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

, NUREG/CR-1864 BNL-NUREG-51317 VOL of NUREGCR1864V-1 ~ "1R2 ~~I~~I~~~~~~I!I"- ~ ~' ASTUDY OF NONEQUILIBRIUM FLASHING OF WATER IN ACONVERGING-DIVERGING NOZZLE VOLUME - EXPERIMENTAL VOLUME MODELING VOLUME 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 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 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 U.S Department of Commerce 5285 Port Royal Road Springfield, VA 22161 NTIS price codes: Printed Copy: A08; Microfiche Copy: AOI , 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 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 INTRODUCTION • REVIEW OF THE LITERATURE • 3 EXPERIMENTAL FACILITY AND TECHNIQUES 3.1 Flow Loop •• 3.2 Test Section 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 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 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 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 6.3.2 141 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 - SUMMARY AND CONCLUSIONS 253 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 - II 15 88888888 gg gg 19 23 +0( ggOg o go c a .= 180 Booooooooooooooooooooooo 000 0000 00 W 0::: :::> 160 (f) 0 00 00 RUNS 383-387 a RUNS 370-372 o (f) W 0:: a 140 00 00 0000 120 A o o 0 o o « 0.6 0::: D I.L o o 0.4 o o DO o o 0 0 0 0 0 0 0 a o o o 0.2 o o o o o o ~ o o o 000 0 000000 30 40 DISTANCE (c m) Figure 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 (BNL Neg No 9-623-80) - 128 - FLOW ~ TAP NO 200 15 II 19 23 27 oooooooeoe eeABg66 00 o 31 35 39 43 47 ~ p (T) S In ~180 o 6 o 66 OOOen w 0::: :::> 00 6600000 160 o (f) (f) wl40 0::: a 00 RUNS 373,374, 3375 RUNS 390 -392 o 00 00 00 o 120 A 1.0 6 z 0.8 6 0 ~ u 0.6 ",6 « 0::: 6 0 LL 0 0.4 6 > 0.2 6 o 6 0 6 6 0 666 0 o 0000 B 10 Figure 5.77 40 20 30 AXIAL DISTANCE (c m) 50 60 Axial Distributions of Pressure (A) and Area Averaged Void Fraction (B) for Two Runs Performed at an Inlet Temperature of l2loC, Two-Phase Inlet Conditions, and Two Inlet Mass Fluxes of 1510 kgjm2 s (Runs 373, 374, 3375) and 1065 kgjrn Z s (Runs 390 to 392) (BNL Neg No 9-625-80 ) - 129 - A method is presented here for determining the cro~s section averaged net vapor generation rate per unit volume f v • from the measured pressure and void fraction distributions along the test section The following definitions of cross section averaged quantities are well documented in the literature On two-phase flow + (5.6) Quality (5.7) = (5.3> «1 - (5.4) a.)PtUj"> / The densities Pv and Pt of the vapor and liquid phases are assumed to be given by the saturation values corresponding to the local pressure p ahd therefore to be constant over a cross section Moreover the vapor drift velocity (5.8) is also assumed to be constant over a cross section By combining Equations (5.7) and (5.3) and using the drift velocity Equation (5.3) the following expression is obtained: = + (5.9) Introduction of the distribution parameter Co / gives which may be expressed as Pv [c ( < x> < G> P v + < 1- x> - 130 - P£ when Equations (5.6) (5.3) and (5.4) are inserted Solving for the cross section averaged quality and replacing the liquid and vapor densities with their saturation values gives an expression for the quality: • [c ~ + P~~j] o P f = - C Pf - Pf o (5.10) Pg - The vapor drift velocity is assumed to be given by the expression for the churn-turbulent upflow of a bubbly mixture V gJ • K ["g(P fp : Pg )] 1/4 (5.11) where the coefficient K has a value of 1.41 according to Kroeger and Zuber (1968) For a given set of test section inlet conditions Co is assumed to remain constant in the test section and the variation of the liquid density Pf is negligible Thus Vgi varies only weakly with P • and it is roughly constant in the test sectIon Hence may be cons~dered as an explicit function of the local cross section averaged void fraction the vapor density and the mixture mass flux From conservation of vapor mass the vapor generation rate can be expressed as (5.12) d/dz • which after dropping the symbol < > leads to Gx a r da+Gx(l dz Pg v dPg aC o ) dp dp_OPgVgj dz G dG dz (5.13) - aCo(pf - Pg ) /Pf where dPg/dz has been replaced by [(dp /dp)(dp/dz)] The quantities da/dz and dp/dz in Equation (5.13) can be ob~ained from the experiments and dPg/dp is given by