Anisotropic Reaction Force Model in Two-way Coupling Simulation for a Smaller Particle Than Grid Spacing Based on Volume Averaging

In the framework of local volume-averaging for two-way coupling simulation of particle-laden flows, we have developed a force model that represents the particle reaction to the fluid. By considering the stress profile on the surface of finite size particles, our previous model was capable of representing the reaction force distribution even without fully resolving the boundary layer around the particle of comparable size to the grid spacing. In our method, the anisotropy of the surface stress is reasonably taken into account in the reaction force. To extend the applicability for particles smaller than the grid spacing, a smoothing method is developed in a consistent way with the discretization of the numerical simulation. The effectiveness of the smoothing method is demonstrated by applying to the following four fundamental fluid-particle interaction problems; a stationary particle in a uniform flow, a moving particle in a vortical flow, a rotating particle in fluid at rest and a particle suspension in a shear flow. The anisotropic contribution of the reaction force is reasonably represented by the smoothing method applied to the volume averaging technique particularly for rotating particle case. For the suspension in the shear flow, the non-physical effect of the grid size is suppressed by the smoothing method. Therefore, the developed reaction force model is effective for the case that the effects of shear and rotation are dominant.