Study of nonequilibrium flashing of water in a converging diverging nozzle volume 1 experimental v1

,

NUREG/CR-1864
BNL-NUREG-51317
VOL. 1 of 3

NUREGCR1864V-1 ~------------"1R2
.~~I~~I~~~~~~I!I"- __ ~

~'

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

----REPRODUCED BY:

--,

~

u.s. Department of Commerce .
National Technical Information Service
Springfield, Virginia 22161


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
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,

fI


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 research. 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 with him during his involvement with 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-27l38 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-260Sl, 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-S0997, March 1979; also Rev. Sci. Instrum., 50(10),
pp. 1260-1263, 1979.
ABUAF, N., WU, 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 Subcoo1ed Inlet Conditions," BNL-NUREG-27512, March 1980; also
"Polyphase Flow and Transport Technology, R. A. Bajura ed., ASME, Aug. 1980.
ABUAF, N., WU, 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 SARA, 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 Info 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-S0907, 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-50661,
BNL-NUREG-50683,
BNL-NUREG-50747,
BNL-NUREG-S0785,
BNL-NUREG-50820,
BNL-NUREG-S0883,
BNL-NUREG-5093l,
BNL-NUREG-50978,
BNL-NUREG-S101S,
BNL-NUREG-S108l,
BNL-NUREG-S1131,
BNL-NUREG-Sl178,
BNL-NUREG-5l2l8,
BNL-NUREG-S1225 ,
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. 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° < 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 ICAT IONS

iv

ABSTRACT. • •

vi

LIST OF FIGURES.

xi

LIST OF TABLES

xxiv

NOMENCLATURE •

xxvi

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 Fr action Measur ements •

17

4.3.1
4.3.2
4.3.3
5

15

Low Activity 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

EXPERIMENTAL RESULTS • • •
5.1

27

Pressure Distributions and Photographic Observations.
5.1.1

Single-Phase Pressure Calibration • • • . • •

- vii -

27

27


5.1.2

5.2

·
....·

Pressure Distributions Under Flashing Cond i t ions.

..

A.

Re pr od ucib il i t Y Stud i e s

B.

Operational Effects (Effect of Back Pr essur e)

C.

Parametric Ef fect s.

38

D.

Flashing Upstream

45

........
of the Throat .
...·

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

5.2.2

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

5.4

5.5

5.6

32

45

60

Axial Distributions of the Centerline Diametrical
Averaged Void Fractions for Flashing Upstream
fr om. the Thr 0 at. . . . . . . . . . . . . . . . . .

5.3

32

45

5.2.1

5.2.3

27

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

66

66.

5.3.1

Calibrations ••

66

5.3.2

Transverse Void Distributions and Area Averaged
Void Fractions. • • • • • • • •

72

Axial Distributions of Area Averaged Vo id Fr actions
Obtained by Means of the High Activity Single Beam
Gamma Densitometer. • •
• •••

84

5.4.1

Calibrations.

84

5.4.2

Transverse Void Distributions and Area Averaged
Void Fractions. • • • •
• • • • • • •

86

Summary of Experimental Results:
and Area Averaged Void Profiles.

Pressure Distributions
• • • •

86

5.5.1

149 C Inlet Temperature Runs.

100

5.5.2

121 C Inlet Temperature Runs • • • • • • • • •

104

5.5.3

100 C Inlet Temperature Runs.

119

5.5.4

Two-Phase Inlet Conditions.

123

CalculatiQns of Net Vapor generation Rates Under Flashing
Condi t ions . . . . . . . . . . . . .

- viii -

. . . . ..

123


VOLUME II - MODELING
6

ANALYTICAL MODELING AND COMPARISON WITH EXPERIMENTS •
6.1

Introduction ••

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 . • •
6.3.1

6.3.2

7

141

Bubbly Flow.

Low Void Fraction Model (a

162

< 0.30)..

A.

Model.

162

B.

Application to Pipe Flows •

170

General 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
Void Fractions. • • • • • • • • • • • • • • • • • • • • ••

217

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

223

7.2.1
7.2.2
7.2.3

Comparison with Runs Performed at a Nominal
Inlet Temperatur e of 100°C. . • • • • • • •

228

Comparison with Runs Performed at a Nominal
Inlet Temperature of 121°C• • • • • • • • •

228

Comparison with Runs Performed at a Nominal
Inlet Temperature of 149°C • • • • • • • • •

240

- ix -


8

SUMMARY AND CONCLUSIONS.

253

9

ACKNOWLEDGEMENTS.

