Research Papers: Flows in Complex Systems

Computational Fluid Dynamics Modeling of Flashing Flow in Convergent-Divergent Nozzle

[+] Author and Article Information
Quang Dang Le

Department of Energy,
Politecnico di Milano,
via Lambruschini 4,
Milan 20156, Italy
e-mail: lequang.dang@polimi.it

Riccardo Mereu

Department of Energy,
Politecnico di Milano,
via Lambruschini 4,
Milan 20156, Italy
e-mail: riccardo.mereu@polimi.it

Giorgio Besagni

Department of Energy,
Politecnico di Milano,
via Lambruschini 4,
Milan 20156, Italy
e-mail: giorgio.besagni@polimi.it

Vincenzo Dossena

Department of Energy,
Politecnico di Milano,
via Lambruschini 4,
Milan 20156, Italy
e-mail: vincenzo.dossena@polimi.it

Fabio Inzoli

Department of Energy,
Politecnico di Milano,
via Lambruschini 4,
Milan 20156, Italy
e-mail: fabio.inzoli@polimi.it

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 20, 2017; final manuscript received April 2, 2018; published online May 7, 2018. Assoc. Editor: Ioannis K. Nikolos.

J. Fluids Eng 140(10), 101102 (May 07, 2018) (22 pages) Paper No: FE-17-1169; doi: 10.1115/1.4039908 History: Received March 20, 2017; Revised April 02, 2018

In this paper, a computational fluid dynamics model of flashing flow, which considers the thermal nonequilibrium effect, has been proposed. In the proposed model, based on the two-phase mixture approach, the phase-change process depends on the difference between the vaporization pressure and the vapor partial pressure. The thermal nonequilibrium effect has been included by using ad hoc modeling of the boiling delay. The proposed model has been applied to the case of two-dimensional axisymmetric convergent-divergent nozzle, which is representative of well-known applications in nuclear and energy engineering applications (e.g., the primary flow in the motive nozzle of ejectors). The numerical results have been validated based on a benchmark case from the literature and have been compared with the numerical results previously obtained by different research groups. The proposed approach has shown a good level of agreement as regards the global and the local experimental fluid dynamic quantities. In addition, sensitivity analyses have been carried out concerning (a) grid independency, (b) turbulence modeling approaches, (c) near-wall treatment approaches, (d) turbulence inlet parameters, and (e) semi-empirical coefficients. In conclusion, the present paper aims to provide guidelines for the simulation of flash boiling flow in industrial applications.

