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

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)-$\gamma$ model. By taking SA-$\gamma$ 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-$\gamma$ model. Furthermore, the ANN model proves to exhibit a higher calculation efficiency and better convergence quality than traditional SA-$\gamma$ model.