The uniqueness of polynomials representing the integral quantities of a compressible boundary layer on a cylinder rotating in a flow

Experimental and theoretical results are presented from a study of the shock wave-laminar boundary layer interaction by a cylinder fitted with a skirt and rotating at high speed in a supersonic flow. An integral method is applied to the problem, as well as adjustments to the equations of circumferential motion defined by Lees and Reeves (1964). A procedure is formulated for characterizing the polynomials for the integral quantities within the boundary layer in order to obtain similarity solutions. The polynomials are generated by means of the Falkner-Skan equations for the similar velocity profiles in a compressible boundary layer. The rotation parameter is chosen and the polynomials are configured for accelerated, constant, and decelerated attached flows. Empirical evidence is presented that each parametric value is unique for a given rotational velocity.