Inviscid Flow Through a Cascade of Thick, Cambered Airfoils: Part 2—Compressible Flow

Abstract

Evaluation of two-dimensional, inviscid, compressible flow through a cascade of airfoils must involve numerical methods. Some of the associated problems are avoided if the flow field is mapped to the interior of a unit circle as the airfoil boundaries become grid points of the regular array in this domain. Further, far upstream and far downstream map to points in this circle so the uniform inlet and outlet flows are simply defined. For a solution obtained in terms of a stream function the compressible flow may be derived as a numerical perturbation from an analytical, incompressible stream function. A method incorporating these features is described in detail and some results for thick, cambered airfoils in cascade are presented. As supersonic patches can exist on the airfoils for high subsonic inlet Mach numbers, a unique method of relating the density to the stream function is employed in order to enable such flows to be calculated.