A COMBINED NEURAL NETWORK AND MULTIPLE MODIFICATION STRATEGY FOR REYNOLDS-AVERAGED NAVIER-STOKES TURBULENCE MODELING

Solving the Reynolds-averaged Navier-Stokes (RANS) equation remains an effective and practical approach in engineering applications, but the uncertainty of Reynolds stress modeling will lead to discrepancies in the prediction accuracy of this approach. With the development of artificial intelligence, the data-driven method of turbulence model combined with machine learning algorithm is more effective than the original RANS model, however, the stability and prediction accuracy of the data-driven method could still be further improved. In the present paper, a fully connected neural network is constructed to predict the eddy viscosity, and this neural network is called as Eddy Viscosity Neural Network (EVNN). Additionally, a tensor-based neural network (TBNN) is also applied to predict the higher-order eddy viscosity relationship between the unclosed quantity and the analytical quantity, and the basis tensors are used to ensure the Galilean invariance. Finally, the closed-loop accuracy of the predicted flow field is realized through multiple modifications. For the method above, the neural network which is combined by EVNN and TBNN, is trained by using the high-fidelity data generated by the large eddy simulation (LES) and the baseline data obtained by the RANS simulation. Compared with the high-fidelity LES results, the results of the modified model exhibit significantly higher accuracy in the posterior velocity field, the mean pressure coefficient, and the mean friction coefficient than the original RANS model. It can be found that the implicit treatment of the linear part of the Reynolds stress can enhance the numerical stability, and the modification of the nonlinear part of the Reynolds stress can better predict the anisotropic characteristics of the flow field. Furthermore, the prediction accuracy is further improved through the multiple modification strategy. Therefore, the combined neural network and multiple modification strategy developed in this paper, have strong potentials in data-driven turbulence modeling and engineering applications in the future.