Direct Coupling Between Eulerian and Lagrangian Approaches in Turbulent Gas-Solid Flows

The purpose of this paper is both to present and validate the methodology of a hybrid method coupling a Eulerian and a Lagrangian approaches in turbulent gas-particle flows. The knowledge of the dispersed phase is displayed in terms of a joint fluid-particle probability density function (pdf) which obeys a Boltzmann-like equation. We chose two different ways of resolution of this equation, depending on the required level of description. The first one is a stochastic Lagrangian approach which embeds a Langevin equation for the fluid velocity seen along the particle path. The second one is a Eulerian second-order momentum approach derived in the same frame as the preceding one. These two approaches are then coupled through half-fluxes. This procedures allows well-posed boundary conditions stemmed from previous time-step statistics for the two approaches. The aim is to provide a methodology able to take into account physical phenomena such as particle bouncing on rough walls or deposition in inhomogeneous flows with a reasonable numerical cost. The paper present the methodology and validations in the case of inert monodispersed particle in a turbulent shear flow without two-way coupling. Comparisons of the results of the hybrid method with each approach and LES/DPS results indicate that the hybrid method could become a powerful simulation tool for gas-particle flows.