A Review of Droplet Dynamics and Vaporization Modeling for Engineering Calculations

The present paper reviews the methodologies for representing the droplet motion and vaporization history in two-phase flow computations. The focus is on the use of droplet models that are realistic in terms of their efficient implementation in comprehensive spray simulations, representation of important physical processes, and applicability under a broad range of conditions. The methodologies available at present to simulate droplet motion in complex two-phase flows may be broadly classified into two categories. First one is based on the modified BBO equation. This approach is more comprehensive, but requires modifications and/or correlations at higher droplet Reynolds number. The second approach aims at developing correlations, using detailed numerical simulations or laboratory experiments, for the effects of flow nonuniformity and droplet relative acceleration on the instantaneous drag and lift coefficients. Recent advances made in the droplet vaporization models are also discussed. The advanced vaporization models include the effects of transient liquid heating, gas-phase convection, and variable thermophysical properties. All of these models are discussed, and recommendations are made for their inclusion in comprehensive two-phase computations.

[1]  P. Libby,et al.  Droplet behavior in counterflowing streams , 1989 .

[2]  J. McLaughlin Inertial migration of a small sphere in linear shear flows , 1991, Journal of Fluid Mechanics.

[3]  M. C. Yuen,et al.  On Drag of Evaporating Liquid Droplets , 1976 .

[4]  William A. Sirignano,et al.  A comparison of vaporization models in spray calculations , 1984 .

[5]  N. Kato,et al.  Experiments on the unsteady drag and wake of a sphere at high reynolds numbers , 1991 .

[6]  S. Penner,et al.  On the burning of single drops of fuel in a oxidizing atmosphere , 1954 .

[7]  W. Sirignano,et al.  Droplet vaporization model for spray combustion calculations , 1989 .

[8]  W. Sirignano Fuel droplet vaporization and spray combustion theory , 1983 .

[9]  H. Dwyer,et al.  A sphere in shear flow at finite Reynolds number: effect of shear on particle lift, drag, and heat transfer , 1990, Journal of Fluid Mechanics.

[10]  Chung King Law,et al.  Recent advances in droplet vaporization and combustion , 1982 .

[11]  Wallis S. Hamilton,et al.  Forces on a sphere accelerating in a viscous fluid , 1964, Journal of Fluid Mechanics.

[12]  Z. H. Chen,et al.  Premixed Flames in Counterflow Jets Under Rigid-Body Rotation , 1985 .

[13]  D. B. Spalding,et al.  The combustion of liquid fuels , 1953 .

[14]  P. Saffman The lift on a small sphere in a slow shear flow , 1965, Journal of Fluid Mechanics.

[15]  William A. Sirignano,et al.  Theory of convective droplet vaporization with unsteady heat transfer in the circulating liquid phase , 1979 .

[16]  Calculations of unsteady reacting droplet flows , 1989 .

[17]  Fuat Odar Unsteady motion of a sphere along a circular path in a viscous fluid , 1968 .

[18]  S. Prakash,et al.  Liquid fuel droplet heating with internal circulation , 1978 .

[19]  L. G. Leal,et al.  Particle Motions in a Viscous Fluid , 1980 .

[20]  R. Mei An approximate expression for the shear lift force on a spherical particle at finite reynolds number , 1992 .

[21]  B. Wood,et al.  The effects of chemical and physical parameters on the burning rate of a liquid droplet , 1955 .

[22]  J. Jarosiński A survey of recent studies on flame extinction , 1986 .

[23]  S. Aggarwal,et al.  On the Structure of Unconfined Turbulent Spray Flames , 1992 .

[24]  R. Eichhorn,et al.  Experiments on the lift and drag of spheres suspended in a Poiseuille flow , 1964, Journal of Fluid Mechanics.

[25]  R. Ingebo,et al.  Drag coefficients for droplets and solid spheres in clouds accelerating in airstreams , 1956 .

[26]  S. Corrsin,et al.  On the equation of motion for a particle in turbulent fluid , 1956 .

[27]  D. Drew The force on a small sphere in slow viscous flow , 1978, Journal of Fluid Mechanics.

[28]  M. Renksizbulut,et al.  Transient droplet evaporation with variable properties and internal circulation at intermediate reynolds numbers , 1988 .

[29]  G. Godsave Studies of the combustion of drops in a fuel spray—the burning of single drops of fuel , 1953 .

[30]  C. H. Chiang,et al.  Numerical analysis of convecting, vaporizing fuel droplet with variable properties , 1992 .

[31]  C. Tchen,et al.  Mean Value and Correlation Problems connected with the Motion of Small Particles suspended in a turbulent fluid , 1947 .

[32]  W. Sirignano,et al.  ANALYSIS OF VAPORIZING DROPLET WITH SLIP, INTERNAL CIRCULATION, AND UNSTEADY LIQUID-PHASE AND QUASI-STEADY GAS-PHASE HEAT TRANSFER. , 1983 .

[33]  S. Temkin,et al.  Droplet drag in an accelerating and decelerating flow , 1982, Journal of Fluid Mechanics.

[34]  W. Sirignano,et al.  Multicomponent droplet vaporization in a high temperature gas , 1984 .

[35]  K. T. Leffek,et al.  Secondary Kinetic Isotope Effects in Bimolecular Nucleophilic Substitutions. IV. The Temperature Dependence of the Deuterium Effect for the Reaction of N,N-Dimethyl-d6-aniline and Methyl p-toluenesulfonate. Correlation of Isotope Effects on Activation Parameters , 1971 .

[36]  Sung Soo Kim,et al.  Droplet motion induced by weak shock waves , 1980, Journal of Fluid Mechanics.

[37]  Gerard M. Faeth,et al.  CURRENT STATUS OF DROPLET AND LIQUID COMBUSTION , 1977 .

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

[39]  R. Clift,et al.  Motion of entrained particles in gas streams , 1971 .

[40]  W. E. Ranz,et al.  Evaporation from drops , 1952 .

[41]  J. Shuen,et al.  A time-accurate algorithm for chemical non-equilibrium viscous flows at all speeds , 1992 .

[42]  A. Hjelmfelt Stokes Flow Behavior of an Accelerating Sphere , 1967 .

[43]  J. A. Weston,et al.  Evaporation rates and drag resistance of burning drops , 1967 .

[44]  M. Renksizbulut,et al.  Numerical Study of Droplet Evaporation in a High-Temperature Stream , 1983 .

[45]  Alan Williams,et al.  Combustion of droplets of liquid fuels: A review , 1973 .

[46]  H. Dwyer,et al.  A detailed study of burning fuel droplets , 1988 .

[47]  Fuat Odar,et al.  Verification of the proposed equation for calculation of the forces on a sphere accelerating in a viscous fluid , 1966, Journal of Fluid Mechanics.

[48]  M. Renksizbulut,et al.  A Detailed Examination of Gas and Liquid Phase Transient Processes in Convective Droplet Evaporation , 1989 .

[49]  Chung King Law,et al.  Unsteady droplet combustion with droplet heating , 1976 .

[50]  J. Riley,et al.  Equation of motion for a small rigid sphere in a nonuniform flow , 1983 .

[51]  Chung King Law,et al.  Unsteady droplet combustion with droplet heating—II: Conduction limit , 1977 .