Self-induced velocity disturbance correction with consideration of weak-inertia and transient effects in Euler-Lagrange simulations

The velocity disturbance developing out of the transfer of momentum from a moving point-particle to the underlying fluid is known to limit the accuracy of the Euler-Lagrange (EL) simulation of particle-laden flows. In EL simulations, the fluid forces acting on each particle are estimated using reduced models, which require knowing the local undisturbed fluid velocity. This conceptual velocity can be recovered by substracting the particle's self-induced velocity disturbance from the local disturbed fluid velocity. In recent years, a variety of models have been proposed for its estimation, however they mostly rely upon steady Stokes flow solutions, augmented with semi-empirical corrections for inertial and transient effects. In this work, we propose a novel unified correction that intrinsically considers these effects for the recovery of the undisturbed fluid velocity. It is based on the solution to the linearised governing equations of the particle's self-induced flow disturbance, expressed as the linear combination of regularised fundamental singular solutions to the unsteady Stokes flow equations, and does not require the introduction of empirical or ad hoc parameters. The proposed correction is validated and compared to other published corrections with relevant test-cases.