. ,NITE0 STATES PARTMENT OF COMMERCE

PUBLICATION NBS TECHNICAL NOTE 606

U.S.

DEPARTMENT

OF

COMMERCE

National

*C Bureau

00 of ;'7S3indards

>.wt

fjl.

Cryogenic Flow Research

Facility Provisional

Accuracy Statement
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards1 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 measure- ment system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Center for Computer Sciences and

Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consistent 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 a Center for Radiation Research, an Office of Measurement Services and the following divisions: Applied Mathematics—Electricity—Heat—Mechanics—Optical Physics—Linac

Radiation2—Nuclear Radiation2—Applied Radiation2—Quantum Electronics3—

Electromagnetics3—Time and Frequency3 —Laboratory Astrophysics3—Cryogenics3

. THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research lead- ing to improved methods of measurement, standards, and data on the properties of

well-characterized materials needed by industry, commerce, educational institutions, and

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provides liaison between NBS and national and international engineering standards

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THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and accessibility of scientific information generated within NBS and other agencies of

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Relations.

1 Headquarters and Laboratories at Gaithersburg. Maryland, unless otherwise noted; mailing address Washington, D.C. 20234.

-'Part of the Center for Radiation Research.

3 Located at Boulder, Colorado 80302.
UT10NAL BUffAU OF SlteOHtita

UNITED STATES DEPARTMENT OF COMMERCE

Maurice H. Stans, Secretary

5 NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

If -7/

NBS

iTECHNICAL NOTE 606

ISSUED JULY 1971

Nat. Bur. Stand. (U.S.), Tech. Note 606, 40 pages (July 1971) CODEN: NBTNA

Cryogenic Flow Research Facility

Provisional Accuracy Statement

J. W. Dean, J. A. Brennan, D. B. Mann, and C. H. Kneebone

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide

a means for making available scientific data that are

of transient or limited interest. Technical Notes may

be listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

(Order by SD Catalog No. C 13.46:606), Price 45 cents Stock Number 0303-0875
PREFACE

It is the policy of the National Bureau of Standards to use the

International System of Units (SI) in its reports unless this usage would

lead to confusion or a lack of understanding. In this report SI units have

not been used because it is standard practice in the industry to use English units and the use of SI units would be unduly cumbersome. The

folio-wing conversions are given so the reader can convert the values

in the report to SI units if he desires.

feet 3 x 0.028317 = meter3

gallons x 0. 0037854 = meters 3

gallons /minute x 0. 00006309 = meters 3 /second

inches x 0. 0254 = meters

pounds x 0. 45359 = kilograms

pounds/inch2 x 6894. 757 = newtons /meter 2

The authors want to thank Dr. Brian Joiner and Dr. Peter Tryon

of the Statistical Engineering Laboratory of NBS for their assistance in

this test program. The test schedules they prepared and the assistance

in analyzing the data has been invaluable.
Contents

Page

1. Introduction .......... 1

2. Provisional Accuracy Statement .....

2. 1 Mass Flow .........

2. 2 Volumetric Flow .......

3. Methods of Obtaining the Accuracy Statement

4. Weigh System Calibration .......

4. 1 Mass Calibration .......

4. 1. 1 Gravitational and Buoyancy Corrections.

4. 2 Voltmeter- Load Cell Calibration ....

5. Static Imprecision of the Weigh System ....

6. Imprecision of the Density. ......

7. Systematic Errors ........

8. Interlaboratory Comparison ......

9. Tests of Meters .........

10. Provisional Accuracy Statement Summary

11. References ..........

Appendix A. Standard Masses Report of Calibration.

Appendix B. Load Cell Manufacturers Certificate

Illustrations

Figure 1. Schematic of Measurement System ....

Figure 2. Load Cell Control Chart ......

List of Tables

Table 1. Voltmeter- Load Cell Calibration Data

Table 2. Sensitivity Determinations ......

Table 3. Least Squares Estimate of Sensitivity as a Function

of Pressure .........

Table 4. Errors Due to Pressure and Temperature Measurements. 1 7 Table 5. Systematic Errors . . . . . . . . .21

1

2

2

3

5

7

9

10

14

14

18

22

22

23

25

A-l

B-l

6

15

11

12

13

CRYOGENIC FLOW RESEARCH FACILITY

PROVISIONAL ACCURACY STATEMENT

J. W. Dean, J. A. Brennan, D. B. Mann, and C. H. Kneebone

The National Bureau of Standards and the Compressed

Gas Association have jointly sponsored a research program

on cryogenic flow measurement. A cryogenic flow research

facility was constructed and was first used to evaluate commercially available cryogenic flowmeters operating with

liquid nitrogen on a positive displacement principle.

The performance of the flow facility was simultaneously being evaluated during the meter tests. This is a summary report of the performance evaluation of the flow

facility. An accuracy statement is given for both totalized

mass and volumetric flow.

Key Words: Accuracy statement; cryogenic; flow facility;

liquid nitrogen; measurement.

1. Introduction

The historical background, design, and operation of the Cryogenic

Flow Research Facility have been given in Mann [1971]. This report

describes the present status of our knowledge of our ability to make

cryogenic flow measurements after a year of operation of the facility.

The error analysis presented here details just the contribution of the

flow facility itself to the uncertainty of flow measurements. Subsequent

reports will deal with the problems and uncertainties in using the facility

in research measurements and in evaluation of flowmeters. The uncertainties given here are, in a sense, limits to the discrimination possible

in those investigations.

2. Provisional Accuracy Statement

The following accuracy statements should be considered provisional and are currently restricted to flow rates between 20 and 100 gpm,

pressures from 50 to 100 psig, and temperatures of 80 to 90 K, and for
ideal conditions where operational or equipment malfunctions are not

present. As results of future tests become known, the accuracy state- ments will be improved.

