MODELING OF FLASHING TWO-PHASE FLOW

A review of the published work on the flashing of a two-phase flow system, owing to a sudden depressurization of a compressed liquid, is presented. Of concern is the two-phase flow transient occurring during a failure of a pressurized tube or vesselblowdown. Abrupt depressurization of a confined liquid can bring the liquid to a superheated state. If this occurs, an intense nucleation process is triggered. The level of superheating at which the nucleation process begins is referred to as the "flashing inception" point. The rapidity of the bubble nucleation and growth processes substantial influence the mixture blowdown scenario that sometimes can be in the form of a Boiling Expanding Vapor Explosion (BLEVE). The current review deals with flashing of a single pure substance. First, the models of bubble formation and growth are presented. This is followed by a description on the incorporation of these models into two-phase flow transport models. The two-phase models are used for analysis of the blowdown scenario. This subject is of critical importance for the investigation of the safety of compressed liquid systems.

[1]  Hsi-Jen Chen,et al.  Modeling a Boiling-Liquid, Expanding-Vapor Explosion Phenomenon with Application to Relief Device Design for Liquefied Ammonia Storage , 1999 .

[2]  J. H. McFadden,et al.  Heat transfer and friction correlations required to describe steam--water behavior in nuclear safety studies , 1975 .

[3]  Michael Epstein,et al.  Vapor‐Liquid disengagement in atmospheric liquid storage vessels subjected to external heat source , 1985 .

[4]  Bubble dynamics on the evolving bubble formed from the droplet at the superheat limit , 1995 .

[5]  J. R. Chen,et al.  Modelling of two-phase blowdown from pipelines—II. A simplified numerical method for multi-component mixtures , 1995 .

[6]  Michel Giot,et al.  Fundamentals of two-phase flow by the method of irreversible thermodynamics , 2002 .

[7]  D. Drew Mathematical Modeling of Two-Phase Flow , 1983 .

[8]  R. Hampel,et al.  Transient two-phase flow in arbitrary inclined tubes caused by depressurization of liquid with dissolved gases , 2001 .

[9]  Gary Z. Watters Analysis and Control of Unsteady Flow in Pipelines , 1979 .

[10]  Dimos Poulikakos,et al.  Pressure and power generation during explosive vaporization on a thin-film microheater , 2000 .

[11]  Rex Britter,et al.  ATMOSPHERIC DISPERSION OF DENSE GASES , 1989 .

[12]  A. Asai,et al.  Bubble Dynamics in Boiling Under High Heat Flux Pulse Heating , 1991 .

[13]  B. Webbon,et al.  Dynamics of vapour bubbles in nucleate boiling , 1996 .

[14]  N. Zuber,et al.  Drag coefficient and relative velocity in bubbly, droplet or particulate flows , 1979 .

[15]  John H. Lienhard,et al.  Correlation of Pressure Undershoot During Hot-Water Depressurization , 1981 .

[16]  K. Yeo,et al.  The numerical simulations of explosion and implosion in air: use of a modified Harten's TVD scheme , 1999 .

[17]  C. Lackme Incompleteness of the flashing of a supersaturated liquid and sonic ejection of the produced phases , 1979 .

[18]  Teruaki Akamatsu,et al.  Effects of the non-equilibrium condensation of vapour on the pressure wave produced by the collapse of a bubble in a liquid , 1980, Journal of Fluid Mechanics.

[19]  A model involving break-up to explain peculiarities of the boiling liquid efflux process , 1992 .

[20]  Bradford Sturtevant,et al.  Rapid evaporation at the superheat limit , 1982, Journal of Fluid Mechanics.

[21]  J. Lienhard Corresponding States Correlations of the Spinodal and Homogeneous Nucleation Limits , 1982 .

[22]  Yuri V. Fairuzov,et al.  Modeling of Conjugate Two-Phase Heat Transfer During Depressurization of Pipelines , 2000 .

[23]  Visualization of boiling bubble dynamics using a flat uniformly heated transparent surface , 2002 .

[24]  A. Robinson,et al.  Bubble growth in a uniform and spatially distributed temperature field , 2001 .

[25]  G. Yadigaroglu,et al.  An investigation of microscale explosive vaporization of water on an ultrathin Pt wire , 2002 .

