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NUREGCR1864V2

NUREG/CR·1864
BNL·NUREG·51317
VOL. 2 of 3

1111111111111111111111111111111111111111111111111

ASTUDY OF NONEQUILIBRIUM FLASHING OF WATER
IN A CONVERGING-DIVERGING NOZZLE
VOLUME 2 . MODELING
B.J.e. Wu. N. Abuaf. and P. Saha

Date Published: June 1981

EXPERIMENTAL MODELING GROUP
DEPARTMENT OF NUCLEAR ENERGY, BROOKHAVEN NATIONAL LABORATORY
UPTON, NEW YORK 11973

Prepared for the U,S, Nuclear Regulatory Commission
Office of Nuclear Regulatory Research
Washington, D,C. 20555

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REPRODUCED BY,

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U.S. Department or Commerce
National Technh:allnfonnalion Service
Springfield, Virginia 22161



NRC

FORM

335


(7·771

1 HI 1'0fn NlJMBE R (AIJ,,,n"rlIJv DOC!

U.S. NUCLEAR REGULATORY COMMISSION

BIBLIOGRAPHIC DATA SHEET
4. TITLE AND SUBTITLE (Add Volume No., If apprO(Jflare'

']

A STUDY OF NONEQUILIBRIUM FLASHING OF WATER
IN A CONVERGING-DIVERGING NOZZLE
VOLUME 2 - MODELING

NUREG/CR-1864, Vol. 2
BNL -NUREG-51317, Vol.2
of J
IL ,."." hlan.'

3 RECIPIENT'S ACCESSION NO.

7. AUTHOR IS)

5. DATE REPORT COMPLE TED

B.J.C. Wu

N. Abuaf


P. Saha

I YE AR

MON1H

1981

June
9. PERFORMING ORGANIZATION NAME AND MAILING ADDRESS (Include Z,p Code)

DATE REPORT ISSUED

Department of Nuclear Energy
Brookhaven National Laboratory
Upton, New York
11973

Ma~lch

TVEf982

6. (Leave blank'

8. (Leave blank'
12. SPONSORING ORGANIZATiON NAME ANO MAl LING ADDRESS (Include Z,p Code)
10. PROJECT/TASK/WORK UNIT NO.

U.S. Nuclear Regulatory Commission
Office of Nuclear Regulatory Research

Washington, D. C. 20555
13. TYPE OF REPORT

15. SUPPLEMENTARY NOTES

11. CONTRACT NO.

FIN No. A3045

I

PE R I OD COV ERE D (InclUSive dares)

114.

(LeBve blank)

16. ABSTRACT (200 words or less)

A steady water loop with well controlled flow and thermodynamic conditions
was designed, built, and made operational for the measurement of net vapor
generation rates under nonequilibrium conditions. The test section consists of
a converging-diverging nozzle with 49 pressure taps and two observation windows
at the exit. Pressure distributions, photographic observations, diamet rical
averaged centerline void fraction distributions, detailed transverse distributions of the chordal averaged void fractions at 27 axial locations, and area
averaged void fraction distributions along the nozzle were recorded under various flashing conditions. The effects of the various parameters such as inlet
pressure (140 < Pin < 766 kPa), inlet temperature (100 0 < Tin < 149°C), mass
flux (1000 < Gin < 6720 kg/m 2 s), and back pressure on the pressure and void
distributions were investigated and are reported here. Since no information on
the phase velocities was recorded during the present experiments, the calculation of vapor generation rates from the available experimental data involved the

assumption of a slip model between the two phases.

17. KEY WORDS AND DOCUMENT ANALYSIS

17a. DESCRIPTORS

17b. IDENTIFIERS/OPEN·ENDED TERMS

18. AVAILABILITY STATEMENT

Unlimited
NRC FORM 33517·77)

19. SE5UR~TY Cl.../'r~

(Tef'! report)

nc aSSl le

20. SE6UR,TY CLAfS (~/S page)

nc aSSl le

21. NO. OF PAGES
22. PRICE

.s

I




NUREG/CR·1864
BNL·NUREG·51317
VOl. 2 of 3
AN,R2

ASTUDY OF NONEQUILIBRIUM FLASHING OF WATER
IN ACONVERGING-DIVERGING NOZZLE
VOLUME 1 - EXPERIMENTAL
VOLUME 2 - MODELING
VOLUME 3 - DATA (MICROFICHE)
N. Abuaf, B.J.C. Wu, G.A. Zimmer, and P. Saha

Manuscript Completed: December 19aO
Date Published: June 19a1

Prepared for the
UNITED STATES NUCLEAR REGULATORY COMMISSION
OFFICE OF NUCLEAR REGULATORY RESEARCH
CONTRACT NO. DE·AC02·76CH00016
FIN NO. A-3045

I

((J-.;


DISCLAIMER
This report was prepared as an account of work sponsored by an agency of the

United States Government. Neither the United States Government nor any agency
thereof. nor any of their employees, nor any of their contractors. subcontractors. or
their employees, makes any warranty, express or implied. or assumes any legal
liability or responsibility for the accuracy. completeness, or usefulness of any
information, apparatus, product. or process disclosed. or represents that its use
would not infringe privately owned rights. Reference herein to any specific commercial product, process. or service by trade name, trademark, manufacturer. or
otherwise, does not necessarily constitute or imply its endorsement. recommendation, or favoring by the United States Government or any agency, contractor or
subcontractor thereof. The views and opinions of authors expressed.herein do not
necessarily state or reflect those of the United States Government or any agency.
contractor or subcontractor thereof.

