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Nisr United States Department of Commerce

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NIST Technical Note 1409

Laser Doppler Velocimeter Studies of the

Pipeflow Produced by a Generic Header

T. T. Yeh and G. E. Mattingly

QC

100

U5753

N0.1/I09

1995
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NIST Technical Note 1409

Laser Doppler Velocimeter Studies of the

Pipeflow Produced by a Generic Header

T. T. Yeh and G. E. Mattingly

Chemical Science and Technology Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-0001

April 1995

/ V \

*^4rES o*

U.S. Department of Commerce

Ronald H. Brown, Secretary

Technology Administration

Mary L Good, Under Secretary for Technology

National Institute of Standards and Technology

Arati Prabhakar, Director
National Institute of Standards U.S. Government Printing Office For sale by the Superintendent of and Technology Washington: 1995 Documents

Technical Note 1409 U.S. Government Printing Office

Natl. Inst. Stand. Techno!. Washington, DC 20402

Tech. Note 1409

79 pages (April 1995)

CODEN: NTNOEF
PREFACE

The research results reported in this document were produced with the support of a National Institute of Standards and Technology (NIST) initiated industrygovernment consortium. This is an established cooperative research effort on

generic technical issues to produce industry-needed flow metering improvements.

In this mode of operation, there is a high degree of interaction between the

representatives of the consortium member companies and the NIST researchers.

These interactions include: (1) the planning of the specific focus of the NIST

research efforts, (2) the discussions and analyses of the results obtained, and (3) the

conclusions drawn for the particular phase of the work. For this reason, it is

pertinent to acknowledge both the support given to this phase of the research

program and the teclmical contributions made by the representatives of the

consortium members.

The current consortium as of October 1993 is, alphabetically:

1

British Columbia Hydro & Power Auth. (Canada)

2. Chevron Oil

3. Consohdated Edison

4. Controlotron

5. Dow Chemical Co.

6. E.I. Dupont de Nemours

7. Fisher Precision Systems, Inc.

8. Ford Motor Co.

9. Gas Unie (The Netherlands)

10. Inst, of Paper Science & Tech.

1 1Instrument Testing Assoc.

1 2Ketema-McCrometer

13. Ketema-Schutte and Koerting

14. Kimmon Mfg. Ltd. (Japan)

15. NRTC (NOVACOR Res. Tech. Corp.)

16. Pacific Gas & Electric Co.

17. Rosemount

HI
TABLE OF CONTENTS

PREFACE iii

ABSTRACT 1

INTRODUCTION 2

TEST CONFIGURATION: A Generic Header 4

EXPERIMENTAL RESULTS 6

A) LDV Velocity Measurements 6

1Downstream of the Header 6

2. Velocity Comparisons Among Different Configurations 8

3. Velocity Downstream of the Header and 19-Tube Tube Bundle 9

B) Characteristics of the Mean Velocity Profile 11

SUMMARY AND CONCLUSIONS 16

REFERENCES 17

FIGURES 19-49

APPENDIX A A1-A12

APPENDIX B B1-B12

IV
Laser Doppler Velocimeter Studies of the Pipeflow

Troduced by A Generic Header

T.T. Yeh

G.E. Mattingly

Fluid Flow Group

Process Measurements Division

Chemical Science and Technology Laboratory

National Institute of Standards and Technology

Gaithersburg, Maryland 20899

ABSTRACT

This report presents recent results obtained in a consortium-sponsored research

program on flowmeter installation effects being conducted at NIST. The piping

element tested and reported here is a generic header which has a specific arrangement

of one inlet and two outlets. Laser Doppler velocimetry (LDV) velocity measurements

are reported for the pipeflows produced downstream of the header with and without a conventional 19-tube concentric tube bundle flow conditioner.

The results indicate that the secondary flow produced by the generic header is very

similar to that produced by the closely coupled double elbows out-of-plane piping

configuration. The axial velocities are slower than the ideal flow near the pipe center

and higher near the walls. Transverse velocity distributions show a very strong swirl

eddy flow pattern produced by this header. This swirl eddy is relatively stable and

organized and its dissipation is slower than that observed for the double elbows out-ofplane. The 19-tube tube bundle is quite effective in reducing the transverse velocities

associated with the energetic, swirl flow from this header.

Several profile indexes are presented to characterize the swirl intensity of the header

flow and the shape of tlie velocity profiles. These indexes can also be used to develop

criteria for improving flow meter perfonnance in the outlet piping from this header.
INTRODUCTION

In many cases, flowmeters are being retrofitted into fluid systems that were not

designed for tliem. Tliis invariably means the meters are being inserted into "nonideal"

installation conditions where the upstream piping conditions produce pipeflow

distributions tliat differ from those ideal installation conditions used to design the meter.

"Ideal" installation conditions are where the meter location is preceded by sufficiently

long, straight lengths of constant diameter piping that the meter's performance is not

affected when the meter is installed fiirther downstream.

The prevalent concern in the flow measurement cominunity is for increased metering

accuracy levels. These levels are desired for existing meter systems - either by

upgrading the flow conditions at meter's entrance or by replacing the device's auxiliary

components so tliat accuracy levels are increased. Various flow conditioning devices

are frequently recoininended for improving flowmeter perfonnance where installation

conditions are not ideal. However, the pipeflows generated by these devices have to

be considered with respect to the type and design of flowmeter installed downstream

of the specific piping configuration. It has been shown previously[l-7]' that certain

flow conditioner installations can produce serious deviations from the performance of

specific meters in ideal installation conditions.

The NIST industry-government consortimn research program on flowmeter installation

effects is designed to help to improve fluid metering perfonnance when installation

conditions are not ideal. This program has the main objective of producing a basic

understanding of the flow phenomena that are produced in prevalently encountered,

nonideal installation conditions and to quantify these phenomena relative to the pipe

flow in ideal installation conditions. The experimental program is based upon the

measurements of pipe flows from selected piping configurations using laser Doppler

velocimetry (LDV). The program uses basic experimental research tools available to

the fluid dynamicist to measure, imderstand, and parameterize the salient features of the

pipeflow phenomena. The successive phase of the prograin is to evaluate quantitatively

how these phenomena influence selected types of fluid meters and how to use these

evaluations to produce satisfactory flow measurements.

^ Square bracketed integers refer to references given in the reference section on page 17.

2
This research effort has also included experimental studies of the flow into and out of

several tube bundle flow conditioners. These results have produced detailed

descriptions of the effects these devices have on different pipe flows. The

performances of both orifice and turbine flowmeters have also been determined for

different installation locations downstream of selected pipeline elements, both without

and with tube bundle flow conditioners. The results show that while the conventional

19-tube tube bundle successfully removes swirl from these pipeflows it apparently

produces other effects in the streamwise velocity profiles that cause several different

types of perturbations both on orifice and turbine meters perfonnance [1].

Previous phases of this research program have produced LDV measurements for a

single elbow, double elbows-out-of-plane, the tee-used-as-an-elbow, the concentric

reducer, and tlie 45° elbow. Conventional, long-radius elbows are used in all of these

studies; the radius of the centerline tlirough these elbows is 1.5 pipe diameters.

Detailed results of these studies can be found in [1-5]; summary descriptions of these

studies are given in [6-8].

In all these studies, the working fluid is water and the piping is 52.5 mm (2 in

diameter), smooth, stainless steel. Water temperature is controlled using a heat

exchanger to maintain a set temperature of 21+0.5 °C. The pertinent parameters

considered important in the experiments are Reynolds number, and pipe relative

rougliness. Tlie relative rougliness of this pipe has been measured with a profilometer

to indicate a value of 0.006% based on interior pipe diameter. The diametral Reynolds

number in the test section was 10^ using bulk average velocity.

This report presents the recent results obtained in the flowmeter installation effects

program. The primary piping element tested and reported is a generic header

configuration. Header or manifold configurations are commonly found in various,

industrial plants. One of the most coininon reasons to use header configurations is to

improve the overall rangeability of flow rate measurements by using headers with

multi-outlet meter stations. Other purposes of header configurations in multi-nm meter

pipings are to reduce capital costs in making flow rate measurements. Headers or flow

manifolds are also used to rearrange the flow loop direction or to serve as a settling

chamber in designing flow loops. Despite the wide spread industrial use of headers,

there is very little infonnation available regarding the flow patterns emerging from

headers or the effects of these flows on meter perfonnance. Recently, flow
disturbances caused by special headers aiid tlieir effects on metering performance have

been the subjects of various investigations [9,10]. However, many of the

configurations used in tliese investigations are the combinations of the specific header

and various upstream piping elements such as single elbow, reducer, riser, etc. It seems evident that the flow upstream entering a pipe element such as an elbow,

reducer, etc. or a header may greatly influence the flow pattern exiting the element or header. Rather than test the combination of a header with some complicated or unknown upstream/downstream piping elements, the objective of the present study is

to study the flow pattern produced solely by the generic header. To do this, the piping

configuration upstream of tlie header was installed to insure that the entering pipe flow

is an otherwise, fiilly developed, equilibrated one.

TEST CONFIGURATION: A Generic Header

Figure 1 shows a sketch of the generic header geometry, that is denoted H342. This

generic header consists of one inlet and two outlets having the same pipe size. The

direction of the inlet pipe is nonnal both to the header and to the outlet pipes. The

diameters of tlie inlet, the header, and outlet pipes are 77 mm (3 in), 103 mm (4 in), and

52 mm (2 in), respectively. H342 denotes the relative diameter ratios of 3:4:2. In the

test, the header is installed vertically and the upper outlet (the one near the inlet) is

outlet #1 and the lower outlet (the one far from the inlet) is outlet #2. Other parameters

needed to be specified for this header test are the flow rates in each outlet and the

outlet selected for the velocity measurement. To identify a specific test and flow

condition, tlie complete designafion will be H342-Fl/F2-n. Wliere F1/F2 gives the ratio

of the flow rates flowing tlirougli the outlet #1 and ouflet #2. The last digit "n" is used

to denote the outlet for the test. In the test described in this report, Fl/F2=100/0 and

n=l . That is, all flow is going tlirough outlet #1 and no flow exits outlet #2 and tests are perfonned at the outlet #1. The test results include flow measurements with and

without the conventional 19-tube concentric tube bundle flow condifioner. Although

other flow divisions can be arranged, it was thought that, in this condition, the effect

of the header on the flow downstream will be most significant, i.e., the worst case for

downstream meter perfonnance, due to the largest possible flow rate in the outlet pipe.

Tests for other flow divisions are in progress.

Figure 2 shows the piping arrangement and the coordinate system used in the test. A

right handed coordinate system is used which has the origin (i.e., X=Y=Z=0) in the
entrance plane of the outlet pipe (the exit plane of the header at the header tank

diameter) and at the pipe centerline. The positive Z direction is downstream; the

positive Y direction is upward; the X direction is, therefore, to the right looking

upstream. The mean velocities in the X, Y, and Z directions are U, V, and W,

respectively; and the corresponding turbulence velocities are u', v', and w', respectively.