[26]  Milton Blander Bubble nucleation in liquids , 1979 .

[27]  Robert C. Reid,et al.  Rapid Phase Transitions from Liquid to Vapor , 1983 .

[28]  G. Yadigaroglu,et al.  Effects of vapour/aerosol and pool formation on rupture of vessels containing superheated liquid , 1990 .

[29]  J. Sherwood The force on a growing bubble in potential flow , 1999 .

[30]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[31]  Antonio C. M. Sousa,et al.  A study of the effect of the tank diameter on the thermal stratification in LPG tanks subjected to fire engulfment , 1990 .

[32]  Souad Harmand,et al.  Experimental study of flash evaporation of a water film , 2002 .

[33]  Yuri V. Fairuzov Numerical solution for slowdown of pipeline containing flashing liquid , 1998 .

[34]  W. E. Martinsen,et al.  BLEVEs: Their causes, effects and prevention , 1986 .

[35]  D. Abdollahian,et al.  Homogeneous non-equilibrium critical flow model , 1982 .

[36]  V. Carey Liquid-Vapor Phase-Change Phenomena , 2020 .

[37]  David L. Frost,et al.  Effects of Ambient Pressure on the Instability of a Liquid Boiling Explosively at the Superheat Limit , 1984 .

[38]  S. Levy,et al.  A mechanistic non-equilibrium model for two-phase critical flow , 1983 .

[39]  O. Jones,et al.  Nucleation and flashing in nozzles—1. A distributed nucleation model , 1993 .

[40]  John A. Davenport,et al.  A survey of vapor cloud explosions: Second update , 1993 .

[41]  Highlights of two-phase critical flow: On the links between maximum flow rates, sonic velocities, propagation and transfer phenomena in single and two-phase flows , 1976 .

[42]  K. Ardron A two-fluid model for critical vapour-liquid flow , 1978 .

[43]  B. R. Sehgal,et al.  Numerical investigation of bubble growth and detachment by the lattice-Boltzmann method , 2001 .

[44]  T. Ytrehus,et al.  Kinetic theory approach to interphase processes , 1996 .

[45]  W. T. Hancox,et al.  Numerical Standards for Flow-Boiling Analysis , 1977 .

[46]  I. Owen,et al.  Heterogeneous flashing in water drops , 1991 .

[47]  D.R.H. Beattie,et al.  A note on the calculation of two-phase pressure losses , 1973 .

[48]  Duu-Jong Lee,et al.  Bubble nucleation in microchannels: statistical mechanics approach , 2001 .

[49]  Robert E. Henry,et al.  The Two-Phase Critical Flow of One-Component Mixtures in Nozzles, Orifices, and Short Tubes , 1971 .

[50]  Kunito Okuyama,et al.  Boiling nucleation on a very small film heater subjected to extremely rapid heating , 1994 .

[51]  Gad Hetsroni,et al.  Handbook of multiphase systems , 1982 .

[52]  J. R. Travis,et al.  A Nonequilibrium Vapor Production Model for Critical Flow , 1980 .

[53]  I. Swift Developments in emergency relief system design , 1984 .

[54]  E. S. Starkman,et al.  Flashing flow of initially subcooled water in convergent--divergent nozzles , 1977 .

[55]  A. Gany,et al.  An exact solution for the moving boiling boundary problem , 2001 .

[56]  J. Cleaver,et al.  Influence of surrounding bubbles on the rate of nucleation , 1993 .

[57]  John H. Lienhard,et al.  An Experimental Study of the Rapid Depressurization of Hot Water , 1980 .

[58]  C. Avedisian,et al.  Measuring bubble nucleation temperature on the surface of a rapidly heated thermal ink-jet heater immersed in a pool of water , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[59]  P. Dergarabedian Observations on bubble growths in various superheated liquids , 1960, Journal of Fluid Mechanics.

[60]  Jan Stawczyk,et al.  Experimental evaluation of LPG tank explosion hazards. , 2003, Journal of hazardous materials.

[61]  Yuri V. Fairuzov,et al.  Blowdown of pipelines carrying flashing liquids , 1998 .

[62]  J. Cleaver,et al.  Blowdown from a vented partially full vessel , 1996 .

[63]  Sung Won Bae,et al.  Single bubble growth in saturated pool boiling on a constant wall temperature surface , 2003 .