Printed in the United States of America
Available from
National Technical Information Service
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5285 Pan Royal Road
Springfield, VA 22161
NTIS price codes:
Printed Copy: A08; Microfiche Copy: AOI

I

JI


FOREWORD
The authors would like to acknowledge Dr. o. C. Jones, Jr. as initiator of
the program and the original principal investigator who conceptualized the research and experiment, supervised the design and construction of the flow loop
and defined the measurement techniques to obtain the necessary data. He also
put the Experimental Modeling and the Systems, Control and Data Acquisition

Groups together to perform the res~arch. The authors would also like to express
their appreciation to Dr. Jones, Jr. for his technical contributions to the
project both in the experiment and the analytical modeling areas and for fruitful discussions that the authors had wi th him during his involvement wi th the
program.
The final series of experimental runs (Runs 254-397), the required data reduction and analysis, and the development of the general void growth model were
performed by the present authors. They also assume responsibility for the
organization and content of this final report.
During this research several reports and papers have been published and a
detailed list of all of them is herewith presented. Two specific reports,
BNL-NUREG-26003 and BNL-NUREG-27138 have been transmitted as preliminary data
analysis reports. The present final report summarizes all the data obtained and
the analytical work performed.

-

iii -


PUBLICATIONS

The following is a list of publications during the total period of this
activity:
ABUAF, N., JONES, O. C., Jr. and ZIMMER, G. A., "Optical Probe for Local Void
Fraction and Interface Velocity Measurements," BNL-NUREG-5079l, March 1978;
also Rev. Sci Instrum. 49(8), pp. 1090-1094, 1978.
ABUAF, N., JONES, O. C., Jr., ZIMMER, G. A., LEONHARDT, W. J., and SARA, P.,
"BNL Flashing Experiments: Test Facility and Measurement Techniques,"
BNL-NUREG-24336, 1978; also Proc. of the CSMI Spec. Meeting on Transient
Two-Phase Flow, Paris, France, June, 1978 (in press).
ABUAF, N., JONES, o. C., Jr., and ZIMMER, G. A., "Response Characteristics of

Optical Probes," ASME paper 78-WA/HT-3, presented at the Winter Annual
Meeting, San Francisco, Calif., December 1978.
ABUAF, N., ZIMMER, G. A., and JONES, O.C., Jr., "BNL Instrumentation Research
Program," BNL-NUREG-2605l, April 1979; also NUREG/CP/0006, May 1979.
ABUAF, N., FEIERABEND, T. P., ZIMMER, G. A., and JONES, O. C., Jr., "Radio
Frequency (R-F) Probe for Bubble Size and Velocity Measurements,"
NUREG/CR-0769, BNL-NUREG-50997, March 1979; also Rev. Sci. Instrum., 50(10),
pp. 1260-1263, 1979.
ABUAF, N., WV, B. J. C., ZIMMER, G. A., and JONES, O. C., Jr., "Preliminary Data
Analysis Report; Vol. I, I I and III," BNL-NUREG-27138, Jan. 1980.
ABUAF, N., JONES, O. C., Jr., and WU, B. J. C., "Critical Flashing Flows in
Nozzles with Subcooled Inlet Conditions," BNL-NUREG-275l2, March 1980; also
"Polyphase Flow and Transport Technology, R. A. Bajura ed., ASME, Aug. 1980.
ABUAF, N., WV, B. J. C., ZIMMER, G. A., SARA, P., and JONES, O. C., Jr.,
"Nonequilibrium Vapor Generation Rates of Flashing Water Flows," Proc. of the
ANS/ASME International Topical Meeting on Nuclear Reactor Thermal Hydraulics,
Oct. 1980.
JONES, O. C., Jr., and SAHA, P., "Nonequilibrium Aspects of Water Reactor
Safety," BNL-NUREG-23143, July 1977; also in Symp. on the Thermal and
Hydraulics Aspects of Nuclear Reactor Safety, Vol. 1: Light Water Reactors, O.
C. Jones, Jr. and S. G. Bankoff ed. ASME, 1977.
JONES, o. C., Jr., ABUAF, N., ZIMMER, G. A., and FEIERABEND, T. P., "Void
Fluctuation Dynamics and Measurement Techniques," BNL-NUREG-26466, June 1979;
also presented at the Joint U.S.-Japan Inf. Exch. on Two-Phase Flow Dynamics,
Japan, 1979.

- iv -


JONES, o. C., Jr., "Inception and Development of Voids in Flashing Liquids,"

BNL-NUREG-26464, June 1979; also presented at the Joint U.S.-Japan Inf. Exch.
on Two-Phase Flow Dynamics, Japan 1979.
JONES, O. C., Jr., "Flashing Inception in Flowing Liquids," BNL-NUREG-26134,
1979.
SARA, P., "A Review of Two-Phase Steam-Water Critical Flow Models with Emphasis
on Thermal Nonequilibrium," BNL-NUREG-50907, Sept. 1978.
WU, B. J. C., SAHA, P., ABUAF, N., and JONES, o. C., Jr., "A One-Dimensional
Model of Vapor Generation in Steady Flashing Flow," BNL-NUREG-25709, March
1979; also ANS Trans., 32, pp. 490-491, 1979.
ZIMMER, G. A., WU, B. J. C., LEONHARD, W. J., ABUAF, N., and JONES, O. C., Jr.,
"Pressure and Void Distributions in a Converging-Diverging Nozzle with
Nonequilibrium Water Vapor Generation," BNL-NUREG-26003, April 1979.
ZIMMER, G. A., WU, B. J. C., LEONHARD, W. J., ABUAF, N., and JONES, O. C., Jr.,
"Experimental Investigations of Nonequilibrium Flashing of Water in a
Converging-Diverging Nozzle," BNL-NUREG-2S716 , Aug. 1979; also "Nonequilibrium
Interfacial Transport Processes," J. C. Chen and S. G. Bankoff eds., ASME,
1979.
Water Reactor Safety Research Division,
Quarterly Progess Report, Jan.-March 1977
"
"
April-June 1977
July-Sept. 1977
Oct.-Dec. 1977
Jan.-March 1978
April-June 1978
July-Sept. 1978
Oct .-Dec. 1978
Jan.-March 1979
April-June 1979

