Modified thin shock layer method for supersonic flow past an oscillating cone

Abstract

The problem of supersonic flow past a circular cone oscillating about its vertex is considered. The amplitude and the frequency parameter of the oscillation are assumed to be small, and a perturbation solution in the amplitude and frequency is sought. Furthermore, thin shock layer expansion is used to derive the flowfield solution in the form of a series. The first three terms in the series are obtained, showing that the series solution tends to converge when the shock layer is very thin and otherwise it tends to diverge. The technique of parameter straining then is applied which greatly improves the accuracy and extends the range of applicability of the thin shock layer solution. In particular, simple explicit formulas for the stability derivatives are valid for moderate as well as high freestream Mach numbers and for thick as well as slender cones. Variations of the stability derivatives with the freestream Mach number, specific heat ratio, and the cone semiangle are investigated and comparisons with existing theories are included. The relation of limiting gasdynamic theory with unsteady Newtonian flow theory also is discussed. k £ MOO m n p r t t utv,w