Effect of flow disturbance around a particle for fluid force estimation in two-way coupling simulation

In two-way coupling simulations of particle-laden flows, obtained flow field is disturbed by particles and spatially averaged on a grid scale. For estimating the fluid force on particles, the effect of the flow disturbance in the averaged field needs to be considered. In a direct numerical simulation containing particles of comparable size to the minimum length scale of a background flow, the effect of the flow disturbance becomes important because the grid size also becomes comparable. In the present study, a steady viscous force and a pressure gradient force are modelled as functions of averaged velocity and pressure. The effect of the size of the averaging volume is reflected in the models. For the case that the particle is fixed in a uniform flow, the effectiveness of the present estimation model of the steady viscous force is highlighted. The present models are applied to cases of uniform straining flow. The pressure gradient force is reasonably obtained. As the present model is based on the disturbed field, a fluid force contribution due to the local velocity gradient of the undisturbed flow is represented.