Evolution of heat transfer at the stagnation point during the detached bow shock establishment

The diffraction of a shock wave over a stationary body is a problem of interest associated with the starting of shock tubes and expansion tubes which are well suited to studies of hypersonic flows. However, these facilities are characterized by very short test times. The transient parameters during the establishment of the detached bow shock in such impulsive facilities are important for both data processing and experimental design. In the present study, numerical simulations are conducted to investigate the diffraction of a normal shock wave over a sphere and the subsequent transient phenomena in a viscous perfect-gas flow field. The incident shock Mach number ranges from 3 to 5 with a specific heat ratio of 1.4. Based on the theoretical description of the reflected shock position during bow shock formation, approximate solutions for the time histories of the stagnation-point heat flux are also derived. The analytical and numerical results agree well. The results show that the stagnation-point pressure and heat flux approach their steady-state values much more rapidly than the shock detachment distance does.