Direct numerical simulation is conducted to uncover the response of a supersonic turbulent boundary layer to streamwise concave curvature and the related physical mechanisms at a Mach number of 2.95. Streamwise variations of mean flow properties, turbulent statistics and turbulent structures are analyzed. A method to define the boundary layer thickness based on the principal strain rate is proposed, which is applicable for boundary layer subjected to wall-normal pressure and velocity gradients. While the wall friction grows with the wall turning, the friction velocity decreases. A logarithmic region with constant slope exists in the concave boundary layer. However, with smaller slope, it is located lower than that of the flat boundary layer. Streamwise varying trends of the velocity and the principal strain rate within different wall-normal regions are different. The turbulent level is promoted by the concave curvature. Due to the increased turbulent generation in the outer layer, secondary bumps are noted in profiles of streamwise and spanwise turbulent intensity. Peak positions in profiles of wall-normal turbulent intensity and Reynolds shear stress are pushed outward because of the same reason. Attributed to the Görtler instability, the streamwise extended vortices within the hairpin packets are intensified and more vortices are generated. Through accumulations of these vortices with similar sense of rotation, large-scale streamwise roll cells are formed. Originated from the very large-scale motions and by promoting the ejection, sweep and spanwise events, the formation of large-scale streamwise roll cells is the physical cause of the alterations of mean properties and turbulent statistics. The roll cells further give rise to the vortex generation. The large amount of hairpin vortices formed in the near-wall region lead to the improved wall-normal correlation of turbulence in the concave boundary layer.

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A hypervelocity imperfect gas nozzle with a shared wave-elimination contour is designed by the residual correction method, allowing the test Mach number to be varied by changing the throat contours. Owing to imperfect gas effects, the nozzle designed by the classical method of characteristics with boundary layer correction does not produce a uniform flow field, resulting in significant deviation from the target Mach number. In this work, the computational fluid dynamics solver is used as an independent module without being coupled to the optimization code, reducing the design complexity. Designers can choose the appropriate solver according to the specified physical characteristics to consider imperfect gas effects. The Mach 15 hypervelocity nozzle designed by the residual correction method better eliminates the Mach waves and achieves a much higher flow uniformity than the nozzle designed by the classical method. On this basis, the dependence domain of the shared wave-elimination contour and the influence domain of the transonic solution are solved by the method of characteristics, and a replaceable throat contour is rigorously designed from aerodynamics theory. Quantitative evaluations show that the nozzles with a shared wave-elimination contour have the same level of flow uniformity, achieving high flow quality at Mach 13–15. The evaluation results validate the design's feasibility, supporting the future construction of hypervelocity tunnels.