PDF model based on Langevin equation for polydispersed two-phase flows applied to a bluff-body gas-solid flow,

TL;DR

This paper presents a detailed theoretical and numerical model for turbulent polydispersed two-phase flows using Langevin equations within the PDF formalism, validated through simulation of a bluff-body gas-solid flow with two-way coupling.

Contribution

It introduces specific enhancements to the PDF-based Langevin model for two-phase flows, including an extra term for two-way coupling and detailed numerical evaluation methods.

Findings

Model accurately simulates bluff-body flow with recirculation.

Inclusion of two-way coupling improves physical realism.

Numerical validation confirms model's effectiveness.

Abstract

The aim of the paper is to discuss the main characteristics of a complete theoretical and numerical model for turbulent polydispersed two-phase flows, pointing out some specific issues. The theoretical details of the model have already been presented [Minier and Peirano, Physics Reports, Vol. 352/1-3, 2001 ]. Consequently, the present work is mainly focused on complementary aspects, that are often overlooked and that require particular attention. In particular, the following points are analysed : the necessity to add an extra term in the equation for the velocity of the fluid seen in the case of twoway coupling, the theoretical and numerical evaluations of particle averages and the fulfilment of the particle mass-continuity constraint. The theoretical model is developed within the PDF formalism. The important-physical choice of the state vector variables is first discussed and the model is then expressed as a stochastic differential equation (SDE) written in continuous time (Langevin equations) for the velocity of the fluid seen. The interests and limitations of Langevin equations, compared to the single-phase case, are reviewed. From the numerical point of view, the model corresponds to an hybrid Eulerian/Lagrangian approach where the fluid and particle phases are simulated by different methods. Important aspects of the Monte Carlo particle/mesh numerical method are emphasised. Finally, the complete model is validated and its performance is assessed by simulating a bluff-body case with an important recirculation zone and in which two-way coupling is noticeable.