Direct numerical simulations (DNS) were performed to investigate the laminar–turbulent transition in a boundary layer on a sharp cone with an isothermal wall at Mach 6 and at zero angle of attack. The motivation for this research is to make a contribution towards understanding the nonlinear stages of transition and the final breakdown to turbulence in hypersonic boundary layers. In particular, the role of second-mode fundamental resonance, or (K-type) breakdown, is investigated using high-resolution ‘controlled’ transition simulations. The simulations were carried out for the laboratory conditions of the hypersonic transition experiments conducted at Purdue University. First, several low-resolution simulations were carried out to explore the parameter space for fundamental resonance in order to identify the cases that result in strong nonlinear interactions. Subsequently, based on the results from this study, a set of highly resolved simulations that proceed deep into the turbulent breakdown region have been performed. The nonlinear interactions observed during the breakdown process are discussed in detail in this paper. A detailed description of the flow structures that arise due to these nonlinear interactions is provided and an analysis of the skin friction and heat transfer development during the breakdown is presented. The controlled transition simulations clearly demonstrate that fundamental breakdown may indeed be a viable path to complete breakdown to turbulence in hypersonic cone boundary layers at Mach 6.

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.

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