Prediction of reynolds stress anisotropic tensor by neural network within wide speed range

Tensor based neural network (TBNN) is constructed based on Pope's effective viscosity hypothesis, and it's used to produces a mapping from the mean strain rate tensor, mean rotation rate tensor calculated by Reynolds averaged Navier-Stokes (RANS) to the high resolution Reynolds stress anisotropy tensor. The high resolution data is used to train TBNN, then TBNN will give prediction results of Reynolds stress anisotropic tensor from the RANS result. The prediction of TBNN will be compared with high resolution numerical simulation and wind tunnel results to evaluate the prediction ability of TBNN. This work expands the predictive ability of TBNN from the low speed domain to hypersonic conditions. Small sample training is performed on low speed channel flow, NACA0012 and hypersonic boundary layer and the prediction accuracy is satisfactory. In addition, the TBNN trained with channel flow accurately predicts the boundary layer of the low-speed flat plate, which verifies the generalization ability of the model. For the extrapolation channel flow at low-speed, TBNN can predict the Reynolds stress anisotropy tensor well in the range of y+ > 5, the error between direct numerical simulation (DNS), experiment and TBNN is inside 10%. Although the prediction accuracy of the low-speed airfoil is slightly lower than that of the channel flow, the cloud images predicted in the key area have significant improvement compared with RANS. For the hypersonic boundary layer, TBNN shows good predictive ability in the boundary layer, and the error between TBNN and DNS is also within 10% in the range of y+ > 5. Although Pope's constitutive law is proposed for most incompressible flows, TBNN can still predict the Reynolds stress anisotropy tensor under hypersonic conditions. The predictive ability of this method in a wide speed range is confirmed and the generalization ability of the model has also been verified. Copyright © 2022 Chinese Journal of Theoretical and Applied Mechanics. All rights reserved.