In this study, only two velocity components, the axial velocity, W and the vertical

velocity, V are measured. The horizontal component, U is not measured. In what

follows, nondimensionalized quantities will be used to describe and to plot results.

Lengths and velocities are normalized using the pipe diameter, D and average-bulk

velocity, W,,, respectively.

To study the flow effects produced by the generic header configuration, efforts have

been made to ensure a fully developed pipe flow that is fi^ee from other disturbances

enters the header configuration. The upstream piping was arranged so that over 45 pipe

diameters of straiglit, constant diameter piping preceded the header. This inlet pipe

section was a single piece of standard piping to assure a concentric constant diameter

along the entire section without any misalignment that could result fi^om joints.

Upstream of this straight lengtli of piping, tlie inlet flow was arranged to have a special,

radial inlet so that no axial vorticity was produced by tliis entrance condition. Although

the pipeflow entering the header was not directly measured, all LDV measurements

fi^om previous phases of our program made downstream from a single elbow showed

that the effects of the elbow were negligibly small after about 30 pipe diameters for

Reynolds number 10^ Since in this 75 mm (3 in) diameter pipe, the Reynolds number

was 66000 (corresponding to 10^ in the 52 mm pipe), the pipeflow entering the header

was assumed to be fully developed. With these reference profiles entering the header,

the exiting pipeflows can be interpreted, for this conventional piping configuration, to

be due solely to this generic header.

A conventional, 19 tube, concentric tube bundle flow conditioner was also tested with

the generic header. The results for the combined configuration are presented below.

In this report only velocity measurement results will be presented. The results for the

flowmeter performance downstream of this generic header configuration will be

presented separately [11].
EXPERIMENTAL RESULTS

A) LDV Velocity Measurements

1. Downstream of the Header

The LDV results obtained downstream from the generic header piping configuration

are presented in tabular format iii Appendix A, Mean and Turbulence Velocity Profiles

for Header H342-100/0-1.

Figure 3 shows LDV measurements of the mean axial velocity profiles, WAV^, versus

horizontal radial position, X/D, at successive downstream locations, Z/D, from the

header for Re=10^ The solid curve is the fully developed, equilibrated pipeflow

distribution put forth by Bogue and Metzner [12]. The data clearly indicate that the

header significantly modifies the axial velocity profile as the fluid passes through the

header. These axial velocity profiles are symmetric about the pipe centerline along the

horizontal diameter, hi the region near the pipe center, tlie flow is slower than the fully

developed pipe flow, while near the pipe walls the flow velocities exceed the fiilly

developed pipe flow. The centerline deviation from the ideal profile at the most

upstream location of Z/D=3.35 is about 22% of the bulk velocity. Near the wall the

deviations are about 15% of the bulk velocity in excess of ideal profile values. These

deviations decrease with downstream distance. However, even for the measured

location of Z/D=30, the profile is still very unifonn over about 80% of the center core of the pipeflow. At this location, the centerline velocity is about 12% of the bulk

velocity below the ideal velocity.

Figure 4 presents the mean axial velocity profile, WAV^, versus the vertical radial

position, Y/D, at successive downstream locations, Z/D, from the header for

Re = 10^ Again, the solid curve is the fiilly developed, equilibrated pipeflow

distribution of Bogue and Metzner. These axial velocity profiles are also symmetric

about the pipe centerline along the vertical diameter. With downstreain distance, these

deviations decrease so that at Z/D=30, the central core flow is only about 10% of the

bulk velocity below the ideal values. At this location, the profile is considerably more

smoothly varying than the fully developed distribution. Both figures 3 and 4 indicate

that, for these conditions, these axial mean velocity profiles do not conform well to the

fully developed distribution even 30 diameters from the header.
Figure 5 presents vertical mean velocity profiles, VAVb, versus horizontal radial

position, X/D at successive downstream positions from the header for Re = 10^ Here,

the ideal, fully developed pipeflow is zero as shown by the solid line. The velocity

profiles indicate that tliis pipe flow has a severe, clock-wise swirl. These data indicate

that the swirl distribution is essenfially that of a rigid body rotation. The peaks in the

vertical velocity component are located near the pipe walls. Due to the nonslip

condition, the velocity at the walls is zero. However, the velocity at or near the wall

was not measured. It has been deemed not worthwliile to make the LDV measurements

in the sub-layers of the flow near the wall owing both to the difficulty and to the nature

of tliis flow, hiside the sub-layer, the tangential velocity gradient should be very large

for this highly swirled flow field. At the location nearest the header, Z/D=3.35, the

upward and downward vertical velocities near the pipe walls are about 22% and -35%

of the bulk velocity, respectively. With downstream distance these deviations diminish

slightly so that at Z/D=30.0, the most distant location measured, the peak vertical

velocity is about 20% of the bulk velocity upward near the -x side wall and is about

-18% downward near the wall at the +x axis. This single eddy flow is very similar to

that from the closely-coupled double elbows out-of-plane configuration [3,4,9]. The

major difference between these flows and those from the double elbows out-of-plane

is that there is little rotation present in the exiring flow at the center of the pipe for the

double elbows out-of-plane, wliile the header flow shows essentially solid body rotation

even at the nearest measured location. With increased downstream distance, the swirl

produced by the double elbows out-of-plane approaches solid body rotation except near

the pipe walls where the usual wall boimdary condition appears. Tlie decay of the swirl

from tlie header seems to be slower than that observed from the double elbows out-ofplane configuration.

Figure 6 shows the vertical mean velocity profiles versus the vertical radial position at

successive downstream locafions from the header for Re = 10^ Again, the solid line

shows tliat the ideal flow distribution is zero everywhere. These profiles indicate that

all vertical velocities are small, being slighfly downward nearer the header at Z/D=3.35

and slightly upward ftirther from the header at Z/D=30.0.

Figures 7 and 8 present, respectively, the distributions for the root-mean-square (r.m.s.)

values of the axial component of the turbulent velocity, w'AV^,, versus the horizontal and

vertical radial positions from the pipe centerline for Re=10^ Figures 9 and 10 present

profiles of the r.m.s. values of the vertical component of the turbulent velocity, v'/W^
for Re = 10^ These measurements for different downstream distances from the header

are plotted with the results measured by Laufer as shown via the solid curve for

Re=41000 (see [13]).

These results indicate that the turbulent intensity profiles are all higher than the ideal

values (Laufer's results) and are symmetric about the pipe centerline, along either

horizontal or vertical diameters. The distributions of the axial turbulence intensities are fairly smoothly varying across the pipe cross section, while there are high levels of

turbulence in the vertical component of the turbulent velocity at the pipe centerline.

Close to the header exit, at Z/EN3.35, the axial component of the turbulent velocity is

about 13% of the bulk velocity across most of the pipe cross section, as shown in

figures 7 and 8, and the vertical component of the turbulent velocity is about 14% of

the bulk velocity at pipe centerline as shown in figures 9 and 10. With downstream

distance, these turbulence levels decrease and approach the ideal values of Laufer.

However, even at Z/D= 30.0 all the turbulence intensities are still larger than, and the

profiles are more uniform than, Laufer's data. Both the mean and turbulence velocity

profiles indicate that the pipe flow in this outlet pipe is still in developing stages 30D

downstream from the header.

2. Velocity Comparisons Among Different Configurations

Since the header arrangement and test conditions are very similar to the double elbow

configuration studied previously, it is interesting to compare the respective exiting

velocity profiles, hi tliis section the velocity profiles, produced by the generic header,

denoted according to the convention described above as H342- 100/0-1 are compared

with those from two double elbows out-of-plane configurations: a) the closely coupled

double elbows, denoted by 2L0, and b) an arrangement having 2.4D of straight pipe

between the elbows denoted 2L2.4. The data are compared at similar locations; one

near the outlet at Z/D=3 and the other fiirther downstream at about Z/D=30.

Figure 1 1 shows comparisons of the axial velocity profiles along the horizontal

diameter at two axial locations downstream from the different piping configurations for

Re = 10^ Figure 12 shows a similar comparison along the vertical diameter. In both

figures, the upper figure is for Z/D=3, approximately, and the lower figure is

essentially for Z/D=30. The solid curve is the fiilly developed, equilibrated pipeflow

by Bogue and Metzner [12]. At the near location, all three flows are very different

8
from the ideal velocity profile with the header flow more uniform across the entire cross

section of the pipe and the double elbow flows having maxima flows nearer the wall.

These seem to indicate that the header configuration has provided more time for the

swirl to be estabhshed in the header and thus the swirl is more completely established

as it leaves the header, while the time for the fluid to pass through the double elbows

is relatively short and thus the exiting flows are still developing. Although there are some differences in the quantitative details of the profiles, all three configurations

basically produce slower axial mean velocities near the pipe center. Further

downstream as shown in the lower figures, the header flow at Z/D=30D is still very

different from the ideal profile while the flow for the 2.4D spaced double elbows is

fairly close to the ideal profile. Tliis seems to indicate that the header flow swirl is

more coherent and stable and thus its decay is much slower.

Figures 13 and 14 show comparisons of the vertical velocity profiles at two axial

locations downstream from the tliree piping configurations for Re = 10^ In figure 13

the results along the diameter parallel to X, the direction of the inlet flow, are presented, while in figure 14 the measurements along Y, the diameter normal to the

inlet flow direction are shown. Also, the upper plot in these figures is for locations

near Z/D=3 while the bottom figure is for Z/D near 30. Here, the fially developed

pipeflow is zero as indicated by the solid line. The data indicate again that the three

configurations produce qualitatively similar vertical velocity profiles. The radial

velocities, as shown in figure 14, are very small for all three cases. The swirl

velocities, as shown in figure 13, are significant for all tliree cases. The header flow

seems to produce the most energetic, stable swirl among the tliree configurations.

Near the header exit, the flow is essentially solid body rotation, while the two double

elbows out-of-plane configurations produce very Httle swirl near the center of the pipe.

Further downstream, as shown on the lower figure, all tliree flows exliibit essentially

solid body rotation and the intensity of the swirl for the header flow is the strongest

among the three cases.

3. Velocity Downstream of the Header and 19-Tube Tube Bundle

hi this section, the resuhs of the velocity measurement obtained in the pipe downstream

of the header and the l9-tube tube bundle are presented. The LDV results for the

generic header configuration with a l9-tiibe tube bundle downstream of the header are presented, in detail, in tabular fonnat in Appendix B, Mean and Turbulence Velocity
Profiles for Header H342- 100/0-1 and a 19-Tube Tube Bundle.

Figure 15 shows the sketch of the header configuration and the tube bundle installation

location. The tube bundle is installed at a fixed location relative to the header. The

upstream and downstream ends of the tube bundle are at Z=4.26D and 6. 2D,

respectively. The distance downstream fi-om the exit plane of the tube bundle flow

conditioner is denoted by the length, C, in diameters. The arrangement of the tube

bundle is also shown in the figure 15. The tube bundle used is tlie conventional 19 tube

concentric design. The unit is a geometrically scaled version of the prevalent unit used

in large pipe sizes according to orifice meter teclmology (see [14]). It is comprised of

tubes having a diameter of 9.5 mm, wall thickness of 0.4 mm, and tube length of 101 .6

mm (approximately 2D length).