[64]  J. C. Leung,et al.  A generalized correlation for one‐component homogeneous equilibrium flashing choked flow , 1986 .

[65]  J. Cleaver,et al.  Determination of the heterogeneous nucleation factor during a transient liquid expansion , 1992 .

[66]  S. J. Board,et al.  Spherical Vapour Bubble Growth in Superheated Liquids , 1971 .

[67]  Alejandro Clausse,et al.  Non-equilibrium effects in void fraction distribution , 1995 .

[68]  F. J. Moody,et al.  Maximum Flow Rate of a Single Component, Two-Phase Mixture , 1965 .

[69]  J. Kestin,et al.  Physical aspects of the relaxation model in two-phase flow , 1990, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[70]  Gecheng Zha,et al.  Numerical solutions of Euler equations by using a new flux vector splitting scheme , 1993 .

[71]  K. Kobe The properties of gases and liquids , 1959 .

[72]  J. Lienhard,et al.  Early Response of Hot Water to Sudden Release from High Pressure , 1978 .

[73]  J. E. S. Venart,et al.  The boiling liquid collapsed bubble explosion (BLCBE): A preliminary model , 1996 .

[74]  G. Sod A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws , 1978 .

[75]  D. Drew,et al.  The Relationship Between Standing Waves, Pressure Pulse Propagation, and Critical Flow Rate in Two-Phase Mixtures , 1989 .

[76]  Joaquim Casal,et al.  Calculating overpressure from BLEVE explosions , 2004 .

[77]  N. Zuber ON THE DISPERSED TWO-PHASE FLOW IN THE LAMINAR FLOW REGIME. , 1964 .

[78]  E. Michaelides,et al.  Relaxation Models for Wave Phenomena in Liquid-Vapor Bubble Flow in Channels , 1998 .

[79]  O. C. Jones,et al.  Critical Flashing Flows in Nozzles With Subcooled Inlet Conditions , 1983 .

[80]  Russell A Ogle,et al.  Explosion caused by flashing liquid in a process vessel. , 2004, Journal of hazardous materials.

[81]  N. Zuber,et al.  Bubble Growth in Variable Pressure Fields , 1978 .

[82]  H. Kwak,et al.  Explosive boiling of liquid droplets at their superheat limits , 2005 .

[83]  Donald A. Drew,et al.  An Analysis of Wave Propagation in Bubbly Two-Component, Two-Phase Flow , 1985 .

[84]  N. Zuber,et al.  The dynamics of vapor bubbles in nonuniform temperature fields , 1961 .

[85]  Milton S. Plesset,et al.  On the Dynamics of Small Vapor Bubbles in Liquids , 1954 .

[86]  V. Dhir,et al.  Taylor instability in boiling, melting and condensation or evaporation , 1980 .

[87]  Q. Tran,et al.  Transient simulation of two-phase flows in pipes , 1998 .

[88]  J. A. Geurst Virtual mass in two-phase bubbly flow , 1985 .

[89]  N. Afgan Boiling Liquid Superheat , 1975 .

[90]  G. Birkhoff,et al.  Spherical Bubble Growth , 1958 .

[91]  D. Fletcher,et al.  A simple kinetic theory treatment of volatile liquid-gas interfaces , 2001 .

[92]  J. Hinze Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes , 1955 .

[93]  Steven R. Hanna,et al.  Guidelines for use of vapor cloud dispersion models , 1987 .

[94]  R. L. Ferch,et al.  Method of characteristics solutions for non-equilibrium transient flow-boiling , 1979 .

[95]  A. E. Bergles,et al.  Wave Propagation in Gas-Liquid Media , 1993 .

[96]  G. Saville,et al.  Modelling of two-phase blowdown from pipelines—I. A hyperbolic model based on variational principles , 1995 .

[97]  A. M. Birk,et al.  The boiling liquid expanding vapour explosion , 1994 .

[98]  G. M. Armstrong Dust explosions: The potent power of powder , 2004 .

[99]  Ron Darby,et al.  On two-phase frozen and flashing flows in safety relief valuesRecommended calculation method and the proper use of the discharge coefficient , 2004 .

[100]  S. A. Zwick Growth of Vapor Bubbles in a Rapidly Heated Liquid , 1960 .

