Data-driven turbulence modeling has been considered an effective method for improving the prediction accuracy of Reynolds-averaged Navier–Stokes equations. Related studies aimed to solve the discrepancy of traditional turbulence modeling by acquiring specific patterns from high-fidelity data through machine learning methods, such as artificial neural networks. The present study focuses on the unsmoothness and prediction error problems from the aspect of feature selection and processing. The selection criteria for the input features are summarized, and an effective input set is constructed. The effect of the computation grid on the smoothness is studied. A modified feature decomposition method for the spatial orientation feature of the Reynolds stress is proposed. The improved machine learning framework is then applied to the periodic hill database with notably varying geometries. The results of the modified method show significant enhancement in the prediction accuracy and smoothness, including the shape and size of separation areas and the friction and pressure distributions on the wall, which confirms the validity of the approach.

Turbulence modeling within the Reynolds-averaged Navier-Stokes (RANS) equations' framework is essential in engineering due to its high efficiency. Field-inversion and machine-learning (FIML) techniques have attempted to improve RANS turbulence models' predictive capabilities for separated flows. However, FIML-generated models often lack interpretability, limiting physical understanding and manual improvements based on prior knowledge. Additionally, these models typically struggle with generalization in flow fields distinct from the training set. This study addresses these issues by employing symbolic regression (SR) to derive an analytical relationship between the correction factor of the baseline turbulence model and local flow variables, enhancing the baseline model's ability to predict separated flow across diverse test cases. The shear-stress-transport (SST) model undergoes field inversion on a curved backward-facing step case to obtain the corrective factor field $\beta$, and SR is used to derive a symbolic map between local flow features and $\beta$. The SR-derived analytical function is integrated into the original SST model, resulting in the SST-SR model. The SST-SR model's generalization capabilities are demonstrated by its successful predictions of separated flow on various test cases, including 2D-bump cases with varying heights, periodic hill case where separation is dominated by geometric features, and the three-dimensional Ahmed-body case. In these tests, the model accurately predicts flow fields, showing its effectiveness in cases completely different from the training set. The Ahmed-body case, in particular, highlights the model's ability to predict the three-dimensional massively separated flows. When applied to a turbulent boundary layer with $R{e}_L=1.0\times {10}^7$, the SST-SR model predicts wall-friction coefficient and log layer comparably to the original SST model, maintaining the attached boundary-layer prediction performance.

Field inversion and machine learning are implemented in this study to describe three-dimensional (3D) separation flow around an axisymmetric hill and augment the Spalart–Allmaras (SA) model. The discrete adjoint method is used to solve the field inversion problem, and an artificial neural network is used as the machine learning model. A validation process for field inversion is proposed to adjust the hyperparameters and obtain a physically acceptable solution. The field inversion result shows that the non-equilibrium turbulence effects in the boundary layer upstream of the mean separation line and in the separating shear layer dominate the flow structure in the 3D separating flow, which agrees with prior physical knowledge. However, the effect of turbulence anisotropy on the mean flow appears to be limited. Two approaches are proposed and implemented in the machine learning stage to overcome the problem of sample imbalance while reducing the computational cost during training. The results are all satisfactory, which proves the effectiveness of the proposed approaches.

Aerodynamic prediction of glaze-ice accretion on airfoils and wings is studied using the Reynolds-averaged Navier–Stokes method. Two separation fixed turbulence models are developed by considering ...

The inlet is one of the most important components of a hypersonic vehicle. The design and optimization of the hypersonic inlet is of great significance to the research and development of hypersonic vehicles. In recent years, artificial intelligence techniques have been used to improve the efficiency of aerodynamic optimization. Deep generative models, such as variational autoencoder (VAE) and generative adversarial network (GAN), have been used in a variety of flow problems in the last two years, making fast reconstruction and prediction of the full flow field possible. In this study, a hybrid multilayer perceptron (MLP) combined with a VAE network is used to reconstruct and predict the flow field of a two-dimensional multiwedge hypersonic inlet. The obtained results show that the VAE network can reconstruct the overall flow structure of the hypersonic flow field with high accuracy. The reconstruction accuracy of complex flow structures, such as shockwaves, boundary layers, and separation bubbles, is satisfactory. The flow field prediction model based on the MLP-VAE hybrid model has a strong generalization and generation ability, achieving relatively accurate flow field prediction for inlets with geometric configurations outside the training set.