Variational problem of optimum side wall design for a narrow supersonic three-dimensional nozzle (Q1317693)

The optimum design of the side walls of the supersonic section of a three-dimensional nozzle with two planes of symmetry is considered in the narrow channel model approximation, which reduces three-dimensional to two-dimensional flow. This nozzle realizes maximum thrust for given sonic or supersonic inlet flow, upper and lower walls, maximum permissible length and pressure outside the nozzle. In general, an approximate solution of the variational problem can be obtained by the indeterminate control contour method. A rather complex relation is established between the thrust of the optimum configurations constructed and the shape of their inlet cross sections.