Figures 16 and 17 present, respectively, profiles of the time-averaged, streamwise

velocity components along the horizontal radial positions for Re=10^ The solid curve

is the fiiUy developed, equilibrated pipeflow distribution put forth by Bogue and

Metzner [12]. The 19-tube tube bundle is installed as shown in figure 15 at the fixed

position of Z-C=6.2D and the velocity profiles are measured at several axial distances,

C , downstream of this tube bundle. These results show, just downstream from the 19-

tube tube bundle at C/D = 2.0, tlie jetting effects of tlie flows from the individual tubes.

These jetting effects diminish very quickly so they caimot be seen at C/D=6.0 These

results show that, even the tube bundle does not alter significantly the axial mean

velocity profile near the tube bundle ( e.g., at C/D=6), the tube bundle does enhance

the process of changing the axial mean velocity to the ideal fiiUy developed profile.

At C/D=22, the axial mean velocity is fairly close to the profile of Boque and Metzner.

Figures 18 and 19 present measurement results for the vertical component of the timeaveraged velocity profile along the X and Y diameters downstream of the header and

19-tube tube bundle for Re = 10^ At all stations measured, the mean vertical velocities are very small and below 2%. These show that the 19-tube tube bundle is very

effective in reducing the transverse velocities. Particularly, figure 18 shows that the

energetic, single eddy flow generated by the header and clearly visible via the vertical

velocity component along the X axis as shown in figure 5 is reduced by tliis tube bundle

to 2% or less just downstream of the tube bundle exit. Further downstream, the vertical

velocities are below 1% of the bulk velocity, except at a small region near the wall at

negative X.

10
Figures 20-23 present r.m.s. distributions of the streamwise and vertical components

of the turbulent velocity measured downstream of the header and 19-tube tube bundle

along the X and Y diameters. The profiles measured nearest the tube bundle exit show,

via the peaks in these distributions, the effects of the interactions between the jetting

flows fi"om the individual tubes. The ideal distributions fi"om Laufer's work at

Re==41000 are shown via the solid lines. The decay of the turbulence is so rapid that

only the value at the first measured location is larger than those of the Laufer data. At

all other measured stations, the turbulence intensity is lower than the Laufer data.

Also, these measured profiles are more uniform across the pipe cross-section. These

data indicate the turbulence distribution is still dominated by the effects of the multi-jet

mixing flows and the pipeflow is still developing downstream of the 1 9-tube tube

bundle even at C/D=22. These results indicate that these pipeflows are still decaying

at these locations downstream of the tube bundle, apparently due to the multi-jet

turbulence. The viscous effects of the pipe wall boundary layer have not completely

traversed the entire pipe cross section and equilibrated these flows. Thus, it is

concluded that these pipeflows are still evolving toward ftilly developed distributions.

B) Characteristics of the Mean Velocity Profile

The results presented above include both the mean and turbulence velocity profiles

downstream of the selected header. The next effort is to characterize and understand

these velocity profiles in order to find some criteria for improving the meter

performance prediction prospects in these nonideal conditions.

Different piping configurations produce different velocity profiles. These velocity

profiles change the pipe flow characteristics fi"om those of the fijlly developed

distributions of ideal flow and these in turn can significantly affect flowmeter

performance. Based on the measured velocities, important flow field parameters can

be defined and quantified. Depending on the particular piping configuration some

parameters may be more important than the others in affecting meter perfonnance.

Previous research results have shown that swirling flows produced by several different

pipe configurations can have very strong effects on the meter perfonnance of selected

meters [1,6,7].

Various parameters can be used to characterize the degree of the swirl flow. The swirl

angle at a point in the flow, defined by the vertical inclination angle of the velocity

11
vector as (|) = arctaii (VAV), is good example. It is a measure of the flow vector's

deviation from tlie ideal streamline direction. Figure 24 shows the profiles of the point

swirl angle (\) vs. horizontal radial position at different downstream locations from the

header. Tlie swirl produced by tlie header configuration is quite similar to that from the

closely-coupled double elbows out-of-plane configuration. At the upstream location

of Z=3.35D, tlie swirl angle approxiiuates +16° near one side of the pipe wall and -20° near tlie otlier side. These swirl angles change as the distance downstream increases.

In the absence of flow conditioners, this swirl is still very strong (+ 12'') at the 30D

distance downstream. Figure 25 shows point swirl angle distributions at different

downstream locations from the header and the 19-tube tube bundle. Except near the

exit of tlie tube bundle, tiie point swirl angles are all very small and less than V. These

data show again that the tube bundle flow conditioner is very effective in removing

swirl from pipe flow.

It is noted that tliere is only one large swirl eddy produced in this header configuration.

To characterize the decay of the swirl flow, a mean swirl angle, S^, is defined as

S^ = (<*, + #)_)/ 2 (1)

where ([)+ and (|). are, respectively, the maximum magnitudes of the point swirl angles

in tlie positive and negative X directions along the horizontal diameter at a given axial

location Z.

Figure 26 shows the comparisons of the decays of the mean swirl angles downstream

from different piping configurations. Data are shown for five piping configurations:

header H342- 100/0-1; double elbows out-of-plaiie(closely coupled, 2.42D spaced, and

5.32D spaced); and header with tube bundle. These data show the header produces

the most energetic swirl and has tlie slowest decay rate among the five cases. At axial

position, Z/D=30, the mean swirl angles are about 12°, T, and 2° for the header, closed

coupled double elbows out-of-plane, and 2.42D spaced double elbows out-of-plane,

respectively. The mean swirl angles for the other two cases are negligibly small. This

is further testimony to the severity of the swirl produced by this header piping

configuration. Tlie large initial mean swirl angle for the double elbows out-of-plane is

due to the large point swirl angle near the wall. These large swirl eddies decay very

rapidly due to the wall boundary condition as well as the dififiision of the vorticity to

the pipe center as they move downstream. The initial diffusion of the swirl for the

12
double elbows out-of-plane is enlianced due to the fact that the initial axial vorticity is

small in the pipe center for the double elbows out-of-plane configuration. The decay

of swirl flows can also be quantified by a pipe swirl number defined as follows:

0.5

S,= 4 I "^^^^ I ^ ' d(X») (2)

The swirl number, S,, corresponds to an integral of the angular momentum over the

entire pipe cross-section. Figure 27 shows the streamwise distributions of the swirl

numbers for Re = 10^ for the same five piping configurations (H342- 100/0-1, L+X-Ys

with three different spacings, s=0, 2.42 and 5.32D, and H342-1 00/0-1 with tube

bundle). These data indicate that the header piping produces very energetic, longlasting, single-eddy, swirled flows. As noted for the mean swirl angle, the swirl

number, S, for tlie header is tlie largest and shows the slowest decay with downstream

distance among tlie five configurations. Tlie Sj values for closely coupled (s=0) double

elbows-out-of-plane are much smaller than those for the header. The values of Sj for

spaced (s = 2.4 and 5.3 diameters) double elbows-out-of-plane and for the header with

the tube bundle are all negligibly small.

Aiiotlier usefiil quantity regarding the pipe flow profile is the degree of the flatness or peakness of the mean velocity profile. To quantify the peakness of the velocity profiles

produced by tlie piping configurations, a number of peakness parameters are introduced

(see [15]). These include:

P, - W. / W, - 1 (3)

Pr W/ / W,^ -1 (4)

P, = 1- W, / W^ (5)

P4 - W, / W„ (6)

13
6

f *°VrW) d(r/D) / W, (7)

J-0.5

*''(W/-W^) d(r^) / W,' (8)

'-0.5

*0.5W(W^-W) dl(r/D) / W^"^ (9)

'-0.5

where W^ is the velocity at tlie pipe centerline location aiid W^ is the velocity at a point

near the wall, defined as r=0.475D. All the parameters have similar meaning for

characterizing the velocity profile peakness. A larger peakness index will mean high

flow velocities near the pipecenter, i.e., a more "peaky" profile near the center core. Both Pj and P3 show the overshoot of the centerline velocity from the average bulk

velocity, except Pj is nomialized by the averaged bulk velocity while P3 is normalized

by the centerline velocity. Pj quantifies the excess of the centerline dynamic pressure

over the dynamic pressure based on the averaged velocity. P4 is the ratio between the

centerline velocity and the velocity near tlie pipe wall (at 2.5% diameter from the wall).

The parameters Pj, P2, and P3 are obtained only by the single point velocity at the pipe

centerline. P4 is detennined by two local velocities, while P5, P(, and P7 are determined

from integrations of velocities over the pipe diameter. These integrated quantities are

similar to the displacement thickness and momentum thickness parameters commonly

used in studying boundary layer flows.

Other investigators have introduced some of these parameters in their studies. For

example, Klein [16,17] called P3 a blocking factor in studying turbulent, developing

pipe flow and the effects of inlet conditions on conical-diffuser performance. In

studying the effect of flow profiles on orifice meter perfonuance Ghazi [18] has

introduced the parameters F, and F2 which are closely related to the peakness

parameters, P3 and P4 respectively; in which Fi=l-P3 and F2 = I/P4.

Besides these peakness parameters, other parameters that quantify how the flow is

displaced from the center of the pipe can also be used. A more peaky flow means that

14
the flow is faster at and near the pipe center with slower flow further from the pipe

centerline. A displacement parameter is introduced to quantify the average flow

displacement from the pipe centerline for a selected quantity as follows:

f

"^rW "^ " dr

ju

ran- —— no^

i.,TV2- . ^ ^

J-Dn

In this report, the results for only two flow displacement parameters will be presented.

D20 is for the dynamic pressure, W^, and D21 is for the first radial moment of the

dynamic pressure, Wh. Likewise, only two peakness parameters, Pj and P^, are presented here.

These profile peakness and flow displacement parameters are determined as functions

of the axial distance downstream from different piping configurations for Re=10^

Figure 28 shows the evolution of the profile peakness, P2 downstream from different

piping configurations. In the figure the change of the peakness from the ideal flow

condition is plotted. Figure 29 shows the evolution of the profile peakness, Pg for the

flow from five piping configurations as noted. Figures 30 and 31 show the evolutions

ofthe profile displacements D20 and D21, respectively, for the same five configurations.

Again, all these flow profile indexes presented are given by the values that differ

significanfly from the ideal condition. Thus, if a profile is flatter than the ideal profile

the change of the peakness relative to the ideal will be negative. In this case, the flow

field is displaced from the centerline and the change of the displacement relative to the

ideal should be positive. On the other hand, if the change of the peakness is positive, or the relative change of the displacement is negative, the axial mean velocity profile

is more peaked at the pipe center.

These data show that, for small values of Z/D, the changes in the peakness, paraineter are negative and the changes in the displacement are positive. With downstream

distance, the values tend to approach the ideal values. Tliey also show that the header

flow with no flow conditioning has profile indexes that deviate more from the ideal

values than most of other configurations.

