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

TL;DR

This paper develops a physics-based uncertainty quantification method for RANS simulations of flow over an SD7003 airfoil, focusing on perturbing the Reynolds stress tensor to better capture model uncertainties in transitional flows.

Contribution

It introduces a novel regression-based amplitude perturbation approach with a switch marker function to improve RANS UQ in transitional flow simulations.

Findings

Uncertainty bounds increase monotonically with perturbations.

The switch marker function effectively prevents over-perturbation.

The method shows promising results in modeling flow over the 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.