Bayesian-Optimization-Based Delay Control of Hypersonic Boundary-Layer Transition

This study is dedicated to delaying the transition induced by broad-spectrum disturbances in a Mach 5.86 hypersonic flat-plate boundary layer through local steady blowing–suction control. The optimal blowing–suction parameters, including the position and amplitude of a single blowing suction as well as the positions of the dual blowing–suction with fixed amplitudes, are determined through direct numerical simulation employing Bayesian optimization. It is revealed that the effective single blowing–suction is located at a certain distance downstream of the synchronization point of the fast/slow mode corresponding to the dominant second mode. The effective dual blowing–suction positions are distributed around the position of the single blowing–suction. Within the parameter range considered in the study of the dual blowing–suction, the transition delay effect tends to improve with an increase in the sum of control amplitudes. The analysis of the transition mechanism found that the baseline transition case involves the presence of broad-spectrum second modes, oblique second modes, and first-mode oblique waves, resulting in the coexistence of multiple canonical transition mechanisms. Analysis of the control mechanism reveals that the transition delay primarily depends on the significant attenuation of the second mode and the maintenance of [Formula: see text]-shaped vortices induced by the first mode along the streamwise direction. A detailed investigation of the linear and nonlinear mechanisms behind the transition delay is conducted using resolvent analysis and wavelet bispectrum analysis. Results show that the optimized blowing–suction can suppress both the broad-spectrum second and first modes. Furthermore, the wavelet bispectrum analysis indicates that the suppressed nonlinear interactions between the second mode and the first mode oblique wave result in the inhibition of the evolution of [Formula: see text]-shaped vortices to the hairpin vortices. Finally, the robustness of the control strategy is explored. As the broad-spectrum disturbances present stronger three-dimensional effects, the transition delay effect weakens but eventually converges to half of the optimal delay effect.