The stability of a hypersonic boundary layer on a flared cone was analysed for the same flow conditions as in earlier experiments (Zhang et al., Acta Mech. Sinica, vol. 29, 2013, pp. 48–53; Zhu et al., AIAA J., vol. 54, 2016, pp. 3039–3049). Three instabilities in the flared region, i.e. the first mode, the second mode and the Görtler mode, were identified using linear stability theory (LST). The nonlinear-parabolized stability equations (NPSE) were used in an extensive parametric study of the interactions between the second mode and the single low-frequency mode (the Görtler mode or the first mode). The analysis shows that waves with frequencies below 30 kHz are heavily amplified. These low-frequency disturbances evolve linearly at first and then abruptly transition to parametric resonance. The parametric resonance, which is well described by Floquet theory, can be either a combination resonance (for non-zero frequencies) or a fundamental resonance (for steady waves) of the secondary instability. Moreover, the resonance depends only on the saturated state of the second mode and is insensitive to the initial low-frequency mode profiles and the streamwise curvature, so this resonance is probably observable in boundary layers over straight cones. Analysis of the kinetic energy transfer further shows that the rapid growth of the low-frequency mode is due to the action of the Reynolds stresses. The same mechanism also describes the interactions between a second-mode wave and a pair of low-frequency waves. The only difference is that the fundamental and combination resonances can coexist. Qualitative agreement with the experimental results is achieved.

Transition and turbulence production in a hypersonic boundary layer is investigated in the Mach 6 wind tunnel at Peking University, using Rayleigh-scattering visualization, fast-response pressure measurements, and particle image velocimetry. Detailed analysis of the experimental observations is provided. It is found that, although the second mode is primarily an acoustic wave, it causes the formation of high-frequency vortical waves. Moreover, the second mode interacts strongly with low-frequency waves, which leads to immediate transition to turbulence.freestream velocity, m∕s u = velocity vector, m∕s u = x component of the velocity, m∕s v = y component of the velocity, m∕s w = z component of the velocity, m∕s x = streamwise coordinate along the cone's surface, mm y = coordinate normal to the cone's surface, mm z = transverse coordinate normal to the x-y plane, mm= viscous normal stress, Pa ρ = density, kg∕m 3 τ f = flow time scale, s τ p = particle relaxation time, s Φ = viscous dissipation function per unit volume, kg∕m · s 3 ω = vorticity, 1∕s

The evolution of second-mode instabilities in hypersonic boundary layers and its effects on aerodynamic heating are investigated. Experiments are conducted in a Mach 6 wind tunnel using fast-response pressure sensors, fluorescent temperature-sensitive paint, and particle image velocimetry. Calculations based on parabolic stability equations and direct numerical simulations are also performed. It is found that second-mode waves, accompanied by high-frequency alternating fluid compression and expansion, produce intense aerodynamic heating in a small region that rapidly heats the fluid passing through it. As the second-mode waves decay downstream, the dilatation-induced aerodynamic heating decreases while its shear-induced counterpart keeps growing. The latter brings about a second growth of the surface temperature when transition is completed.

Instability evolution in a transitional hypersonic boundary layer and its effects on aerodynamic heating are investigated over a 260 mm long flared cone. Experiments are conducted in a Mach 6 wind tunnel using Rayleigh-scattering flow visualization, fast-response pressure sensors, fluorescent temperature-sensitive paint (TSP) and particle image velocimetry (PIV). Calculations are also performed based on both the parabolized stability equations (PSE) and direct numerical simulations (DNS). Four unit Reynolds numbers are studied, 5.4, 7.6, 9.7 and $11.7\times 10^{6}~\text{m}^{-1}$ . It is found that there exist two peaks of surface-temperature rise along the streamwise direction of the model. The first one (denoted as HS) is at the region where the second-mode instability reaches its maximum value. The second one (denoted as HT) is at the region where the transition is completed. Increasing the unit Reynolds number promotes the second-mode dissipation but increases the strength of local aerodynamic heating at HS. Furthermore, the heat generation rates induced by the dilatation and shear processes (respectively denoted as $w_{\unicode[STIX]{x1D703}}$ and $w_{\unicode[STIX]{x1D714}}$ ) were investigated. The former item includes both the pressure work $w_{\unicode[STIX]{x1D703}1}$ and dilatational viscous dissipation $w_{\unicode[STIX]{x1D703}2}$ . The aerodynamic heating in HS mainly arose from the high-frequency compression and expansion of fluid accompanying the second mode. The dilatation heating, especially $w_{\unicode[STIX]{x1D703}1}$ , was more than five times its shear counterpart. In a limited region, the underestimated $w_{\unicode[STIX]{x1D703}2}$ was also larger than $w_{\unicode[STIX]{x1D714}}$ . As the second-mode waves decay downstream, the low-frequency waves continue to grow, with the consequent shear-induced heating increasing. The latter brings about a second, weaker growth of surface-temperature HT. A theoretical analysis is provided to interpret the temperature distribution resulting from the aerodynamic heating.

Transition and turbulence production in a hypersonic boundary layer is investigated in a Mach 6 wind tunnel using Rayleigh-scattering visualization, fast-response pressure measurements, and particle image velocimetry. It is found that the second-mode instability is a key modulator of the transition process. Although the second-mode is primarily an acoustic wave, it causes the formation of high-frequency vortical waves, which triggers a fast transition to turbulence.