Derivation of jump conditions for the turbulence k−ϵ model at a fluid/porous interface

The boundary conditions that must be imposed at a fluid/porous interface for the turbulence k-ϵ model is investigated in a two-step up-scaling framework, already introduced to study the laminar case [Chandesris, M., Jamet, D., 2006. Boundary conditions at a planar fluid–porous interface for a Poiseuille flow. Int. J. Heat Mass Transfer 49, 2137–2150]. The form of the momentum, 〈k〉 and 〈ϵ〉 fluxes jump conditions are derived using a surface-excess theory of interfacial transport processes. These jump conditions are related to surface-excess quantities. These excess quantities are evaluated for a particular geometry of the porous medium for which DNS results are available [Breugem, W.P., Boersma, B.J., 2005. Direct numerical simulations of turbulent flow over a permeable wall using a direct and a continuum approach. Phys. Fluids 17 (2), 025103]. A very good agreement is obtained between the k-ϵ model and the DNS results. The study of this particular configuration also allows to show for the first time the validity of the macroscopic turbulent viscosity modeling for flows in porous media.