Integral quantification and phase space analysis of heat transfer in a particle-laden shearless turbulent flow

We present a discussion of the enthalpy transport at the interface between two homothermal regions in a particle-laden turbulent flow, in order to quantify the role of inertial particles and of fluid-particle thermal interaction. We use a phase-space analysis of particles in a reduced phase space, and a formulation of a moment of total enthalpy integral (MTEI) applied to data from direct numerical simulations (DNS) at a Taylor microscale Reynolds number equal to 56 in a thermally coupled two-way regime. This allows us to identify the main features of particle statistics and to measure the effects of particle inertia and turbulent convection of the heat transfer, providing a quantitative and interpretable evaluation of the process which does not require any hypothesis of self-similarity. We show how particles dominate the transport mechanisms, bridging enthalpy across eddy structures, in particular when their Stokes number approaches unity, making them accumulate across temperature fronts.