the equation of state of the vapor or the steam table The mixture continuity ~quation can be written as dG G dz dA = - (5.14) A dz = - (A/A+) To account properly for the frictional effects the effective cross sectional area distribution (A/A+)eff determined from single-phase calibrations was used instead of the geometrical area distribution in the reported calculations This is probably a good assumption for the convergent part of the test section where the favorable pressure gradient is expected to keep the wall boundary layers thin and attached but it may be questionable for the divergent part - 131 - where the boundary layer displacement in two-phase flow may differ significantly from that in single-phase flow under adverse pressure gradients Thus, all terms in Equation (5.13) may be evaluated as a function of z, and the net vapor generation rate may be calculated Figure 5.78 shows an early example of f v thus determined for the convergent part of the test section The top graph shows the pressure and void distributions measured in the experiments, with least-square polynomial fits to the measured data given for comparison The derivatives of a and p can be evaluated along the fitted polynomials, rather than through the actual data points, which may lead to considerable scatter The f v values calculated from Equation (5.13) are shown in the bottom graphs These experiments attain rv values of the order of 10 kg/m s, which are approximately in the same range as those observed by Reocreux (1974) The value of f v was found to be strongly dominated by the variation of a with z in these experiments For example, for Runs 82/821 at z = 254 mm, the values of the three terms in the numerator in Equation (5.13) are (Gx/a)da/dz = 22.53 kg/m s, (Gx/Pg) (1 - aCo) (dPg/dp) (dp/dz) (a PgVgj/G)dG/dz = 0.33 kg/m s, ,= - 2.66 kg/m s, where Vgj = 0.21 m/s Thus, the term involving dG/dz, which is directly proportional to the drift velocity assumed, contributes about % to the value of f v Any uncertainty in the assumption of Vgj is therefore expected to lead to insignificant errors in rv thus determined Figure 5.78, shows rv calculated for zero drift velocity and for a tenfold increase in Vgj (taking K = and 14.1, in Equation (5.11» The differences between the three curves are indeed small Recently Thang and Davis (1979) measured the diametrical distribution of void fraction and slip in air-water two-phase flows in a converging-diverging nozzle From the geometry of their nozzle, the fluid acceleration and deceleration in their experiments are estimated to be greater than those in the BNL experiments by a factor of two to four Their measurements indicated that Vgj increased from 0.58 m/s to about 0.83 m/s for an increase of a = 0.3 to a = 0.5 The sensitivity calculations above, covering a range for V j of to 2.1 mis, showed that the possible error in Vgj , being within one or~er of magnitude, is not expected to affect the rv calculation appreciably Additional data with diametrical averaged void fraction are shown in Figure 5.79, in which the smoothing and interpolation routines of the IMSLX computer program package were used to obtain piecewise continuous least-squares cubic spline curve fits to the pressure and void distribution data The locations of the "knots," where neighboring pieces of the spline fit are joined, are optimized by the computer on the basis of initial guesses specified in the input The cubic spline fit thus computed is continuous and has continuous first and second derivatives The initial guesses regarding the locations of knots, and the number of knots specified, influence the cubic splines computed Hence, - 132 - 400. -,r r -r ,0.4 Psat 10 o 20 30 AXIAL DISTANCE (em) Figure 5.78 Top: Measured Pressure (0) and Void Fraction (aD Distributions in the Converging Part of the Test Section in Runs 82/821 and the Least-Square Polynomial Fit to Data Bottom: Calculated Net Vapor Generation Rate Based on the Least Square Fit to the a and p Data (BNL Neg No 3-1226-79) - 133 - f-' ~ W ~ IDeUI 200.0 \ Z "II" ~.i) 100.0 1t'O.D / Z ,,,"I ]W.O / 4OC'_::l / I I 1\ -.m.D /' I c &m.D oUIl.O ~DD D.O \ GAMMA vS Z PLOT, CQ " 1.00 0.0 ~ 'Sm.G o ~ ~ "'0 ~~ -0 ~§ ~ § '" o ~ D.D HXI.D 4!W.a / Z ':1r11 'DJ.O 1/ / sm.o ccy- m.o / GAMMA VS Z PLOT, A 6lJ].a -1 ".DD 1-21 6-25-79 0.0 o &m.O 10 o