Turbulence Kinetic Energy Distribution and Heat Transfer in a Porous Layer Induced by Bluff Body Vortex Shedding

Abstract

When a turbulent vortex impinges on a porous layer, it creates a complex multiscale interaction: the wake structures that form in the free fluid engage with the intricate geometry of the pores, and this interplay governs both the turbulent energy budget and the rate of heat transfer. Here we use interface-resolved two-dimensional direct numerical simulations (DNS) to examine how a bluff-body wake impinges on an in-line porous array heated to maintain a constant wall temperature. The Reynolds number is fixed at Re = 10000, and the porosity is varied between $\phi$ = 0.80 and $\phi$ = 0.95. In all cases, the incoming von K\'arm\'an vortices undergo rapid breakdown at the porous/fluid interface and do not persist as coherent macroscale structures within the porous layer. The interface instead acts as a spectral filter: large-scale wake energy is strongly attenuated, while turbulence is regenerated locally within the matrix via shear layers and microscale vortex shedding around individual obstacles. Thermal statistics show that the lower-porosity medium produces higher local and surface-averaged Nusselt numbers across representative interface and interior locations. This is consistent with the stronger shear and enhanced fluid/solid thermal interaction associated with the larger surface-area-to-volume ratio. These results clarify the mechanisms by which wake-driven turbulence is converted into pore-scale motions and how porosity tunes the balance between turbulence attenuation and convective heat transfer in porous coatings and inserts.