15
SUMMARY AND CONCLUSIONS

Experimental measurements have been made, using laser Doppler velocimetry in the

pipe flows produced by a generic header. With a limited set of measurements of fluid

velocity, the profile characteristics of the mean velocity downstream of a header are described both qualitatively and quantitatively. Several profile indexes are introduced

to characterize the profile swirl, peaknesses, and flow displacements. These indexes

could be used to develop criteria for improving flow meter performance in nonideal

installation conditions. The velocity data indicate that the header produces, initially,

a velocity profile that is highly swirled and more smoothly varying than the fiilly

developed distribution that is pertinent to the Reynolds number and relative roughness

conditions.

The secondary flow produced by the header is very similar to that for the closelycoupled double elbows out-of-plane configurations. As compared to fiilly developed

pipe profile, the header flow velocities near tlie pipe center are much slower, and those

near the pipe walls are faster. At the location, 30D downstream from the header, the

profile is fairly flat across most of the center core of the pipe, and it is symmetric. A

strong single eddy swirl distribution is generated by tiie turning action of this header

configuration. Results indicate that tlie single eddy produced by the header is relatively

stable and organized and its dissipation is slower than the swirl from previously studied

double elbows out-of-plane cases. Additionally, these flows are accompanied by levels

of turbulence that are slightly lower tlian tiiose for tlie double elbows out-of-plane. The

net results are that the flow effects from the header dissipate more slowly than those

from the double elbows out-of-plane. Data for the conditions tested show that the

single-eddy swirl pattern produced by the header persist to well beyond 30D from the

exit of the header. The extent to wliich tliis swirl propagates down the pipe has not yet

been completed. The flow also has smootiily varying turbulence distributions across

the pipe even at Z=30D and the flow is still developing toward a fiilly developed

pipeflow condition.

The results obtained when a tube bundle is installed in the outlet piping show that, just

downstream of the 19 tube bundle, the pipeflow is dominated by the effects of the

multi-jets from the individual tubes. The axial velocity profiles exliibit very smoothly

varying velocity distributions in which the major portion of the center core of the

pipeflow is quite slow in comparison with the fiilly developed distributions. The 19-

tube bundle is quite effective in reducing transverse velocities. At 22D downstream of

16
the tube bundle, the effect of the pipe wall boundary layer has not yet completely

propagated over the entire pipe cross section and thus the pipeflow is still in the

process of evolving toward the fully developed distribution.

REFERENCES

[1] Mattingly, G.E. and Yeh, T.T., NIST's Industry-Government Consortium

Research Program on Flowmeter Installation Effects: Report of Results for the

Research Period Nov. - May 1989, NISTIR 4310, Apr. 1990.

[2] Mattingly, G.E. and Yeh, T.T., Summary Report ofNIST's Industry-Government

Consortium Research Program on Flowmeter Installation Effects With Emphasis

on the Research Period January-September 1991 : The Reducer, NISTIR 4779,

December 1991.

[3] Mattingly, G.E. and Yeh, T.T., NIST's Industry-Government Consortium

Research Program on Flowmeter Installation Effects: Report of Results for the

Research Period July - December 1987. NISTIR-88-3898, May 1988.

[4] Mattingly, G.E. and Yeh, T.T., Effects of Pipe Elbows and Tube Bundles on

Selected Types of Flowmeters, Journal of Flow Measurements and

Instrumentation, Vol. 2, pp. 4-13, January, 1991.

[5] Yeh, T.T. and Mattingly, G.E., Summary Report of NIST's Industry-Government

Consortium Research Program on Flowmeter Installation Effects: The 45°

Elbow, NIST Teclmical Note 1408, October, 1994.

[6] Mattingly, G.E. and Yeh, T.T., Flowmeter Installation Effects Due to Several

Elbow Configurations, Proceedings of the 2nd International Symposium on

Fluid Flow Measurement, pp. 271-283, June, 1990.

[7] Mattingly, G.E. and Yeh, T.T., Robertson, B. and Kothari, K., NBS Research on

In- Situ Flowmeter Installations, Procs, AGA Distribution and Transmission

Confr. Las Vegas, NV, May 1987.

[8] Yeh, T.T. and Mattingly, G.E., Mixing Motions Produced by Pipe Elbows,

NISTIR 89-4029 January 1989.

17
[9] Harbrmk, B., Zimig, W., Hassenpflug, H., Kerber, W. and Zimmermann, H.; The

Disturbance of Flow Through an Orifice Plate Meter Run by the Upstream

Header, 5th International IMEKO=Conference on Flow Measurement

FLOMEKO, Dusseldorf(FRG), pp. 75-90, October, 1989.

[10] WiUiamson, ID., Botros, K.K. and Price, G.R.; Flow Characteristics and Orifice

Meter Error Caused by Upstream Headers in Multi-Run Meter Stations. ASME

Fluid Measurements and Instrumentation Forum, FED-Vol. 161, 1 993

[11] Yeh, T.T. and Mattingly, G.E., Flowmeter Installation Effects due to a Generic

Header. (To appear as NIST Technical Note)

[12] Bogue, D.C. and Metzner, A.B., Velocity Profiles in Turbulent Pipe Flow, I&EC

Fundamentals Vol. 2, No. 2, May 1963, pp. 143-9.

[13] Laufer, J., Tlie Structure of Turbulence in Fully Developed Pipe Flow, NBS Rept.

1974, Sept. 1952.

[14] Orifice Metering of Natural Gas and Other Related Hydrocarbon Fluids, Part

2, Specification and Installafion Requirements, AGA Report No. 3, API 14.3,

GPA 8185-90, 3rd Ed., February 1991.

[15] Yeh, T.T. and Mattingly, G.E., Pipeflow Downstream of a Reducer and Its Effects on Flowmeters. ASME Fluid Measurement and Instrumentation Forum,

FED-Vol.161, 1993, pp. 21-28.

[16] Klein, A. Review:Turbulent Developing Pipe Flow. J. of Fluids Engineering, June

1981, Vol.103, pp. 243-249.

[17] Klein,A. Review:Effects of Inlet condifions on Conical-Diffuser Performance.

J. of Fluid Engineering, June 1981, Vol. 103, p. 250

[18] Ghazi, H.S. A Pressure hidex for Predicting tlie effect of Flow Profiles on Orifice

Meter Performance. J. of Basic Engineering, March 1966, pp. 93-100

18
Header H342

One Inlet: 77 mm Dia.

Two Outlets: 52 mm Dia.

Tank Body: 103 mm Dia.

All dimensions are nominal and in mm

Figure 1 The Generic Header Geometry, H342 Consisting

One Inlet and Two Outlets.

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29
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0.2 -

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1 1———1 1 1 1 1 1—

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31
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49

APPENDIX A

Mean and Turbulence Velocity Profiles

for Header H342-100/0-1

Velocities in the Outlet Pipe #1

with Outlet #1 Fully Opened and Outlet #2 Fully Closed.

Water Temperature = 21.5 °C

Water Kinematic Viscosity = 9.71958*10-^ mVs

Pipe Diameter, D = 5.25 cm (2.07 in)

Reynolds Number Re =100000

1) Velocity Profile at Y=Q, and Z=3.35D

X/D W/W^ w'/Wb V/Wi, v'/Wb O.Deg,

1 -0.460 0.950 0.144 0.246 0.150 14.52

2 -0.421 1.012 0.138 0.233 0.138 12.97

3 -0.383 1.030 0.130 0.207 0.132 11.36

4 -0.345 1.023 0.130 0.179 0.125 9.92

5 -0.307 1.014 0.127 0.150 0.125 8.41

6 -0.268 1.010 0.125 0.115 0.128 6.50

7 -0.230 1.000 0.127 0.093 0.130 5.31

8 -0.192 0.997 0.123 0.057 0.133 3.27

9 -0.153 0.996 0.124 0.033 0.136 1.90

10 -0.115 0.992 0.123 0.013 0.140 0.75

11 -0.077 0.991 0.127 -0.001 0.141 -0.06

12 -0.038 0.993 0.132 -0.034 0.146 -1.96

13 0.000 0.990 0.131 -0.050 0.145 -2.89

14 0.038 0.984 0.131 -0.063 0.143 -3.66

15 0.077 0.985 0.132 -0.089 0.138 -5.16

16 0.115 0.986 0.133 -0.109 0.136 -6.31

17 0.153 0.986 0.131 -0.130 0.133 -7.51

18 0.192 0.987 0.131 -0.154 0.132 -8.87

19 0.230 0.993 0.132 -0.175 0.131 -9.99

20 0.268 0.997 0.129 -0.219 0.135 -12.39

21 0.307 1.000 0.129 -0.254 0.139 -14.25

22 0.345 1.005 0.126 -0.291 0.144 -16.15

23 0.383 1.013 0.128 -0.323 0.150 -17.69

24 0.421 1.005 0.130 -0.351 0.153 -19.25

25 0.460 0.972 0.140 -0.355 0.160 -20.06

Al
2) Velocity Profile ab X=0, and Z=3.35D

I Y/D W/Wb w'/W;, V/Wb v'/Wb (t),Deg.

1 -0.460 0.945 0.136 -0.006 0.078 -0.36

2 -0.421 0.993 0.136 -0.014 0.105 -0.81

3 -0.383 0.992 0.132 -0.031 0.106 -1.79

4 -0.345 0.984 0.128 -0.039 0.112 -2.27

5 -0.307 0.984 0.127 -0.044 0.116 -2.56

6 -0.268 0.985 0.128 -0.057 0.120 -3.31

7 -0.230 0.983 0.128 -0.040 0.123 -2.33

8 -0.192 0.975 0.124 -0.050 0.126 -2.94

9 -0.153 0.981 0.128 -0.050 0.130 -2.92

10 -0.115 0.983 0.126 -0.056 0.133 -3.26

11 -0.077 0.983 0.126 -0.047 0.138 -2.74

12 -0.038 0.986 0.127 -0.052 0.141 -3.02

13 0.000 0.989 0.129 -0.049 0.144 -2.84

14 0.038 0.986 0.128 -0.048 0.145 -2.79

15 0.077 0.985 0.126 -0.049 0.141 -2.85

16 0.115 0.979 0.123 -0.040 0.140 -2.34

17 0.153 0.983 0.122 -0.040 0.138 -2.33

18 0.192 0.983 0.122 -0.036 0.138 -2.10

19 0.230 0.982 0.124 -0.028 0.134 -1.63

20 0.268 0.978 0.125 -0.030 0.128 -1.76

21 0.307 0.976 0.123 -0.028 0.120 -1.64

22 0.345 0.968 0.122 -0.026 0.112 -1.54

23 0.383 0.959 0.123 -0.016 0.102 -0.96

24 0.421 0.942 0.126 -0.017 0.096 -1.03

25 0.460 0.875 0.135 0.001 0.085 0.07

A2
3) Velocifcv Profile at Y=0, and Z=7.44D

I X/D W/Wb w'/Wb V/Wb v'/Wfa 0,Deg.

