Adjoint-Based Uncertainty Quantification and Calibration of RANS-Based Transition Modeling

The main objective of the present study is to use a gradient-based optimization framework to perform uncertainty quantification and sensitivity analysis for the closure coefficients of the two-equation Amplification Factor Transport (AFT) model with the aim of improving its prediction capability. Additionally, the critical amplification factor, which directly controls the onset of the transition via the source term of the intermittency equation, is calibrated for a set of canonical flat plate test cases in both bypass and natural transitional regimes. It is shown that by utilizing a sigmoid fitting of the turbulence index profile, the transition onset location can be accurately predicted in a differentiable and smooth fashion that is essential to the adjoint-based sensitivity analysis of the RANS solver. Subsequently, the results of these calibration studies are used for obtaining a new relation via a high-order polynomial regression model that can define the critical amplification factor as a function of the free-stream turbulence intensity. Finally, the efficacy of the calibrated relation is tested for the natural laminar flow NLF(1)-0416 airfoil and the results show significant improvements in predicting the transition onset location as well as lift and drag predictions.