Two-way coupled stochastic model for dispersion of inertial particles in turbulence

Turbulent two-phase flows are characterized by the presence of multiple time and length scales. Of particular interest in flows with non-negligible interphase momentum coupling are the time scales associated with interphase turbulent kinetic energy transfer (TKE) and inertial particle dispersion. Point-particle direct numerical simulations (DNS) of homogeneous turbulent flows laden with sub-Kolmogorov size particles report that the time scale associated with the interphase TKE transfer behaves differently with Stokes number than the time scale associated with particle dispersion. Here, the Stokes number is defined as the ratio of the particle momentum response time scale to the Kolmogorov time scale of turbulence. In this study, we propose a two-way coupled stochastic model (CSM), which is a system of two coupled Langevin equations for the fluctuating velocities in each phase. The basis for the model is the Eulerian-Eulerian probability density function formalism for two-phase flows that was established in Pai & Subramaniam (J. Fluid Mech., vol. 628, 2009, pp. 181-228). This new model possesses the unique capability of simultaneously capturing the disparate dependence of the time scales associated with interphase TKE transfer and particle dispersion on Stokes number. This is ascertained by comparing predicted trends of statistics of turbulent kinetic energy and particle dispersion in both phases from CSM, for varying Stokes number and mass loading, with point-particle DNS datasets of homogeneous particle-laden flows.