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Saha, P. , 1978, A Review of Two-Phase Steam–Water Critical Flow Models With Emphasis on Thermal Non-Equilibrium, U.S. Nuclear Regulatory Commission, Washington, DC.
Wallis, G. B. , 1980, “ Critical Two-Phase Flow,” Int. J. Multiphase Flow, 6(1–2), pp. 97–112. [CrossRef]
Richter, H. J. , 1983, “ Separated Two-Phase Flow Model: Application to Critical Two-Phase Flow,” Int. J. Multiphase Flow, 9(5), pp. 511–530. [CrossRef]
Pinhasi, G. A. , Ullmann, A. , and Dayan, A. , 2005, “ Modeling of Flashing Two-Phase Flow,” Rev. Chem. Eng., 21(3–4), pp. 133–264. [CrossRef]
Xi, X. , Liu, H. , Jia, M. , Xie, M. , and Yin, H. , 2017, “ A New Flash Boiling Model for Single Droplet,” Int. J. Heat Mass Transfer, 107, pp. 1129–1137. [CrossRef]
Reocreux, M. , 1978, “ Contribution to the Study of Critical Flow Rates in Two-phase Water Vapour Flow,” Ph.D. thesis, Scientific and Medical University of Grenoble, Grenoble, France. https://catalog.hathitrust.org/Record/003204018
Schrock, V. E. , Starkman, E. S. , and Brown, R. A. , 1977, “ Flashing Flow of Initially Subcooled Water in Convergent-Divergent Nozzles,” ASME J. Heat Transfer, 99(2), pp. 263–268. [CrossRef]
Abuaf, N. , 1981, A Study of Nonequilibrium Flashing of Water in a Converging-Diverging Nozzle: Volume 1, Experimental, U.S. Nuclear Regulatory Commission, Washington, DC.
Araneo, L. , and Donde', R. , 2017, “ Flash Boiling in a Multihole G-DI Injector—Effects of the Fuel Distillation Curve,” Fuel., 191, pp. 500–510. [CrossRef]
Henry, R. E. , Fauske, H. K. , and McComas, S. T. , 1970, “ Two-Phase Critical Flow at Low Qualities—II: Analysis,” Nucl. Sci. Eng., 41(1), pp. 92–98. [CrossRef]
Ishii, M. , 1975, Thermo-Fluid Dynamics Theory of Two-Phase Flow, Eyrolles, Paris, France.
Bouré, J. A. , 1977, “ The Critical Flow Phenomenon With Reference to Two-Phase Flow and Nuclear Reactor Systems,” Winter Annual Meeting of the American Society of Mechanical Engineers, Atlanta, GA, Nov. 27–Dec. 2, pp. 195–216. https://inis.iaea.org/search/search.aspx?orig_q=RN:10448767
Wendroff, B. , 1979, “ Two-Fluid Models: A Critical Study,” EPRI Workshop on Two-Phase Flow, Tampa, FL, Mar. 2.
Maksic, S. , and Mewes, D. , 2002, “ CFD-Calculation of the Flashing Flow in Pipes and Nozzles,” ASME Paper No. FEDSM2002-31033.
Jones, O. C. , and Zuber, N. , 1978, “ Bubble Growth in Variable Pressure Fields,” ASME J. Heat Transfer, 100(3), pp. 453–459. [CrossRef]
Shin, T. S. , and Jones, O. C. , 1986, “ An Active Cavity Model for Flashing,” Nucl. Eng. Des., 95, pp. 185–196. [CrossRef]
Shin, T. S. , and Jones, O. C. , 1993, “ Nucleation and Flashing in Nozzles—1,” Int. J. Multiphase Flow, 19(6), pp. 943–964. [CrossRef]
Blinkov, V. N. , Jones, O. C. , and Nigmatulin, B. I. , 1993, “ Nucleation and Flashing in Nozzles—2,” Int. J. Multiphase Flow, 19(6), pp. 965–986. [CrossRef]
Marsh, C. A. , and O'Mahony, A. P. , 2009, “ Three-Dimensional Modelling of Industrial Flashing Flows,” CFD2008, Trondheim, Norway, June 10–12.
Blander, M. , and Katz, J. L. , 1975, “ Bubble Nucleation in Liquids,” AIChE J., 21(5), pp. 833–848. [CrossRef]
Mimouni, S. , Boucker, M. , Lavieville, J. , and Bestion, D. , 2008, “ Modelling and Computation of Cavitation and Boiling Bubbly Flows With the NEPTUNE CFD Code,” Nucl. Eng. Des., 238(3), pp. 680–692. [CrossRef]
Robert, M. , Farvacque, M. , Parent, M. , and Faydide, B. , 2003, “ CATHARE 2 V2.5: A Fully Validated CATHARE Version for Various Application,” Tenth International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH 10), Seoul, South Korea, Oct. 5–11, p. 17. https://inis.iaea.org/search/search.aspx?orig_q=RN:36067340