July-Sept. 1979
Oct.-Dec. 1979
Jan.-March 1980
April-June 1980
July-Sept. 1980

- v -

BNL-NUREG-5066l,
BNL-NUREG-S0683,
BNL-NUREG-S0747,
BNL-NUREG-5078S,
BNL-NUREG-S0820,
BNL-NUREG-S0883,
BNL-NUREG-S093l,
BNL-NUREG-S0978,
BNL-NUREG-S101S,
BNL-NUREG-S108l,
BNL-NUREG-Sl13l,
BNL-NUREG-Sl178,
BNL-NUREG-S12l8,
BNL-NUREG-S122S,
BNL-NUREG-S1298,

May 1977 •
Aug. 1977 .
Dec. 1977 .
Feb. 1978.
May 1978.
Aug. 1978.

Nov. 1978.
Mar. 1979.
May 1979.
Sept.1979.
Jan. 1980.
Apr. 1980.
June 1980.
Aug. 1980.
Nov. 1980


ABSTRACT
A steady water loop with well controlled flow and thermodynamic conditions
was designed, built, and made operational for the measurement of net vapor
generation rates under nonequilibrium conditions. The test section consists of
a converging-diverging nozzle with 49 pressure taps and two observation windows
at the exit. Pressure distributions, photographic observations, diametrical
averaged centerline void fraction distributions, ~etailed transverse distributions of the chordal averaged void fractions at 27 axial locations, and area
averaged void fraction distributions along the nozzle were recorded under various flashing conditions. The effects of the various parameters such as inlet
pressure (140 < Pin < 766 kPa), inlet temperature (100° < Tin < 149°C), mass
flux (1000 < Gin < 6720 kg/m 2 s), and back pressure on the pressure and void
distributions were investigated and are reported here. Since no information on
the phase velocities was recorded during the present experiments, the calculation of vapor generation rates from the available experimental data involved the
assumption of a slip model between the two phases.
The development of voids in nonequilibrium flashing flows is shown through
the Oswatitsch integral to be dependent on three major factors of the void
inception point which determines the initial and subsequent liquid superheats
and must be accurately described; of the interfacial mass transfer rates, which
depend on the local superheat and must be specified; and the local interfacial
area density where the mass transfer occurs. The flashing onset correlation of

Alamgir and Lienhard (1979) was extended to predict flashing inception in pipe
and nozzle flows with subcooled inlet conditions. A void development model for
bubbly flows (a< 0.30) was based on a simple concept for interfacial area density in conjunction with a conduction-controlled bubble growth law.
A general
model of vapor generation following flashing inception was also developed. In
this model, bubbly flow, bubbly-slug flow, a transitional flow comprising the
annular and annular-mist regimes and finally fully dispersed droplet flow were
assumed to occur at successively higher void fraction ranges.
On the basis that flashing inception occurred at the throat in nozzle flows
with subcooled inlet conditions, and that the pressure undershoot can be
calculated from the Alamgir-Lienhard correlation, a method of calculating the
critical mass flow rates through nozzles was proposed, and it was checked with
existing data.
Comparison of the BNL experiments with TRAC-PIA predictions revealed that,
although the code gave a good qualitative description of the flow, it was
inadequate in predicting the flashing inception point. This failure led to
significant quantitative discrepancies in the predicted and measured flow parameters for a number of test runs. The inclusion of a nucleation model should
improve the predictive capabilities of the code.

- vi -


CONTENTS

. VOLUME I - EXPERIMENTAL
FOREWORD ••

iii

PUBL IC AT IONS


iv

ABSTRACT . •

vi

LIST OF FIGURES.

xi

LIST OF TABLES

. . ..

xxiv
xxvi

NOMENCLATURE •
1

INTRODUCTION

1

2

REVIEW OF THE LITERATURE •

3


3

EXPERIMENTAL FACILITY AND TECHNIQUES.

7

4

3.1

Flow Loop ••

7

3.2

Test Section.

9

3.3

Loop Operation Conditions and Instrumentation.

14

DATA ACQUIS ITION • • • . • • • •
4.1


General Data Acquisition System ••

15

4.2

Static Pressure Measurement Set Up.

15

4.3

y-Densitometer for Void Fraction Heasurements

17

4.3.1
4.3.2
4.3.3
5

15

Low Activi ty Single-Beam Densitometer for Axial
Distributions of Centerline Void Fractions.

20

Multibeam y-Densitometer for Transverse and
Axial Void Distributions

••...•

20

High Activity Single-Beam y-Densitometer for
Transverse and Axial Void Distributions ••

22
27

EXPERIMENTAL RESULTS • • •
5.1

Pressure Distributions and Photographic Observations.
5.1.1

Single-Phase Pressure Calibration . • • • . •

- vii -

27
27


5.1.2

5.2

5.4


Reproducibility Studies ••

32

B.

Operational Effects (Effect of Back Pressure)

32

C.

Parametr ic Effects.

38

D.

Flashing Upstream of the Throat •

45

5.6

45

5.2.1

Gamma Densitometer Calibration.


45

5.2.2

Axial Distributions of the Centerline Diametrical
Averaged Void Fractions for Flashing Close to
the Throat. . . . . . . . . . . . . . . . . . . • .

60

Axial Distributions of the Centerline Diametrical
Averaged Void Fractions for Flashing Upstream
from the Throat • • • • • •

66

Axial Distributions of Area Averaged Void Fractions
Obtained by Means of the Five-Beam Gamma Densitometer ••

66.

