Boundary layer transition over a lifting body of 1.6 m length at $2^\circ$ angle of attack has been simulated at Mach 6 and a unit Reynolds number $1.0 \times 10^7$ m $^{-1}$ . The model geometry is the same as the Hypersonic Transition Research Vehicle designed by the China Aerodynamics Research and Development Center. Four distinct transitional regions are identified, i.e. windward vortex region, shoulder vortex region, windward cross-flow region and shoulder cross-flow region. Multi-dimensional linear stability analyses by solving the two-dimensional eigenvalue problem (spatial BiGlobal approach) and the plane-marching parabolized stability equations (PSE3D approach) are further carried out to uncover the dominant instabilities in the last three regions as well as the shoulder attachment-line region. The shoulder vortex is conducive to both inner and outer modes of shear-layer instability, of which the latter most likely trigger the vortex breakdown. A novel method is presented to substantially reduce the computational cost of BiGlobal and PSE3D in resolving the cross-flow instabilities in cross-flow regions. The peak frequencies of cross-flow modes lie between 15 and 45 kHz. Whereas oblique second Mack modes are marginally unstable in the windward cross-flow region, they could be strong enough to compete with the cross-flow modes in the shoulder cross-flow region. In the shoulder attachment-line region, there exists only one unstable mode of Mack instability, differing from previous studies that show a hierarchy of modes in the context of symmetrical attachment-line flows. Results of the numerical simulation and multi-dimensional stability analyses are compared when possible, showing a fair agreement between the two approaches and highlighting the necessity of considering non-parallel effects.

In this paper, a direct numerical simulation is performed to study the wake structures of a micro-ramp vortex generator in the hypersonic flow. The whole evolution process of vortical structures of the wake flow has been carefully analyzed. First, the scaling laws for the profiles of mean velocities and fluctuations have been explored. The results show that the scaling laws based on the supersonic experiments can be directly applied in the hypersonic wake flow with a few discrepancies near the wall. Then, the detailed structures of arc-like vortices are examined, and the legs of vortices are found not being connected with each other. No full vortex ring is detected in the present simulation. At the downstream of the wake flow, the intensity of arc-like vortices has been augmented when passing the separation shock. The results reveal that a vortex train composed of arc-like vortices and shear layer is formed. With the help of the proper orthogonal decomposition, the impact of arc-like vortices on the heat flux has been revealed. The alternative positive and negative strips in the streamwise direction suggest the impinging process of arc-like vortices. The frequencies of the corresponding modes further prove that the strips are the footprint of arc-like vortices.

An investigation into the linear instability of streamwise vortices over a yawed blunt cone with a half-angle of 7° at 6° angle of attack, a free-stream Mach number of 6, and a Reynolds number of 1.0 × 10⁷/m was performed. The steady laminar base flow obtained using direct numerical simulation (DNS) has a mushroom structure. Three classes of unstable modes (inner mode, outer mode, and Mack mode modified by the streamwise vortices) were identified using a two-dimensional spatial global stability analysis (bi-global). Among them, the inner mode and the modified Mack mode were discovered for the first time for such a configuration. Notably, the inner mode appears only over a short distance upstream of the cone, and its energy is mainly in the vicinity of the symmetry plane of the mushroom structure. By comparing with DNS results, it was shown that multiple instability modes can coexist physically during the transition in the leeward plane. In addition, the eN method based on global stability theory was used to predict the location of the transition along the centerline on the leeward side of the cone. It was found that the inner modes grow rapidly in the upstream region, while the outer mode near the stem of the mushroom structure dominates the transition in the downstream region. Further analysis suggests that the inner modes dominate the transition only in a noisy environment, whereas the traditional centerline modes dominate the transition in quiet free-stream conditions.

Computational fluid dynamics predictions based on machine learning methods have become an important area of turbulence and transition research. However, the otherwise efficient and low-cost transition models based on Reynolds-averaged Navier–Stokes (RANS) methods have limited capability for dealing with hypersonic conditions, owing to the strong compressibility and multimodal features that are then present. This paper develops an augmented method for transition heat flux prediction. A deep neural network (DNN) is trained using flight test data from the China Aerodynamics Research and Development Center. The subject of the flight test is an inclined blunt cone on which temperature sensors are mounted. The training data consist of RANS solutions and flight test data, with the input being the mean strain/rotation rate tensor from RANS and the output the heat flux values from the flight test. The trained DNN model based on the RANS results can give heat flux values with similar accuracy to those from the flight test. For the blunt cone, the trained DNN model can accurately forecast the heat distribution caused by the Mack mode and the cross-flow transition under various inflow conditions, and the errors in the prediction results are all within 15%. Furthermore, the generalizability of the trained DNN model is also verified on an elliptic cone under different inflow conditions. This paper provides a new transition prediction approach with low computational cost and high accuracy. The proposed method solves the problem that the transition model fails in some working conditions and avoids re-modifying empirical criteria in the RANS model. It has both advantages of a transition model and flight tests and maintains the excellent potential for application.