Archer, A. , 2002, “ A Predictive Model for Cavitation Erosion Downstream Orifices,” ASME Paper No. FEDSM2002-31012.
Janet, J. P. , Liao, Y. X. , and Lucas, D. , 2015, “ Heterogeneous Nucleation in CFD Simulation of Flashing Flows in Converging-Diverging Nozzles,” Int. J. Multiphase Flow, 74, pp. 106–117. [CrossRef]
Lemmert, M. , and Chawla, J. , 1977, “ Influence of Flow Velocity on Surface Boiling Heat Transfer Coefficient,” Heat Transfer Boil, 237, p. 247.
Kurul, N. , and Podowski, M. , 1991, “ On the Modeling of Multidimensional Effects in Boiling Channels,” ANS 27th National Heat Transfer Conference, Minneapolis, MN, July 28–31, pp. 28–31.
Cole, R. , 1967, “ Bubble Frequencies and Departure Volumes at Subatmospheric Pressures,” AIChE J., 13(4), pp. 779–783. [CrossRef]
Kocamustafaogullari, G. , and Ishii, M. , 1983, “ Interfacial Area and Nucleation Site Density in Boiling Systems,” Int. J. Heat Mass Transfer, 26(9), pp. 1377–1387.
Riznic, J. , and Ishii, M. , 1989, “ Bubble Number Density in Vapor Generation and Flashing Flow,” Int. J. Heat Mass Transfer, 32(10), pp. 1821–1833. [CrossRef]
Rohatgi, U. , and Reshotko, E. , 1975, “ Non-Equilibrium One-Dimensional Two-Phase Flow in Variable Area Channels,” Winter Annual Meeting, Houston, TX, Nov. 30–Dec. 5, pp. 47–54. http://adsabs.harvard.edu/abs/1975netp.proc...47R
Wu, B. , Saha, P. , and Abuaf, N. , 1981, A Study of Nonequilibrium Flashing of Water in a Converging–Diverging Nozzle, Vol. 2, NUREG/CR.U.S.N.R.C., Commission, U.N.R., Washington, DC.
Pelletingeas, A. , Dufresne, L. , and Seers, P. , 2016, “ Characterization of Flow Structures in a Diesel Injector for Different Needle Lifts and a Fluctuating Injection Pressure,” ASME J. Fluids Eng., 138(8), p. 081105. [CrossRef]
Giese, T. , Lauren, E. , and Schwarz, W. , 2002, “ Experimental and Numerical Investigation of Gravity-Driven Pipe Flow With Cavitation,” ASME Paper No. ICONE10-22026.
Laurien, E. , and Giese, T. , 2003, “ Exploration of the Two-Fluid Model of Two-Phase flow Towards Boiling, Cavitation and Stratification,” Third International Conference on Computational Heat and Mass Transfer (ICCHMT), Banff, AB, Canada, May 26–30.
Laurien, E. , 2004, “ Influence of the Model Bubble Diameter on Three-Dimensional Numerical Simulations of Thermal Cavitation in Pipe Elbows,” Third International Symposium on Two-Phase Modelling and Experimentation, Pisa, Italy, Sept. 22–25, pp. IV-2113-2120. https://www.tib.eu/en/search/id/BLCP%3ACN058101148/Influence-of-the-model-bubble-diameter-on-three/
Frank, T. , 2007, “ Simulation of Flashing and Steam Condensation in Subcooled Liquid Using ANSYS CFX,” Fifth FZD & ANSYS MPF Workshop, Dresden, Germany, Apr. 25–27, pp. 1–29. http://www.drthfrank.de/publications/2007/Frank_ANSYS_Flashing_Condensation_b.pdf
Liao, Y. , Lucas, D. , Krepper, E. , and Rzehak, R. , 2013, “ Flashing Evaporation Under Different Pressure Level,” Nucl. Eng. Des., 265, pp. 801–813. [CrossRef]
Schaffrath, A. , Krüssenberg, A.-K. , Weiß, F.-P. , Hicken, E. F. , Beyer, M. , Carl, H. , Prasser, H.-M. , Schuster, J. , Schütz, P. , and Tamme, M. , 2001, “ TOPFLOW—A New Multipurpose Thermal Hydraulic Test Facility for the Investigation of Steady State and Transient Two-Phase Flow Phenomena,” Kerntechnik, 66, pp. 209–212. http://www.hzdr.de/publications/PublDoc-111pdf#page=23
