Mean-field/PDF numerical approach for polydispersed turbulent two-phase flows

TL;DR

This paper reviews a numerical approach combining mean-field and PDF methods for simulating polydispersed turbulent two-phase flows, emphasizing multiscale dynamics and stochastic differential equations.

Contribution

It introduces a hybrid numerical method integrating mean-field RANS equations with stochastic particle models, addressing multiscale consistency and numerical integration challenges.

Findings

Effective simulation of three different flow cases.

Demonstrated handling of multiscale particle dynamics.

Validated the numerical approach's robustness.

Abstract

The purpose of this paper is to give an overview in the realm of numerical computations of polydispersed turbulent two-phase flows, using a mean-field/PDF approach. In this approach, the numerical solution is obtained by resorting to a hybrid method where the mean fluid properties are computed by solving mean-field (RANS) equations with a classical finite volume procedure whereas the local instantaneous properties of the particles are determined by solving stochastic differential equations (SDEs). The fundamentals of the general formalism are recalled and particular attention is focused on a specific theoretical issue: the treatment of the multiscale character of the dynamics of the discrete particles, that is the consistency of the system of SDEs in asymptotic cases. Then, the main lines of the particle/mesh algorithm are given and some specific problems, related to the integration of the SDEs, are discussed, for example, issues related to the specificity of the treatment of the averaging and projection operators, the time integration of the SDEs (weak numerical schemes consistent with all asymptotic cases), and the computation of the source terms. Practical simulations, for three different flows, are performed in order to demonstrate the ability of both the models and the numerics to cope with the stringent specificities of polydispersed turbulent two-phase flows.