Epistemic uncertainty quantification for Reynolds-averaged Navier-Stokes modeling of separated flows over streamlined surfaces

Abstract

It is well known that linear eddy-viscosity turbulence models can introduce uncertainty in predictions for complex flow features such as separation and reattachment. The goal of this paper is to advance our understanding of a physics-based approach to quantify this turbulence model form uncertainty in Reynolds-averaged Navier-Stokes simulations of separated flows over streamlined surfaces. The methodology is based on perturbing the modeled Reynolds stresses in the momentum equations; perturbations are defined in terms of a decomposition of the Reynolds stress tensor, i.e., based on the tensor magnitude and the eigenvalues and eigenvectors of the normalized anisotropy tensor. We demonstrate that the accuracy of the predicted Reynolds stress magnitude is strongly influenced by the turbulence production term and subsequently explore the anisotropy tensor eigenvalue and eigenvector perturbations that maximize or minimize turbulence production; these could be expected to provide bounds on the prediction of separation and reattachment locations. The method uses two user-defined parameters to identify the spatial extent of the perturbed region and the magnitude of the eigenvalue perturbations. Results for the flow over a periodic wavy wall and over a three-dimensional hill indicate that the perturbations that increase turbulence production decrease the extent of the separation region, while perturbations that decrease production increase the region of separated flow. The predicted bounds can successfully encompass the reference data, provided the extent of the perturbed region and the eigenvalue perturbation magnitudes are sufficiently large. Importantly, we observed a monotonic behavior of the magnitude of the predicted bounds as a function of the two user-defined parameters.