1 -0.460 0.828 0.138 0.227 0.145 15.33

2 -0.421 0.908 0.123 0.228 0.131 14.10

3 -0.383 0.966 0.118 0.218 0.123 12.72

4 -0.345 0.994 0.113 0.197 0.116 11.21

5 -0.307 1.005 0.113 0.172 0.108 9.71

6 -0.268 1.009 0.111 0.145 0.102 8.18

7 -0.230 1.009 0.109 0.124 0.104 7.01

8 -0.192 1.013 0.108 0.093 0.101 5.25

9 -0.153 1.015 0.107 0.071 0.103 4.00

10 -0.115 1.015 0.103 0.044 0.103 2.48

11 -0.077 1.015 0.105 0.019 0.104 1.07

12 -0.038 1.016 0.102 -0.007 0.107 -0.39

13 0.000 1.018 0.100 -0.025 0.109 -1.41

14 0.038 1.016 0.102 -0.050 0.106 -2.82

15 0.077 1.015 0.102 -0.080 0.102 -4.51

16 0.115 1.018 0.102 -0.101 0.099 -5.67

17 0.153 1.017 0.101 -0.120 0.096 -6.73

18 0.192 1.014 0.102 -0.148 0.092 -8.30

19 0.230 1.016 0.103 -0.179 0.090 -9.99

20 0.268 1.015 0.105 -0.202 0.089 -11.26

21 0.307 1.012 0.109 -0.228 0.087 -12.70

22 0.345 1.008 0.112 -0.251 0.090 -13.98

23 0.383 1.006 0.114 -0.272 0.092 -15.13

24 0.421 0.987 0.119 -0.285 0.096 -16.11

25 0.460 0.956 0.132-0.282 0.126 -16.43

A3
4) Velocity Profile at X=0, and Z=7.44D

I Y/D W/Wb w'/Wb V/Wb v'/W^ (l),Deg,

1 -0.460 0.901 0.121 0.003 0.056 0.19

2 -0.421 0.967 0.107 -0.011 0.065 -0.65

3 -0.383 0.991 0.104 -0.011 0.071 -0.64

4 -0.345 0.993 0.104 -0.018 0.076 -1.04

5 -0.307 0.993 0.103 -0.014 0.084 -0.81

6 -0.268 0.999 0.100 -0.018 0.092 -1.03

7 -0.230 1.005 0.098 -0.018 0.095 -1.03

8 -0.192 1.008 0.099 -0.021 0.098 -1.19

9 -0.153 1.007 0.098 -0.015 0.100 -0.85

10 -0.115 1.013 0.097 -0.018 0.102 -1.02

11 -0.077 1.012 0.101 -0.020 0.102 -1.13

12 -0.038 1.015 0.100 -0.024 0.106 -1.35

13 0.000 1.015 0.101 -0.025 0.109 -1.41

14 0.038 1.017 0.099 -0.024 0.107 -1.35

15 0.077 1.021 0.099 -0.020 0.103 -1.12

16 0.115 1.020 0.098 -0.017 0.100 -0.95

17 0.153 1.017 0.097 -0.017 0.098 -0.96

18 0.192 1.016 0.096 -0.015 0.094 -0.85

19 0.230 1.017 0.098 -0.013 0.089 -0.73

20 0.268 1.015 0.097 -0.014 0.085 -0.79

21 0.307 1.012 0.102 -0.011 0.083 -0.62

22 0.345 0.998 0.099 -0.011 0.081 -0.63

23 0.383 0.989 0.104 -0.009 0.080 -0.52

24 0.421 0.964 0.110 -0.004 0.081 -0.24

25 0.460 0.891 0.127 0.001 0.078 0.06

A4
5) Velocity Profile at Y=Q, and Z=12.44D

I X/D W/Wb w'/Wj, v/v^ v'/W^ (t)/Deg.

1 -0.460 0.926 0.112 0.253 0.115 15.28

2 -0.421 0.984 0.101 0.226 0.103 12.94

3 -0.383 1.010 0.095 0.211 0.095 11.80

4 -0.345 1.015 0.089 0.191 0.093 10.66

5 -0.307 1.021 0.088 0.174 0.090 9.67

6 -0.268 1.022 0.088 0.154 0.089 8.57

7 -0.230 1.024 0.088 0.137 0.085 7.62

8 -0.192 1.026 0.088 0.112 0.085 6.23

9 -0.153 1.027 0.087 0.093 0.090 5.17

10 -0.115 1.027 0.086 0.069 0.091 3.84

11 -0.077 1.027 0.087 0.041 0.094 2.29

12 -0.038 1.024 0.089 0.015 0.096 0.84

13 0.000 1.025 0.090 -0.003 0.096 -0.17

14 0.038 1.024 0.093 -0.022 0.094 -1.23

15 0.077 1.028 0.089 -0.055 0.089 -3.06

16 0.115 1.030 0.089 -0.081 0.086 -4.50

17 0.153 1.030 0.089 -0.103 0.083 -5.71

18 0.192 1.030 0.091 -0.136 0.086 -7.52

19 0.230 1.029 0.092 -0.164 0.086 -9.06

20 0.268 1.024 0.093 -0.182 0.088 -10.08

21 0.307 1.018 0.094 -0.214 0.088 -11.87

22 0.345 1.006 0.096 -0.224 0.091 -12.55

23 0.383 0.986 0.100 -0.245 0.094 -13.95

24 0.421 0.951 0.104 -0.259 0.098 -15.23

25 0.460 0.882 0.108 -0.257 0.110 -16.25

A5
6) Velocibv Profile at X=0, and Z=12.44D

I Y/D W/Wb vf'/K V/Wb V/Wb 0,Deg.

1 -0.460 0.894 0.113 0.000 0.059 0.00

2 -0.421 0.967 0.101 -0.003 0.054 -0.18

3 -0.383 0.997 0.092 -0.005 0.059 -0.29

4 -0.345 1.007 0.092 -0.006 0.061 -0.34

5 -0.307 1.020 0.090 -0.008 0.064 -0.45

6 -0.268 1.025 0.087 -0.007 0.069 -0.39

.7 -0.230 1.030 0.086 -0.010 0.073 -0.56

8 -0.192 1.033 0.084 -0.007 0.077 -0.39

9 -0.153 1.030 0.088 -0.010 0.082 -0.56

10 -0.115 1.026 0.084 -0.007 0.087 -0.39

II -0.077 1.025 0.087 -0.010 0.091 -0.56

12 -0.038 1.025 0.088 -0.007 0.094 -0.39

13 0.000 1.024 0.089 -0.010 0.095 -0.56

14 0.038 1.022 0.089 -0.008 0.094 -0.45

15 0.077 1.023 0.085 -0.006 0.092 -0.34

16 0.115 1.025 0.086 -0.004 0.089 -0.22

17 0.153 1.026 0.088 -0.005 0.086 -0.28

18 0.192 1.026 0.086 -0.008 0.082 -0.45

19 0.230 1.021 0.089 -0.008 0.078 -0.45

20 0.268 1.018 0.088 -0.005 0.072 -0.28

21 0.307 1.013 0.087 -0.006 0.066 -0.34

22 0.345 1.006 0.090 -0.004 0.065 -0.23

23 0.383 0.989 0.094 -0.004 0.062 -0.23

24 0.421 0.956 0.101 -0.005 0.059 -0.30

25 0.460 0.869 0.120 -0.002 0.060 -0.13

A6
7) Velocity Profile at Y=0, and Z=21D

X/D W/W. w'/W. V/Wb v'/Wb (t),Deg.

1 -0.460 0.914 0.100 0.245 0.095 15.01

2 -0.421 0.979 0.091 0.236 0.089 13.55

3 -0.383 1.013 0.086 0.217 0.083 12.09

4 -0.345 1.030 0.082 0.194 0.080 10.67

5 -0.307 1.041 0.080 0.174 0.079 9.49

6 -0.268 1.045 0.078 0.159 0.076 8.65

7 -0.230 1.044 0.075 0.139 0.075 7.58

8 -0.192 1.045 0.074 0.108 0.075 5.90

9 -0.153 1.048 0.073 0.089 0.078 4.85

10 -0.115 1.048 0.072 0.067 0.080 3.66

11 -0.077 1.049 0.071 0.043 0.083 2.35

12 -0.038 1.050 0.071 0.025 0.084 1.36

13 0.000 1.049 0.072 0.011 0.083 0.60

14 0.038 1.052 0.072 -0.017 0.083 -0.93

15 0.077 1.050 0.073 -0.032 0.081 -1.75

16 0.115 1.051 0.072 -0.058 0.080 -3.16

17 0.153 1.050 0.074 -0.080 0.081 -4.36

18 0.192 1.045 0.073 -0.102 0.081 -5.57

19 0.230 1.046 0.074 -0.114 0.082 -6.22

20 0.268 1.046 0.077 -0.140 0.083 -7.62

21 0.307 1.038 0.080 -0.157 0.084 -8.60

22 0.345 1.032 0.083 -0.175 0.086 -9.62

23 0.383 1.013 0.087 -0.194 0.089 -10.84

24 0.421 0.986 0.092 -0.212 0.093 -12.13

25 0.460 0.914 0.102 -0.228 0.100 -14.01

A7
8) Velocity Profile at X=0, and Z=21D

I Y/D W/Wb w'/Wb V/Wb v'/Wj, 0,Deg.

1 -0.460 0.913 0.104 0.003 0.052 0.19

2 -0.421 0.984 0.095 0.002 0.056 0.12

3 -0.383 1.019 0.089 0.001 0.058 0.06

4 -0.345 1.037 0.083 -0.001 0.061 -0.06

5 -0.307 1.049 0.081 -0.001 0.064 -0.05

6 -0,268 1.052 0.078 -0.002 0.068 -0.11

7 -0.230 1.053 0.076 -0.002 0.071 -0.11

8 -0.192 1.057 0.074 -0.001 0.076 -0.05

9 -0.153 1.054 0.073 -0.002 0.080 -0.11

10 -0.115 1.054 0.073 0.002 0.081 0.11

II -0.077 1.056 0.072 0.005 0.082 0.27

12 -0.038 1.054 0.072 0.008 0.083 0.43

13 0.000 1.052 0.072 0.008 0.083 0.44

14 0.038 1.052 0.073 0.007 0.083 0.38

15 0.077 1.053 0.073 0.006 0.081 0.33

16 0.115 1.053 0.073 0.005 0.079 0.27

17 0.153 1.053 0.074 0.005 0.075 0.27

18 0.192 1.056 0.075 0.005 0.072 0.27

19 0.230 1.048 0.076 0.007 0.069 0.38

20 0.268 1.049 0.078 0.005 0.065 0.27

21 0.307 1.041 0.080 0.004 0.059 0.22

22 0.345 1.034 0.084 0.005 0.057 0.28

23 0.383 1.015 0.089 0.006 0.055 0.34

24 0.421 0.983 0.095 0.001 0.054 0.06

25 0.460 0.920 0.108 0.000 0.052 0.00

A8
9) Velocity Profile at Y=0. and Z=25D

X/D W/W^ w ' m V/Wi, v'/Wb 4),Deg.

