Physics-enhanced data-driven turbulence model for flow around submerged bodies

Abstract

Data-driven turbulence modeling is regarded as an effective approach to enhance the predictive performance of Reynolds-Averaged Navier−Stokes (RANS) models. However, the stability and accuracy of such methods still require further improvement. Therefore, we propose a novel modified model based on a combined neural network. Within this framework, we construct a fully connected neural network to predict the eddy viscosity coefficient in the RANS equations, thereby achieving an implicit solution for the linear part of the Reynolds stress. Additionally, we introduce a tensor basis neural network to predict the higher-order eddy viscosity relationships between unclosed quantities and analytical quantities. Furthermore, the model incorporates pressure gradients and turbulent kinetic energy gradients as inputs, fully considering the influence of pressure gradients and strong non-equilibrium effects in turbulence, thereby enhancing the physical foundation of the model. To evaluate the performance of the constructed model in different-dimensional flow fields with higher Reynolds numbers, we conduct validation analyzes on a two-dimensional NACA0012 model and a three-dimensional SUBOFF model without appendages. The results indicate that the modified model consistently outperforms the RANS model, particularly in predicting the velocity field near the leading edge of the NACA0012 hydrofoil. The predictions of the modified model are closer to those of large eddy simulation (LES) results. Specifically, the root mean square error (RMSE) of the interpolated and extrapolated modified models is reduced by 49.2% and 33.3%, respectively, compared to the RMSE of the RANS model. When applied to three-dimensional isolated SUBOFF flows, the modified model’s predictions for the average velocity field and pressure coefficients at both ends of the SUBOFF are in high agreement with LES results, but the prediction accuracy in the middle section is slightly insufficient. Nevertheless, the prediction errors of the interpolated and extrapolated modified models are reduced by 69.5% and 63.6%, respectively, compared to the baseline RANS model, which fully demonstrates the high accuracy of the modified model in predicting the overall pressure distribution of the SUBOFF. The methods developed in this study provide valuable insights into high-precision intelligent modeling for two-dimensional and three-dimensional flows.