Robust experimental data assimilation for the Spalart-Allmaras turbulence model

Abstract

This study presents a methodology focusing on the use of computational model and experimental data fusion to improve the Spalart-Allmaras (SA) closure model for Reynolds-averaged Navier-Stokes solutions. In particular, our goal is to develop a technique that not only assimilates sparse experimental data to improve turbulence model performance, but also preserves generalization for unseen cases by recovering classical SA behavior. We achieve our goals using data assimilation, namely the ensemble Kalman filtering approach, to calibrate the coefficients of the SA model for separated flows. A holistic calibration strategy is implemented via the parametrization of the production, diffusion, and destruction terms. This calibration relies on the assimilation of experimental data collected in the form of velocity profiles, skin friction, and pressure coefficients. Despite using observational data from a single flow condition around a backward-facing step (BFS), the recalibrated SA model demonstrates generalization to other separated flows, including cases such as the two-dimensional (2D) NASA wall mounted hump and the modified BFS. Significant improvement is observed in the quantities of interest, i.e., the skin friction coefficient $\left(C_f\right)$ and the pressure coefficient $\left(C_p\right)$, for each flow tested. Finally, it is also demonstrated that the newly proposed model recovers SA proficiency for flows, such as a NACA-0012 airfoil and axisymmetric jet, and that the individually calibrated terms in the SA model target specific flow-physics wherein the calibrated production term improves the recirculation zone while destruction improves the recovery zone.