5.3.1

Calibrations ••

66

5.3.2

Transverse Void Distributions and Area Averaged

Void Fractions ••

72

Axial Distributions of Area Averaged Void Fractions
Obtained by Means of the High Activity Single Beam
Gamma Densitometer

...

5.5

27

A.

Measurement of the Axial Distribution of the Centerline
Diametrical Averaged Void Fraction by a Low Activity SingleBeam Gamma Densitometer. • • • • • • • ••
••• • •

5.2.3

5.3

Pressure Distributions Under Flashing Conditions..

....

84


5.4.1

Cal ibrations.

·····

84

5.4.2

Transverse Void Distributions and Area Averaged
Void Fract ions.

86

....

Summary of Exper imental Results:
and Area Averaged Void Profiles.

·······

Pressure Distributions

5.5.1

149 C Inlet Temperature Runs.

5.5.2


121 C Inlet Temperatur e Runs.

5.5.3

100 C Inlet Temperatur e Runs •

5.5.4

Two-Phase Inlet Conditions.

86

····
····..

..··
.·······

100
104
119
123

Calculations of Net Vapor generation Rates Under Flashing
Conditions. . . . . . . . . . . . .

- viii -

. . . . ..


123


VOLUME II - MODELING
6

ANALYTICAL MODELING AND COMPARISON WITH EXPERIMENTS •
6.1

Introduc tion . . .

141

6.2

Flashing Inception.

145

6.3

6.2.1

Static Depressurization Results.

145

6.2.2

Flashing Inception in Flowing Systems


147

6.2.3

Pipe Flows . .

151

6.2.4

Nozzle Flows.

153

Vapor Generation Rate.

162

6.3.1

6.3.2

7

141

Bubbly Flow.

Low Void Fraction Model (a


~

0.30)..

A.

Model.

162

B.

Application to Pipe Flows •

170

Gener a1 Model •

177

A.

Model.

177

B.

Application to BNL Nozzle Data.


196

COMPARISON OF TRAC-PIA PREDICTIONS WITH EXPERIMENTAL DATA •
7.1

7.2

162

217

Comparison of TRAC-PIA Predictions with Experimental Data
Consisting of Pressure and Diametrical Averaged Centerline
Vo id Fr ac t ions • • • • • • • • • •

217

Comparison of TRAC-PIA Predictions with Experimental Data
Consisting of Pressure and Area Averaged Void Profiles

223

7.2.1
7.2.2

Comparison with Runs Per formed at a Nominal
Inlet Temperature of lOODC.

228


Comparison with Runs Performed at a Nominal
Inlet Temperat ureof 121 DC.

228

Comparison with Runs Performed at a Nominal
Inlet Temper a tur e of 149°C.

240

············

············

7.2.3

············

- ix -


8

SUHMARY AND CONCLUS IONS •

253

9


ACKNOWLEDGEMENTS.

257

REFERENCES. • • • •

258

10

APPENDICES TO VOLUHE II
Appendix I • • •

264

Appendix II ••

273

VOLUHE III - DATA
(Hicrof iche)
NOTES TO APPENDICES
Appendix A.

Single Phase Calibration Data • • • • • • • • • •

Appendix B.

Pressure Distribution Data Under Flashing
Conditions • • • • • • •


Appendix C.

Pressure and Centerline Diametrical Averaged Void
Fraction Distributions Obtained wi th the Low
Activity Single Beam Densitometer • • • • • • • •

Appendix D.

Pressure and Detailed Transverse and Area Averaged
Void Fraction Di stributions Obtained wi th the
l1ulti Beam Gamma Densitometer • • • • • •

Appendix E.

Pressure and Detailed Transverse and Area Averaged
Void Fr action Di stributions Obtained wi th the
High Activity Single Beam Gamma Densitometer • • •

-

x -


LIST OF FIGURES

3.1

Schematic of BNL Heat Transfer Facility.


3.2

Inside Dimensions of TS-2.

3.3

Deviation From Design of TS-2 Inside Dimensions.

3.4

Schematic Representation of the Test Section.

4.1

Graphical Representation of the Data Acquisition System

4.2

Schematic Representation of y-Densitometer.

4.3

Photograph of the Five Beam Gamma Densitometer.

4.4

Horizontal and Vertical Cross Sections of the Source Holder.

4.5


Schematic Representation of the Detector Holder .

. 5.1

Typical Pressure Distributions Along TS-2 for the Single-Phase Flow
Hydrodynamic Calibration Runs.

5.2

Dimensionless Pressure Distribution for TS-2. Data are Averaged for
All the Hydrodynamic Calibration Runs Performed.

5.3

Typical Representation of an Isothermal Flashing Experiment in the p-T
Diagram.

5.4

Pressure Distributions Under Flashing and Nonflashing Conditions in
TS-2.

5.5

Dimensionless Pressure Distributions in TS-2 Under Flashing Conditions
Compared With Single-Phase Hydrodynamic Calibration Data.

5.6

Comparison of Pressure Distribution in Two Experiments to Show the

Reproducibility of the Results at Low Mass Fluxes, G = 3.03 Mg/m 2 s.

5.7

Comparison of Pressure Distributions in Two Experiments to Show
Reproducibility of the Results at High Mass Flux, G = 4.45 Mg/m 2 s.

5.8

Pressure Distributions Showing the Effect of Condensing Tank Back
Pressure for Identical Nozzle Inlet Conditions.

- xi -


5.9

Photographic Observations for the Experimental Conditions Presented in
Fig. 5.8. In these and all the following photographs, the diameter of
both the front and rear windows is 50 mm.

