A two-fluid approach is proposed for direct numerical simulation of particle-laden turbulent flows in two-way coupling through equilibrium assumption that is valid for particles with sufficiently small time constants. Making this assumption, a 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 and the gravity acceleration. 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 particles on the fluid phase is taken into account through source terms in the momentum equations. For the assessment purposes, particle-laden isotropic turbulence is simulated. The results obtained through this approach are compared against those obtained by a trajectory approach in which the particle equations are solved in the Lagrangian framework. It is shown that there is a good agreement between the results obtained by the proposed two-fluid model and the trajectory approach by comparing the mean turbulent kinetic energy and its dissipation rate of the fluid phase as well as their spectra.
Development of a Two-fluid Drag Law for Clustered Particles using Direct Numerical Simulation and Validation through Experiments
