Statistical and probabilistic modeling of a cloud of particles coupled with a turbulent fluid

TL;DR

This paper introduces a new formalism for simulating particle clouds in turbulent fluids, integrating physics and stochastic processes, with initial results on simplified models and future extensions to energy-conserving interactions.

Contribution

It develops a unified framework combining physical and mathematical models for particle-fluid interactions and provides preliminary validation for simplified scenarios.

Findings

Unified mathematical and physical definitions within a common framework

Preliminary validation of reduced-order models in simplified settings

Extension to energy-conserving interactions in complex scenarios

Abstract

This paper exposes a novel exploratory formalism, which end goal is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Giventhe large panel of expertise of the list of authors, the content of this paper scans a wide range of connexnotions, from the physics of turbulence to the rigorous definition of stochastic processes. Our approachis to develop reduced-order models for the dynamics of both carrying and carried phases which remainconsistant within this formalism, and to set up a numerical process to validate these models. Thenovelties of this paper lie in the gathering of a large panel of mathematical and physical definitionsand results within a common framework and an agreed vocabulary (sections 1 and 2), and in somepreliminary results and achievements within this context, section 3. While the first three sections havebeen simplified to the context of a gas field providing that the disperse phase only retrieves energythrough drag, the fourth section opens this study to the more complex situation when the dispersephase interacts with the continuous phase as well, in an energy conservative manner. This will allowus to expose the perspectives of the project and to conclude.