5.10

Effect of Mass Flux on Pressure Distributions for Identical Nozzle
Inlet Conditions Which are Close to Those For Onset of Flashing in the
Test Section.

5.11

Photographic Observations for the Experimental Conditions Presented

in Fig. 5.10.

5.12

Effect of Mass Flux on the Pressure Distributions in the Test Section.

5.13

Photographic Observations for the Experimental Conditions Presented in
Fig. 5.12.

5.14

Effect of Nozzle Inlet Temperature at Constant Pin-Psat (Tin)
on the Pressure Distribution in the Test Section.

5.15

Photographic Observations for Experimental Conditions Presented in
Fig. 5.14.

5.16

Effect of Nozzle Inlet Temperature at Constant Pin-Psat (Tin)
on the Pressure Distribution in the Nozzle.

5.17

Effect of Nozzle Inlet Temperature at Constant Pin-Psat (Tin)
on the Pressure Distribution in the Nozzle.


5.18

Effect of Nozzle Inlet Temperature at Constant Pin-Psat (Tin)
on the Pressure Distribution in the Nozzle.

5.19

Photographic Observations for Experimental Conditions Presented in
Fig. 5.16 and 5.18.

5.20

Effect of Nozzle Inlet Pressure on the Pressure Distributions in the
Test Section.

5.21

Effect of Nozzle Inlet Pressure on the Pressure Distributions in the
Test Section.

5.22

Effect of Nozzle Inlet Pressure on the Pressure Distributions in the
Test Section.

5.23

Pressure Distributions in the Test Section While The Flashing Onset is
Upstream From the Nozzle Throat.


- xii -


5.24

Nondimensiona1 Pressure Distributions DP* = DP/1/2 Uo in the Test
Section While the Flashing Onset is Upstream From the Nozzle Throat

5.25

Calibration of the test Section Both Empty (Air) and Full of Water as
a Function of Axial Distance.

5.26

Pressure and axial void fraction distributions in the test section.
Plot of the difference between the dimensionless measured pressure
drop and the nondimensiona1 pressure drop measured in the single phase
calibration (DDP = DPi - DP~) as a function of axial distance.

5.27

Pressure and axial void fraction distributions in the test section.
Plot of the difference between the dimensionless measured pressure
drop and the nondimensiona1 pressure drop measured in the single phase
calibration (DDP = DP~ - DP~) as a function of axial distance.

5.28


Pressure and axial void fraction distributions in the test section.
Plot of the difference between the dimensionless measured pressure
drop and the nondimensiona1 pressure drop measured in the single phase
calibration (DDP = DP~ - DP~) as a function of axial distance.

5.29

Pressure and axial void fraction distributions in the test section.
Plot of the difference between the dimensionless measured pressure
drop and the nondimensiona1 pressure drop measured in the single phase
calibration (DDP = DP~ - DP~) as a function of axial distance.

5.30

Pressure and axial void fraction distributions in the test section.
Plot of the difference between the dimensionless measured pressure
drop and the nondimensiona1 pressure drop measured in the single phase
calibration (DDP = DP~ - DP~) as a function of axial distance.

5.31

Pressure and axial void fraction distributions in the test section.
Plot of the difference between the dimensionless measured pressure
drop and the nondimensiona1 pressure drop measured in the single phase
calibration (DDP = DP~ - DP~) as a function of axial distance.

5.32

Pressure and axial void fraction distributions in the test section •
. P1ot of the difference between the dimensionless measured pressure

drop and the nondimensiona1 pressure drop measured in the single phase
calibration (DDP = DPi - DP~) as a function of axial distance.

5.33

Pressure and axial void fraction distributions in the test section
with flashing occurring upstream from the nozzle throat. Plot of the
difference between the dimensionless measured pressure drop and the
nondimensiona1 fressure drop measured in the single phase calibration,
(DDP = DP~ - DP c ) as a function of axial distance.

- xiii -


5.34

Pressure and Axial Void Fraction Distributions in the Test Section
With Flashing Occurring Upstream From The Nozzle Throat. Plot of the
Difference Between the Dimensionless Measured Pressure Drop and the
Nondimensional Pressure Drop Measured in the Single Phase Calibration,
(DDP = DPm*- D~) as a Function of Axial Distance.

5.35

Normalized Calibrations of the Empty Test Section at Five Different
Axial Locations.

5.36

Normalized Calibrations of the Full Test Section at Five Different

Axial Locations.

5.37

Radial Distributions of the Chordal Averaged Void Fractions at Various
Axial Locations Obtained by the Five Beam Gamma Densitometer for
Run 130.

5.38

Radial Distributions of the Chordal Averaged Void Fractions at Various
Axial Locations Obtained by the Five Beam Gamma Densitometer for
Run 130.

5.39

Radial Distributions of the Chordal Averaged Void Fractions at Various
Axial Locations Obtained by the Five Beam Gamma Densitometer for
Run 130.

5.40

Radial Distributions of the Chordal Averaged Void Fractions at Various
Axial Locations Obtained by the Five Beam Gamma Densitometer for
Run 130.

5.41

Radial Distributions of the Chordal Averaged Void Fractions at Various
Axial Locations Obtained by the Five Beam Gamma Densitometer for

Run 130.

5.42

Radial Distributions of the Chordal Averaged Void Fractions at Various
Axial Locations Obtained by the Five Beam Gamma Densitometer for
Run 130.

5.43

Radial Distributions of the Chordal Averaged Void Fractions at Various
Axial Locations Obtained by the Five Beam Gamma Densitometer for
Run 130.

5.44

Axial Distributions of the Area Averaged Void Fractions (A) and of the
Pressure Drop (B) in the Test Section. Runs 129 and 130 were Performed
under the Following Conditions: Pin = 380 kPa~ Tin = 99.9 C,
Pct = 127 kPa at inlet mass flux of 5.97 Mg/m s.

