Numerical Solution of Deforming Evaporating Droplets at Intermediate Reynolds Numbers

Abstract A finite volume numerical model, using a nonorthogonal adaptive grid, has been developed to examine both steady deformed and transient deforming droplet behavior. The model has been tested by comparison with existing numerical solutions and experimental data. Computations of the steady state evaporation of n-heptane droplets in high-temperature air (T∗ ∞ = 1000 K, 10 ≤ Re∞ ≤ 100, We∞ ≤ 10) show deformed oblate shapes with major axes perpendicular to the mean flow direction. Using volume equivalent diameters, predictions based on existing Nusselt and Sherwood number correlations for spherical droplets are in good agreement with the numerical results. A new correlation is presented for the drag coefficient of deformed vaporizing droplets.

[1]  L. G. Leal,et al.  Numerical solution of free-boundary problems in fluid mechanics. Part 2. Buoyancy-driven motion of a gas bubble through a quiescent liquid , 1984, Journal of Fluid Mechanics.

[2]  Michael J. Miksis,et al.  Axisymmetric bubble or drop in a uniform flow , 1981, Journal of Fluid Mechanics.

[3]  H. R. Pruppacher,et al.  A wind tunnel investigation of the internal circulation and shape of water drops falling at terminal velocity in air , 1970 .

[4]  G. D. Raithby,et al.  Transient deformation and evaporation of droplets at intermediate Reynolds numbers , 1994 .

[5]  C. H. Byers,et al.  Characteristics of electric-field-induced oscillations of translating liquid droplets , 1990 .

[6]  J. Masliyah,et al.  NUMERICAL SOLUTION OF HEAT AND MASS TRANSFER FROM SPHEROIDS IN STEADY AXISYMMETRIC FLOW , 1972 .

[7]  C. H. Byers,et al.  Drop oscillations in liquid-liquid systems , 1989 .

[8]  I. Demirdzic,et al.  Space conservation law in finite volume calculations of fluid flow , 1988 .

[9]  D. Jones,et al.  The Shape of Raindrops. , 1959 .

[10]  M. Perić,et al.  FINITE VOLUME METHOD FOR PREDICTION OF FLUID FLOW IN ARBITRARILY SHAPED DOMAINS WITH MOVING BOUNDARIES , 1990 .

[11]  R. Gunn,et al.  THE TERMINAL VELOCITY OF FALL FOR WATER DROPLETS IN STAGNANT AIR , 1949 .

[12]  David S. Dandy,et al.  Buoyancy-driven motion of a deformable drop through a quiescent liquid at intermediate Reynolds numbers , 1989, Journal of Fluid Mechanics.

[13]  N. Cheremisinoff,et al.  Shapes and velocities of single drops and bubbles moving freely through immiscible liquids. , 1976 .

[14]  K. Cliffe,et al.  Isothermal flow past a blowing sphere , 1985 .

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

[16]  M. Renksizbulut,et al.  Experimental Study of Droplet Evaporation in a High-Temperature Air Stream , 1983 .

[17]  L. G. Leal,et al.  Numerical solution of free-boundary problems in fluid mechanics. Part 1. The finite-difference technique , 1984, Journal of Fluid Mechanics.

[18]  G. Raithby,et al.  Transient deformation of freely-suspended liquid droplets in electrostatic fields , 1991 .

[19]  R. Kessler,et al.  Comparison of finite-volume numerical methods with staggered and colocated grids , 1988 .

[20]  A. Reinhart Das Verhalten fallender Tropfen , 1964 .

[21]  J. F. Harper,et al.  The Motion of Bubbles and Drops Through Liquids , 1972 .

[22]  James E. McDonald,et al.  THE SHAPE AND AERODYNAMICS OF LARGE RAINDROPS , 1954 .

[23]  S. Patankar Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[24]  J. G. Hnat,et al.  Spherical cap bubbles and skirt formation , 1976 .

[25]  Xianguo Li,et al.  A mass transfer correlation for droplet evaporation in high-temperature flows , 1991 .

[26]  J. P. V. Doormaal,et al.  ENHANCEMENTS OF THE SIMPLE METHOD FOR PREDICTING INCOMPRESSIBLE FLUID FLOWS , 1984 .

[27]  Numerical investigation of the steady viscous flow past a stationary deformable bubble , 1985 .

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

[29]  K. Asano,et al.  NUMERICAL ANALYSIS OF DRAG COEFFICIENTS AND THE HEAT AND MASS TRANSFER OF SPHEROIDAL DROPS , 1986 .