257

10

REFERENCES. • • •

258

APPENDICES TO VOLUME II
Appendix I ••

264

Appendix II

273

VOLUME III - DATA
(Microfiche)
NOTES TO APPENDICES
Appendix A.
Appendix B.

Single Phase Calibration Data • • • . • •
Pressure Distribution Data Under Flashing
Conditions . • • • . • • • . . . • •

Appendix C.

Pressure and Centerline Diametrical Averaged Void
Fraction Distributions Obtained with the Low

Activity Single Beam Densitometer • • • • • • • •

Appendix D.

Pressure and Detailed Transverse and Area Averaged
Void Fraction Distributions Obtained with the
Multi Beam Gamma Densitometer • • • • • • • • • •

Appendix E.

Pressure and Detailed Transverse and Area Averaged
Void Fraction Distributions Obtained with 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 SO moo.

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

Nondimensional Pressure Distributions DP* = DP/I/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 nondimensional 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 nondimensional 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 nondimensional 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 nondimensional 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 nondimensional 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 nondimensional 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.
Plot of the difference between the dimensionless measured pressure
drop and the nondimensional 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
nondimensional 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 Conditionsr

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 Representation 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. Bottom: 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;CJ, Measured; ---- Cubic Spline Fit;
+, Optimum Knot Locations. (C), (D), and (E): Calculated Value of Rate
of Vapor Generation r v for Three Values of the Distribution Parameter
Co·

5.80

Results of Calculations on Data of Runs 141/142. Pin = 240 kPa,
Tin
121.3 C, Gin = 2.97 Mg/m 2 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/m2 s, Paat (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 al (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 A1amgir 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 -

cr

6.12

Variation of a with
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. o. 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. o. 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. o. Measurements by Reocreux (1974);
----- • Calculations Based on the cr Values Shown.

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 "BestFit" 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-Fi t" 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-Fit" 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 BNL Experimental 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 2 s. Pin = 585 kPa. Tin = l48.3°C.

7.6

Comparison of TRAC-PIA
Pressure Distributions
kPa. Tin = 99.9 C. Gin
Tct = 100.4 C (mexp =

7.7

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

7.8

Comparison of TRAC-PIA 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/so ffiTRAC = 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-PIA 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-PIA 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. Pet = 234 kPa. and
Tct = 121.7 C (m exp = 7.5 kg/so 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/so mTRAC =

Run No.

Predictions With BNL Experimental Data for
and Area Averaged Void Profiles. Pin = 143
= 2.28 Mg/m 2s. Pet = 127 kPa. and
4.6 kg/so ffiTRAC = 4.8 kg/s).

- xxi -

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


7.14

Comparison of Vapor Generation Rates Calculated From Experimental Data
With TRAC-PIA Predictions for Run 133 Presented in Figure 7.13.

7.15

Comparison of Experimentall Measured Pressure Distributions and Area
Averaged Void Profiles as well as Vapor Generation Rates Calculated
from the Experimental Data with TRAC-PlA Predictions. Pin = 464 kPa,
Tin = 121.6 C, Gin = 5.9 Mg/m 2 s, Pct = 234 kPa, Tct = 121.6 C

7.16

Comparison of TRAC-PIA Predictions With BNL Experimental Data for
Pressure Distributions and Area Averaged Void Profiles for Runs 339342. Pin = 320 kPa, Tin 121 C, Gin = 4430 kg/m 2 s, Pct = 240
Tct = 121 C.

7.17

Comparison of TRAC-PIA Predictions With BNL Experimental Data for
Pressure Distributions and Area Averaged Void Profiles for Runs 322325. Pin = 341 kPa, Tin 121 C, Gin = 4410 kg!m 2 s, Pct = 200
Tct = 121 C.

7.18

Comparison of TRAC-PlA Predictions With BNL Experimental Data for
Pressure Distributions and Area Averaged Void Profiles for Runs 313316. Pin = 341 kPa, Tin = 121 C, Gin·= ~430 kg!m 2 s, Pct =
Tct = 119 C.

7.19

Comparison of TRAC-PIA Predictions With BNL Experimental Data for
Pressure Distributions and Area Averaged Void Profiles for Runs 318321. Pin 322 kPa, Tin = 121 C, Gin = 4430 kg!m 2 s, Pct = 156
Tct = 113.5 C.

7.20

Comparison of TRAC-PlA Predictions With BNL Experimental Data for
Pressure Distributions and Area Averag~d Void Profiles for Runs 264266. Pin = 515 kPa, Tin 149 C, Gin = 2860 kg/m 2 s, Pct = 478
Tct = 149 C.