5.45

Normalized Calibrations of the Empty Test Section at Five Different
Axial Locations.

5.46

Normalized Calibrations of the Full Test Section at Five Different
Axial Locations.


- xiv -


5.47

Radial Distributions of the Chordal Averaged Void Fractions at Various
Axial Locations Obtained by the High Activity Single Beam Gamma
Densitometer for Run 310.

5.48

Radial Distributions of the Chordal Averaged Void Fractions at Various
Axial Locations Obtained by the High Activity Single Beam Gamma
Densitometer for Run 310.

5.49

Radial Distributions of the Chordal Averaged Void Fractions at Various
Axial Locations Obtained, by the High Activity Single Beam Gamma
Densitometer for Run 310.

5.50

Radial Distributions of the Chordal Averaged Void Fractions at Various
Axial Locations Obtained by the High Activity Single Beam Gamma
Densitometer for Run 310.

5.51


Radial Distributions of the Chordal Averaged Void Fractions at Various
Axial Locations Obtained by the High Activity Single Beam Gamma
Densitometer for Run 310.

5.52

Radial Distributions of the Chordal Averaged Void Fractions at Various
Axial Locations Obtained by the High Activity Single Beam Gamma
Densitometer for Run 310.

5.53

Axial distributions of the area-averaged and the centerline
diametrical void fractions (A) and of the pressure drop (B) in the
test section. Runs 309 and 310 were performed under the following
conditions: Pin = 555.9 kPa, Tin = 149.1 C, Pct = 378.3 kPa
and at a mass flow rate of 8.8 kg/so

5.54

Axial Distributions of the Pressure (A) and Area Averaged Void Fraction
(B) for Runs Performed at an Inlet Temperature of-149°C and Several
Inlet Mass Fluxes.

5.55

Axial Distributions of Pressure (A) and Area Averaged Void Fraction
(B) for Runs Performed at an Inlet Temperature of 149°C, a Constant
Inlet Mass Flux of 4300 kg/m 2 s, and Decreasing Nozzle Exit or
Condensing Tank, Pressure.

'

5.56

Three Dimensional Representation of the Chordal Averaged Void Fraction
Distributions Along the Test Section.

5.57

Three Dimensional Representation of the Chordal Averaged Void Fraction
Distributions Along the Test Section.

5.58

Radial Distributions of the Chordal Averaged Void Fractions at Four
Axial Locations Obtained by the High Activity Single Beam Densitometer
for Run 306.

- xv -


5.59

Radial Distributions of the Chordal Averaged Void Fractions at Four
Axial Locations Obtained by the High Activity Single Beam Densitometer
for Run 310.

5.60

Comparison of Centerline Diametrical Averaged Void Fraction

Distributions with the Area Averaged Void Fractions at the Same Axial
Locations for Runs 306 and 310.

5.61

Axial Distributions of Pressure (A) and Area Averaged Void Fraction (B)
for Five Runs Performed at an Inlet Temperature of 121°C and Increasing
Inlet Mass Flux.

5.62

Comparison of Axial Distributions of Pressure (A) and Area Averaged
Void Fraction (B) for Two Runs Performed Under "Identical" Conditions.
Data in Runs 133-136 Were Recorded with the Five-Beam Gamma
Densitometer with the High Activity Single Beam Densitometer.

5.63

Axial Distributions of Pressure (A) and Area Averaged Void Fraction (B)
for Runs Performed at an Inlet Temperature of 121°C, a Constant Inlet
Mass Flux, and Decreasing Nozzle Exit or Condensing Tank Pressure

5.64

Three Dimensional Representation of the Chordal Averaged Void Fraction
Distributions Along the Test Section.

5.65

Three Dimensional Representation of the Chordal Averaged Void Fraction

Distributions Along the Test Section.

5.66

Three Dimensional Representation of the Chordal Averaged Void Fraction
Distributions Along the Test Section.

5.67

Three Dimensional Representation of the Chordal Averaged Void Fraction
Distributions Along the Test Section.

5.68

Three Dimensional Representation of the Chordal Averaged Void Fraction
Distributions Along the Test Section.

5.69

Axial Distributions of Pressure (A) and Area Averaged Void Fraction (B)
for Runs 149-153, Performed at an Inlet Temperature of 121°C with MgO
Particulates Present in the Water Loop.

5.70

Axial Distributions of Pressure (A) and Area Averaged Void Fraction (B)
for Five Runs Performed at an Inlet Temperature of 100°C and Increasing
Inlet Mass Fluxes (Five Beam Gamma Densitometer).

- xvi -



5.71

Axial Distributions of Pressure (A) and Area Averaged Void Fraction (B)
for Three Runs Performed with the High Activity Single Beam
Densitometer, at an Inlet Temperature of 100°C, and Increasing Inlet
Mass Fluxes.

5.72

Axial Distributions of Pressure (A) and Area Averaged Void Fraction (B)
for Several Runs Performed at an Inlet Temperature of 121°C and Single
and Two-Phase Inlet Conditions.

5.73

Three Dimensional Representation of the Chordal Averaged Void Fraction
Distributions Along the Test Section.

5.74

Three Dimensional Representation of the Chordal Averaged Void Fraction
Distributions Along the Test Section.

5.75

Three Dimensional ~epresentation of the Chordal Averaged Void Fraction
Distributions Along the Test Section.


5.76

Axial Distributions of Pressure (A) and Area Averaged Void Fraction (B)
for Two Runs Performed at Similar Inlet Conditions but Varying
Condensing Tank Pressure.