2. 1 Mass Flow

At this time the uncertainty of the measurement of totalized

mass flow is estimated to be ±0. 18 percent. This figure includes an uncertainty of ±0. 12 percent for known sources of systematic errors plus an uncertainty of ±0. 06 percent 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.

2. 2 Volumetric Flow

At this time the uncertainty of the measurement of totalized

volumetric flow of liquid nitrogen is estimated to be ±0. 47 percent. This

figure includes an additional uncertainty of ±0. 39 percent for known sources

of systematic error in the density determination, which is added in quadrature to the uncertainty due to systematic error in the mass measurement. The major contribution to the uncertainty in liquid nitrogen volumetric flow measurement is the uncertainty in the liquid density, which

can only be improved by new PVT property measurements.

When the objective of using the accuracy statement is in the

mediation between seller and buyer, where both have accepted the same

values of density, the uncertainty in the density need not be considered.

Under this condition the uncertainty of the measurement of totalized

volumetric flow is ±0. 18 percent, because the contribution of the pressure and temperature measurements error is negligible.
3. Methods of Obtaining the Accuracy Statement

The estimated uncertainty of a measurement is composed of the

estimated imprecision plus an estimate of the limits to possible systematic error. The methods available for determining the imprecision of

cryogenic flow measurement are:

1) Measurement of the static imprecision from repeated

applications of the calibration weights.

2) Measurement of the dynamic imprecision of the combined

meter and flow system.

3) Measurement of the dynamic imprecision of the flow system

by series testing two or more meters and performing an

analysis of variance calculation with the resulting data.

In measuring static imprecision, the flow facility is brought to equilibrium pressure and temperature by circulating liquid nitrogen

through the weigh tank. Repeated application of the calibration weights

combined with the reading of load cell output under these conditions allows

the calculation of the static imprecision of mass measurement. However,

liquid is not being accumulated in the weigh tank and a different imprecision

may be associated with this action. Thus, the static imprecision measurement does not include all the desired information. It is the static

imprecision that is most commonly reported in the literature for cryogenic flow facilities.

Measuring the dynamic imprecision of the combined meter and

flow system includes any effect of accumulating liquid in the weigh tank,

but it also includes the contribution of the volumetric meter imprecision.

Meters have substantial imprecisions that tend to mask the contribution

of the flow system. At best, meters can only indicate an imprecision

that is larger than the true flow system imprecision. Since only volumetric cryogenic flowmeters were available, the imprecision of the
density measurement required to compare the performance of these

volumetric meters to the gravimetric flow system is included.

The best method of separating the dynamic imprecision of the

flow system from the imprecision of the meters is to perform a series

meter test and to make the analysis of variance calculation. Modification

of the flow facility to permit series testing of two meters is underway.

The imprecision reported are found by methods (1) and (2) using the most

consistent meter data available.

Systematic errors may be investigated by:

1. Propagating the effect of the indicated systematic errors in

the calibration of the measuring system components.

2. Plotting the deviations between the meter and flow system

performance as a function of the flow system parameters.

3. Using a flowmeter as a transfer device and intercomparing

the results of tests of the same meter on different facilities.

4. Changing components of the measuring system and comparing

results.

The critical components of the measurement system have been

calibrated by the appropriate groups within NBS.

The deviations of all meters evaluated have been plotted as a function of pressure, liquid temperature, density, weight accumulated,

degree of liquid subcooling, mass flow rate, and the order in which the

data were taken. The presence of a dependency on any of these parameters for all meters would indicate the presence of a systematic error. Some of the volumetric meters tested on the cryogenic flow re- search facility had previously been evaluated on private industrial cryogenic flow facilities. Where appropriate, data obtained on the NBS
and the private facilities are compared. Discrepancies indicate a systematic error, but the systematic error cannot be charged to either

facility -without further information.

The technique of changing components of the flow facility and

comparing the results has not been used to determine the presence of

systematic error because the components are unique. Experimental

evidence from the first three of the above four methods are discussed

below.

4. Weigh System Calibration

A schematic diagram of the flow measurement system is seen in

figure 1. Either the calibration weights or the weigh tank can be supported from the load cell. The load cell receives a 10 volt excitation

and produces an analog output voltage proportional to the applied weight.

Both the excitation and the output signal are read by an integrating

digital voltmeter converting the analog signal to a digital signal that is recorded. The flowmeter under test either generates, or is adapted to generate, a digital output. Integer pulses are counted, timed, and used

to synchronize the reading of the load cell at the start and end of the test draft by the controller.

The performance of the weigh system is determined by the measurement of the load cell sensitivity by the operation of the calibrator.

The load cell sensitivity is described by the relationship

S = Es " E l (1) wv

where E2 and E 1 are the load cell output voltages measured by an integrating digital voltmeter. W is the weight of the brass cylindrical
s

CO

s

U
masses of the calibrator, and V is the load cell excitation voltage measured by the same integrating digital voltmeter. An estimate of the

uncertainty of the ability to determine the load cell sensitivity requires

a knowledge of the systematic and random errors associated with the

brass cylindrical masses and the integrating digital voltmeter-load cell

system. The masses have been calibrated yearly and are used to calibrate the voltmeter-load cell combination.

Recalibration of the four nominal 250-pound brass cylindrical

masses required that the calibrator be removed from the catch and

weigh tanks and disassembled. After recalibrating the masses and re- assembly of the calibrator, the calibrator was placed on a test table and

the load cell sensitivity was determined using the brass cylindrical

masses and four additional cast iron nominal 50-pound masses. The

calibrator was then installed on the catch and weigh tanks and the load

cell sensitivity determined and compared to the value obtained on the

test table.

