Temperature statistics of settling particles in homogeneous isotropic turbulence

Abstract

Heat transfer of settling particles in homogeneous isotropic turbulence is investigated in one-way coupled Eulerian–Lagrangian direct numerical simulations. In the absence of gravity, our observations highlight that there was a correlation between particles concentration and temperature fronts, which are characterized by high-temperature gradients. The particle clustering is mainly influenced by the preferential concentration and the non-local effect, the latter being the memory of their interaction with the flow along their trajectories. Nevertheless, gravity significantly affects the clustering of particles, which further influence the heat transfer of particles with the fluid. We find that the heat transfer of particles is intricately related to particle dynamic inertia and thermal inertia, which can be quantified by the particle Stokes number St and particle thermal Stokes number Stθ, respectively. In this study, we observe that the variance of particle temperature rate of change is independent of Stθ at small thermal inertia but inversely proportional to Stθ2 for large thermal inertia. In the presence of gravity, the variance converges to Stθ−1 for particles with negligible thermal inertia. Our findings reveal that the second-order structure function of the particle temperature, indicating the enhancement of Lagrangian scalar intermittency, adheres to a power-law behavior with limited thermal inertial particles in the dissipation region, denoted as r2. However, as Stθ increases, the power law of the structure function of the particle temperature is disrupted leading to ‘thermal caustics’. The present findings of the heat transfer behavior of settling particles advance the understanding of gravity effect, and are valuable for the modeling of heat transfer in particle-laden turbulent flows.