Two-fluid approach for direct numerical simulation of particle-laden turbulent flows at small Stokes numbers

A two-fluid approach is proposed for direct numerical simulation of particle-laden turbulent flows in two-way coupling where the particle Stokes number is small. An Eulerian velocity field is calculated for the particle phase through a truncated series expansion in terms of the velocity and acceleration of the fluid phase [M. R. Maxey, J. Fluid Mech. 174, 441 (1987)]. This expansion is valid for particles with a sufficiently small Stokes number defined as the ratio of particle time constant to the Kolmogorov time scale. The transport equation of the Eulerian concentration field of particles (particle volume fraction) is solved along with the fluid-phase equations for which the effect of the particles on the fluid phase is taken into account through source terms in the momentum equations. For the assessment purposes, particle-laden decaying isotropic turbulence is studied. The results obtained through the proposed two-fluid approach are compared against those obtained by the trajectory approach in which the particle equations are solved in the Lagrangian framework. It is shown that there is a good agreement between various fluid-phase statistics obtained by these approaches for different small Stokes numbers and mean particle concentrations.