Transonic flow in plane and axisymmetric nozzles

Abstract

The solution of the transonic flow problem in the throat of a convergent-divergent nozzle in which the fluid is continuously accelerated from subsonic to supersonic velocities has been studied by many authors. In particular a first order linearized solution was first reported by Sauer [1]. Higher order solutions using power series correct to fourth order have been developed by Taylor [2] in the two-dimensional case and Hooker [3] in the axisymmetric case. However none of these solutions are applicable to a throat of high curvature necessary in the design of a propulsion nozzle of short length. In this case a solution of the full non linear partial differential equations of compressible fluid flow is required. Full solutions of these equations have been obtained by Cherry [4] and Lighthill [5] for the plane flow case using the hodograph method. Emmons [6] also obtained a single numerical solution for plane flow by relaxation which would be equally applicable to axisymmetric nozzles. This solution was obtained only after a formidable amount of hand computation of a type that would be extremely difficult to mechanise for automatic computation. More recently Holt [7] has had some success using the method of integral relations in which the form of the velocity profile in the direction perpendicular to the axis of the nozzle is prescribed.