The following sections describe the calibrations and calculations

performed in order to better estimate the uncertainty of the load cell

sensitivity. These results are then used to calculate the uncertainty in

the mass determination.

4. 1 Mass Calibration

The four nominal 250-pound brass cylinders used to perform the

in-place calibration of the load cell were calibrated against a set of mass

standards maintained in Boulder by the NBS Electromagnetics Division.

The set of standards consists of one 25-pound and two 50-pound brass

masses, and a set of smaller stainless steel masses which have been

compared to the National Standard of Mass. The test reports and descriptive information are included in Appendix A.
The above mass standards were used to calibrate a working set

of masses consisting of cast iron nominal 50-pound blocks. This calibration was done on a Russell [1955] equal arm balance.

Our nominal 250-pound brass cylinders were calibrated on the

same Russell equal arm balance against the brass, the cast iron, and

the small stainless steel masses as required. This measurement did

not make a correction for the buoyancy of air and the difference of

density of the weights. This results in a possible systematic error

estimated to be +0. 002 percent. The total uncertainty in the 150 pounds

of standard masses used in the comparison is less than ±0. 00008 percent

in 250 pounds. The uncertainty in the 100 pounds of cast iron masses

is somewhat larger, but still sufficiently small that the total uncertainty in the 250 pound brass cylinders is conservatively estimated to be less than ±0. 01 percent.

Additional information available on the stability of the mass

standards includes independent calibration of the 50-pound masses in 1965 and 1971 which agrees to within ±0. 001 percent, and calibrations

of the 250-pound brass cylinders used in sensitivity calculations, in

1968 and 1970, agreed to within ±0. 001 percent.

Since the load cell senses force, it is necessary to determine

what forces were exerted by the individual masses under the conditions

of the experiment. Important experimental conditions were the air

pressure of 12. 3 psia at 70°F and local gravity of 979. 615 cm/s 2

, both measured at the Boulder Laboratories.
sion

4. 1. 1 Gravitational and Buoyancy Corrections

Gravitational corrections -were made on all masses by the expres

B B W = W B g g

W

S (2)

where

g = 979. 615 cm/s 2 at the experiment B

g

= 980. 665 cm/s 2 standard gravity

W - weight at Boulder without buoyancy correction

W = weight at standard conditions of 45° latitude sea level without buoyancy correction.

By definition W is equal to the masses certified by NBS. The value of

g TD /g e

is equal to 0. 998929.

-D O

In order to make buoyancy corrections for the calibration masses,

the density of each mass must be known. The buoyancy corrections made

here are approximations based on handbook values of the density. The

buoyancy force is equal to the volume of the masses times the density

of the displaced gas.

The density of air at 12. 3 psia and 70°F is 0. 063 lbs/ft 3 or F = Mass/density of brass x 0. 063 lbs/ft J

.

The density of brass has been taken as 520 lbs/ft 3

. Thus, the

weight of the flow facility cylindrical brass masses at Boulder are:

Mass Number Boulder Weight

(lb f

)

1 255.34(0.998929-0.063/520) 255.03

2 247.72(0.998929-0.063/520) 247.42

3 252.33(0.998929-0.063/520) 252.03

4 247.53(0.998929-0.063/520) 247.23
4. 2 Voltmeter -Load Cell Calibration

The voltmeter-load cell calibration mechanism was reassembled

and placed on a steel table with a hole cut in its center. This hole allowed

a weigh pan to be attached to the load cell string. Four nominal 50 -pound

working masses were obtained from the NBS Boulder weight calibration

laboratory. Thus, a total of 1200 pounds of mass in 50-pound increments

was available to calibrate the load cell. A statistically designed calibration was performed by repeated application of the calibrated masses

sequenced as follows: 0, 200, 50, 150, and 100 pounds.

The calibration mechanism was operated with the above masses

in the described sequence with 10 ±0. 001 volt energizing the load cell. The millivolt output reading of the load cell was recorded with its corresponding applied force. The results are shown in table 1.

The sensitivity value and the uncertainty of the sensitivity value

needs to be known in order to estimate the uncertainty associated with

weighing a test draft of liquid. Therefore, sensitivity values are determined daily using the brass masses. Table 2 lists the typical results

obtained. Since the load cell is within the pressure environment, it is subjected to system pressure. The sensitivity is a function of this pressure as shown in table 3. The uncertainty of the sensitivity value is estimated to be less than ±0. 02 percent.

The data in tables 1, 2, and 3 are consistent -with the uncertainty

due to non-linearity specified by the manufacturer of ±0. 05 percent

(see Appendix B).

10
TABLE 1 er-Load Cell Calibration Data

Weight Voltage

lb. mV

0.00 0.9M+

255.03 8.616

502. k5 16.061

751+.1+8 23.61+6

1001.71 31.087

751+.1+8 23.61+8

502.1+5 16.061+

255.03 8.617

199.76 6.953

<+5<t.79 lit. 627

702.21 22.071

951+.21+ 29.657

1201.1*7 37.098

95*+. Zh 29.661

702.21 22.077

1+51+.79 li+. 630

199.76 6.956

1+9.91+ 2.1+1+6 301+.97 10. 120

552.39 17.561+

801+.1+2 25.11+9

1051.65 32.589

80it. <+2 25.152

552.39 17.567

301+.97 10.120

1+9. 9k 2.1+1+7 ii+9.82 5.1+50

1+01+.85 13.121+

652.27 20.571

90*+. 30 28.157

1151.53 35.598

90^.30 28.158

652.27 20.573

1+01+.85 13.127

11+9.8 2 5.1+52

99.88 3.950

351+.91 11.621+

602.33 19.069

851+.36 26.653

1101.59 3i+. 091+ 851+.36 26.656

602.33 19.071

35i». 91 11.625

99.88 3.950

11
TABLE 2

Sensitivity Determinations

Excitation System S<snsitivity

Date Voltage Pressure (mV/V-lb)