Yazdani, M. , Alahyari, A. A. , and Dradcliff, T. D. , 2013, “ Numerical Modeling and Validation of Supersonic Two-Phase Flow of CO2 in Converging-Diverging Nozzles,” ASME J. Fluids Eng., 136(1), p. 014503. [CrossRef]
Singhal, A. K. , Athavale, M. M. , Li, H. , and Jiang, Y. , 2002, “ Mathematical Basis and Validation of the Full Cavitation Model,” ASME J. Fluids Eng., 124(3), pp. 617–624. [CrossRef]
Brennen, C. E. , 2005, Fundamentals of Multiphase Flow, Cambridge University Press, Cambridge, UK. [CrossRef]
Nakagawa, M. , Berana, M. S. , and Kishine, A. , 2009, “ Supersonic Two-Phase Flow of CO2 Through Converging-Diverging Nozzles for the Ejector Refrigeration Cycles,” Int. J. Refrig., 32(6), pp. 1195–1202. [CrossRef]
Liao, Y. , and Lucas, D. , 2015, “ 3D CFD Simulation of Flashing Flows in a Converging-Diverging Nozzle,” Nucl. Eng. Des., 292, pp. 149–163. [CrossRef]
Liao, Y. , and Lucas, D. , 2017, “ Possibilities and Limitations of CFD Simulation for Flashing Flow Scenarios in Nuclear Applications,” Energies, 10(1), p. 139.
Jin, M. S. , Ha, C. T. , and Park, W. G. , 2017, “ Numerical Study on Heat Transfer Effects of Cavitating and Flashing Flows Based on Homogeneous Mixture Model,” Int. J. Heat Mass Transfer, 109, pp. 1068–1083. [CrossRef]
Ha, C. T. , Park, W. G. , and Merkle, C. L. , 2009, “ Multiphase Flow Analysis of Cylinder Using a New Cavitation Model,” Seventh International Symposium on Cavitation, Ann Arbor, MI, Aug. 16–20. https://deepblue.lib.umich.edu/handle/2027.42/84283
Manninen, M. , Taivassalo, V. , and Kallio, S. , 1996, “ On the Mixture Model for Multiphase Flow,” VTT Publications 288, Technical Research Center of Finland, Finland. http://www.vtt.fi/inf/pdf/publications/1996/P288.pdf
Zuber, N. , and Findlay, J. A. , 1965, “ Average Volumetric Concentration in Two-Phase Flow Systems,” ASME J. Heat Transfer, 87(4), pp. 453–468. [CrossRef]
Pericleous, K. A. , and Drake, S. N. , 1986, An Algebraic Slip Model of Phoenics for Multi-Phase Applications, Numerical Simulation of Fluid Flow and Heat/Mass Transfer Processes, Springer-Verlag, Berlin.
Verloop, W. C. , 1995, “ The Inertial Coupling Force,” Int. J. Multiphase Flow, 21(5), pp. 929–933. [CrossRef]
Ungarish, M. , 1993, Hydrodynamics of Suspensions: Fundamentals of Centrifugal and Gravity Separation, Springer, Berlin. [CrossRef]
Johansen, S. T. , Anderson, N. M. , and De Silva, S. R. , 1990, “ A Two-Phase Model for Particle Local Equilibrium Applied to Air Classification of Powers,” Power Technol., 63(2), pp. 121–132. [CrossRef]
Morgan, M. J. , and Shapiro, H. N. , 2006, Fundamentals of Engineering Thermodynamics, Wiley, London.
Miyatake, O. , Tanaka, I. , and Lior, N. , 1997, “ A Simple Universal Equation for Bubble Growth in Pure Liquids and Binary Solutions With a Non-Volatile Solute,” Int. J. Heat Mass Transfer, 40(7), pp. 1577–1584. [CrossRef]
Oza, R. D. , and Sinnamon, J. F. , 1983, “ An Experimental and Analytical Study of Flashing Boiling Fuel Injection,” SAE Paper No. 830590.
Barbone, R. , 1994, “ Explosive Boiling of a Depressurized Volatile Liquid,” M.Sc. thesis, McGill University, Montreal, QC, Canada http://digitool.library.mcgill.ca/webclient/StreamGate?folder_id=0&dvs=1524553701156~622.
Sher, E. , Bar-Kohany, T. , and Rashkovan, A. , 2008, “ Flash-Boiling Atomization,” Prog. Energy Combust. Sci., 34(4), pp. 417–439. [CrossRef]
ANSYS, 2016, “User's Guide of ANSYS-FLUENT 16.2,” ANSYS Inc., Canonsburg, PA.
Naumann, Z. , and Schiller, L. , 1935, “ A Drag Coefficient Correlation,” Z. Ver. Dtsch. Ing., 77(3), pp. 318–323.
