Effects of wall temperature on separation structures in supersonic flow over a semi-circular cavity

The influence of wall temperature on the vortex structure and flow characteristics of flow in semi-circular cavities is numerically investigated in this paper. The results show that the separation and reattachment points move downstream, and the secondary vortex increases with increases in wall temperature. In the secondary vortex section, normalized wall shear stress in the polar map has good consistency at different wall temperatures, and the flow properties of the three extreme points on the map are similar to Couette flow. In addition, the secondary vortex region can be regarded as an isobaric high-pressure region, while the pressure gradients slowly vary as the wall temperature increases. We confirm the independence of separation pressure for the wall temperature using pressure distribution and find that the peak and inflection points are at the reattachment points and separation points, respectively. Moreover, using a series of numerical calculations of the positions of the vortex center at different wall temperatures, explicit empirical formulas for estimating the positions of the primary vortex center are put forward. Using a topological mapping method, cavity flow is converted into quasi-one-dimensional steady-state compressible viscous flow through a variable cross-section pipe, and the flow parameter distribution, including the Mach number and pressure, conforms to the rule of quasi-one-dimensional flow.