The influence of cryogenic temperature on the shock structure of impinging under-expanded flow over a convex surface

Abstract

This study comprehensively investigates the effect of cryogenic nozzle inlet temperature on the flow structure and interactions of an under-expanded supersonic jet with a spherical solid surface. A combined experimental and numerical approach was employed to achieve this goal, utilizing high-speed Z-type schlieren visualization and Reynolds-averaged Navier–Stokes simulations with a Redlich–Kwong real gas equation of state. This study is significant as it addresses a relatively unexplored area of research on the flow structure of the cryogenic under-expanded supersonic jet. The study examines the shock pattern and interaction region through varying static inlet temperature (Tin = 178–290 K) and nozzle pressure ratio (NPR 5–14). Additionally, parameters including nozzle exit-to-throat area ratio (A/A* = 1.277), the distance between the sphere and the nozzle (1.5 cm), and the diameter of the sphere (d = 1.5 cm) were considered fixed. The results show that the supersonic jet exhibits a change in shock patterns in the first shock cell concerning the location and width of the Mach disk, accompanied by a shift in the location of the last shock crossing point and the shock plate. The simulation provides a more detailed insight into the flow, indicating a temperature drop to 105 K in the case of the cryogenic nozzle inlet. At such a low temperature, the compressibility factor exhibits a 5% reduction from unity, while in the case of the ambient nozzle inlet, the minimum temperature at the nozzle exit reached 170 K, leading to only a 1% drop in the compressibility factor, which is negligible. It triggers different flow structures concerning the nozzle inlet temperature. These findings can contribute to the complex flow structures of supersonic jets seen in different industrial and scientific fields.