7. Turbulence Equations for a Disperse Phase

This chapter deals with turbulence modeling for a disperse phase embedded in a continuous one. By disperse phase turbulence, we do not mean the turbulence existing in the interior of fluid particles (if any). Instead, we mean the fluctuating motion of the particles themselves, each particle having its own velocity that is different from the mean velocity of the swarm. In order to do this kind of turbulence description, a two-particle Number Density Function (NDF) is introduced (one continuous fluid particle and one discrete particle). Real particles are replaced by “stochastic particles” which are assumed to give the same statistics than the real particles. A Langevin modeling approach is also introduced to model the fluid velocity seen by the particles. All the turbulence equations for the two phases are rewritten according to this formalism, and the compatibility relations between the equations of this chapter and the equations derived in the previous chapters are indicated. The present chapter ends with the introduction of the inter-particles collisions in some of the equations derived, and a summary of the closure issues.