(volts) (psig) First Mass Second Mass Both Masses

11/18/70 10. 0045 93. 5 0. 00300222 0. 00300285 0. 00300253

19 10. 0057 94. 1 0. 00300225 0. 00300007 0. 00300118

20 10. 0057 94. 4 0. 00300225 0. 00300209 0. 00300217

23 10. 0054 59. 2 0. 00300469 0. 00300783 0. 00300624

12/07/70 10. 0043 88. 4 0. 00300267 0. 00300210 0. 00300239

08 10. 0048 67. 2 0. 00300487 0. 00300518 0. 00300502

09 10. 0051 69. 1 0. 00300517 0. 00300711 0. 00300613

1 1 10. 0043 75. 6 0. 00300463 0. 00300332 0. 00300398

14 10. 0046 90. 3 0. 00300219 0. 00300282 0. 00300250

15 10. 0049 88. 2 0. 00300327 0. 00300112 0. 00300221

16 10. 0048 59. 6 0. 00300487 0. 00300640 0. 00300562

17 10. 0047 70. 6 0. 00300412 0. 00300360 0. 00300386

21 10. 0046 51. 5 0. 00300532 0. 00300767 0. 00300648

22 10. 0041 58. 0. 00300508 0. 00300661 0. 00300583

01/19/71 10. 0024 81. 7 0. 00300363 0. 00300389 0. 00300376

20 10. 0014 60. 4 0. 00300511 0. 00300459 0. 00300485

21 10. 0024 92. 2 0. 00300010 0. 00300227 0. 00300117

22 19. 9984 74. 7 0. 00300444 0. 00300388 0. 00300416

25 10. 0018 80. 4 0. 00300381 0. 00300366 0. 00300374

26 10. 0028 75. 9 0. 00300234 0. 00300670 0. 00300463

26 10. 0026 77. 2 0. 00300357 0. 00300625 0. 00300489

27 10. 0037 77. 3 0. 00300402 0. 00300430 0. 00300416

28 10. 0026 69. 4 0. 00300514 0. 00300625 0. 00300569

12
TABLE 3 Least Squares Estimate of Sensitivity as a Function of Pressure

(50 - 100 psig)

Mass Sensitivity, mV/V - lb

First 0. 00301053 - 0. 00000009 P

Second 0. 00301 5 1 - 0. 000000 14 P

Both 0. 00301278 - 0. 00000011 P

13
5. Static Imprecision of the Weigh System

The sensitivity of the load cell is measured each day the flow

research facility is operated. This is done with the pump running,

liquid passing through the weigh tank, and operating temperatures and

pressures established. Known weights are placed on the load cell, the

voltage recorded, and the load cell sensitivity calculated. The calculated sensitivities are normalized by applying the pressure correction.

The standard deviation is calculated from data obtained over several

months of operation, and the uncertainty due to imprecision is then calculated on three times the standard deviation. Since liquid is not ac- cumulated in the weigh tank as the known weights are applied, dynamic

effects are not included. The uncertainty calculated in this manner is defined as the uncertainty due to static imprecision.

Results from the load cell calibration are shown in figure 2 and

the uncertainty due to static imprecision is ±0. 06 percent.

6. Imprecision of the Density

The liquid density is found by measuring the pressure and temperature and calculating the density from a state equation. The liquid

nitrogen density data used are given by an equation of state defined by

Strobridge [1962]. At the time Strobridge did the work, there were very

few experimental data in the liquid region. The data available were

located along the saturated liquid line or at high pressures (above 100

atm). No experimental data were available in the liquid region of

current interest.

Recently, new experimental work has been done for nitrogen in

the saturated and subcooled liquid region. This work has been performed

by Streett [1968] and Terry [1969]. Terry reports that unpublished work

14
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15
of the British Oxygen Company (BOC) on saturated liquid data for molar

volumes is in agreement with his work to ±0. 05 percent. A comparison

was made between Strobridge's calculated density data and the new ex- perimental data in the range from 77 to 95 K and pressures to 100 psia.

The data of Streett, Terry, and BOC give larger molar volumes on the

order of 0. 3 to 0. 4 percent over this region. These differences are

within the average uncertainty in density of ±0. 39 percent claimed by

Strobridge.

The above comparison indicates that the density values, in the

stated pressure and temperature range given by Strobridge, might be

brought into agreement with the new data by multiplying Strobridge's

density data by 0. 9965. This correction has not been made in the present meter performance work in order to facilitate intercomparison

with measurements using the data of Strobridge.

Temperature and pressure measurements must be made to determine the density. The density error associated with these measurements may be estimated from the isothermal compressibility and

the temperature coefficient of the liquid. The isothermal compressibility is defined as

l^BP

pVoP.

and the temperature coefficient as

e

= pC^p

Assuming that the temperature error is not more than ±0. 1 K

and the pressure error is not more than ±0. 25 psi, then the resulting

density errors for liquid nitrogen are:

16
Table 4

Errors Due to Pressure and Temperature Measurements

or /

• % density w

, % density Liquid a - %/psi R - 70/K error error N2 0. 0022 0. 0005 0. 6 0. 06

The pressure measurement is made with a strain gauge type

pressure transducer that is calibrated against a test gauge having a stated accuracy of 0. 1 percent of full scale. Table 4 shows that the

uncertainty in the pressure measurement contributes very little to the

uncertainty in the density.

The temperature measurement requires more care. The temperature measurement system consists of a constant current source of

0. 001 amp feeding a standard resistance, specified at ±0. 02 percent, and

a platinum resistance thermometer. The platinum resistance thermometer has been calibrated against a NBS secondary standard thermometer

at the hydrogen, nitrogen, and ice point. The interpolation between

these temperatures is done by the three point method of Corruccini [I960].

