COMPRESSIBLE FLOW THROUGH A POROUS PLATE

Abstract A simple one-dimensional theory is given for the steady, compressible, adiabatic flow of a perfect gas through a porous plate. The Dupuit-Forcheimer relation, valid for incompressible flow, is replaced by an isentropic compression when the gas enters the plate and a non-isentropic sudden enlargement process when it exits. Darcy's equation is used in a form applicable to compressible adiabatic flow. A consequence of this study is that the Mach number at the downstream surface may be much smaller than unity, even when the flow through the plate is choked. As the pressure at the downstream surface of the plate decreases, the flow remains choked, but the downstream Mach number increases. For a sufficiently small downstream pressure this Mach number will be greater than unity. A wide range of downstream Mach numbers from subsonic to supersonic is thus possible, even though the flow is choked. For incompressible flow, the volumetric flow rate is usually determined by the pressure differential across the plate. The equivalent compressible relation is shown to consist of a plot of upstream Mach number versus the pressure ratio across the plate. The incompressible result can also be shown on this plot; it differs from the compressible one, except when the plate is thick.