5.77

Axial Distributions of Pressure (A) and Area Averaged Void Fraction (B)
for Two Runs Performed at an Inlet Temperature of 121°C, Two-Phase
Inlet Conditions, and at Two Inlet Mass Fluxes.

5.78

Top: Measured Pressure (0) and Void Fraction (Q) Distributions in the
Converging Part of the Test Section in Runs 82/821 and the Least Square
Po1ynomina1 Fit to Data. B,ottom: Calculated Net Vapor Generation Rate
Based on the Least Square Fit to the a and p Data.

5.79

Results of Calculation on Data of Runs 80/801. (A) and (B): Pressure
and Void Fraction Distributions;cr, Measured; ---- Cubic Spline Fit;
+, Optimum Knot Locations. (C), (D), and (E): Calculated Value of Rate
of Vapor Generation rv for Three Values of the Distribution Parame.ter
Co·

5.80

Results of Calculations on Data of Runs 141/142. Pin = 240 kPa,

2
.
Tin
121.3 C, Gin
2.97 Mg/m s, Psat (Tin) = 207 kPa,
Pct = 236 kPa, Tct = 121.6 C.

5.81

Results of Calculations on Data of Runs 145/146. Pin
306 kPa,
Tin
121.2 C, Gin
3.70 Mg/m 2 s, Psat (Tin) = 206 kPa,
Pct = 234 kPa, Tct = 121.7 C.

- xvii -


5.82

Results of Calculations on Data of Runs 133/134. Pin = 350 kPa,
Tin
121.2 C, Gin
4.43 Mg/m 2 s, Psat (Tin) = 206 kPa,
Pct = 233 kPa, Tct = 121.7 C.

5.83

Results of Calculations on Data of Runs 140/139. Pin = 465 kPa,

Tin
121.2 C, Gin
5.91 Mg/m 2 s, Psat (Tin) = 206 kPa,
Pct = 234 kPa, Tct = 121.6 C.

6.1

The Flashing Inception Undershoot (Ps - PFio) Predicted by the
Alamgir-Lienhard Correlation.

6.2

Flashing Inception Undershoots and Equivalent Superheats Computed
by the Alamgir-Lienhard Correlation (1979).

6.3

Comparison of the Flashing Inception Data of Reocreux (1974) and of
Seynhaeve, et al (1976) with the Theory Developed by Jones (1979)
Using the Approximate Static Flashing Overexpansion Value of 18 kPa
for the Computation Jones (1979).

6.4

Pressure Distributions for Two Experiments (Run 36, 51) Under 18.3 and
50°C Subcooled Inlet Conditions (Brown, 1961).

6.5

Variation of the Discharge Coefficient with the Reynolds Number for

Data in a Converging-Diverging Nozzle with Subcooled Liquid Inlet
Conditions. Brown (1961), CD = 0.910 + 0.037; Sozzi and Sutherland
(1975), CD=0.918 ~ 0.058; Zimmer, et aT (1979), CD=0.931+0.039.

6.6

Comparison of the Flashing Inception Predicted by Alamgir and
Lienhard (1979) (solid line) with the Locus of the Liquid
Depressurization History (circles connected by dashed line) in Brown's
Nozzle (1961).

6.7

Comparison of the Flashing Inception Predicted by Alamgir and
Lienhard (1979) (solid line) with the Locus of the Depressurization
History in BNL's Nozzle (Runs 76 to 79).

6.8

Comparison of the Flashing Inception Predicted by Alamgir and Lienhard
(1979) (solid line) with the Locus of the Depressurization History in
Reocreux' Pipe Experiments (1974).

6.9

Variation of Surface Area Density With Void Fraction.

6.10

Comparison of Plesset and Zwick (1954) and Forster and Zuber (1954,

1955) Heat Transfer Coefficient with Measured Instantaneous Heat
Transfer Coefficient of Steam-Water During Variable Liquid Superheating.

6.11

Comparison of Plesset and Zwick (1954) and Forster and Zuber (1954,
1955) Heat Transfer Coefficient with Measured Instantaneous Heat
Transfer Coefficient of Nitrogen During Variable Liquid Superheating.

- xviii -


6.12

Variation of a with ?r and ZNVG in Present Model and Comparison
with Experimental Data of Reocreux.

6.13

Void Fraction Distribution in a Constant Area Channel as a Function
of Mass Flux G. Tin ~ 116 C. 0, Measurements by Reocreux (1974);
, Calculations Based on the
Values Shown.

cr

6.14

Void Fraction Distribution in a Constant Area Channel as a Function of
Mass Flux G. Tin ~ 121 C. 0, Measurements by Reocreux (1974);

----- , Calculations Based on the
Values Shown.

cr

6.15

Void Fraction Distribution in a Constant Area Channel as a Function of
Mass Flux G. Tin ~ 126 C. 0, Measurements by Reocreux (1974);
----- , Calculations Based on the
Values Shown.

cr

6.16

Effect of Expansion Rate on the Pressure at the Point of Net Vapor
Generation.

6.17

Variation of Point of Net Vapor Generation ZNVG with Mass Flux G and
Initial Temperature Tin in Flashing Flow. Values of ZNVG which
Give "Best Fit" to Reocreux's (1974) Data.

6.18

Variation of Cr with Mass Flux G and Initial Temperature Tin in
Flashing Flow, Values of C Which Give "Best Fit" to Reocreux's (1974)
r

Data.

6.19

The Flow Regimes Map for the General Model.

6.20

Comparison of Correlation of Table 6.2 with Experiment.

6.21

Nomenclature of Bubbly-Slug Flow.

6.22

Surface to Volume Ratios for Cylinders and Spherical Caps.

6.23

Heat and Mass Transfer Rates for Spheres.

6.24

Comparison Between the Void Fraction Data for Run 353 and The "BestFi t" Calculation Using the General Model.

