Integral quantification of heat transfer in a particle-laden shearless turbulent flow

Understanding thermal mixing in turbulent flows laden with inertial particles is crucial for various industrial and natural applications. Recent studies have identified inertia, thermal inertia, turbulence characteristics, and mixing dynamics as key factors influencing this process. Our study aims to elucidate heat transfer between two homothermal regions, where fluid temperature is passively advected by a homogeneous and isotropic turbulent flow, seeded by heavy particles with a finite thermal capacity. Direct numerical simulations (DNS) reveal a substantial enhancement in heat flux, resulting in a thermal mixing layer evolving in a quasi-self-similar manner. One of the key findings is that the particle-to-fluid thermal capacity ratio is pivotal in quantifying the particles' role in enhancing thermal mixing. This enhancement is consistently observed with a fixed value exceeding unity, particularly when the ratio of particle thermal response time to particle momentum response time is higher than one. For the sake of simplicity, our analysis focuses on the role of Stokes numbers at single Taylor Reynolds number. To quantify the global impact of suspended particles on heat transfer across the entire flow domain, we introduce a novel approach involving the Total Enthalpy Integral (TEI), which provides a comprehensive measure of the heat transport process through spatially integrated moments of the total enthalpy equation. This integral encompasses diffusive, convective, and particle thermal contents. The TEI concept, successfully applied in other flow regimes (Kianfar et al., AIAA J., 2023), allows rigorous measurement of global thermal mixing augmentation in the presence of inertial particles compared to unladen turbulent flow. This offers a deeper understanding of the thermal role of particles in the mixing process, improving the prediction of turbulent flows laden with inertial particles for various applications.