Estimation of fluid forces on a spherical particle for two-way coupling simulation based on the volume averaging

The relationship between the flow field numerically obtained by the two-way coupling simulation and the fluid force on each particle is discussed. For estimating the fluid force on a particle, the effect of the disturbance by the particle needs to be considered. In the present study, for a particle located in a steady ambient flow, the fluid force is modelled as a function of the averaged velocity and pressure over an explicitly-defined averaging volume in the disturbed field. The gradients of the pressure and velocity induced by the particle are also modelled. It is found that the discretised gradients are almost independent of the distance between the reference points for sufficiently small distances. This fact makes the gradient models independent of the grid width of the two-way coupling simulation. The proposed steady viscous force model implicitly includes the correction terms due to the strain of the undisturbed flow and the history effect as the model is constructed with the disturbed flow. For the radius of the averaging volume smaller than 5 times the particle radius, the present force estimation method based on the disturbed flow particularly works well. The results suggest that the present method is effective in the two-way coupling simulation with the particles of comparable size to the minimum length scale of the background flow. (C) 2019 Elsevier Ltd. All rights reserved.