Undisturbed velocity recovery with transient and weak inertia effects in volume-filtered simulations of particle-laden flows

In volume-filtered Euler-Lagrange simulations of particle-laden flows, the fluid forces acting on a particle are estimated using reduced models, which rely on the knowledge of the local undisturbed flow for that particle. Since the two-way coupling between the particle and the fluid creates a local flow perturbation, the filtered fluid velocity interpolated to the particle location must be corrected prior to estimating the fluid forces, so as to subtract the contribution of this perturbation and recover the local undisturbed flow with good accuracy. In this manuscript, we present a new model for estimating a particle's self-induced flow disturbance that accounts for its transient development and for inertial effects related to finite particle Reynolds numbers. The model also does not require the direction of the momentum feedback to align with the direction of the particle's relative velocity, allowing force contributions other than the steady drag force to be considered. It is based upon the linearization of the volume-filtered equations governing the particle's self-induced flow disturbance, such that their solution can be expressed as a linear combination of regularized transient Stokeslet contributions. Tested on a range of numerical cases, the model is shown to consistently estimate the particle's self-induced flow disturbance with high accuracy both in steady and highly transient flow environments, as well as for finite particle Reynolds numbers.