Supersonic nozzle design of arbitrary cross-section

An investigation, both theoretical and experimental in nature, has been undertaken to develop a simple method for the design of supersonic nozzles and, indeed, inlets of quite complex shapes from known or calculated axisymmetric flowfields. 1he axisymmetric flowfield is determined using a computer program based on the method of characteristics. Streamlines are calculated by direct integration of the axisymmetric stream function. 7he desired shape is chosen at the exit of the computed axisymmetric nozzle having the desired length and Mach number. Its describing points are then traced along the corresponding streamlines back to the throat. Streamsheets formed by these streamlines define the new shape. Following this approach, two three-dimensional nozzles were designed : one of elliptical cross-section and a two-dimensional wedge. Flows within the two configurations were further simulated using a general purpose three-dimensional CFD code, "PHOENICS", while the elliptical nozzle was subsequently manufactured and submitted to experimental tests. Results from the experimental tests and three-dimensional numerical simulation, as well as predictions of the performance of the nonaxisymmetric nozzles and their axisymmetric counterparts were obtained and compared. Good agreement was achieved between the several components of the study demonstrating that it is possible, using this relatively simple method, to design satisfactory three-dimensional nozzles.