Secondary instability of Mack mode disturbances in hypersonic boundary layers over micro-porous surface

Abstract

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.

Numerical Analysis of Porous Coatings Stabilizing Capabilities on Hypersonic Boundary-Layer Transition

“…The subsequent unstable modes, derived from the compressible inviscid Euler equations, are of acoustic nature and typically dominate the laminar-turbulent transition process beyond Mach 4 [5]. Such instabilities have been experimentally [3,6,7] and numerically [2,[8][9][10][11][12] visualized as rope-like density waves wrapped around the critical layer in close vicinity to the wall. The acoustic analogy is further supported by the work of Kuehl [13] detailing how the wall-normal gradient of the acoustic impedance would form an impedance well which physically acts as an acoustic wave-guide inside the boundary layer.…”

Effect of cone rotation on the nonlinear evolution of Mack modes in supersonic boundary layers

“…As reported by the experimental studies of Brad et al (2009), Chou et al (2011) and Chynoweth et al (2019), the streak component in this regime is always much greater than the other SI modes, forming longitudinal streak patterns. This phenomenon was later confirmed by the SI analysis based on a base flow including the saturated Mack second mode (Chen et al 2017;Xu et al 2020).…”

Spatial–temporal transformation for primary and secondary instabilities in weakly non-parallel shear flows

“…Satisfactory accuracy was also observed when this transformation was applied to subharmonic secondary instability of Mack modes in supersonic boundary layers (Xu et al. 2020). However, the transformation failed for secondary instability of fundamental resonance form.…”