An Inviscid Supersonic Nozzle Design Approach to Perfect Flow Uniformity for Wind Tunnel Applications

A large number of papers have been published on supersonic nozzle design since Prandtl and Buseman first applied the Method of Characteristics in a paper published in 1929. This study explores a method by Evvard and Marcus published in 1952 for 2D supersonic wind tunnel nozzle designs. Based on the Method of Characteristics, this nozzle design method achieves continuous wall curvature avoiding disturbances to the supersonic flow field and providing the curvature continuity needed for variable Mach number flexible-walled nozzles. In the current study, the method is found to be capable of creating perfectly uniform test section air flow for a fixed-block nozzle design for supersonic Mach numbers ≤ 5.5. Moreover, simultaneously achieving perfect flow uniformity, smooth curvatures, and single inflection point, the nozzle contours for the range of Mach numbers can span a common length which is required in a flexible-walled nozzle. In addition, the current study also develops a visualization capability to inspect the characteristics network and resultant nozzle flow field. It is discovered that as the accelerating Mach numbers turn constant and uniform in the rhombus region, the accompanying compression (right-running characteristic) waves become perfectly linear and their reflections remain so downstream. No wave cancellation is implemented or observed, which differs from the description in other design methods.