Numerical investigation of the development of three-dimensional wavepackets in a sharp cone boundary layer at Mach 6

Abstract

Direct numerical simulations were performed to investigate wavepackets in a sharp cone boundary layer at Mach 6. In order to understand the natural transition process in hypersonic cone boundary layers, the flow was forced by a short-duration (localized) pulse. The pulse disturbance developed into a three-dimensional wavepacket, which consisted of a wide range of disturbance frequencies and wavenumbers. First, the linear development of the wavepacket was studied by forcing the flow with a low-amplitude pulse (0.001 % of the free-stream velocity). The dominant waves within the resulting wavepacket were identified as the second-mode axisymmetric disturbance waves. In addition, weaker first-mode oblique disturbance waves were also observed on the lateral sides of the wavepacket. In order to investigate the nonlinear transition regime, large-amplitude pulse disturbances (0.5 % of the free-stream velocity) were introduced. The response of the flow to the large-amplitude pulse disturbances indicated the presence of a fundamental resonance mechanism. Lower secondary peaks in the disturbance wave spectrum were identified at approximately half the frequency of the high-amplitude frequency band, suggesting the possibility of a subharmonic resonance mechanism. However, the spectrum also indicated that the fundamental resonance was much stronger than the subharmonic resonance. A secondary stability investigation using controlled disturbances confirmed that fundamental resonance is indeed a dominant mechanism compared to subharmonic resonance. Furthermore, strong peaks in the disturbance wave spectrum were also observed for low-azimuthal-wavenumber second-mode oblique waves, hinting at a possible oblique breakdown mechanism. Thus, the wavepacket simulations indicate that the second-mode fundamental resonance and oblique breakdown mechanisms are the strongest for the investigated flow. Hence, both mechanisms are likely to be relevant in the natural transition process for a cone boundary layer at Mach 6.

Transition in Hypersonic Boundary Layers: Role of Dilatational Waves

“…Experimental work comparing the linear growth of second mode with the results of the linear stability theory (LST) has been undertaken both in quiet [12,15,16] and noisy tunnels [13,17,18]. The nonlinear stages of the second-mode evolution and its relevance to turbulence development was investigated both by direct numerical simulations (DNS) [19][20][21][22][23] and experiments [24][25][26][27]. Issues related to the effect of the surface roughness have also been discussed [28][29][30].…”

“…They attributed these waves to be "triggered by the upstream first-or second-mode LST waves." Sivasubramanian and Fasel [22] performed DNS of the development of 3-D wavepackets in a sharp cone boundary layer at Mach 6. The packets are generated by pulsing the wall-normal velocity in a circular area on the cone's surface with broadband frequencies centered on the dominant frequency of the second mode.…”

Thermoacoustic Interpretation of Second-Mode Instability

“…For relatively sharp bodies at hypersonic speeds in particular, the transition is dominated by second-mode waves, or fast-slow modes [3], which are manifest as convectively amplified streamwise-propagating disturbances with a distinctive acoustic signature, typically in the ultrasonic range. Many numerical [4][5][6][7][8][9][10] and experimental [11][12][13][14][15][16][17][18][19][20] works have confirmed the existence of such instabilities.…”

Numerical Investigation of Second Mode Attenuation over Carbon/Carbon Surfaces on a Sharp Slender Cone

“…43 The first one is a spatially and temporally broadband pulse applied for a finite amount of time ( figure 3). This perturbation aims at mimicking a natural transition scenario and determining the most amplified frequency inside the boundary layer, and it was first used by Gaster and Grant 44 in incompressible boundary layer transition simulations and by Sivasubramanian et al 43 in hypersonics. The pulse is applied for 3.3 µs and the amplitude was chosen small enough to trigger only the linear growth mechanisms.…”