Porosity effects in laminar fluid flow near permeable surfaces

This work analyzes the porosity effects on laminar flow and drag reduction of Newtonian fluids flowing over and through permeable surfaces. A fully developed laminar flow in a channel partially replaced with a porous material is considered. The analytical solutions for the velocity and shear stress are given and examined to identify the influence of the porosity on the flow. The scaling laws in the porous media are determined using asymptotic analysis in the limit of infinitely small permeability. Direct numerical simulations are performed and the transport equation for the kinetic energy is examined to establish the dependency of the porosity on the flow. We found that the impact of the porosity depends on the permeability. For high permeability, the higher porosity induces the increase of driving force and accelerates the flow while it decelerates the flow for low permeability by causing stronger viscous drag of the porous medium.