The planar spread of a liquid jet and hydraulic jump on a porous layer

Abstract

The flow of a planar liquid free surface jet impinging on a porous layer is theoretically examined, with particular emphasis on the influence of porosity ϕ, stress jump coefficient χ, and depth of the porous layer on the super- and sub-critical regions. Despite the numerous studies in the literature on the flow over a porous medium, the jet impingement on a porous layer has not been studied. An averaging integral approach is adopted to capture the flow in the developing boundary-layer and fully viscous regions upstream of the hydraulic jump. Asymptotic analyses for small distance from impingement, small porosity, and small porous layer depth are also conducted, elucidating the various mechanisms behind the behavior predicted numerically. We find a domain of validity for the stress jump coefficient χ in which numerical and experimental values of χ from the literature seem to fall. The transition point, where the outer edge of the boundary layer intersects the film surface, moves downstream with increasing porosity and stress jump coefficient accompanied by a drop in the film thickness. While the height of the hydraulic jump generally decreases with increasing ϕ for any permeability, the jump location decreases for small χ and increases for large χ.