Force model for a stationary finite-size spherical particle in compressible turbulence

Abstract

In this study, the force model for a finite-size stationary spherical particle in a compressible turbulent flow is numerically investigated from particle-resolved direct numerical simulations at various Mach numbers with a ghost-point immersed boundary method. We first show that it makes insignificant difference whether the volume-averaged or surface-averaged physical quantity is used in the force model, and whether the Reynolds and Mach numbers are obtained by using averaged parameters (e.g., average slip velocity, density, viscosity) or by averaging the local Reynolds and Mach numbers, respectively. Averaging followed by differentiation is better than differentiation followed by averaging for the calculation of the momentum derivative term in the inviscid-unsteady force. From our results, it is a good choice to just use the quasi-steady and undisturbed forces to predict the force on the finite-size particles in compressible turbulence, particularly for the supersonic case with the particle Mach number above 1. For the subsonic case, the inclusion of the inviscid-unsteady force improves the prediction accuracy for the streamwise force and the inclusion of all types of forces is most accurate for the lateral force. When the slip velocity is calculated from the disturbed average fluid velocity on a spherical surface, the surface with the radius being one particle diameter provides the best prediction for the quasi-steady force on the particle in turbulence. However, the accuracy of this method for the prediction of the instantaneous force is much lower than the approach of calculating the undisturbed velocity from the simulation without the particle.