A stochastic model for the residence time of solid particles in turbulent Rayleigh-B\'enard Flow

TL;DR

This paper develops a simple stochastic model to predict the residence times of particles in turbulent Rayleigh-Bénard flow, capturing the effects of gravity, inertia, and convective structures with quantitative accuracy.

Contribution

The study introduces a novel stochastic model that accurately describes particle residence times in turbulent convection, incorporating effects of gravity and inertia.

Findings

Model accurately predicts residence time distributions.

Gravity and inertia independently influence residence times.

Residence times are governed by convective trip durations and particle settling probabilities.

Abstract

The Pi Chamber, located at Michigan Technological University, generates moist turbulent Rayleigh-B\'{e}nard flow in order to replicate steady-state cloud conditions. We take inspiration from this setup and consider a particle-laden, convectively-driven turbulent flow using direct numerical simulation (DNS). The aim of our study is to develop a simple stochastic model that can accurately describe the residence times of the particles in the flow, this time being determined by the complex competition between the gravitational settling of the particles, and the interaction of the particles with the turbulent structures in the flow. A simple conceptual picture underlies the stochastic model, namely that the particles take repeated trips between the top and bottom boundaries, driven by the convective cells that occur in Rayleigh-B\'{e}nard turbulence, and that their residence times are determined by the time it takes to complete one of these trips, which varies from one trip to another, and the probability of falling out to the bottom boundary after each trip. Despite the simplicity of the model, it yields quantitatively accurate predictions of the distribution of the particle residence times in the flow. We independently vary the Stokes numbers and settling velocities in order to shed light on the independent roles that gravity and inertia play in governing these residence times.