[101]  Roman Kwidziński,et al.  Evaluation of the relaxation time of heat and mass exchange in the liquid-vapour bubble flow , 1996 .

[102]  R. L. Seliger,et al.  Variational principles in continuum mechanics , 1968, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[103]  Amos Ullmann,et al.  Numerical Model for Bubbles Break-up During Blowdown , 2005 .

[104]  D. Sharp An overview of Rayleigh-Taylor instability☆ , 1984 .

[105]  S. A. Zwick,et al.  THE GROWTH OF VAPOR BUBBLES IN SUPERHEATED LIQUIDS. REPORT NO. 26-6 , 1953 .

[106]  G. Taylor The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[107]  E. Elias,et al.  Bubble transport in flashing flow , 2000 .

[108]  M. M. El-Wakil,et al.  Investigations of liquid flashing and evaporation due to sudden depressurization , 1984 .

[109]  T. G. Theofanous,et al.  Universal relations for bubble growth , 1976 .

[110]  G. Eitelberg,et al.  Studies of the transient flows in high enthalpy shock tunnels , 1998 .

[111]  D. Weihs,et al.  Stability of rapidly evaporating droplets and liquid shells , 2001 .

[112]  J. Straub,et al.  Analysis of the evaporation coefficient and the condensation coefficient of water , 2001 .

[113]  F. R. Steward,et al.  Initiation step of boiling liquid expanding vapour explosions , 1990 .

[114]  U. S. Rohatgi,et al.  Non-equilibrium one-dimensional two-phase flow in variable area channels , 1975 .

[115]  Y. Hsu On the Size Range of Active Nucleation Cavities on a Heating Surface , 1962 .

[116]  Victor H. Ransom,et al.  A CHOKED-FLOW CALCULATION CRITERION FOR NONHOMOGENEOUS, NONEQUILIBRIUM, TWO-PHASE FLOWS , 1982 .

[117]  H. Merte,et al.  Explosive vapor bubble growth in uniformly superheated liquids: R-113 and mercury , 2005 .

[118]  H. No,et al.  Subcooled water critical pressure and critical flow rate in a safety valve , 2001 .

[119]  L. Chambers Linear and Nonlinear Waves , 2000, The Mathematical Gazette.

[120]  M. Dalle Donne,et al.  THE GROWTH OF VAPOR BUBBLES IN SUPERHEATED SODIUM , 1975 .

[121]  Costas P. Grigoropoulos,et al.  Pressure generation and measurement in the rapid vaporization of water on a pulsed-laser-heated surface , 1996 .

[122]  N. Zuber,et al.  Growth of a Vapor Bubble in a Superheated Liquid , 1954 .

[123]  Graham B. Wallis,et al.  Critical two-phase flow , 1980 .

[124]  H. Palmer,et al.  The hydrodynamic stability of rapidly evaporating liquids at reduced pressure , 1976, Journal of Fluid Mechanics.

[125]  S. Bankoff,et al.  Bubble growth on a solid wall in a rapidly-depressurizing liquid pool , 1991 .

[126]  F. J. Moody,et al.  MAXIMUM TWO-PHASE VESSEL BLOWDOWN FROM PIPES , 1965 .

[127]  Andrea Prosperetti,et al.  Vapour-bubble growth in a superheated liquid , 1978, Journal of Fluid Mechanics.

[128]  R. E. Nieman,et al.  One-dimensional models for transient gas-liquid flows in ducts , 1980 .

[129]  N.H.A. Versloot,et al.  Expansion-controlled evaporation: a safe approach to BLEVE blast , 2004 .

[130]  R C Reid,et al.  Possible Mechanism for Pressurized-Liquid Tank Explosions or BLEVE's , 1979, Science.

[131]  S. Bankoff Entrapment of gas in the spreading of a liquid over a rough surface , 1958 .

[132]  Mamoru Ishii,et al.  Interfacial area and nucleation site density in boiling systems , 1983 .

[133]  L. E. Scriven On the dynamics of phase growth , 1995 .

[134]  G. A. Melhem,et al.  Data summary of the national fire protection association's BLEVE tests , 1993 .

[135]  P. Saha,et al.  Study of nonequilibrium flashing of water in a converging-diverging nozzle. Volume 2. Modeling , 1981 .

