Applicability analysis of Sivells' method in nozzle designwith high Mach number and low total pressure

At present, the Sivells' method is widely used for the design of the inviscid hypersonic axisymmetric nozzle contour. And then, the nozzle contour viscous correction is performed by solving the axisymmetric momentum equation. This design procedure is validated by nozzles in conventional hypersonic wind tunnels and shock wind tunnels, which are operated under high Mach number and high total pressure conditions. Meanwhile, there are few validation studies of this procedure under high Mach number and low total pressure conditions. In this study, the nozzle design procedure based on the Sivells' method is used for Mach 6, 8, 10, and 12 nozzle contour design under the low total pressure condition. Furthermore, in order to analyze nozzle flowfields, numerical simulation and wind tunnel experiment are carried out. It can be found that, the flowfields in Mach 6 nozzle and Mach 8 nozzle are consistent with expectation and the jet flowfields are so good that are suitable for test. In contrast, there are some over-expanded areas in the flowfields of Mach 10 nozzle and Mach 12 nozzle, which results in higher Mach number than expectation in those areas. The jet flowfield quality of Mach 10 nozzle is better than that of Mach 12 nozzle. It can be concluded that, under the condition of low total pressure, the Sivells' method still works well for Mach 6 nozzle and Mach 8 nozzle design. Meanwhile, the method is less effective when applied to the Mach 10 nozzle and Mach 12 nozzle design.