1 -0.460 0.859 0.102 0.209 0.089 13.67

2 -0.421 0.952 0.092 0.208 0.080 12.32

3 -0.383 0.999 0.087 0.201 0.076 11.38

4 -0.345 1.019 0.083 0.182 0.072 10.13

5 -0.307 1.034 0.078 0.166 0.069 9.12

6 -0.268 1.045 0.075 0.149 0.067 8.11

7 -0.230 1.053 0.072 0.126 0.066 6.82

8 -0.192 1.059 0.072 0.108 0.067 5.82

9 -0.153 1.062 0.071 0.093 0.069 5.00

10 -0.115 1.061 0.069 0.068 0.071 3.67

11 -0.077 1.059 0.069 0.051 0.073 2.76

12 -0.038 1.059 0.068 0.029 0.073 1.57

13 0.000 1.060 0.068 0.014 0.074 0.76

14 0.038 1.059 0.069 -0.002 0.073 -0.11

15 0.077 1.061 0.069 -0.020 0.072 -1.08

16 0.115 1.059 0.069 -0.036 0.071 -1.95

17 0.153 1.060 0.069 -0.053 0.071 -2.86

18 0.192 1.061 0.070 -0.072 0.072 -3.88

19 0.230 1.057 0.070 -0.086 0.073 -4.65

20 0.268 1.056 0.072 -0.108 0.074 -5.84

21 0.307 1.052 0.074 -0.123 0.073 -6.67

22 0.345 1.044 0.079 -0.139 0.076 -7.58

23 0.383 1.026 0.083 -0.159 0.079 -8.81

24 0.421 1.004 0.088 -0.170 0.082 -9.61

25 0.460 0.925 0.096 -0.174 0.088 -10.65

A9
10) Velocity Profile at X=Q, and Z=25D

Y/D W/Wi, w'/Wb V/Wb v'/Wb (t),Deg.

1 -0.460 0.907 0.101 0.004 0.051 0.25

2 -0.421 0.973 0.092 0.003 0.052 0.18

3 -0.383 1.012 0.087 0.004 0.054 0.23

4 -0.345 1.030 0.082 0.003 0.056 0.17

5 -0.307 1.042 0.079 0.005 0.058 0.27

6 -0.268 1.054 0.076 0.006 0.060 0.33

7 -0.230 1.059 0.072 0.005 0.063 0.27

8 -0.192 1.061 0.071 0.005 0.065 0.27

9 -0.153 1.064 0.070 0.007 0.068 0.38

10 -0.115 1.064 0.069 0.009 0.071 0.48

11 -0.077 1.067 0.068 0.009 0.073 0.48

12 -0.038 1.065 0.068 0.009 0.074 0.48

13 0.000 1.064 0.068 0.006 0.074 0.32

14 0.038 1.064 0.069 0.007 0.073 0.38

15 0.077 1.065 0.069 0.007 0.072 0.38

16 0.115 1.061 0.069 0.007 0.070 0.38

17 0.153 1.060 0.070 0.008 0.067 0.43

18 0.192 1.054 0.071 0.010 0.065 0.54

19 0.230 1.053 0.073 0.012 0.061 0.65

20 0.268 1.045 0.076 0.010 0.058 0.55

21 0.307 1.045 0.078 0.010 0.056 0.55

22 0.345 1.034 0.082 0.010 0.053 0.55

23 0.383 1.012 0.086 0.009 0.052 0.51

24 0.421 0.974 0.090 0.008 0.051 0.47

25 0.460 0.914 0.098 0.002 0.050 0.13

AlO
11) Velocity Profile at Y=Q, and Z=30D

X/D W/W^ w'/K V/Wj, v'/Wj, 0,Deg,

1 -0.460 0.869 0.097 0.197 0.081 12.77

2 -0.421 0.961 0.089 0.193 0.075 11.36

3 -0.383 1.004 0.084 0.187 0.070 10.55

4 -0.345 1.025 0.080 0.170 0.067 9.42

5 -0.307 1.039 0.077 0.156 0.064 8.54

6 -0.268 1.053 0.073 0.131 0.062 7.09

7 -0.230 1.059 0.071 0.113 0.060 6.09

8 -0.192 1.065 0.070 0.091 0.059 4.88

9 -0.153 1.070 0.068 0.076 0.059 4.06

10 -0.115 1.074 0.067 0.060 0.061 3.20

11 -0.077 1.074 0.067 0.041 0.064 2.19

12 -0.038 1.075 0.065 0.025 0.064 1.33

13 0.000 1.079 0.066 0.008 0.064 0.42

14 0.038 1.077 0.066 0.002 0.064 0.11

15 0.077 1.074 0.067 -0.014 0.064 -0.75

16 0.115 1.076 0.068 -0.029 0.063 -1.54

17 0.153 1.075 0.067 -0.048 0.061 -2.56

18 0.192 1.072 0.068 -0.063 0.060 -3.36

19 0.230 1.070 0.069 -0.077 0.062 -4.12

20 0.268 1.067 0.070 -0.097 0.063 -5.19

21 0.307 1.062 0.074 -0.106 0.066 -5.70

22 0.345 1.040 0.079 -0.122 0.069 -6.69

23 0.383 1.015 0.083 -0.137 0.071 -7.69

24 0.421 0.988 0.087 -0.144 0.076 -8.29

25 0.460 0.927 0.097 -0.155 0.082 -9.49

All
12) Velocity Profile at X=0, and Z=30D

I Y/D W/Wb w'/Wb V/Wj, v'/Wj, (t),Deg.

1 -0.460 0.895 0.098 -0.002 0.050 -0.13

2 -0.421 0.969 0.090 -0.002 0.053 -0.12

3 -0.383 1.006 0.084 -0.003 0.055 -0.17

4 -0.345 1.031 0.080 -0.002 0.057 -0.11

5 -0.307 1.045 0.077 -0.004 0.058 -0.22

6 -0.268 1.057 0.073 0.000 0.059 0.00

7 -0.230 1.064 0.071 -0.001 0.061 -0.05

8 -0.192 1.068 0.069 0.000 0.061 0.00

9 -0.153 1.070 0.068 0.000 0.061 0.00

10 -0.115 1.073 0.067 0.000 0.062 0.00

II -0.077 1.076 0.066 0.002 0.064 0.11

12 -0.038 1.078 0.066 0.004 0.065 0.21

13 0.000 1.077 0.066 0.005 0.066 0.27

14 0.038 1.079 0.066 0.007 0.066 0.37

15 0.077 1.076 0.067 0.005 0.065 0.27

16 0.115 1.073 0.067 0.006 0.063 0.32

17 0.153 1.073 0.067 0.009 0.062 0.48

18 0.192 1.070 0.070 0.010 0.058 0.54

19 0.230 1.065 0.071 0.009 0.056 0.48

20 0.268 1.058 0.074 0.010 0.053 0.54

21 0.307 1.054 0.077 0.017 0.052 0.92

22 0.345 1.037 0.080 0.013 0.051 0.72

23 0.383 1.020 0.084 0.012 0.050 0.67

24 0.421 0.984 0.088 0.011 0.049 0.64

25 0.460 0.919 0.096 -0.002 0.049 -0.12

A12
APPENDIX B

Mean and Turbulence Velocity Profiles

for Header H342-100/0-1 and a 19-Tube Tube Bundle.

Velocities in the Outlet Pipe #1

with Outlet #1 Fully Opened and Outlet #2 Fully Closed

19-Tube Tube Bundle in Outlet #1

Tube Bundle Entrance Location, Z= 4.26D

Tube Bundle Exit Location, Z= 6. 2D

Water Temperature = 2L5 °C

Water Kinematic Viscosity = 9.71958*10-^ mVs

Pipe Diameter, D = 5.25 cm (2.07 in)

Reynolds Number Re =100000

1) Velocity Profile at Y=0, Z=8.2D, and C=2D

X/D W/Wb w'/Wi, V/Wb v'/Wb 0,Deg.

1 -0.460 1.052 0.105 0.019 0.070 1.03

2 -0.421 1.054 0.108 0.011 0.065 0.60

3 -0.383 1.047 0.101 0.010 0.063 0.55

4 -0.345 1.030 0.088 0.012 0.060 0.67

5 -0.307 1.014 0.076 0.016 0.055 0.90

6 -0.268 1.009 0.067 0.020 0.057 1.14

7 -0.230 1.045 0.078 0.016 0.065 0.88

8 -0.192 1.092 0.091 0.008 0.062 0.42

9 -0.153 1.088 0.096 0.003 0.054 0.16

10 -0.115 1.060 0.087 0.009 0.055 0.49

11 -0.077 1.014 0.073 0.014 0.058 0.79

12 -0.038 1.043 0.081 0.015 0.066 0.82

13 0.000 1.098 0.092 0.004 0.062 0.21

14 0.038 1.099 0.090 0.007 0.055 0.36

15 0.077 1.065 0.083 0.010 0.060 0.54

16 0.115 1.017 0.072 0.013 0.060 0.73

17 0.153 1.011 0.081 0.005 0.061 0.28

18 0.192 1.070 0.091 -0.001 0.056 -0.05

19 0.230 1.083 0.087 -0.001 0.058 -0.05

20 0.268 1.047 0.078 0.005 0.063 0.27

21 0.307 1.016 0.072 0.004 0.065 0.23

22 0.345 1.041 0.085 0.002 0.067 0.11

23 0.383 1.064 0.093 0.001 0.067 0.05

24 0.421 1.059 0.097 -0.006 0.069 -0.32

25 0.460 1.046 0.094 -0.006 0.068 -0.33

Bl
2) Velocity Profile at X=0, Z=8.2D, and C=2D

I Y/D W/Wb w'/Wb V/Wb v'/Wb 0,Deg.

1 -0.460 0.966 0.100 0.001 0.066 0.06

2 -0.421 1.016 0.095 0.001 0.063 0.06

3 -0.383 1.026 0.083 0.004 0.060 0.22

4 -0.345 1.011 0.074 0.006 0.056 0.34

5 -0.307 0.975 0.066 0.006 0.051 0.35

6 -0.268 0.962 0.062 0.008 0.046 0.48

7 -0.230 1.001 0.067 0.009 0.055 0.52

8 -0.192 1.027 0.078 0.007 0.058 0.39

9 -0.153 1.021 0.082 0.010 0.052 0.56

10 -0.115 1.009 0.070 0.014 0.056 0.79

II -0.077 1.028 0.073 0.006 0.059 0.33

12 -0.038 1.067 0.081 0.011 0.062 0.59

13 0.000 1.093 0.089 0.018 0.062 0.94

14 0.038 1.075 0.086 0.012 0.058 0.64

15 0.077 1.025 0.079 0.011 0.052 0.61

16 0.115 1.005 0.073 0.012 0.057 0.68

17 0.153 1.043 0.082 0.014 0.055 0.77

18 0.192 1.069 0.087 0.015 0.051 0.80

19 0.230 1.033 0.081 0.008 0.059 0.44

20 0.268 0.992 0.073 0.007 0.058 0.40

21 0.307 0.978 0.066 0.003 0.056 0.18

22 0.345 1.008 0.077 -0.002 0.057 -0.11

23 0.383 1.032 0.087 -0.005 0.060 -0.28

24 0.421 1.022 0.093 -0.004 0.060 -0.22

25 0.460 0.961 0.093 -0.002 0.060 -0.12

B2
3) Velocity Profile at Y=0, Z=12.2D, and C=6D

I X/D W/Wb W/Wj. V/Wb v'/W^ (|)/Deg.

