Machine learning based uncertainty quantification of turbulence model for airfoils

Reynolds-averaged Navier-Stokes (RANS)-based transition modeling is widely used in aerospace applications but suffers inaccuracies due to the Boussinesq turbulent viscosity hypothesis. The eigenspace perturbation method can estimate the accuracy of a RANS model by injecting perturbations to its predicted Reynolds stresses. However, there lacks a reliable method for choosing the strength of the injected perturbation, while existing machine learning models are often complex and data craving. We examined two light-weighted machine learning models to help select the strength of the injected perturbation for estimating the RANS uncertainty of flows undergoing the transition to turbulence over a Selig-Donovan 7003 airfoil. On the one hand, we examined polynomial regression to construct a marker function augmented with eigenvalue perturbations to estimate the uncertainty bound for the predicted skin friction coefficient. On the other hand, we trained a convolutional neural network (CNN) to predict high-fidelity turbulence kinetic energy. The trained CNN acts as a marker function that can be integrated into the eigenspace perturbation method to quantify the RANS uncertainty. Our findings suggest that the light-weighted machine learning models are effective in constructing an appropriate marker function that is promising to enrich the existing eigenspace perturbation method to quantify the RANS uncertainty more precisely.