[136]  Larry C. Witte,et al.  The Vapor Explosion , 1970 .

[137]  Numerical Model for Boiling Liquid Vapor Explosion (BLEVE) , 2004 .

[138]  K. Nishikawa,et al.  Nucleate Boiling Heat Transfer and Its Augmentation , 1990 .

[139]  John H. Lienhard,et al.  Homogeneous Nucleation and the Spinodal Line , 1981 .

[140]  Keun-Shik Chang,et al.  Pressure wave speeds from the characteristics of two fluids, two-phase hyperbolic equation system , 1998 .

[141]  E. Hahne,et al.  Evaporation waves in flashing processes , 2000 .

[142]  Jean-Marie Seynhaeve,et al.  A Model for Choked Flow-through Cracks With Inlet Subcooling , 1993 .

[143]  The role of thermal disequilibrium in critical two-phase flow , 2002 .

[144]  L. G. Leal,et al.  NONLINEAR BUBBLE DYNAMICS , 1997 .

[145]  S. M. Sami,et al.  A Transient Model for Predicting Nonhomogeneous Nonequilibrium Critical Two-Phase Flows , 1989 .

[146]  N. Abuaf,et al.  A Nonequilibrium Vapor Generation Model for Flashing Flows , 1984 .

[147]  A. Prosperetti,et al.  Bubble Dynamics and Cavitation , 1977 .

[148]  J. Cleaver,et al.  The role of nucleation in the initial phases of a rapid depressurization of a subcooled liquid , 1990 .

[149]  The analytical solution of an unsteady gas flow with shocks , 1997 .

[150]  Ho Sung Lee,et al.  Spherical vapor bubble growth in uniformly superheated liquids , 1996 .

[151]  J. L. Xu,et al.  Nonequilibrium Modeling of Two-Phase Critical Flow , 1995 .

[152]  R. Henry,et al.  Bubble Growth During Decompression of a Liquid , 1981 .

[153]  Van P. Carey,et al.  Thermal bubble formation on polysilicon micro resistors , 1998 .

[154]  Daniel Lhuillier,et al.  A mean-field description of two-phase flows with phase changes , 2003 .

[155]  N. Zuber Nucleate boiling. The region of isolated bubbles and the similarity with natural convection , 1963 .

[156]  J. E. S. Venart,et al.  To BLEVE or not to BLEVE: Anatomy of a boiling liquid expanding vapor explosion , 1993 .

[157]  J. Sherwood,et al.  Bubble motion in a potential flow within a Venturi , 2000 .

[158]  J. Barták A study of the rapid depressurization of hot water and the dynamics of vapour bubble generation in superheated water , 1990 .

[159]  Andrea Prosperetti,et al.  Averaged equations for inviscid disperse two-phase flow , 1994, Journal of Fluid Mechanics.

[160]  D. J. Lewis The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. II , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[161]  G. Yadigaroglu,et al.  Explosive vaporization of superheated liquids by boiling fronts , 2001 .

[162]  G. Kocamustafaogullari,et al.  Breakup criteria for fluid particles , 1989 .

[163]  Léon Bolle,et al.  The non-equilibrium relaxation model for one-dimensional flashing liquid flow , 1996 .

[164]  R. Schrage A theoretical study of interphase mass transfer , 1953 .

[165]  R. Furzeland,et al.  Rapid evaporation at the superheat limit , 1988 .

[166]  H. J. Richter,et al.  Separated two-phase flow model: application to critical two-phase flow , 1983 .

[167]  P. A. Thompson,et al.  Shock waves and phase changes in a large-heat-capacity fluid emerging from a tube , 1986, Journal of Fluid Mechanics.

[168]  Yoshiaki Oka,et al.  Numerical analysis of boiling on high heat-flux and high subcooling condition using MPS-MAFL , 2002 .

[169]  D. Hsieh Some Analytical Aspects of Bubble Dynamics , 1965 .

[170]  B. B. Mikic,et al.  On bubble growth ratesSur les vitesses de croissance des bullesÜber blasenwachstumsratenO cкopocти pocтa пyзыpькoв , 1970 .

[171]  J. D. Parker,et al.  Bubble Growth and Collapse in Liquid Nitrogen , 1968 .

[172]  R. Clift,et al.  Bubbles, Drops, and Particles , 1978 .