1 -0.460 0.979 0.071 0.012 0.061 0.70

2 -0.421 1.009 0.064 0.012 0.052 0.68

3 -0.383 1.027 0.058 0.009 0.043 0.50

4 -0.345 1.016 0.052 0.011 0.037 0.62

5 -0.307 1.018 0.047 0.008 0.031 0.45

6 -0.268 1.035 0.044 0.007 0.030 0.39

7 -0.230 1.058 0.041 0.004 0.029 0.22

8 -0.192 1.076 0.039 0.001 0.029 0.05

9 -0.153 1.077 0.038 0.002 0.028 0.11

10 -0.115 1.074 0.037 0.001 0.027 0.05

11 -0.077 1.073 0.035 0.001 0.026 0.05

12 -0.038 1.074 0.036 0.002 0.026 0.11

13 0.000 1.073 0.035 -0.002 0.026 -0.11

14 0.038 1.073 0.036 0.000 0.027 0.00

15 0.077 1.072 0.037 0.000 0.027 0.00

16 0.115 1.068 0.037 -0.001 0.026 -0.05

17 0.153 1.067 0.038 -0.001 0.028 -0.05

18 0.192 1.066 0.039 0.002 0.028 0.11

19 0.230 1.067 0.040 0.002 0.029 0.11

20 0.268 1.064 0.041 -0.004 0.029 -0.22

21 0.307 1.061 0.044 -0.001 0.032 -0.05

22 0.345 1.053 0.049 -0.002 0.033 -0.11

23 0.383 1.041 0.056 -0.003 0.041 -0.17

24 0.421 1.018 0.069 -0.003 0.050 -0.17

25 0.460 0.994 0.080 -0.005 0.063 -0.29

B3
4) Velocity Profile at X=0, Z=12.2D, and C=6D

I Y/D W/Wj, w'/Wj, V/Wj, v'/Wb (p^Deg.

1 -0.460 0.968 0.067 -0.001 0.055 -0.06

2 -0.421 1.011 0.056 -0.002 0.041 -0.11

3 -0.383 1.028 0.051 0.002 0.032 0.11

4 -0.345 1.043 0.046 0.003 0.030 0.16

5 -0.307 1.061 0.043 0.000 0.029 0.00

6 -0.268 1.065 0.041 0.003 0.028 0.16

7 -0.230 1.070 0.038 -0.001 0.027 -0.05

8 -0.192 1.072 0.037 -0.002 0.027 -0.11

9 -0.153 1.074 0.037 -0.001 0.027 -0.05

10 -0.115 1.075 0.036 0.000 0.026 0.00

II -0.077 1.075 0.035 0.002 0.026 0.11

12 -0.038 1.076 0.035 0.001 0.026 0.05

13 0.000 1.075 0.035 0.001 0.025 0.05

14 0.038 1.070 0.035 0.003 0.025 0.16

15 0.077 1.069 0.035 0.001 0.026 0.05

16 0.115 1.070 0.035 0.002 0.026 0.11

17 0.153 1.065 0.036 0.001 0.026 0.05

18 0.192 1.063 0.037 -0.001 0.026 -0.05

19 0.230 1.058 0.038 -0.001 0.026 -0.05

20 0.268 1.053 0.040 0.001 0.028 0.05

21 0.307 1.043 0.043 0.001 0.029 0.05

22 0.345 1.039 0.049 0.001 0.032 0.06

23 0.383 1.028 0.059 0.003 0.035 0.17

24 0.421 0.993 0.071 0.004 0.041 0.23

25 0.460 0.936 0.077 0.001 0.055 0.06

B4
5) Velocity Profile at Y=0, Z=16.2D, and C=10D

X/D W/Wb w'/Wb V/Wj, v'/Wj, (t),Deg.

1 -0.460 0.931 0.081 0.021 0.063 1.29

2 -0.421 0.992 0.069 0.017 0.054 0.98

3 -0.383 1.020 0.063 0.016 0.046 0.90

4 -0.345 1.036 0.056 0.013 0.039 0.72

5 -0.307 1.044 0.051 0.007 0.032 0.38

6 -0.268 1.059 0.046 0.006 0.028 0.32

7 -0.230 1.072 0.042 0.001 0.026 0.05

8 -0.192 1.087 0.039 0.003 0.026 0.16

9 -0.153 1.099 0.037 0.000 0.025 0.00

10 -0.115 1.103 0.035 -0.002 0.025 -0.10

11 -0.077 1.108 0.034 -0.002 0.024 -0.10

12 -0.038 1.111 0.034 -0.002 0.024 -0.10

13 0.000 1.107 0.033 -0.002 0.024 -0.10

14 0.038 1.109 0.033 -0.002 0.024 -0.10

15 0.077 1.106 0.034 -0.003 0.025 -0.16

16 0.115 1.102 0.034 -0.002 0.024 -0.10

17 0.153 1.099 0.035 -0.002 0.026 -0.10

18 0.192 1.096 0.037 -0.002 0.026 -0.10

19 0.230 1.092 0.038 -0.003 0.026 -0.16

20 0.268 1.084 0.041 -0.002 0.027 -0.11

21 0.307 1.076 0.046 -0.003 0.027 -0.16

22 0.345 1.058 0.054 -0.003 0.029 -0.16

23 0.383 1.042 0.065 -0.004 0.042 -0.22

24 0.421 1.012 0.075 -0.002 0.053 -0.11

25 0.460 0.982 0.086 -0.002 0.064 -0.12

B5
6) Velocity Profile at X=0, Z=16.2D, and C=10D

I Y/D W/Wj, w'/W^ V/Wj. v'/Wb 0/Deg.

1 -0.460 0.949 0.078 -0.002 0.058 -0.12

2 -0.421 1.003 0.058 0.004 0.047 0.23

3 -0.383 1.047 0.048 0.002 0.038 0.11

4 -0.345 1.064 0.044 0.001 0.032 0.05

5 -0.307 1.081 0.042 0.000 0.029 0.00

6 -0.268 1.090 0.039 -0.002 0.028 -0.11

7 -0.230 1.095 0.037 -0.001 0.026 -0.05

8 -0.192 1.099 0.036 -0.001 0.025 -0.05

9 -0.153 1.102 0.035 -0.002 0.025 -0.10

10 -0.115 1.105 0.035 -0.001 0.024 -0.05

11 -0.077 1.105 0.034 0.000 0.023 0.00

12 -0.038 1.107 0.034 0.000 0.023 0.00

13 0.000 1.109 0.034 0.000 0.023 0.00

14 0.038 1.109 0.034 0.000 0.023 0.00

15 0.077 1.103 0.034 -0.001 0.023 -0.05

16 0.115 1.103 0.035 -0.002 0.023 -0.10

17 0.153 1.094 0.036 -0.003 0.024 -0.16

18 0.192 1.086 0.036 -0.003 0.025 -0.16

19 0.230 1.080 0.037 0.001 0.025 0.05

20 0.268 1.074 0.039 -0.003 0.027 -0.16

21 0.307 1.062 0.045 0.000 0.028 0.00

22 0.345 1.043 0.049 0.003 0.033 0.16

23 0.383 1.018 0.059 0.001 0.039 0.06

24 0.421 0.981 0.069 0.002 0.046 0.12

25 0.460 0.922 0.083 -0.001 0.056 -0.06

B6
7) Velocibv Profile at Y=Q, Z=19.7D, and C=13.5D

I X/D W/Wb w'/Wb V/Wb v'/Wj, (J),Deg.

1 -0.460 0.904 0.083 0.014 0.067 0.89

2 -0.421 0.966 0.074 0.013 0.057 0.77

3 -0.383 1.004 0.067 0.011 0.052 0.63

4 -0.345 1.044 0.062 0.008 0.046 0.44

5 -0.307 1.054 0.056 0.009 0.038 0.49

6 -0.268 1.072 0.052 0.008 0.034 0.43

7 -0.230 1.081 0.048 0.007 0.030 0.37

8 -0.192 1.096 0.043 0.007 0.028 0.37

9 -0.153 1.107 0.039 0.005 0.027 0.26

10 -0.115 1.115 0.036 0.004 0.026 0.21

II -0.077 1.125 0.035 0.002 0.025 0.10

12 -0.038 1.133 0.034 0.001 0.025 0.05

13 0.000 1.134 0.033 0.001 0.024 0.05

14 0.038 1.132 0.033 0.002 0.024 0.10

15 0.077 1.132 0.034 -0.001 0.024 -0.05

16 0.115 1.129 0.035 0.002 0.024 0.10

17 0.153 1.127 0.036 0.001 0.024 0.05

18 0.192 1.123 0.037 0.000 0.024 0.00

19 0.230 1.118 0.039 0.001 0.026 0.05

20 0.268 1.105 0.043 -0.001 0.027 -0.05

21 0.307 1.092 0.050 -0.001 0.028 -0.05

22 0.345 1.072 0.059 -0.002 0.031 -0.11

23 0.383 1.031 0.071 -0.002 0.045 -0.11

24 0.421 0.981 0.080 0.000 0.056 0.00

25 0.460 0.911 0.089 -0.003 0.067 -0.19

B7
8) Velocity Profile at X=0, Z=19.7D> and C=13.5D

I Y/D W/Wb w'/Wb V/Wb v'/Wb 0,Deg.

1 -0.460 0.925 0.084 0.000 0.052 0.00

2 -0.421 0.971 0.067 -0.004 0.048 -0.24

3 -0.383 1.015 0.060 -0.001 0.044 -0.06

4 -0.345 1.049 0.054 0.000 0.039 0.00

5 -0.307 1.073 0.045 0.002 0.034 0.11

6 -0.268 1.096 0.042 0.004 0.031 0.21

7 -0.230 1.112 0.039 0.005 0.029 0.26

8 -0.192 1.121 0.036 0.004 0.029 0.20

9 -0.153 1.128 0.034 0.003 0.028 0.15

10 -0.115 1.132 0.034 0.002 0.028 0.10

II -0.077 1.135 0.034 0.004 0.027 0.20

12 -0.038 1.134 0.033 0.005 0.026 0.25

13 0.000 1.136 0.033 0.004 0.026 0.20

14 0.038 1.135 0.033 0.002 0.027 0.10

15 0.077 1.135 0.033 0.002 0.027 0.10

16 0.115 1.130 0.032 0.005 0.027 0.25

17 0.153 1.128 0.033 0.006 0.027 0.30

18 0.192 1.122 0.032 0.004 0.028 0.20

19 0.230 1.114 0.034 0.004 0.029 0.21

20 0.268 1.107 0.037 0.004 0.030 0.21

21 0.307 1.091 0.047 0.005 0.032 0.26

22 0.345 1.064 0.057 0.005 0.036 0.27

23 0.383 1.012 0.067 0.004 0.043 0.23

24 0.421 0.972 0.076 -0.001 0.050 -0.06

25 0.460 0.907 0.086 -0.002 0.054 -0.13

B8
9) Velocibv Profile at Y=0, Z=23.7D, and C=17.5D

I X/D W/Wb w'/Wb V/Wj, ^r'/K <l)/Deg.