7.21

Comparison of TRAC-PIA Predictions With BNL Experimetnal Data for
Pressure Distributions and Area Averaged Void Profiles for Runs 291295. Pin = 502 kPa, Tin = 148.9 C, Gin = 3170 kg/m 2 s, Pct =
Tct = 148.9 C.

7.22

Comparison of TRAC-PlA Predictions With BNL Experimental Data for
Pressure Distributions and Area Averaged Void Profiles for Runs 284288. Pin = 530 kPa, Tin = 149.2 C, Gin = 3580 kg/m 2 s, Pct =
Tct = 149.2 C.

7.23

Comparison of TRAC PIA Predictions With BNL Experimental Data for
Pressure Distributions and Area Averaged Void Profiles for Runs 273277. Pin = 573 kPa, Tin = 148.7 C, Gin = 4290 kg/m 2 s, Pct =
Tct = 148.8 C.

7.24

Comparison of TRAC-PIA Predictions With BNL Experimental Data for
Pressure Distributions and Area Averaged Void Profiles for Runs 279283. Pin = 688 kPa, Tin = 148.8 C, Gin = 5730 kg/m 2 s, Pct =
Tct = 148.8 C.

- xxii

7.25

Comparison of TRAC-PIA Predictions With BNL Experimental Data for
Pressure Distributions and Area Averaged Void Profiles for Runs 309311. Pin = 556 kPa, Tin = 149.1 C, Gin = 4330 kg/m 2 s, Pct =
Tct = 142 C.

A.l

Schematic Representation of a One-Dimensional Nonequilibrium
Vaporization Front.
Hugoniot Curve of Vaporization Front at PI
Experiment Run 77.

80 kPa in BNL Flashing

A.3

Comparison of Experimental Mass Flux Gexp and Critical Mass Flux
Gcr at C-J Point in BNL Experiment Run 77.

A.4

Comparison of Experimental Mass Flux Gexp and Critical Mass Flux
Gcr at C-J Point in Run 56 of Schrock, et al., (1977).

A.5

Comparison of Critical Throat Mass Fluxes Measured by Powell (1961)

with Those Calculated by the Present Method for Different Nozzle Inlet
Pressures and Temperatures.
Comparison of Calculated with Measured Critical Throat Mass Fluxes
(Powell, 1961) for Various Nozzle Inlet Conditions.

- xxiii -


LIST OF TABLES
3.1

Operational Range of the Facility.

3.2

Test Section Instrumentation.

4.1

Typical Pressure Drop Data.

4.2

Typical Output for the Five-Beam Gamma Densitometer.

4.3

Typical Output for the High Activity Single-Beam Gamma Densitometer.

5.1

Summary of Experimental Conditions.
Pressure Calibrations.

5.2

Summary of Experimental Conditions for Pressure Distribution
Measurements Under Flashing Conditions.

5.3

Summary of Experimental Conditions for Diametrical Averaged Void
Fraction Data with Single Beam Gamma Densitometer.

5.4

Calibration of the Test Section Both Empty (Air). IE' and Full
of Water. IF.

5.5

Distance From Pressure Tap 47 for the 27 Axial Locations (Five Beam
Gamma Densitometer).

5.6

Transverse Radial Locations for Each Y-Beam Center During Axial Scan.

5.7

Summary of Experimental Conditions.
Source Gamma Densitometer).

5.8

Distance from Pressure Tap 47 for the 27 Axial Locations (Single Beam
Gamma Densitometer).

5.9

Transverse Radial Locations for y-Beam Center During Axial Scan.

5.10

Summary of Experimental Conditions for Flashing Experiments (Single
Source Gamma Densitometer).

6.1

Conditions in Flashing Flow of Water in a Constant Area Pipe.

6.2

Bubble Rise Velocities.

6.3

Free Rise Velocities of Steam Bubbles in Water.

6.4

Summary of Test Conditions and BNL Model Calculations.

7.1

Comparison of 100 C Inlet Temperature Runs with TRAC-PIA Predictions.

- xxiv -

Cold and Hot Single Phase

Flashing Experiments (Five


7.2

Comparison of 121 C Inlet Temperature Runs with TRAC-PlA Predictions.

7.3

Comparison of 149 C Inlet Temperature Runs with TRAC-PlA Predictions.

A.l

Comparison of the Critical Mass Fluxes Calculated by the Jump
Conditions and the Experimental Value Measured by Reocreux
(Run 423)(1974).

- xxv -