A theoretical study of annular supersonic nozzles

Abstract

This paper is concerned with the design of annular supersonic nozzles to produce uniform flow in supersonic wind tunnels which are axi-symmetrical and which have an internal coaxial circular cylinder throughout. Symmetrical two-dimensional and conventional axi-symmetrical nozzles are special cases of annular nozzles. Proposals are made for design criteria sufficient to ensure that the flow inside a nozzle is free from limit lines and shock waves; the criteria for (symmetrical) two-dimensional and (conventional) axi-symmetrical nozzles are new. The two outstanding procedures for designing two-dimensional and axi-symmetrical nozzles are generalised to apply to annular nozzles. One of the design procedures is mainly analytical and the other is mainly numerical; the analytical expressions in both procedures are made much more complicated by the presence of the internal cylinder but the numerical process (the method of characteristics) is not. The design criteria and the mainly numerical design procedure are successfully applied to the design of a particular annular nozzle.