  Accurate simulation of turbulent flow with separation is an important but
challenging problem. In this paper, a data-driven Reynolds-averaged turbulence
modeling approach, field inversion and machine learning is implemented to
modify the Spalart-Allmaras model separately on three cases, namely, the S809
airfoil, a periodic hill and the GLC305 airfoil with ice shape 944. Field
inversion based on a discrete adjoint method is used to quantify the model-form
uncertainty with limited experimental data. An artificial neural network is
trained to predict the model corrections with local flow features to extract
generalized modeling knowledge. Physical knowledge of the nonequilibrium
turbulence in the separating shear layer is considered when setting the prior
model uncertainty. The results show that the model corrections from the field
inversion demonstrate strong consistency with the underlying physical mechanism
of nonequilibrium turbulence. The quantity of interest from the observation
data can be reproduced with relatively high accuracy by the augmented model. In
addition, the validation in similar flow conditions shows a certain extent of
generalization ability.
