A Lagrangian probability-density-function model for collisional turbulent fluid-particle flows. I. Model derivation

Abstract

Inertial particles in turbulent flows are characterised by preferential concentration and segregation and, at sufficient mass loading, dense particle clusters may spontaneously arise due to momentum coupling between the phases. These clusters, in turn, can generate and sustain turbulence in the fluid phase, which we refer to as cluster-induced turbulence. In the present theoretical work, we tackle the problem of developing a framework for the stochastic modelling of moderately dense particle-laden flows, based on a Lagrangian formalism, which naturally includes the Eulerian one. A rigorous formalism and a general model have been put forward focusing, in particular, on the two ingredients that are key in moderately dense flows, namely, two-way coupling in the carrier phase, and the decomposition of the particle-phase velocity into its spatially correlated and uncorrelated components. Specifically, this last contribution allows to identify in the stochastic model the contributions due to the correlated fluctuating energy and to the granular temperature of the particle phase, which determines the time scale for particle-particle collisions. Applications of the Lagrangian probability-density-function model developed in this work to moderately dense particle-laden flows are discussed in a companion paper.

References in corpus (8)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows
• Shear thickening in non-Brownian suspensions: an excluded volume effect
• PDF model based on Langevin equation for polydispersed two-phase flows applied to a bluff-body gas-solid flow,
• Forcing homogeneous turbulence in DNS of particulate flow with interface resolution and gravity
• Lagrangian filtered density function for LES-based stochastic modelling of turbulent dispersed flows
• Turbulence modulation in heavy-loaded suspensions of tiny particles
• A note on the consistency of Hybrid Eulerian/Lagrangian approach to multiphase flows

Cited by in corpus (3)

• Neural stochastic differential equations for particle dispersion in large-eddy simulations of homogeneous isotropic turbulence
• Sparse identification of multiphase turbulence closures for coupled fluid--particle flows
• Developing a Non-Newtonian Fluid Model for Dust, for Application to Astrophysical Flows