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Wall temperature is a crucial factor for the transition of hypersonic boundary layers. This paper investigates the wall temperature effects on the hypersonic boundary-layer transition over an inclined blunt cone with two wall temperatures by direct numerical simulations and instability analysis. The breakdown processes of leeward streamwise vortices and crossflow vortices are both studied. Inner modes with lower phase velocities and outer modes with higher phase velocities are responsible for the breakdown of leeward streamwise vortices, respectively, in cooled- and heated-wall cases. A higher wall temperature will promote the boundary layer transition in the vicinity of the leeward centerline due to the collision of nearby crossflow vortices with the leeward mushroom structure, instead of by destabilizing inner and outer modes. In the crossflow-dominated region, the transition is triggered by the interaction between second modes and crossflow vortices for the cooled-wall case. Increasing the wall temperature will promote the transition in this region even though second modes are suppressed.

The purpose of this work is to improve the efficiency of sample selection with the recursive method for wall-bounded turbulent flows. In the proposed physics-assisted recursive method, the flow field is divided into several sub-regions along the wall distance. Since the distributions of the flow variables have certain similarity along the wall normal direction, fast clustering of similar data can be achieved, which paves the way for the rapid elimination of redundant data. Then, the recursive method is used for sample selection in each sub-region. The effectiveness of the proposed method is investigated through several cases. The results show that the proposed method has good convergence and grid independence and improves the computational efficiency of the recursive method for sample selection. Since the amount of training data is reduced, the time consumption of model training is decreased. In addition, it is demonstrated that sample selection can also be helpful to achieve more balanced model performance by changing the distribution of training data.

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.