Statistical modelling of mass transfer in turbulent two-phase dispersed flows — 1. Model development

Abstract A closed equation for probability density function (PDF) of particles coordinates and velocities in a nonhomogeneous turbulent flow is obtained. On the base of the equation for PDF, a closed system of balance equations for concentration, momentum and energy of a chaotic motion of dispersed phase in Eulerian variables is derived. For the system of balance equations boundary conditions, describing particles interaction with a surface in a two-phase flow are found.

[1]  M. Fichman,et al.  A MODEL FOR TURBULENT DEPOSITION OF AEROSOLS , 1988 .

[2]  Green's function approach to the solution of the time dependent Fokker-Planck equation with an absorbing boundary , 1986 .

[3]  M. Wells,et al.  The effects of crossing trajectories on the dispersion of particles in a turbulent flow , 1983, Journal of Fluid Mechanics.

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

[5]  Robert E. Street,et al.  Mathematical Methods In Kinetic Theory , 1970 .

[6]  W. Uijttewaal,et al.  Particle dispersion and deposition in direct numerical and large eddy simulations of vertical pipe flows , 1996 .

[7]  G. Ahmadi,et al.  Analysis of Particle Motion in the Near-Wall Shear Layer Vortices— Application to the Turbulent Deposition Process , 1995 .

[8]  E. Ganić,et al.  Investigation of droplet deposition from a turbulent gas stream , 1981 .

[9]  V. Protopopescu,et al.  Hydrodynamic boundary conditions from kinetic theory , 1983 .

[10]  A. B. Hedley,et al.  particle deposition behaviour from turbulent flows , 1984 .

[11]  Kazuo Yamamoto,et al.  Lagrangian measurement of fluid-particle motion in an isotropic turbulent field , 1987, Journal of Fluid Mechanics.

[12]  M. Reeks.  On the continuum equations for dispersed particles in nonuniform flows , 1992 .

[13]  S. Pope.  PDF methods for turbulent reactive flows , 1985 .

[14]  Goodarz Ahmadi,et al.  Direct simulation of charged particle deposition in a turbulent flow , 1998 .

[15]  I. Derevich,et al.  Particle deposition from a turbulent flow , 1988 .

[16]  Carlo Cercignani,et al.  Mathematical Methods in Kinetic Theory , 1970 .

[17]  M. Reeks,et al.  PARTICLE DEPOSITION FROM A TURBULENT FLOW. I: A STEADY-STATE MODEL FOR HIGH INERTIA PARTICLES , 1994 .

[18]  J. Lumley,et al.  Some measurements of particle velocity autocorrelation functions in a turbulent flow , 1971, Journal of Fluid Mechanics.

[19]  K. Squires,et al.  Comparison between two-fluid model predictions and large eddy simulation results in a vertical gas-solid turbulent channel flow , 1997 .

[20]  K. Razi Naqvi,et al.  Reduction of the Fokker-Planck Equation with an Absorbing or Reflecting Boundary to the Diffusion Equation and the Radiation Boundary Condition , 1982 .