectral information about velocity

fluctuations that we always considered important but rarely measured

because of the enormous effort involved in acquiring and reducing the

data.

It no longer appears visionary to expect on line instrumentation

systems to automatically account for spatial changes in state variables

in real time. Existing integrated circuit technology makes relatively

large volume data storage for use with complex algorithms economically

possible. We can now acquire data at a high rate and manipulate large

data bases with inexpensive reliable solid state devices. The technology

is available to handle problems with a large number of parameters quite

easily. Our difficulty is that instrumentation and computing technology

is well ahead of our understanding of the parameters which control the

flow processes in metering devices. In the relatively recent past, this

was not true, which diminished our drive to increase our knowledge. We

should recognize that times have changed; the need exists, the technology

to exploit additional knowledge exists, and now our lack of understanding

is holding us back.

I believe that we should and can move vigourously with programs

which enlarge our understanding, confident in the knowledge that the

results of such efforts will be used quickly in the international field.

959
AUTHOR INDEX

Abernathy, F. H. 957

Allion, H. 33

Annett, John 145

Appell, Gerald 109

Bajura, R. A. 523

Baker, Milton 803

Ball, John M. 847

Baumoel, J. 267

Berte' , Frank J. 447

Bradshaw, J. E. 293

Brennan, J. A. 881

Brower, W. B. Jr. 719

Bruner, Ronald F. 277

Clark, M. E. 479

Cullen, J. T. 549

Dang, Clement 187

Davis, L. M. 55

Davis, R. W. 219, 491

DeCarlo, J. P. 549

Delisi, Donald P. 423, 783

Dijstelbergen, H. H. 935

Durgin, William W. 471

Dussauge, J. P. 649

Edgerly, D. E. 921

Fabris, Gracio 659

Flandro, G. 335

Flemons, R. S. 319

Gad-el-Hak, Mohamed 571

Gaviglio, J. 649

Gold, D. S. 621

Grant, D. M. 91

Greenleaf, J. F. 335

Guthrie, D. L. 173

Halmi, Dezsoe 61

Haney, Robert A. 755

Hayward, A. T. J. 1

Holley, E. R. 395

Irwin, L. K. 895

Jennings, Roger 821

Johnson, S. A. 335

Kempf, D. 361

Kirchhoff, Robert H. 783

Koenig, H. L. 145

Kondic, N. N. 765

Kulin, G. 123

Kullman, C. G. 25

LaNasa, Paul J. 871

Lin, Jung-Tai 423

Liu, Hsien-Ta 423

Lowell, Francis C. Jr. 243

Lynnworth, L. C. 293

Mann, D. B. 881

Martig, Kenneth W. Jr. 83

Mattingly, G. E. 33, 491

McQuivey, S. 109

Meagher, Thomas F. V. 687

Mero, Thomas 109

Miller, R. W. 549

Moore, E. 33

Morel, P. R. 293

Morgan, W. H. 361

Neale, Lawrence C. 471

O'Brien, Joseph F. 145

Peckham, Vernon D. 687

Pedersen, N. E. 293

Pellegrin, M. T. 523

Phillips, R. E. 361

Pierce, F. J. 621

Pontius, P. 33

Replogle, John A. 201

Robben, Frank A. 423

Robertson, J. M. 479

Rudland, R. S. 705

Ruff, James F. 187

960
Sachs, Donald C. 687

Saxton, Keith 187

Scottron, V. E. 737

Servoz, Alan 719

Seward, Wallace N. 929

Singley, G. Wayne 145

Skridulls, James 145

Spencer, E. A. 947

Suhoke, Robert B. 597

Tabler, J. H. 25

Tanaka, M. 335

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BIBLIOGRAPHIC DATA

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1. PUBLICATION OR REPORT NO.

SP 484 -- Volume 2

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Flow Measurement in Open Channels and Closed Conduits

Volume 2

5. Publication Date October 1977

6. Performing Organization Code

7. AUTHOR(S)

Lafayette K. Irwin, Editor

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

National Bureau of Standards

13. Type of Report & Period

Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 77-14243

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

The wide range and complexity of problems and potential solutions that must be considered for useful flow measurements are emphasized by the papers contained in these

proceedings. Fifty-three presentations cover: characteristics of new and improved

instruments; applications of traditional and new measuring devices in field environments: procedures for identifying and analyzing errors or uncertainties in data under specific conditions; uses of physical and numerical models; politico-economic changes

that affect international standards for flow measurement; and philosophical bases for

making measurements. The fluids of most interest are water and waste water, petroleum

and related refined products, air, natural gas and stack gas.

Experimental and analytical investigations on instrument performance and interpretation of results include innovative applications of traditional and new flow measurement

techniques to fluid flows in open channels and closed conduits. The traditional devices

or techniques include weirs, flumes, current meters, orifice plates, turbines, hot-wires, pitot-static tubes, velocity traverses, dye-dilution, and others. More recent instru- mentation developments and procedures such as laser doppler anemometry, acoustic and

thermal imaging, acoustic pulse velocity and doppler anemometry, numerical modeling,

vortex shedding and digital computation are covered for particular measurement purposes

The most significant trend reflected in these presentations is the general awareness

that uncertainties in measured quantities at the lowest point in the measurement chain,

i.e., in the field or plant, are more important than accuracy statements derived from

controlled laboratory studies. Other trends in evidence are the rising importance of

turbine meters for use as transfer standards and in-line measurements of liquids and

gases m filled pipes and the increasing number of applications for acoustics and laser

technology for flow measurements in hnfh open channels and closed conduits

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Acoustic flow meters; closed conduit flows: current meters; dye-dilution methods; errors in r. low measurement; flow measurement; fluid flow modeling; fluid velocity; flumes; gas tlow standard; hot-wire anemometry; international flow standards; laser anemometry; open

channel flows; orifice meters; pitot-static meters: turbine meters; weirs

18. AVAILABILITY | [ Unlimited

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19. SECURITY CLASS

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21. NO. OF PAGES

490

22. Price

$12.25 Per

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