Robustness and weakness of the classical nonlinear model for circular cones at supersonic speed: New closed-forms solutions, Crossed regions, and a new theoretical lower boundary

Abstract

Any analytical closed-form solution can offer a deep insight into understanding the fundamentals of the associated theory, but it is not always available at a particular time. For example, in modern compressible flow literature, Anderson 2003, the author claimed that the equation of Taylor and McColl did not have closed form solution and must be solved numerically and that had been true for many years. In fact, just the numerical solution of the Taylor-Maccoll formulation, not the analytical one, has existed since 1933. In the original work, a conical body of circular cross section at zero angle of attack inside a supersonic flow and the corresponding shock wave were studied, ( Taylor & Maccoll 1933 and Stone 1948 and 1952)