Predicting the boundary-layer transition process is a hot research issue in aerodynamics as well as an engineering demand for aircraft design. The e^N method based on linear stability theory is widely regarded as the most scientific method for transition prediction, which has been applied in engineering practices. However, this method has theoretical shortcomings as it traditionally ignores the receptivity of the boundary layer to external disturbances, i.e., the process of exciting boundary-layer unstable waves by external disturbances. The influence factors of receptivity are numerous, but at present, their influence laws are relatively less studied and not systematically understood yet. In this study, the high-speed cone boundary layer is taken as the object to investigate the influence of key parameters such as nose bluntness, wall temperature, unit Reynolds number, and frequency on the receptivity of boundary layers to freestream slow acoustic waves. The used methods include numerical simulations of receptivity and linear stability theory. It is found that, overall, the receptivity coefficient decreases as the nose bluntness increases, and increases as the wall temperature decreases, but is almost unaffected by the unit Reynolds number. For freestream disturbances with different frequencies, the unstable mode excited in the boundary layer under adiabatic or heated wall temperature conditions include the first and second modes, among which the receptivity coefficient of the first mode is 1-2 orders of magnitude higher than that of the second mode. In addition, the receptivity coefficient decreases with increasing frequency in the first-mode excited frequency range, while it is mainly affected by the nose bluntness in the second-mode excited frequency range. The receptivity coefficient decreases first then increases with the frequency for small bluntness, decreases monotonically with the frequency for medium bluntness, and increases first then decreases for large bluntness.

The theoretical model for calculating the thermodynamic parameters of high enthalpy gases, widely used in two-temperature model solvers, has the shortcomings such as low program operation efficiency and poor numerical stability in specific applications. A simpler and more effective method for calculating the thermodynamic energy system of the two-temperature model is developed. Drawing on the fitting expressions of the thermodynamic equilibrium energy in the one-temperature model, the representation forms of the internal energy modes are reconstructed to obtain separately a linear energy term characterized by translational temperature and a nonlinear energy term characterized by vibrational temperature. Meanwhile, Chemkin’s fitting polynomials are introduced to characterize and calculate the nonlinear energy term, so as to avoid the potential numerical problems arising from the use of exponential expressions in the theoretical model. Numerical studies indicate that the new method has reliable computational accuracy in predicting thermochemical nonequilibrium flows and their associated aerodynamic characteristics, and has higher computational efficiency compared to the solvers that use the theoretical model. The average time of single step iteration can be reduced by about 12%, and the computational time for convergence can be reduced by more than 10%, which has a positive effect on improving the efficiency of simulation of thermochemical nonequilibrium flows, and has good prospects for engineering applications.

The two-dimensional global stability analysis method (BiGlobal) was employed to investigate the instability characteristics of asymmetric streamwise vortex structures at the waist of a hypersonic transition research vehicle (HyTRV), with parameters set as model length 1 600 mm, 0° angle of attack, freestream Mach number 6, unit Reynolds number 1.0×10⁷/m, and static temperature 79 K. The laminar base flow field was obtained through direct numerical simulation by a high-order finite difference method under an isothermal wall condition (300 K). The results indicate that low-velocity fluids near the top of the upper surface and along the long axis of the lower surface converge at the waist, forming streamwise vortices. The pressure gradient disparity between the two sides leads to asymmetric development of these vortices, with the one on the lower side exhibiting more pronounced curling. Stability analysis reveals that the unstable modes of asymmetric streamwise vortices at the lifting body's waist can be categorized into inner modes, outer modes, and Mack modes, aligning with previous research findings. The inner modes are primarily influenced by spanwise velocity shear, whereas the outer modes are predominantly affected by normal velocity shear. The disturbance shape functions are primarily distributed on the side where the streamwise vortex exhibits stronger curling, which is different from the traditional symmetrical streamwise vortex. Utilizing the e^N method based on global stability analysis, it is concluded that the N factor of the Mack mode is higher in the upstream region. This suggests that the Mack mode is more likely to initiate transition in a noisy environment. Conversely, the N factor of the outer mode is more pronounced in the downstream region, indicating a higher potential for transition in a quiet environment.

Boundary layer transition has a significant impact in the design of flight vehicles. At high Mach numbers, the temperature in the boundary layer rises rapidly, leading to a series of high-temperature effects, which affect the boundary layer transition process. Some physicochemical models are often introduced to reflect these effects in the numerical simulations, which greatly increases the computational cost. In the meantime, different models may give different results in the flow stability analysis. Currently, relevant research in this field is not sufficient, and the effects of typical physicochemical models have not been considered. In the present study, the linear stability theory (LST) for chemical non-equilibrium flow was developed, and the influence of chemical non-equilibrium effects on the flow stability of blunt wedge boundary layers was investigated. The differences in the boundary layer stability calculation results caused by physicochemical models such as the thermal models, the transport models, and the chemical models were analyzed. The results show that the chemical non-equilibrium effects mainly affect the N factors by changing the basic flow, thus, they can be considered merely in the basic flow calculation in order to improve the computational efficiency. The transition prediction result is insensitive to the selection of physicochemical models for second-mode dominant transition in the chemical non-equilibrium flow. However, when the contribution of the third mode to the N values is large, the influence of physicochemical model on the transition prediction cannot be ignored.