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

The averaged equations of motion including the Clausius-Duhem inequality for multiphase mixtures are considered and the thermodynamics of the mean motion is studied. Based on the averaged entropy inequality, constitutive equations are formulated, and the thermodynamical constraints on material parameters are obtained. The resulting expressions for phasic stresses are anisotropic, rate-dependent and exhibit normal stress effects. It is shown that the present theory contains the recently developed turbulence models for-dilute two-phase flows and kinetic models for dense granular flows as special cases. Using these limiting conditions, the material coefficients of the model for a two-phase mixture are evaluated. The special case of simple shear flows of dense two-phase mixtures are studied in details. It is shown that the model predictions are in good agreement with the experimental data for glass beads in water and air.