6.25

Comparison Between the Void Fraction Data for Run 358 and the
"Best-Fit" Calculation Using the General Model.


6.26

Comparison Between the Void Fraction Data for Run 362 and the
"Best-Fit" Calculation Using the General Model.

6.27

Comparison Between the Void Fraction Data for Run 145 and the
"Best-Fit" Calculation Using the General Model.

6.28

Comparison Between the Void Fraction Data for Run 137 and the
"Best-Fit" Calculation Using the General Mode.

- xix -


6.29

Comparison Between the Void Fraction Data for Run 137 and the
"Best-Fit" Calculation Using the General Model.

6.30

Comparison Between the Void Fraction Data for Run 344 and the
"Best-Fit" Calculation Using the General Model.

6.31


Comparison Between the Void Fraction Data for Run 291 and the
"Best-Fit" Calculation Using the General Model.

6.32

Comparison Between the Void Fraction Data for Run 284 and the
"Best-Fit" Calculation Using the General Model.

6.33

Comparison Between the Void Fraction Data for Run 273 and the
"Best-Fit" Calculation Using the General Model.

6.34

Comparison Between the Void Fraction Data for Run 278 and the
"Best-Fi t" Calculation Using the General Model.

6.35

Comparison Between the Void Fraction Data for Run 296 and the
"Best-Fit" Calculation Using the General Model.

6.36

Comparison Between the Void Fraction Data for Run 268 and the
"Best-Fit" Calculation Using the General Model.

6.37


Comparison Between the Void Fraction Data for Run 304 and the
"Best-Fit" Calculation Using the General Model.

6.38

Comparison Between the Void Fraction Data for Run 309 and the
"Best-Fit" Calculation Using the General Model.

6.39

The Optimum Bubble Number Density at the Inception Point vs.
the Liquid Superheat at the Inception Point.

6.40

The Interfacial Area Density at the Inception Point vs. the
Liquid Superheat at the Inception Point.

7.1

Comparison of TRAC Predictions with BNL Experimental Results.
79. Gin = 2270 kg/m 2 s, Pin = 124 kPa, Tin = 99.4°C.

Run No.

7.2

Comparison of TRAC Predictions with BNL Experimental Results.
78. Gin = 2610 kg/m 2 s, Pin = 138 kPa, Tin = 99.3°C.


Run No.

7.3

Comparison of TRAC Predictions and Homogeneous Equilibrium Calculations
with BNL Experimental Results. Run No. 77. Gin = 3060 kg/m 2 s,
Pin = 157 kPa, Tin = 99.4°C.

- xx -


7.4

Comparison of TRAC Predictions and Homogeneous Equilibrium Calculations
with BNLExperimental Results. Run No. 76. Gin = 6040 kg/m 2 s,
Pin = 395 kPa, Tin = 99.3°C.

7.5

Comparison of TRAC Predictions with BNL Experimental 'Results.
80-801 •. Gin = 4360 kg/m 2s, Pin = 585 kPa, Tin = l48.3°C.

7.6

Comparison of TRAC-PIA Predictions With BNL Experimental Data for
Pressure Distributions and Area Averaged Void Profiles. Pin = 143
kPa, Tin = 99.9 C, Gin = 2.28 Mg/m 2s, Pct = 127 kPa, ~nd
Tct = 100.4 C (mexp =4.6 kg/s, IIlTRAC = 4.8 kg/s).


7.7

Comparison of TRAC-PlA Predictions with BNL Experimental Data for
Pressure Distributions and Area Averaged Void Profiles. Pin = 171
kPa, Tin = 100.2 G, Gin = 3.01 Mg/m 2 s, Pct = 133 kPa, and
Tet = 100.7 C (m exp = 6.1 kg/s, mTRAC = 6.0 ,kg/s).

7.8

Comparison of TRAC-PlA Predictions With BNL Experimental Data for
Pressure Distributions and Area Averaged Void Profiles. Pin = 248
kPa, Tin = 100 C, Gin = 4.49 Mg/m 2s, Pet = 127 kPa, and
Tct = 100.5 C (mexp = 9.1 kg/s, IIlTRAC = 8.6 kg/s).

7.9

Comparison of TRAC-PIA Predictions With BNL Experimental Data for
Pressure Distributions and Area Averaged Void Profiles. Pin = 247
kPa, Tin = 100 C, Gin = 4520 kg/m 2 s, Pet = 113 kPa, and
Tct = 100 C.

7.10

Comparison of Experimentally Measured Pressure Distributions and Area
Averaged Void Profiles, as well as Vapor Generation Rates Calculated
From the Experimental Data With TRAC-PlA Predictions. Pin =241 kPa,
Tin 121.3 C, Gin = 2.97 Mg/m 2 s, Pet = 237 kPa, Tct = 121.7 C.

7.11


Comparison of TRAC-PlA Predictions With BNL Experimental Data for
Pressure Distributions and Area Averaged Void Profiles.' Pin = 305
kPa, Tin = 121.2 C, Gin = 3.7 Mg/m 2 s, Pct = 234 kPa, and
Tct= 121.7 C (m exp = 7.5 kg/s, mTRAC = 7.0 kg/s).

7.12

Comparison of Vapor Generation Rates Calculated From Experimental Data
With TRAC-PIA Predictions for Run 145 Presented in Figure 7.11.

7.13

Comparison of TRAC-PIA Predictions With
Pressure Distribution and Area Averaged
Tin
121.2 C, Gin = 4430 kg/m 2 s, Pet =
Tct = 121.7 C (mexp = 8.9 kg/s, mTRAC =

- xxi -

Run No.

BNL Experimental Data for
Void Profiles. Pin = 349
233 kPa, and
8.4 kg/s).