Hydrodynamic development along the fluid-porous medium interface in a coupled channel-porous cavity flow via particle image velocimetry and analytical approach

The hydrodynamic development along the fluid-porous medium interface in a coupled channel-porous cavity flow was investigated. A numerical solution was obtained by solving simultaneously the Navier-Stokes' equations for fluid flow in the channel and the modified Brinkman's equations for fluid flow through the porous cavity. Appropriate boundary conditions were prescribed at the interface. It was observed that at moderate dimensionless porous cavity permeability, $\rm k \approx O(10\sp{-3}),$ the viscous shear was confined to within the thickness of $\rm O(\surd k)$ and the horizontal velocity component at the interface reached a maximum after a distance of $\rm O(Re\sb{i}k),$ where $\rm Re\sb{i}$ is the Reynolds number based on the mean inlet velocity and channel height. This length characterizes the distance to which the thickness of the boundary layer developed by the viscous shearing effect at the surface of the porous cavity reaches a constant value. In the experimental investigation, a model of the porous cavity was constructed from a packed-bed of spheres arranged in cubic formation. Velocity field measurement along the interface was made possible by matching the refractive indices of the solid and the liquid phases. The particle image velocimetry (PIV) technique was employed to quantitatively observe the hydrodynamic development of the velocity along the interface and to measure the velocity field across the channel and the surface of the porous cavity. The results of the experimental investigation were compared with those obtained from the numerical model and a satisfactory match was obtained. The detailed quantitative observation of the hydrodynamic development and the subsequent analysis represent a first effort in the direct investigation of the phenomena occurring at the fluid-porous medium interface.