Performance differences and design method improvement of Laval nozzles under superatmospheric and subatmospheric conditions

To enhance the performance of subatmospheric supersonic wind tunnels, this study explores the design of Laval nozzle profiles using the method of characteristics. For Mach numbers ranging from 1.2 to 1.8, various nozzle designs are validated using numerical simulations, and the performance differences between superatmospheric and subatmospheric conditions are analyzed. An improved formula for boundary layer correction under subatmospheric conditions is developed using the least-squares method, and its reliability is numerically verified. All nozzle designs considered in this study perform outstandingly in superatmospheric conditions, with outlet Mach number errors of less than 0.2%. Under subatmospheric conditions, the outlet Mach number errors increase by a factor of ten, and the maximum total pressure loss coefficient approaches 5.57%, representing an increase in almost 30% over the superatmospheric case. The reduced Reynolds number of subatmospheric conditions causes areas of high total pressure loss to accumulate near the wall boundary layer, which induces an increase in the boundary layer displacement of 0.2–0.4 mm and reduces the effective expansion ratio by 0.24%–0.67%. The improved boundary layer correction formula has broad applicability for Mach 1.1–2.0 nozzles under subatmospheric conditions. In such scenarios, the improved nozzles reduce the total pressure loss by 22.18%–32.37% compared with unimproved nozzles.