What we can learn from direct numerical simulation of turbulence in porous media : modeling turbulent flow in composite porous/fluid domains

Abstract

Our recently published papers reporting results of Direct Numerical Simulation (DNS) of forced convection flows in porous media suggest that in a porous medium the size of turbulent structures is restricted by the pore scale. Since the turbulent kinetic energy is predominantly contained within large eddies, this suggests that turbulent flow in a porous medium may carry less energy that its counterpart in a clear fluid domain. We use this insight to develop a practical model of turbulent flow in composite porous/fluid domains. In such domains, most of the flow is expected to occur in the clear fluid region; therefore, in most cases the flow in the porous region either remains laminar or starts its transition to turbulence even if the flow in the clear fluid region is fully turbulent. This conclusion is confirmed by comparing appropriate Reynolds numbers with their critical values. Therefore, for most cases, using the Forchheimer term in the momentum equation and the thermal dispersion term in the energy equation may result in a sufficiently good model for the porous region. However, what may really affect turbulent convection in composite domains is the roughness of the porous/fluid interface. If particles or fibers that constitute the porous medium (and the pores) are relatively large, the impact of the roughness on convection heat transfer in composite porous/fluid domains may be much more significant than the impact of possible turbulence in the porous region. We use the above considerations to develop a practical model of turbulent flow in a composite porous/fluid domain, concentrating on the effect of interface roughness on turbulence.