Model of interfacial term in turbulent kinetic energy equation and computation of dissipation rate for particle-laden flows

In this paper, we demonstrate that the original Troshko-Hassan model with the correction coefficient being unity should be chosen for an interfacial term in the turbulent kinetic energy equation at the statistically steady state based on the theoretical analysis and interface-resolved direct numerical simulations of the particle sedimentation in a periodic domain and an upward turbulent channel flow. In addition, the computational schemes for the viscous dissipation near the particle surface with the non-boundary-fitted mesh are examined, and the results show that the second-order single-sided differentiation for the velocity gradient at the fluid grids in the immediate vicinity of the particle surface can reduce the computational error significantly, compared to the two-sided differentiation.