Thin Airfoil in Fields of Nonuniform Density, Part 1: Single Density Interface

Abstract

The classical theory of thin airfoils in unsteady low-speed flow, for example, von Karman and Sears extended to the circumstance where the undisturbed flow contains certain regions of strong density variation. The unique feature of this situation is the vorticity generated in the regions of density gradient, which, in turn, induces additional loading on the airfoil in much the same manner as does the trailing vortex sheet in conventional unsteady airfoil theory. In a special case of this problem, Marble introduced two concepts that substantially simplified an otherwise complicated situation. One was the application of Kelvin's theorem to flows where the fluid density had discontinuities that were transported with the fluid. The second and more essential simplication of the analysis was the development of a representation for the vorticity induced on a convected density interface in the form of image vortices of appropriate strength and location. The present analysis generalizes thin airfoil theory to include a single density interface convected past the airfoil at any angle with respect to the airfoil