Lee, W. H. , 1980, “ A Pressure Iteration Scheme for Two-Phase Flow Modeling,” Multi-Phase Transport Fundamentals, Hemisphere Publishing, Washington, DC. [CrossRef]
Hinze, J. O. , 1975, Turbulence, 2nd ed., McGraw-Hill, New York.
Colombo, E. , Inzoli, F. , and Mereu, R. , 2012, “ A Methodology for Qualifying Industrial CFD: The Q3 Approach and the Role of a Protocol,” Comput. Fluids, 54, pp. 56–66. [CrossRef]
Launder, B. E. , and Spalding, D. B. , 1972, Lectures in Mathematical Models of Turbulence, Academic Press, London.
Shih, T.-H. , Liou, W. W. , Shabbir, A. , Yang, Z. , and Zhu, J. , 1995, “ A New kε Eddy-Viscosity Model for High Reynolds Number Turbulent Flows—Model Development and Validation,” Comput. Fluids, 24(3), pp. 227–238. [CrossRef]
Yakhot, V. , Orszag, S. A. , Thangam, S. , Gatski, T. B. , and Speziale, C. G. , 1992, “ Development of Turbulence Models for Shear Flows by a Double Expansion Technique,” Phys. Fluids A, 4(7), pp. 1510–1520. [CrossRef]
Launder, B. E. , Reece, G. J. , and Rodi, W. , 1975, “ Progress in the Development of a Reynolds-Stress Turbulence Closure,” J. Fluid Mech., 68(3), pp. 537–566. [CrossRef]
Wilcox, D. C. , 1988, “ Reassessment of the Scale-Determining Equation for Advanced, Turbulence Models,” AIAA J., 26(11), pp. 1299–1310. [CrossRef]
Wilcox, D. C. , 1993, “ Comparison of Two-Equation Turbulence Models for Boundary Layers With Pressure Gradients,” AIAA J., 31(8), pp. 1414–1421. [CrossRef]
Wilcox, D. C. , 1993b, Turbulence Modelling for CFD, DCW Industries, La Canada, CA.
Wilcox, D. C. , 1994, “ Simulating Transition With a Two-Equation Turbulence Model,” AIAA J., 32(2), pp. 247–255. [CrossRef]
Menter, F. R. , 1992, “ Performance of Popular Turbulence Models for Attached and Separated Adverse Pressure Gradient Flow,” AIAA J., 30(8), pp. 2066–2072. [CrossRef]
Menter, F. R. , 1992, “ Improved Two-Equation k–ω Turbulence Models for Aerodynamic Flows,” Ames Research Center, Mountain View, CA, NASA Technical Memorandum No. 103975. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930013620.pdf
Menter, F. , 1994, “ Two-Equation Eddy-Viscosity Turbulence Model for Engineering Applications,” AIAA J., 32(8), pp. 1598–1605. [CrossRef]
Menter, F. R. , Kuntz, M. , and Langtry, R. , 2003, “ Ten Years of Industrial Experience With the SST Turbulence Model,” Fourth International Symposium on Turbulence, Heat and Mass Transfer, Antalya, Turkey, Oct. 12–17. http://citeseerx.ist.psu.edu/viewdoc/download?doi=
Launder, B. E. , and Spalding, D. B. , 1974, “ The Numerical Computation of Turbulent Flows,” Comput. Methods Appl. Mech. Eng., 3(2), pp. 269–289. [CrossRef]
Kim, S.-E. , and Choudhury, D. , 1995, “ A Near-Wall Treatment Using Wall Functions Sensitized to Pressure Gradient,” Symposium on Fluids Engineering and Laser Anemometry Conference, Separated and complex flows, Hilton Head, SC, pp. 273–280. https://www.tib.eu/en/search/id/BLCP%3ACN013245860/A-Near-Wall-Treatment-Using-Wall-Functions-Sensitized/
Besagni, G. , and Inzoli, F. , 2017, “ Computational Fluid-Dynamics Modeling of Supersonic Ejectors: Screening of Turbulence Modeling Approaches,” Appl. Therm. Eng., 117, pp. 122–144. [CrossRef]
Besagni, G. , Mereu, R. , Chiesa, P. , and Inzoli, F. , 2015, “ An Integrated Lumped Parameter-CFD Approach for Off-Design Ejector Performance Evaluation,” Energy Convers Manage, 105, pp. 697–715. [CrossRef]
Roache, P. J. , 1998, Verification and Validation in Computational Science and Engineering, Albuquerque, Hermosa Publishers, Socorro, NM.


