Model form uncertainty quantification of Reynolds-averaged Navier-Stokes modeling of flows over a SD7003 airfoil

Abstract: It is well known that the Boussinesq turbulent viscosity hypothesis can yield inaccurate predictions when complex f low features are involved, e.g. laminar-turbulent transition. The focus of the study is to explore the capability of a physics-based uncertainty quantification (UQ) approach to quantify the model-form uncertainty in Reynolds-averaged Naiver-Stokes (RANS) simulations of laminar-turbulent transitional flows over an Selig-Donovan (SD) 7003 airfoil. This methodology perturbs the modeled Reynolds stress tensor in the momentum equations; perturbations are injected into the amplitude, eigenvalues and eigenvectors of the anisotropy Reynolds stress tensor undergone an eigen-decomposition. In this study, our analyses focus upon the amplitude perturbation. We observed a monotonic behavior of the magnitude of the predicted uncertainty bounds for different quantities of interest. High-order regressions based on the turbulence kinetic energy discrepancies are used to develop a novel switch marker function Mk to introduce perturbations in a non-uniform manner over different regions of the domain based upon prior knowledge of the limitations of the model. Importantly, the compound effect of Mk and eigenvalue perturbations show a synergy behavior, e.g., dramatically increased uncertainty bounds to account for the discrepancy in the RANS prediction; and the Mk function effectively avoids over-perturbation to the amplitude of the anisotropy Reynolds stress tensor. In this context, regression based amplitude perturbation of the anisotropy Reynolds stress tensor makes a new contribution to the RANS UQ methodology in the simulations of the airfoil transitional flows, which shows very encouraging results.