Analytical Euler Solution for Two Dimensional Compressible Ramp Flow with Experimental Comparison

Abstract

A newly developed procedure for obtaining analytical asymptotic solutions of the two-dimensional steadystate Euler equations is applied to compressible flow past a ramp to further demonstrate its general utility. The procedure has been shown to be applicable into the low transonic range (shock free). The equations are written in natural streamline coordinates with mass flux and flow angle as dependent variables. Higher-order effects, for example, compressibility, appear as nonhomogeneous forcing terms. This new solution procedure does not require aG reen’s function for the forcing terms and has general applicability to many other disciplines, for example, heat transfer, besides fluid dynamics. Application of the new approach to flow problems having geometric corners, for example, ramp, reveals the typical singularity compounding at higher order. The analytical nature of the solution guides implementation of a nonconformal mapping and a new type of coordinate straining strategy to control the phenomenon and ensure uniform validity. Understanding of the nature of the inviscid flow near a geometric corner can be used to devise improved computational fluid dynamics surface boundary conditions at such singular points, for example, airfoil trailing edge. The analytical validity of the ramp solution is corroborated for this purpose by