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Fig. 1

Physical behavior of flashing flow: (a) thermodynamic diagram of phase change of water with equilibrium assumption and (b) start of vaporization

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Fig. 2

Vertical circular convergent-divergent nozzle in Abuaf [8]

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Fig. 3

Mesh and boundary condition of convergent-divergent nozzle

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Fig. 4

Influence of y+ on the velocity profile at cross section I (x = 0.458 m) and cross section N (x = 0.577 m)

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Fig. 5

Section description and radial vapor profile with effects of turbulence RANS models

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Fig. 6

Influence of turbulence inlet intensity to numerical results: (a) vapor fraction along center line and (b) radial vapor profile at x = 0.577 m

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Fig. 7

Artificial coefficients sensitivity in BNL309: (a) vapor profile and static pressure along nozzle with fixed dp = 75 Pa and (b) vapor profile and static pressure along nozzle with fixed β = 1.2

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Fig. 8

Averaged vapor fraction and absolute pressure along nozzle compared to experimental data and Liao and Lucas model [43]

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Fig. 9

Averaged vapor fraction and absolute pressure along nozzle compared to experimental data and Janet model [24]

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Fig. 10

Radial void fraction profile at positions along divergent nozzle

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Fig. 11

Radial vapor profile of BNL309 compared to experiment data and Liao and Lucas model [43]

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Fig. 12

Turbulence kinetic energy field

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Fig. 13

Radial vapor fraction in comparison with results of Ref. [24] — x = 0.59 m

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Fig. 14

Radial vapor fraction in comparison with results of Ref. [24]: (a) x = 0.59 m and (b) x = 0.59 m

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Fig. 15

Artificial coefficients sensitivity for BNL284: (a) vapor profile and static pressure along nozzle with fixed dp = 75 Pa and (b) vapor profile and static pressure along nozzle with fixed β = 0.8

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Fig. 16

Artificial coefficients sensitivity for BNL273: (a) vapor profile and static pressure along nozzle with fixed dp = 75 Pa and (b) vapor profile and static pressure along nozzle with fixed β = 1.05

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Fig. 17

Artificial coefficients sensitivity for BNL268: (a) vapor profile and static pressure along nozzle with fixed dp = 75 Pa and (b) vapor profile and static pressure along nozzle with fixed β = 1.0

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Fig. 18

Artificial coefficients sensitivity for BNL304: : (a) vapor profile and static pressure along nozzle with fixed dp = 75 Pa and (b) vapor profile and static pressure along nozzle with fixed β = 1.11



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