It is estimated that the uncertainty of the calibration and the interpolation

does not exceed ±0. 05 K, which results in a density uncertainty of ±0. 03

percent. The stability of the current source is monitored by reading the

voltage drop across the standard resistor on the 0. 1 volt scale of the

voltmeter. The current is adjusted to within ±0. 05 percent which is the

capability of the voltmeter. This translates into a possible density error

of ±0. 01 percent.

The stability of the constant current source has been checked

over a period of 1 5 days throughout each day. The uncertainty of the current reading, calculated on three times the standard deviation, is ±0. 0036

percent, which results in an uncertainty in the density of ±0. 002 percent.

17
The thermometer protrudes into the flow stream with liquid

sweeping around the tubular support of the platinum sensor. Flow

velocities are between 0. 5 to 5 ft/s passing the thermometer. The

velocity head of liquid passing the thermometer is about 0. 3 ft. Thus,

the pressure on the downstream side of the thermometer tube should

not be depressed more than 0. 25 psi below the liquid static pressure.

Since the static pressure is 10 to 75 psi above the liquid vapor pressure,

it is believed that liquid cavitation does not contribute to the thermometer imprecision.

From the above discussion of the instrumentation, it is seen that

the major uncertainty in the density measurement is in the uncertainty

of the state equation for nitrogen.

7. Systematic Errors

Four different types of positive displacement, volumetric

cryogenic flowmeters have been evaluated. The deviation between the

meter reading and the flow system measurement has been plotted for

the parameters: liquid temperature, weight of liquid accumulated, gas

space temperature, degree of liquid subcooling, pressure, mass flow

rate, and the order in which the data 'were taken. Of all these parameters, only liquid temperature consistently showed a trend for all meters.

The deviations were consistently higher at high liquid temperatures.

This effect was traced to a systematic error made in calculating the

buoyancy correction.

Previously an analysis of the gas in the catch and weigh tank

had shown a predominance of helium. Thus, the buoyancy calculation was consequently made on the basis of helium. That gas analysis proved

to be in error, and subsequent analysis of the gas showed that at higher
temperatures the higher vapor pressure of liquid nitrogen causes a predominance of nitrogen vapor in the gas space. Therefore, an equation of state for the helium-nitrogen gas mixture was written into the

data reduction program to calculate the buoyancy of the accumulated

liquid.

Once the buoyancy correction is made, there remains the question of how well the correction has been made. The ability to make this

correction depends upon how well the average temperature of the displaced gas is measured and the uncertainty of the state equation for the

helium-nitrogen mixture. Currently, there is a problem in obtaining a uniform temperature environment for the weigh tank. When liquid is dumped from the weigh tank, gas is displaced from the catch tank. This

gas prefers to circulate up the outside of the weigh tank neck, across

the warm flange, and down the inside of the weigh tank neck, rather than

through the vents provided. This action causes a temperature gradient

to exist across the gas space of the catch and weigh tank. The temperature of the displaced gas is taken as the average temperature across the

gas space as measured by two platinum resistance thermometers. The

uncertainty of the buoyancy force for the temperature extremes encountered can be quite large; therefore, tests are not conducted until temperatures

are within specified limits. Large errors in this area would be indicated

by a systematic deviation as a function of gas space temperature. Since

there is no such deviation apparent in the data, it is believed that errors from this source are not large.

The binary mixture state equation is believed accurate to within

±3 to 5 percent in the range of interest. Errors from this source would

be a function of liquid temperature and would result in only a ±0. 07

percent error in the liquid weight at the higher temperatures. The effect

19
would be much less at lower temperatures. The absence of a systematic

trend as a function of liquid temperature is evidence that errors from

this source are not large.

Considering both of the above mentioned sources of error, the

estimate of limits to the systematic error associated with the buoyancy

calculations is ±0. 1 percent. This is the largest source of error in the

mass measurement. Improvement will be made in this area when better

temperature control is obtained.

The liquid diffuser is submerged in the weigh tank giving a buoyancy force that is equal to the product of the diffuser volume and

the liquid density. Again a large density error will result in only a small weighing error. However, the density of the liquid and the volume

of the diffuser are reasonably well known. It is estimated that the resulting uncertainty in v/eighing from this source does not exceed ±0. 03 percent.

Table 5 summarizes the available evidence on estimated limits

to systematic error from all known or suspected sources. The source and limits to the magnitude of the error are listed according to the

type and amount of information available on that error source. The

estimated limit to total systematic error has been computed by adding

the components in quadrature, i. e. ,

(0. 01) 2 + (0. 05) s + + (0. 01) 2 = ±0.12%.

This procedure may be justified whenever there is no "correlation"

among the several sources of error. For example, the error due to the voltmeter is positive, this does not influence the chances that any

of the other errors will be positive or negative.

20
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21
8. Interlaboratory Comparison

It is quite informative to have the same meter checked by another

flow facility operating on a different principle. Such comparisons help

to locate unsuspected sources of systematic error and to lend confidence

to the validity of an accuracy statement. Extensive data have been taken on two positive displacement type meter elements at NBS and at a static

gravimetric flow facility operated by a meter supplier. Due to the

possibility of leaks occurring in these particular meters, in the meter

bowls, or in the meter element-bowl joints which bypass the measuring

chamber, it is necessary to calibrate such devices as units — element

and bowl combined. Unfortunately, this was not discovered until the

calibration data had been taken, with elements calibrated in different

bowls by NBS and the meter supplier. The result is an uncertainty of

±0. 5 percent in the differences between NBS and supplier calibrations

which were negligible by comparison (less than 0. 1 percent). Despite

this loss of resolution, the results indicate that there is no major

(> 0. 5 percent) discrepancy between the two measurement facilities.

