Scaling analysis of incident shock wave / boundary layer interaction in the presence of expansion fan

In this paper, the incident shock wave/turbulent boundary layer interaction (SWTBLI) in the presence of an expansion corner is investigated by numerical simulations. With the emphasis on the influence mechanism of the expansion fan for the interaction scale, the effects of the expansion corner angle and the relative positions between the shock impinging point and the expansion corner on the flow field structure and the distributions of the wall pressure and the wall friction coefficient in the interaction zone are discussed respectively. The study has found that as the expansion corner is located downstream of the shock impinging point and the expansion corner angle is larger than the incident shock deflection angle, the scale of the interaction zone is only related to the relative position between the expansion corner and the shock impinging point, and is not affected by the expansion corner angle. A scale-prediction method is proposed for the interaction flow under this flow condition. Considering the effect of the expansion fan as a weakening of the intensity of the incident shock, the corrected incident shock deflection angle under the effect of the expansion fan is defined. Then based on the results of the wide-range numerical simulations, the fitting equation of the corrected incident shock deflection angle is determined. Finally, according to the corrected shock deflection angle and the classical scaling method of SWTBLIs, the scale of the interaction zone influenced by the expansion fan can be solved. Published experimental results and high-precision simulation results are employed to verify the accuracy of the prediction method proposed in this paper.