Calibration of the Critical Amplification Factor for Reynolds-Averaged Navier–Stokes-Based Transition Modeling

Abstract

The present study uses an adjoint-based gradient optimization framework to perform calibration of the critical amplification factor for transition models based on the linear stability theory. More specifically, the two-equation amplification factor transport model is used, and 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, which is essential to the adjoint-based sensitivity analysis of the Reynolds-averaged Navier–Stokes solver. Subsequently, the results of these calibration studies are used for obtaining a new relation via a high-order polynomial regression model relating the critical amplification factor to the freestream turbulence intensity. Finally, the prediction capability of the calibrated relation is tested for natural transitional flows past NLF(1)-0416 and S809 airfoils. The numerical results show significant improvements in predicting the transition onset location as well as lift and drag predictions.