[173]  L. J. Clarke,et al.  An experimental study of vapour growth at the superheat limit temperature , 1988 .

[174]  W. S. Winters,et al.  Experiments and Nonequilibrium Analysis of Pipe Blowdown , 1979 .

[175]  Lei Zhang,et al.  Nucleation site interaction in pool boiling on the artificial surface , 2003 .

[176]  J. Tu,et al.  On numerical modelling of low-pressure subcooled boiling flows , 2002 .

[177]  F. Dobran Nonequilibrium Modeling of Two-Phase Critical Flows in Tubes , 1987 .

[178]  Pasquale M. Sforza Two-Phase Flows and Heat Transfer , 1979 .

[179]  John A. Davenport Hazards and protection of pressure storage and transport of LP-gas , 1988 .

[180]  O. C. Jones,et al.  Flashing Inception in Flowing Liquids , 1980 .

[181]  John H. Lienhard,et al.  The Dominant Unstable Wavelength and Minimum Heat Flux During Film Boiling on a Horizontal Cylinder , 1964 .

[182]  J. A. Geurst Variational principles and two-fluid hydrodynamics of bubbly liquid/gas mixtures , 1986 .

[183]  H. John,et al.  Critical two-phase flow through rough slits , 1988 .

[184]  Ezra Elias,et al.  Two-phase critical flow , 1994 .

[185]  David L. Frost,et al.  Dynamics of explosive boiling of a droplet , 1988 .

[186]  V. E. Schrock,et al.  Two-phase critical flow in slits , 1983 .

[187]  P. Souers,et al.  Thermophysical Properties of Liquids in the Metastable (Superheated) State , 1989 .

[188]  A. R. Edwards,et al.  STUDIES OF PHENOMENA CONNECTED WITH THE DEPRESSURIZATION OF WATER REACTORS. , 1970 .

[189]  S. J. Board,et al.  Detonation of fuel coolant explosions , 1975, Nature.

[190]  C. Avedisian The Homogeneous Nucleation Limits of Liquids , 1985 .

[191]  Raymond F. Bishop,et al.  Thermo-fluid Dynamic Theory of Two-Phase Flow , 1975 .

[192]  G. R. Moore Vaporization of superheated drops in liquids , 1959 .

[193]  M. Ishii,et al.  Bubble number density and vapor generation in flashing flow , 1989 .

[194]  T. G. Theofanous,et al.  A theoretical study on bubble growth in constant and time-dependent pressure fields , 1969 .

[195]  Chong-fang Ma,et al.  Study on bubble dynamics for pool nucleate boiling , 2000 .

[196]  Stanley M. Walas,et al.  Phase equilibria in chemical engineering , 1985 .

[197]  Jinliang Xu,et al.  Acoustic wave prediction in flowing steam–water two-phase mixture , 2000 .

[198]  O. Jones,et al.  Nucleation and flashing in nozzles—2. Comparison with experiments using a five-equation model for vapor void development , 1993 .

[199]  Y. Zvirin,et al.  Bubble growth predictions by the hyperbolic and parabolic heat conduction equations , 1990 .

[200]  L. Rayleigh VIII. On the pressure developed in a liquid during the collapse of a spherical cavity , 1917 .

[201]  V. Dhir BOILING HEAT TRANSFER , 1998 .

[202]  Albert Mosyak,et al.  Explosive boiling of water in parallel micro-channels , 2005 .

[203]  D. Weihs,et al.  Kinetic theory analysis of explosive boiling of a liquid droplet , 2000 .

[204]  A. M. Birk,et al.  State of the art review of pressure liquefied gas container failure modes and associated projectile hazards , 1991 .

[205]  Gerd E. A. Meier,et al.  Wave splitting in a fluid of large heat capacity , 1987, Journal of Fluid Mechanics.

[206]  E. Wacholder,et al.  A two-fluid model for critical flashing flows in pipes , 1993 .

[207]  Ron Darby,et al.  On two-phase frozen and flashing flows in safety relief values , 2004 .

[208]  R. Duffey,et al.  Acoustic wave propagation in a flowing liquid-vapour mixture , 1978 .

[209]  Y. Mori,et al.  Vaporization of single liquid drops in an immiscible liquid Part I: Forms and motions of vaporizing drops , 1977 .