Present plans include the use of fixed meter element/meter bowl

configurations to establish future interlaboratory comparison.

9. Tests of Meters

When the facility is used to test meters the resulting uncertainties

necessarily incorporate a component of variation arising from the performance of the meter itself. Four different types of meters have been

tested, some with substantial imprecision. The tests of these meters

were evaluated through a pressure range of 50 to 100 psig, a temperature range of 80 to 90 K, and a flow range of 20 to 50 gpm. The resulting standard deviation was based on 36 points taken on the meter with

22
best performance. The uncertainty due to combined dynamic imprecision

of the volumetric meter, the density measurement required to compare

the meter to the mass system and the cryogenic flow facility, calculated on three times the standard deviation, is ±0. 3 percent.

10. Provisional Accuracy Statement Summary

As may be garnered from the above discussions, it is a tedious

and difficult process to demonstrate the validity of an accuracy statement. It seems desirable at this time to gather a moderate amount of

additional evidence prior to issuing a formal accuracy statement. The

following statements summarize the accuracy information presently

available on the NBS gravimetric flow system.

At this time the uncertainty of the measurement of totalized

mass flow is estimated to be ±0. 18 percent. This figure includes an

uncertainty of ±0. 12 percent for known sources of systematic errors

plus an uncertainty of ±0. 06 percent for random error. The estimated

uncertainty due to the random error is three times the standard deviation

calculated for 23 applications of the calibrated masses over a period of

three months.

At this time the uncertainty of the measurement of totalized volumetric flow of liquid nitrogen is estimated to be ±0. 47 percent. This

figure includes an additional uncertainty of ±0. 39 percent for known

sources of systematic error in the density determination. The major

contributor to the uncertainty of liquid nitrogen volumetric flow measurement is the uncertainty in the liquid density.

When the objective of using the accuracy statement is in the

mediation between seller and buyer, where both have accepted the same

values of density, the uncertainty in the density need not be considered.

23
Under this condition the uncertainty of the measurement of totalized

volumetric flow is ±0. 18 percent, because the contribution of the pressure and temperature measurements error is negligible.

This accuracy statement should be considered provisional and is currently restricted to flow rates between 20 and 100 gpm, pressures

from 50 to 100 psig, and temperatures from 80 to 90 K, for ideal conditions where operational or equipment malfunctions are not present.

The error analysis is continuing and will be updated as more information

is acquired.

24
1 1. References

1. R. J. Corruccini, "Interpolation of Platinum Resistance Thermometer 20 to 273. 15 K, " Rev. Sci. Inst. 31_, 6 (I960), p. 637.

2. D. B. Mann, "Cryogenic Flowmetering Research at NBS, " Cryogenics, Vol. 11, No. 3, (June 1971).

3. H. H. Russell, "The National Bureau of Standards 1 , 000 Pound

Balance, " Notes of the National Conference of Weights and Measures, May 18, 1955, p. 31.

4. W. B. Streett and L. A. K. Staveley, "PVT Behavior of Liquid

Nitrogen at Temperatures from 77 to 120 K and Pressures to 680

Atmospheres, " Advances in Cryogenic Engineering , Vol. 13

(Plenum Press, New York 1968), p. 363.

5. T. R. Strobridge, "The Thermodynamic Properties of Nitrogen

from 64 to 300 K between 0. 1 and 200 Atmospheres, " NBS Tech.

Note 129 (1962).

6. M. J. Terry, J. T. Lynch, M. Bunclark, K. R. Mansell, and

L. A. K. Staveley, "The Densities of Liquid Argon, Krypton,

Xenon, Oxygen, Nitrogen, Carbon Monoxide, Methane, and Carbon

Tetrafluoride Along the Orthobaric Liquid Curve, " J. Chem.

Thermodynamics, 1 (1969), p. 413.

25

APPENDIX A

Standard Masses Report of Calibration

A-l
National Bureau of Standards

Report of Calibration Comp. No.

U. S. Department of Commerce

3050

For Section 2 1Z. 31

Item Set of mass standards 50LB-6, 50LB-Z6, and 25LB-26

Stated density 50LB-6 8. 3909 G per cm3 at 20C

50LB-26 8. 3909 G per cm3 at 20C

25LB-26 8. 3909 G per cm3 at 20C

The above items have the mass values shown with reference to the national standard of mass. See attached supplement for limitations

in the use of apparent mass value and uncertainty from error in density.

App. Mass True Mass

Item Nominal Corr. Corr.

Microlb. Microlb.

50LB-6 50. 116. 7 116. 8 50LB-26 50. - 8. 4 - 8. 4

25LB-26 25. 6.9 6.9

Uncertainty Vol. at 20

Microlb. (cm) 3

44. 2702. 8 44. 2702. 8 40. 1351. 4

The uncertainty figure is an expression of the overall uncertainty

using three standard deviations as a limit to the effect of random errors

of measurement, the magnitude of systematic errors from known sources

being negligible.

For the Director,

Test completed June 4, 1965

Washington, D. C. 20234

Signed by

Paul E. Pontius, Chief

Mass and Volume Section

Metrology Division

A-2
UNITED STATES DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

Washington 2 5, D. C. Comp No. 3009

Set A

NATIONAL BUREAU OF STANDARDS

TEST REPORT

on

Set of Avoirdupois Weights

Maker: W & L. E. Gurley, Inventory No. NBS 968 50

Submitted by: National Bureau of Standards

Division 2, Section 6

Material and Assumed Density: 10 lb to 0. 002 lb, stainless steel,

7. 92 g/cm3 at 20°C; 0. 001 lb to 0. 0001 lb, 80% Ni - 20% Cr, 8. 4 g/cm3 at 20 °C.

