Heat-fluid-solid coupling model for turbulent forced convection within porous media
Phys. Rev. Fluids 10, 064502 – Published 25 June, 2025
DOI: https://doi.org/10.1103/67vg-cfqb
Abstract
The momentum dispersion model of flows in porous media has been validated and successfully applied by Rao and Jin [J. Fluid Mech. 937, A17 (2022)]. However, the modeling of heat-fluid-solid coupling in turbulent forced convection requires further development. This research identifies two primary scaling laws for the heat transfer coefficient between the fluid and solid: with for the Darcy regime and for the Forchheimer regime, both taking into account the Prandtl number. The transition between the two scaling regimes occurs around . To effectively connect these two regimes, a bridge function is employed. The influence of thermal dispersion on energy transport is approximated using a Laplacian term, analogous to the momentum dispersion model. A Taylor expansion is utilized to calculate the effective thermal diffusivity in relation to the local Reynolds number . The first two leading-order terms of the series are adopted. The corresponding model coefficients are determined by fitting direct numerical simulation (DNS) results. The effective thermal diffusivity approaches molecular diffusivity as porosity approaches 1, while it tends toward infinity as porosity approaches zero. The macroscopic energy equation is applied in conjunction with our previous macroscopic momentum equation and has been validated across four typical scenarios. The results indicate that the proposed coupled macroscopic models maintain a high level of accuracy across a wide range of Darcy numbers, Reynolds numbers, porosities, and Prandtl numbers. The coupled macroscopic equations, though calibrated with statistically stationary DNS data, can predict not only statistically stationary temperature distributions but also overall temperature evolutions successfully, which is addressed in this research.
