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-Forchheimer 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. A generalized form of Darcy's equation is used that is applicable to adiabatic flow. It retains the convective term, which is necessary if the flow is compressible. An important 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 ratio across the plate decreases, the flow remains choked, but the downstream Mach number increases. In fact, this Mach number will be greater than unity for a sufficiently small pressure ratio, in which case the downstream flow is supersonic. Thus, a wide range of downstream Mach numbers from subsonic to supersonic is possible, even though the flow is choked. For incompressible flow, the volumetric flow rate varies linearly with 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1966
- Accession Number
- AD0801622
Entities
People
- George Emanuel
- John P. Jones
Organizations
- The Aerospace Corporation