Self-induced velocity disturbance correction in Euler-Lagrange simulations of dense particle-laden flows

When simulating dense particle-laden flows with the volume-filtered Euler-Lagrange (VFEL) method, the flow disturbance caused by the transfer of momentum from a moving point-particle to the underlying fluid is known to introduce an error in the estimation of the fluid forces acting on this particle. This flow disturbance indeed prevents direct access to the local undisturbed fluid velocity, which is needed to estimate fluid-particle forces with reduced models. Over the past years, several models have been proposed so as to correct this error. However, they mostly rely on steady Stokes/Oseen flow solutions, augmented with semi-empirical factors accounting for inertial and/or transient effects. In this work, we present a model that considers both (weak) inertia and transient effects, together with the local volume fraction, for recovering the undisturbed velocity at the location of a point-particle in VFEL simulations. The model is obtained from discretising the linearised governing equations of the particle's self-induced flow disturbance, themselves originating from the governing volume-filtered equations of the Eulerian phase. As such, its convergence in time and space can be proven, and it does not necessitate ad-hoc or empirical parameters. The proposed model is validated with several representative test-cases.