Evaluation of physics constrained data-driven methods for turbulence model uncertainty quantification

In order to achieve a virtual certification process and robust designs for turbomachinery, the uncertainty bounds for computational fluid dynamics have to be known. The formulation of turbulence closure models implies a major source of the overall uncertainty of Reynold-averaged Navier Stokes simulations. We discuss the common practice of applying a physics constrained eigenspace perturbation of the Reynolds stress tensor in order to account for the model form uncertainty of turbulence models. Since the basic methodology often leads to generous uncertainty estimates, we extend a recent approach of adding a machine learning strategy. The application of a data-driven method is motivated by striving for the detection of flow regions, which are prone to suffer from a lack of turbulence model prediction accuracy. In this way any user input related to choosing the degree of uncertainty is supposed to become obsolete. This work especially investigates an approach, which tries to determine an a priori estimation of prediction confidence, when there is no accurate data available to judge the prediction. The flow around the NACA 4412 airfoil at near-stall conditions serves to demonstrate the successful application of the data-driven eigenspace perturbation framework. We especially highlight the objectives and limitations of the underlying methodology finally.