Direct Numerical Simulation of Particle-Laden Homogeneous Isotropic Turbulent Flows Using a Two-Fluid Model Formulation

Abstract A DNS approach for Eulerian-Eulerian dispersed particles simulation is presented in which a stress term corresponding to the uncorrelated motion of dispersed particles is identified. Two models for this stress terms are proposed. The first model uses an isentropic approximation that relates the local amount of uncorrelated particle kinetic energy to the particle number density. The second model uses a transport equation comparable to the transport equation for the internal energy in the Navier Stokes equations. The validity of the Eulerian-Euler formulation is discussed by comparing to a Lagrangian particle tracking simulation using identical carrier phase realisation. It is found that the dispersed phase behaves in both simulations like a very compressible gas when the Stokes number is close to unity. The resulting strong gradients in the particle number density field can not be resolved on the grid which is sufficient for DNS of the carrier phase. Spectral analysis of the correlated particle velocity shows the limits of validity of the present simulations.