This set of weights is accepted for calibration and conforms to Class S-l

specifications for design and construction. It does not conform to Class

S-l requirements for accuracy of adjustment in that the weights designated

(0. 2 lb). , (0. 05 lb), (0. 02 lb). . , and (0. 005 lb) have corrections larger

than the tolerances for those denominations. All weights of this set are

adjusted within Class A tolerances.

This certifies that the values are correct within the accuracy specified

for the Class S-l calibration.

The weights from 10 lb to 0. 05 lb, inclusive, are marked with the letters

SA.

Designation Apparent Mass vs. Brass

(10 lb). 10 lb +12 mg

(10 ). . 10 +

( 5 5 ' +22

( 2 j. 2 - 2.

( 2 )• • 2 + 4. 3

( 1 ' 1 '

' + 2. 2

( 0. 5 ' 0. 5 + 2. 2

( 0. 2 ). 0. 2 - 1. 16 '

( 0. 2 )• • 0. 2 + 0. 16 '

( 0. 1 0. 1 - 0. 43 '

A-3
Comp. No. 3009, Set A, (continued)

Designation Apparent Vtass vs. Brass

( 0. 5 11)) 0. 05 lb + 0. 50 m|

( 0. 02 ' '). 0. 02 ' ' - o. 13 '

( 0. 02 ' '). . 0. 02 ' ' - o. 64 '

( 0. 01 ' ') 0. 01 ' + o. 05 '

( 0. 005 ' ') 0. 005 ' + o. 141 '

( 0. 002 ' '). 0. 002 ' ' - 0. 048 '

( 0. 002 ' '). . 0. 002 '

' - 0. 065 '

( 0. 001 ' ') 0. 001 ' + 0. 014 '

( 0. 0005 ' ') 0. 0005' + o. 023 '

( 0. 0002 ' '). 0. 0002' + o. 012 '

( 0. 0002 ' ')„ . 0. 0002' - o. 037 '

( 0. 0001 ' ) o. ooor + o. 014 '

Test completed:

July 12, 1961

CLCrbvh

L. B. Macurdy

Chief, Mass Unit

Mass and Scale Section

Metrology Division

A-4
Supplement for Precise Laboratory Standards of Mass

1. Basis for Values. Values under the heading Apparent Mass versus Brass are those which the weights appear to have when compared in air under Normal Conditions against Normal Brass standards, no correction being made for the buoyant effect of the air. Normal Conditions are 20° C and

air density of 1.2 mg/cm'. Normal Brass has a density of 8.4

g/cra' at 0° C and coefficient of cubical expansion of 0.000 054/deg C. True Mass values are those which might

be observed in air of zero density, i. e., in a vacuum.

2. Accuracy. The accuracy is the extent to which the measured values, as given, are in agreement with the true values of the mass of the weights. The divergence of the measured value from the true value is the inaccuracy. The methods of weight calibration employed at the National Bureau of Standards include checks against numerical

errors, observational blunders and other sources of uncertainty that would detract from the accuracy. The methods involve more than the minimum number of observations necessary

to obtain the values, and derive the values from more than

one standard, with some mathematical treatment to obtain

the best value. A statistical estimate of the inaccuracy in- cludes allowance for uncertainty or bias in the standards and

for the precision of the weighings. The estimated bias of the standards is small relative to the precision and is included

in the limits stated below for the inaccuracy of values under

the various classes. These limits are at least three times the standard deviations of the calibrated values. In rounding

off the computed values those digits that are uncertain by 16

units or more are dropped by rounding off to one less dec- imal place.

Class J: For microbalance weights adjusted to nominal

values in a series which permits appropriate intercomparisons

of the weights the inaccuracy is within 0.2 microgram. For

weights of odd amounts the inaccuracy iswithin0.3 microgram.

Class M: 1 part in 10'for weights lOg and above; 0.01 mg

for weights 10 g to 1 g, inclusive; 0.001 mg for weights below

If?.Class S and S-l: 3 parts in 10' for weights 10 g and above:

0.03 mg for weights 10 g to 1 g, inclusive; 0.003 mg for weights below 1 g. For 1 g weights of such materials as platinum, tantalum or gold the inaccuracy is within 0.01 mg.

3. Volumes. Under Class M the volumes are determined

for weights of 1 g and larger as the basis for computation of True Mass values. In other cases True Mass values are computed by the use of assumed densities. When the density

is assumed to be that of normal brass, only the Apparent Mass values are given.

4. Computation of True Mabs of Objects. If it is desired to compute the true mass of an object it is necessary

to make proper allowance for any systematic effects. Since

air exerts an appreciable buoyant effect it is necessary to make an appropriate correction to the results of a weighing

in air. When the volumes of the object and the weights are known it is convenient to use formula I.

I- Mn = M, + p(V„-V.),

where M„=true mass of unknown object, M,=true mass of standard weights necessary to bring the balance into equilibrium, p=air density, F„=volume of unknown mass, and K,= volume of standards. When apparent mass values are used for M, the volume, V„ Is the volume of normal brass.

When the volume of the unknown mass has not been measured the true mass may be computed from the densities by the approximate formula II.

II. M„=M.[l+,(-L--I-)]

where D„ and D, are densities.

For values of D„=2 g/cm! or greater and for D, = 8.4 g/cm!

