In laminar hypersonic boundary layers, it is known that secondary instability plays a crucial role in transition to turbulence. The secondary instability usually includes fundamental mode, subharmonic mode and the detuned mode. Considerable research exists on the secondary instability mechanism in hypersonic boundary layers with the smooth wall condition. The topic of using micro-porous surfaces for disturbance stabilization has recently drawn interest. The stabilization and thus a possible delay in transition, arises due to a reduction in the growth rate of the primary Mack mode by the porous surface. The paper focuses on investigating whether the secondary instability mechanism of Mack modes can also be affected by a surface porosity condition. It is known that the primary Mack mode linear disturbances are changed significantly on the porous surface, how it subsequently influences the secondary instability of the modified time varying basic flow is our concern. The analysis demonstrates that on the porous surface, as the amplitude of the primary Mack mode increases, the fundamental mode is not stable. Instead, the fundamental mode amplifies rapidly with increasing primary amplitudes. At larger secondary instability spanwise wavenumbers, when the primary amplitude exceeds a certain threshold value, the fundamental modes surpass the subharmonic modes and dominate the secondary instability. However, when the spanwise wavenumber is relatively small, especially at the spanwise wavenumber corresponding to the maximum growth rate of the subharmonic mode, the fundamental modes are weakened and lose their dominant position. We find that corresponding to different amplitudes of primary Mack mode disturbances affected by the porosity parameters, there are no strongly preferred interaction modes that dominate the secondary instability; this contrasts with smooth wall findings. We further find that the larger the pore size or porosity, the more severe is the suppression of the fundamental mode.

It is key points to improve the aerodynamic efficiency and decrease the sonic-boom intensity for the supersonic aircraft design. Sonic-boom prediction method with high precision combining the near-field sonic-boom prediction based on Reynolds-Averaged Navier-Stokes equations and the far-field sonic-boom prediction based on waveform parameter method is firstly established. Then the gradient of sonic boom with respect to the design variables is calculated by the finite difference method and is combined with the gradient of the aerodynamic object by the discrete adjoint technique, acting as the gradient of the weighed object function. Assembling two gradients, the optimization system couples Free Form Deform method、the dynamic mesh technique based on Inverse Distance Weighting interpolation method、the gradient-based optimization algorithm based on the sequential quadratic programming. Using the aerodynamic optimization system considering the sonic boom intensity, the paper conducts a nose angle deflection optimization design and an elaborate aerodynamic optimization including huge design variables and constraints on a supersonic business jet, while the optimization objects are the weighed object and the supersonic cruise drag coefficient. The results show that the nose is deflected downward and the shock wave pattern is changed, leading to a lower far-field maximum overpressure; the drag is decreased by 15.8 counts, and the wing load is moved inboard, also, the pressure drag of the outer wing reduces. Meanwhile, the pressure distribution in the outer wing has a weaker adverse pressure gradient and a more gentle pressure recovery. After optimization, the low-drag and low-sonic boom configuration is obtained, which verified the effectiveness of the optimization system.

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In hypersonic boundary layers, Mack mode disturbances play an important role in laminar–turbulence transition. Understanding the secondary instability mechanism of Mack mode disturbances will provide physical insight into turbulence generation for the researchers, which is also meaningful for transition control. According to the previous studies over straight cones and flared cones, it seems that a pressure gradient may affect the primary instability and secondary instability of Mack mode disturbances obviously. In this paper, we are trying to make it clear that what the pressure gradient effect on the secondary instability of Mack modes is and what the influence rule is. Four hypersonic flat plate cases with various pressure gradients at Mach 6 are analyzed through linear stability theory, non-linear parabolized stability equations, and spatial secondary instability theory methods. We found that the essence of the pressure gradient influence on the secondary instability mechanism is by affecting the primary amplitude of Mack modes, rather than other routes or factors. An adverse pressure gradient can enlarge both the primary instability and secondary instability growth rates and advance the transition. Moreover, an adverse pressure gradient will form a larger primary amplitude of the Mack mode, leading to a fundamental resonance dominated secondary instability. In contrast, the favorable pressure gradient will suppress the primary amplitude so that the subharmonic resonance may dominate the secondary instability. Therefore, it is very meaningful and valuable for transition prediction and turbulence generation to conduct the present study of pressure gradient effects on the secondary instability of Mack mode disturbances.

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