Artificial neural network-based one-equation model for simulation of laminar-turbulent transitional flow

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• This paper is intended to provide a new artificial neural network (ANN) strategy for turbulence modeling of Reynolds stress towards Reynolds-averaged Navier Stokes (RANS) simulation of laminar-to-turbulent transitional flows, especially those induced by laminar separations. In the proposed two-way coupling data-driven model, the ANN structure maps the relation between the RANS mean flow variables and an intermittency factor function, which is substituted for solving the intermittency factor governing equation in the Mentor’s gamma transition model. This transition-enabled ANN model proves to have excellent generalization capability and be more efficient than the benchmark SA-gamma model with much stronger robustness and higher convergence rate and accuracy. This is an important attempt for ANN technique to be incorporated into the traditional turbulence modeling framework with physical features and domain knowledge involved in the model training procedure. The present study may be of particular interest to the community of turbulence modeling with the aid of ANN or machine leaning. This paper not only provides people with an efficient engineering-practical RANS model, but suggests a new ANN-based strategy for turbulence model towards both RANS simulation and large-eddy simulation of transition-characterized flows. A mapping function between the Reynolds-averaged Navier-Stokes mean flow variables and transition intermittency factor is constructed by fully connected artificial neural network (ANN), which replaces the governing equation of the intermittency factor in transition-predictive Spalart-Allmaras (SA)- γ model. By taking SA- γ model as the benchmark, the present ANN model is trained at two airfoils with various angles of attack, Mach numbers and Reynolds numbers, and tested with unseen airfoils in different flow states. The a posteriori tests manifest that the mean pressure coefficient, skin friction coefficient, size of laminar separation bubble, mean streamwise velocity, Reynolds shear stress and lift/drag/moment coefficient from the present two-way coupling ANN model almost coincide with those from the benchmark SA- γ model. Furthermore, the ANN model proves to exhibit a higher calculation efficiency and better convergence quality than traditional SA- γ model.