Self-induced temperature correction for inter-phase heat transfer in Euler-Lagrange point-particle simulation

Highlights: • Rigorous analytic derivation of self-induced thermal correction in Euler-Lagrange methodology. • Extension of the low Reynolds number theory to higher Reynolds numbers through numerical simulation. • A composite thermal correction model that has been tested in the context of slow and rapid thermal evolution. • A simple criterion provided for when thermal correction is needed and when quasi-steady model is sufficient. -- Abstract: In a two-way coupled Euler-Lagrange simulation, particles are approximated as point sources and their momentum and energy exchange with the surrounding flow are modeled through point-particle force and heat transfer models. As the particle size increases and approaches the Eulerian grid, the feedback force and heat transfer become large and strongly affect the local flow at the particle location. The fluid velocity and temperature computed in the EL simulation when interpolated to the particle location will be substantially different from the corresponding undisturbed values. In this work we will follow the approach pursued in Balachandar et al. (2018) [1] for self-induced velocity correction to develop an analogous correction procedure for self-induced temperature. We obtain analytical solutions for the self-induced thermal perturbation for a steady uniform cross flow past a Gaussian filtered heat source under both steady and unsteady conditions. The analytical results are extended to finite Peclet number using numerical simulations. The resulting quasi-steady and unsteady models are tested with a simple problem of exponential thermal evolution against the corresponding EL simulation results. We also provide a simple criterion for when the self-induced temperature correction is needed in an Euler-Lagrange simulation.