A THERMODYNAMICALLY CONSISTENT RATE-DEPENDENT MODEL FOR TURBULENT 2-PHASE FLOWS

The averaged equations of motion including the Clausius-Duhem inequali ty for multiphase mixtures are considered and the thermodynamics of th e mean motion is studied. Based on the averaged entropy inequality, co nstitutive equations are formulated, and the thermodynamical constrain ts on material parameters are obtained. The resulting expressions for phasic stresses are anisotropic, rate-dependent and exhibit normal str ess effects. It is shown that the present theory contains the recently developed turbulence models for-dilute two-phase flows and kinetic mo dels for dense granular flows as special cases. Using these limiting c onditions, the material coefficients of the model for a two-phase mixt ure are evaluated. The special case of simple shear flows of dense two -phase mixtures are studied in details. It is shown that the model pre dictions are in good agreement with the experimental data for glass be ads in water and air.