Coupled modelling of turbulent forced thermal convection in anisotropic porous media

The momentum dispersion model for flows in isotropic porous media has been validated and successfully applied by Rao & Jin (2022, J. Fluid Mech., vol. 937, A17). However, the anisotropic coupled models concerning heat–fluid–solid interactions in turbulent forced convection requires further development. This research proposes various anisotropic physical coefficient tensors to model the total drag Rᵢ , interphase energy resistance H , momentum dispersion and thermal dispersion accounting for both anisotropic and isotropic scenarios. The effective physical coefficients of the Darcy–Forchheimer equation regarding Rᵢ are adapted to accommodate anisotropy. The heat transfer coefficient h between the solid and fluid, despite being a scalar, is also required to depend on the local flow direction in anisotropic cases. Two scaling laws of h with respect to a local Reynolds number ReK are found: h~ ReK² for the Darcy regime, and h~ ReK1/2 for the Forchheimer regime, with a transition at ReK~ 1 . The influence of momentum and thermal dispersions, along with the modelling errors of Rᵢ and H originating from heterogeneity, are approximated using a second-order pseudo-stress tensor and a pseudo-flux vector, respectively. The effective viscosity and thermal diffusivity tensors are simplified into longitudinal and transverse components using tensor symmetries, and are assumed to rely mainly on another local Reynolds number Red . Both components of the effective viscosity are positive in isotropic cases, whereas the longitudinal component may be negative in anisotropic cases, mainly serving as a compensation of overestimated drag. The coupled models are applied to simulate turbulent forced thermal convection in porous media with one or two length scales across a wide range of Reynolds numbers. The comparisons with direct numerical simulations results imply that the coupled macroscopic models can accurately predict not only statistically stationary distributions but also real-time changes in velocity and temperature.