1 -0.460 0.888 0.086 0.010 0.069 0.65

2 -0.421 0.955 0.079 0.014 0.060 0.84

3 -0.383 1.001 0.071 0.013 0.054 0.74

4 -0.345 1.027 0.067 0.011 0.048 0.61

5 -0.307 1.056 0.062 0.009 0.044 0.49

6 -0.268 1.076 0.057 0.008 0.040 0.43

7 -0.230 1.096 0.053 0.008 0.036 0.42

8 -0.192 1.108 0.049 0.008 0.032 0.41

9 -0.153 1.127 0.043 0.007 0.029 0.36

10 -0.115 1.137 0.038 0.007 0.027 0.35

II -0.077 1.153 0.036 0.005 0.026 0.25

12 -0.038 1.163 0.035 0.002 0.025 0.10

13 0.000 1.167 0.035 0.001 0.025 0.05

14 0.038 1.168 0.035 0.001 0.025 0.05

15 0.077 1.168 0.036 0.001 0.025 0.05

16 0.115 1.159 0.037 -0.001 0.025 -0.05

17 0.153 1.156 0.039 0.001 0.024 0.05

18 0.192 1.144 0.042 0.002 0.026 0.10

19 0.230 1.131 0.045 0.003 0.026 0.15

20 0.268 1.116 0.048 0.002 0.027 0.10

21 0.307 1.099 0.055 0.002 0.027 0.10

22 0.345 1.071 0.064 0.002 0.034 0.11

23 0.383 1.040 0.075 0.003 0.045 0.17

24 0.421 0.993 0.082 -0.001 0.058 -0.06

25 0.460 0.882 0.091 -0.002 0.065 -0.13

B9
10) Velocity Profile ab X=0, Z=23.7D, and C=17.5D

Y/D W/W^ w'/Wb V/Wb v'/W^, (t),Deg.

1 -0.460 0.865 0.087 0.003 0.049 0.20

2 -0.421 0.943 0.074 0.004 0.049 0.24

3 -0.383 0.991 0.066 0.004 0.046 0.23

4 -0.345 1.031 0.058 0.003 0.043 0.17

5 -0.307 1.065 0.050 0.004 0.038 0.22

6 -0.268 1.094 0.046 0.003 0.033 0.16

7 -0.230 1.118 0.041 0.001 0.032 0.05

8 -0.192 1.134 0.036 0.002 0.030 0.10

9 -0.153 1.150 0.035 0.002 0.029 0.10

10 -0.115 1.154 0.034 0.002 0.029 0.10

11 -0.077 1.161 0.034 0.003 0.028 0.15

12 -0.038 1.164 0.033 0.002 0.027 0.10

13 0.000 1.165 0.034 0.003 0.026 0.15

14 0.038 1.167 0.034 0.003 0.026 0.15

15 0.077 1.164 0.034 0.004 0.025 0.20

16 0.115 1.160 0.034 0.005 0.026 0.25

17 0.153 1.154 0.034 0.005 0.026 0.25

18 0.192 1.144 0.036 0.006 0.027 0.30

19 0.230 1.130 0.038 0.005 0.028 0.25

20 0.268 1.113 0.045 0.005 0.031 0.26

21 0.307 1.079 0.054 0.005 0.036 0.27

22 0.345 1.041 0.062 0.005 0.042 0.28

23 0.383 1.005 0.071 0.005 0.047 0.29

24 0.421 0.965 0.078 0.002 0.051 0.12

25 0.460 0.891 0.087 -0.002 0.052 -0.13

BIO
11) Velocity Profile at Y=0, Z=28.2D, and C=22D

I X/D W/W^ w'/W^ v/K v/w^ <t)/Deg.

1 -0.460 0.878 0.090 0.014 0.065 0.91

2 -0.421 0.943 0.081 0.014 0.061 0.85

3 -0.383 0.996 0.075 0.011 0.056 0.63

4 -0.345 1.032 0.070 0.008 0.052 0.44

5 -0.307 1.064 0.064 0.003 0.048 0.16

6 -0.268 1.087 0.060 0.005 0.045 0.26

7 -0.230 1.104 0.055 0.003 0.042 0.16

8 -0.192 1.119 0.052 0.005 0.038 0.26

9 -0.153 1.137 0.047 0.004 0.033 0.20

10 -0.115 1.157 0.042 0.003 0.029 0.15

11 -0.077 1.168 0.038 0.003 0.027 0.15

12 -0.038 1.182 0.036 0.000 0.026 0.00

13 0.000 1.189 0.036 0.000 0.025 0.00

14 0.038 1.193 0.036 -0.002 0.025 -0.10

15 0.077 1.192 0.037 -0.001 0.026 -0.05

16 0.115 1.190 0.038 -0.001 0.025 -0.05

17 0.153 1.184 0.041 -0.002 0.026 -0.10

18 0.192 1.163 0.044 0.000 0.027 0.00

19 0.230 1.144 0.048 -0.001 0.029 -0.05

20 0.268 1.124 0.054 0.001 0.033 0.05

21 0.307 1.093 0.060 0.003 0.038 0.16

22 0.345 1.065. 0.069 -0.001 0.046 -0.05

23 0.383 1.033 0.076 -0.001 0.054 -0.06

24 0.421 0.972 0.082 -0.003 0.061 -0.18

25 0.460 0.886 0.090 0.000 0.065 0.00

Bll
12) Velocity Profile at X=0, Z=28.2D, and C=22D

Y/D W/Wj, w'/Wb V/Wi, v'/Wb ({),Deg.

1 -0.460 0.853 0.089 -0.001 0.050 -0.07

2 -0.421 0.939 0.080 -0.001 0.051 -0.06

3 -0.383 0.989 0.073 0.004 0.048 0.23

4 -0.345 1.031 0.067 0.004 0.045 0.22

5 -0.307 1.066 0.062 0.003 0.042 0.16

6 -0.268 1.097 0.057 0.004 0.038 0.21

7 -0.230 1.123 0.051 0.002 0.034 0.10

8 -0.192 1.142 0.046 0.001 0.033 0.05

9 -0.153 1.161 0.041 0.000 0.032 0.00

10 -0.115 1.170 0.039 0.002 0.030 0.10

11 -0.077 1.176 0.038 0.003 0.029 0.15

12 -0.038 1.181 0.036 0.002 0.028 0.10

13 0.000 1.183 0.036 0.004 0.027 0.19

14 0.038 1.185 0.037 0.005 0.027 0.24

15 0.077 1.184 0.037 0.004 0.026 0.19

16 0.115 1.178 0.038 0.004 0.027 0.19

17 0.153 1.166 0.039 0.004 0.028 0.20

18 0.L92 1.151 0.043 0.002 0.031 0.10

19 0.230 1.126 0.048 0.002 0.034 0.10

20 0.268 1.101 0.056 0.003 0.036 0.16

21 0.307 1.069 0.063 0.002 0.040 0.11

22 0.345 1.041 0.068 0.003 0.044 0.17

23 0.383 1.001 0.075 0.003 0.049 0.17

24 0.421 0.962 0.081 0.003 0.050 0.18

25 0.460 0.871 0.089 0.001 0.050 0.07

B12


NIST.Technical Publications

Periodical

Journal of Research of the National Institute of Standards and Technology—Reports NIST research and

development in those disciplines of the physical and engineering sciences in which the Institute is active. These include physics, chemistry, engineering, mathematics, and computer sciences. Papers cover a broad

range of subjects, with major emphasis on measurement methodology and the basic technology underlying

standardization. Also included from time to time are survey articles on topics closely related to the Institute's technical and scientific programs. Issued six times a year.

Nonperiodicals

Monographs—f^ajor contributions to the technical literature on various subjects related to the Institute's scientific and technical activities. Handbooks—Recommended codes of engineering and industrial practice (including safety codes) developed

in cooperation with interested industries, professional organizations, and regulatory bodies.

Special Publications—Include proceedings of conferences sponsored by NIST, NIST annual reports, and

other special publications appropriate to this grouping such as wall charts, pocket cards, and bibliographies.

National Standard Reference Data Series—Provides quantitative data on the physical and chemical

properties of materials, compiled from the world's literature and critically evaluated. Developed under a

worldwide program coordinated by NIST under the authority of the National Standard Data Act (Public Law

90-396). NOTE: The Journal of Physical and Chemical Reference Data (JPCRD) is published bi-monthly for NIST by the American Chemical Society (ACS) and the American Institute of Physics (AlP). Subscriptions,

reprints, and supplements are available from ACS, 1155 Sixteenth St., NW, Washington, DC 20056.

Building Science Series—Disseminates technical information developed at the Institute on building

materials, components, systems, and whole structures. The series presents research results, test methods,

and performance criteria related to the structural and environmental functions and the durability and safety

characteristics of building elements and systems.

Technical Notes—Studies or reports which are complete in themselves but restrictive in their treatment of a

subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of the

subject area. Often serve as a vehicle for final reports of work performed at NIST under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under procedures published by the Department of Commerce in Part 1 0, Title 1 5, of the Code of Federal Regulations. The standards establish nationally recognized

requirements for products, and provide all concerned interests with a basis for common understanding of the

characteristics of the products. NIST administers this program in support of the efforts of private-sector

standardizing organizations.

Order the following NIST publications—FIPS and NISTIRs—from the National Technical

Information Service, Springfield, VA 22161.

Federal Information Processing Standards Publications (FIPS PUB>—Publications in this series collectively constitute the Federal Information Processing Standards Register. The Register serves as the official source

of information in the Federal Government regarding standards issued by NIST pursuant to the Federal

Property and Administrative Services Act of 1949 as amended. Public Law 89-306 (79 Stat. 1 127), and as implemented by Executive Order 11717 (38 FR 12315, dated IVIay 11, 1973) and Part 6 of Title 15 CFR

(Code of Federal Regulations).

NIST Interagency Reports (NISTIR)—A special series of interim or final reports on work performed by NIST

for outside sponsors (both government and nongovernment). In general, initial distribution is handled by the sponsor; public distribution is by the National Technical Information Service, Springfield, VA 22161, in paper

copy or microfiche form.