A numerical study of the interfacial transport characteristics outside spheroidal bubbles and solids

Abstract In this paper, the interfacial transport characteristics to or from spheroidal bubbles are studied numerically and the results of numerical simulations are reported. The numerical modelling uses the SIMPLE method with a non-orthogonal, boundary fitted staggered grid. The aim of this paper is to provide an understanding of the interfacial transport characteristics of inviscid spheroidal bubbles, of different geometric parameters, rising in a stagnant hot or bi-solution liquid. The flow and concentration (or temperature) fields around bubbles and similarly sized rigid spheroids are computed. Detailed analyses of the pressure and vorticity distributions at surfaces of the inviscid spheroidal bubbles are made and compared with those of similar rigid spheroids. Drag coefficients for and wake lengths behind rigid spheroids and inviscid spheroidal bubbles are also presented. Local and mean Sherwood numbers and Nusselt numbers at bubble and rigid spheroid surfaces are compared, as well as their change with the Reynolds and Schmidt numbers and geometric parameters.

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

[2]  S. Cheng,et al.  Numerical Solution of a Uniform Flow over a Sphere at Intermediate Reynolds Numbers , 1969 .

[3]  Calculation of Boundary Layers and Separation on a Spheroid at Incidence , 1982 .

[4]  S. Dennis,et al.  Calculation of the steady flow past a sphere at low and moderate Reynolds numbers , 1971, Journal of Fluid Mechanics.

[5]  Jacques Magnaudet,et al.  Accelerated flows past a rigid sphere or a spherical bubble. Part 1. Steady straining flow , 1995, Journal of Fluid Mechanics.

[6]  K. Wang,et al.  Three-dimensional separated flow structure over prolate spheroids , 1990, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[7]  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.

[8]  Yoichiro Matsumoto,et al.  Numerical Analysis of a Single Rising Bubble Using Boundary-Fitted Coordinate System , 1995 .

[9]  Joe F. Thompson,et al.  Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies , 1974 .

[10]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[11]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[12]  Separation of three-dimensional laminar boundary layers on a prolate spheroid , 1988 .

[13]  P. D. Thomas,et al.  Direct Control of the Grid Point Distribution in Meshes Generated by Elliptic Equations , 1980 .

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

[15]  Bengt Fornberg,et al.  Steady viscous flow past a sphere at high Reynolds numbers , 1988, Journal of Fluid Mechanics.

[16]  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.

[17]  L. G. Leal,et al.  Numerical solution of free-boundary problems in fluid mechanics. Part 3. Bubble deformation in an axisymmetric straining flow , 1984, Journal of Fluid Mechanics.

[18]  H. R. Pruppacher,et al.  A Numerical Study of the Drag on a Sphere at Low and Intermediate Reynolds Numbers , 1970 .

[19]  S. Komori,et al.  Comparison of using Cartesian and covariant velocity components on non‐orthogonal collocated grids , 1999 .

[20]  Wei Shyy,et al.  Computational Fluid Dynamics with Moving Boundaries , 1995 .

[21]  Andrea Prosperetti,et al.  EFFECT OF GRID ORTHOGONALITY ON THE SOLUTION ACCURACY OF THE TWO-DIMENSIONAL CONVECTION-DIFFUSION EQUATION , 1994 .

[22]  J. A. Schetz,et al.  Effect of Injection Angle on Liquid Injection in Supersonic Flow , 1980 .

[23]  Emergence of three-dimensional separation over a suddenly started prolate spheroid at incidence , 1991 .

[24]  J. Masliyah,et al.  Numerical study of steady flow past spheroids , 1970, Journal of Fluid Mechanics.