Effect of small radius of curvature on transonic flow in axisymmetric nozzles.

Abstract

An analysis was made of the transonic flow in axisymmetric nozzles having wall radii between one-quarter and three times the throat radius. Entrance angles were varied from 30° to 75°. The analysis is based on Friedrichs' equations, by which the flowfield is developed for a prescribed velocity distribution along the nozzle axis. Each variable is expressed as a series in terms of the stream function, and fourth order terms are retained to give an accurate solution for a small throat radius of curvature. The usual assumption of steady, isentropic, irrotational flow is made, and the specific heat ratio is constant. In the throat region, the solution has been found to compare favorably with available experimental data for both small and large throat curvatures. With a large wall radius of curvature, the solution is comparable to those of Sauer, Oswatitsch, and Hall. With a small radius of curvature, the sonic line is found to differ appreciably from the parabolic sonic line of Sauer's solution. For the wall radii equal to or less than the throat radius, an inflection point occurs in the sonic line near the nozzle wall. The entrance angle influences the flow in the transonic region only when the wall radius is less than 1J times the throat radius.