Classic shock-expansion theory provides the surface pressure of a single body moving through a two-dimensional inviscid continuum fluid at supersonic speeds. Shockwaves are assumed to be infinitely thin and attached so that there are no subsonic regions relative to the body. The flow outside of the shockwaves is assumed to be isentropic, calorically perfect, steady, and irrotational. All wave interactions are assumed to be complete attenuation or amplification, with negligible reflection or transmission. This last assumption in particular is what restricts its range of application to the near-field of single bodies. Inlet flows, supersonic blade cascades, Bussemann biplanes, wing-tail analysis, nozzle flows, supersonic exhaust, far-field sonic booms, formation flying, wind tunnel wall effects; none of these challenging examples can be properly evaluated without modeling the wave interactions.
In this post, I will present my results in attempting to model these wave interactions. I am likely not the first to apply this method and my code is currently far from efficient, but for a limited number of problems, this method could be much faster than Euler based computational fluid dynamics while avoiding some of the problems with shockwaves that the method of characteristics encounters. There will not be much discussion of the math here, but I intend to one day write another post that goes into much more detail when I have rewritten my code. For now, I have selected three cases to present. Continue reading “An Extension of Shock-Expansion Theory to Include Wave Interactions”