  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.