, formula II gives values correct within 1 part in one million. For values of D„ less than 2 g/cm3 or for weighing to higher

precision than 1 in 10s the following exact formulae may be

required. 1-

III. M„=M. D.

IK

The precision needed for p is determined by the size of the

difference between V„ and V,. For quartz versus brass V„— V, is +0.258 cm3 per gram. With a precision of weighing

of 4 in 107

, and with p known to 0.2 percent the weighing wiB. be correct to 1 part on 10°. For a precise computation of p

it is necessary to determine the temperature, pressure, and

relative humidity of the air and to apply the following corrections: (1) Instrument correction for barometer, (2) barometric

reduction from local to standard gravity, (3) reduction of barometric pressure to the pressure for dry air of equivalent

density, and (4) thermometer correction to international temperature 6cale. Instructions and tables for computing

the various terms required for the density of the air are given

in the Smithsonian Meteorological Tables. When "Apparent Mass versus Brass" is used for M, the standards must then be assumed to have the same density as normal brass. This assumption introduces no error when

weighings are made under normal conditions. At altitudes

to 6,000 ft. apparent mass values and the assumed volumes

of the weights may still be used with actual air densities since the discrepancies arising from the assumption regarding volume do not exceed the accuracy of the Class S calibration. For higher accuracy than the accuracy of the Class S cali- bration or under more extreme conditions it may be desirable to compute the true mass values for the weights in order to provide a more precise determination of the buoyant effect of the air. When true mass values are used for M, then the

actual density of the standards must be used for D,. True mass values of the weights may be computed by

applying the following corrections to the "Apparent Mass"

values:

Material Density Correction

Aluminum . Stainless steel Stainless steel Brass Tantalum

Gold Platinum

g/cm2 2.7

7.8 8.0 8.4

16. 6 18.0 21.5

mglg +0. 302 + .011 +.007

.000 -.071 -.076 -.087

Corrections are to be added to apparent mass to get true mass.

U. I. 0OVCNNMINT MINTING OFFICR 16—71709-3

A-5

APPENDIX B

Load Cell Manufacturers Certificate

B-l
^

{certificate of L^alihiration

Date. J"~- 7L1Z-6, £

Transducer Model Nn. ^'2-^- B<^^

Customer

RangE t/*° & Serial Mn. «? ?- * ?*/*

Customer P.O. No. 7/ £ /5~$- .Sales Nn. /JJTJz.

Excitation VoltageInput Resistance (RW /^f & ohms

Sensitivity

Hnrnprpssinn *?-<y*»~2- mv/v Tension J? r ^ «? ? mv/v

Linearity (L) within «£>*" %f.S.

Repeatability (R) within <t> 2~ % F.s.

/ d .volts ac/dc

Output Resistance fRn) ^"^^ohms

THESE FACTORS ARE WITHIN -+- « ' ° %

OF NOMINAI _£ MV/VF. S. OUTPUT IN THE DIRECTION OF STANDARDIZATION.

Hysteresis (H) within _£_^2_%F.S.

Combined L,H,R, within ' "

~? %F.S.

"boubLa shunt Calibration with 9t,/TS nhms /&;>•?/ %F.S. in compression

Wiring Diagram ^^ < /^ %F.S. in tension

TEMPERATURE AND

FACTOR RESISTOR TEMPERATURE AND

FACTOR RESISTOR rA/WV

TERMINAL RESISTANCE —WW

WWi

STANDARDIZED IN. _ + Rj

Terminal Connections /%- / Neg. Output

^^^ Pos. Output

R~£- Neg. Input

^~Q~H _pos. Input ""

Shield

THIS TRANSDUCER WAS MANUFACTURED TO RIGID QUALITY CONTROLLED STANDARDS AND CALIBRATED WITH DEAD

WEIGHTS, A DEAD WEIGHT AND LEVER SYSTEM LOAD

APPLICATOR OR LABORATORY STANDARD TRANSDUCER

CALIBRATED BY THE NATIONAL BUREAU OF STANDARDS

OR TRACEABLE THERETO.

Cnnnectnr 7^//-/-/2-- /o f

^>i^t&e&z?'.

QUALITY CONTROL

B-2
i NBS-114A (1-71) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS-TN-6062. Gov't Accession No.3. Recipient's Accession No.

4. TITLE AND SUBTITLE Cryogenic Flow Research Facility Provisional Accuracy

Statement

5. Publication Date July 1971

6. Performing Organization Code

7. AUTHOR(S)

J. W. Dean, J. A. Brennan, D. B. Mann, and C. H. Kneebone

8. Performing Organization

10. Project/Task/Work Unit No. 2750360

9. PERFORMING ORGANIZATION NAME AND ADDRESS NATIONAL BUREAU OF STANDARDS DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

11. Contract/Grant No.

12. Sponsoring Organization Name and Address NBS and Compressed Gas Association, Inc. 500 Fifth Avenue

New York, New York 10036

13. Type of Report & Period Covered _Interim

Jan. 1968 - June 1971

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

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 National Bureau of Standards and the Compressed Gas Association

have jointly sponsored a research program on cryogenic flow measurement. A

cryogenic flow research facility was constructed and -was first used to evaluate

commercially available cryogenic flowmeters operating with liquid nitrogen on a positive displacement principle.

The performance of the flow facility was simultaneously being evaluated

during the meter tests. This is a summary report of the performance evaluation

of the flow facility. An accuracy statement is given for both totalized mass and

volumetric flow.

17. KEY WORDS (Alphabetical order, separated by semicolons) Accuracy statement; cryogenic; flow facility; liquid nitrogen; measurement.

18. AVAILABILITY STATEMENT

2D UNLIMITED.

I I FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

40

22. Price 45 cents

-DC 66244- P71 GPO 836 - 328

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areas of interest to the consumer. Easily understandable language and illustrations provide useful back- ground knowledge for shopping in today's technological marketplace.

NBS Special Publication 305, Supplement 1, Publications of the NBS, 1968-1969. When ordering, include Catalog No. C13. 10:305. Price $4.50;

foreign, $5.75.

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