Kinetic and turbulence models for granular and twophase flows
Abstract
Kinetic and turbulent models are being developed for granular and twophase flows. A kinetic model is introduced and the kinetic equation governing the evolution of the firstorder distibution function including the fluid drag force is presented. The particlefluid interactions are analyzed and the first order particlate distribution function is determined. The system of equations governing the mean granular velocity, solid volume fraction, and fluctuation energy are developed. The special case of a simple shear flow is studied and the predictions of the present model are compared with those of other models and the available data. Turbulent flows of dispersed multiphase solidfluid mixtures are considered. From the global equations of balance for each phase and via a special ensemble averaging technique, the local conservation laws for the mean motion are developed. The thermodynamics of the mixture in the turbulent state is studied. The concept of coldness of turbulence for each phase induced, the free energy function is discussed, and several thermodynamic relationships are established. Based on the averaged entropy inequality, constitutive equations for the stresses, energy, and heat fluxes of various species are developed. It is shown that the model contains the recently developed turbulence models for dilute twophase flows and dense granular flows as special limiting factors. Using the turbulence model, simple shear flows of a dense solidfluid mixture are studied. The equations governing the transport of mass, momentum, and fluctuation kinetic energy for different phases are considered.
 Publication:

Ph.D. Thesis
 Pub Date:
 1987
 Bibcode:
 1987PhDT........42M
 Keywords:

 Kinetic Equations;
 Particle Interactions;
 Prediction Analysis Techniques;
 Stresses;
 Turbulence Models;
 Turbulent Flow;
 Two Phase Flow;
 Boundary Value Problems;
 Conservation Laws;
 Drag;
 Mass Transfer;
 Mathematical Models;
 Momentum Transfer;
 Fluid Mechanics and Heat Transfer