In aerodynamic discrete adjoint optimization design systems for aircraft, the accuracy and robustness of the flow field transport equations and adjoint equations are primarily influenced by the numerical discretization schemes used for the inviscid terms. Since the adjoint equations solve the differential information of the flow field, the adjoint variables are more sensitive than the flow field transport variables, making the proper treatment of inviscid terms critically important. To address this issue, the discrete adjoint equations and sensitivity equations based on the AUSMPW+ scheme were systematically derived, and a novel discrete adjoint optimization method employing the low-dissipation AUSMPW+ scheme was proposed. The effectiveness of the proposed method was thoroughly validated through representative numerical examples, including the transonic M6 wing and the NASA common research model (CRM) wing-body configuration. The optimization results achieved remarkable total drag reductions of 28.1 counts and 32.3 counts, respectively. Extensive computational and design results consistently demonstrate that the adjoint equation solver using the low-dissipation scheme exhibits excellent robustness and high accuracy in gradient calculations. This method is applicable to three-dimensional, complex, high-precision flow field solutions and aerodynamic optimization design for modern aircraft configurations, providing a reliable and efficient numerical tool for large-scale design variable optimization problems in practical engineering applications.

The typical large sweep angle wing laminar flow design of supersonic aircraft faces the problem of boundary layer transition induced by crossflow instability. The standard e^N method based on linear stability theory involves solving eigenvalue problems and requires frequent interactive operations, which cannot meet the needs of fast transition prediction and iterative design. To address the above difficulties, a linear stability analysis is conducted on the similarity solution of the three-dimensional compressible boundary layer to generate a large number of eigenvalue samples. The powerful spatial feature extraction ability of convolutional layers is utilized to achieve automatic recognition of the input baseflow profile features, and together with the flow parameters and disturbance parameters at the outer edge of the boundary layer, they are mapped to eigenvalue or local growth rates through fully-connected layers, thus constructing an e^N convolutional neural network model suitable for predicting the instability and transition of supersonic stationary crossflow waves. By conducting stability analysis on a series of variable operating conditions and geometries of infinite swept wings, the neural network model's prediction results of disturbance amplification factors are in good agreement with the standard e^N method. Finally, based on the stability analysis and flight test data of a supersonic swept wing crossflow transition model developed by NASA, the neural network model's ability to predict transition in real three-dimensional configurations was verified. The results showed that this model has strong generalization ability and ensures high accuracy, making it a relatively simple and reliable modeling method.

The e^N method based on linear stability theory (LST) is one of the more reliable methods in the prediction of boundary layer transition. In order to greatly simplify and automate the solution process of the traditional LST eigenvalue problem, the convolutional neural network (CNN) is trained on the LST analysis sample set of the boundary layer similarity solution. For the streamwise and crossflow instabilities, the local growth rate, N factor and transition location are predicted by CNN on a naturally laminar airfoil and an infinite swept-back wing respectively, which are in good agreement with the results of standard LST. It is verified that CNN can encode the velocity derivative information of the boundary layer profile into a scalar feature that satisfies the Galilean invariance, and plays a role in characterizing the pressure gradient in the boundary layer of an airfoil or the crossflow intensity in the boundary layer of a swept-back wing. Based on the prediction of LST eigenvalues by CNN, the total loss function is constructed by the governing equations of LST, the boundary conditions and the trivial solution penalty term to train the physics-informed neural network (PINN), which realizes an accurate prediction of LST eigenfunctions without relying on samples. The results show that the PINN model can provide an effective modeling method for the eigenfunction problem of LST.

After nearly half a century’s research, it is known that the e^N method based on linear stability theory (LST) is one of the most reliable methods for the boundary layer transition prediction. However, the traditional LST is difficult to be applied to complex aerodynamic configurations due to its complicated process of searching for the solution. With the rapid development of local-variable-based transition models, it has become a research hotspot to model the analysis process of the traditional LST, that is, to transform the LST analysis into a computational fluid dynamics (CFD) problem. After Coder & Maughmer developed the transport equation for the amplification factor of two-dimensional Tollmien-Schlichting (T-S) waves, the amplification factor transport equation for stationary crossflow waves in incompressible boundary layers was first proposed in 2019 and then extended to transonic flows in 2020 by the present authors. In this study, a wind-tunnel test model that only targets the crossflow transition of a transonic swept wing boundary layer was selected to verify the rationality and accuracy of the method. It is shown that, the proposed local prediction formula for the key indicator factor of crossflow is reasonable, and the prediction results based on the amplification factor are in good agreement with the standard LST and wind tunnel test results.