Optimization of Parameter Values in the Turbulence Model Aided by Data Assimilation

This study proposes a data assimilation methodology for estimating the optimal parameter values of turbulence models. The proposed methodology was applied to the estimation of the parameter a(1) in the modified Menter k-omega shear-stress transport turbulence model. For this purpose, a fundamental turbulent flow, namely, the flow over a two-dimensional backward-facing step, was employed. The estimated value of a(1) (1.0) differed from its original value (i.e., 0.31). The modified Menter k-omega shear-stress transport turbulence model with a(1) = 1.0 was validated on several turbulent flow calculations; flows over a two-dimensional backward-facing step and a two-dimensional flat-plate boundary layer, two-dimensional transonic flows around the RAE 2822 airfoil, and three-dimensional transonic flows around the ONERA M6 wing. In simulations, the modified Menter k-omega shear-stress transport turbulence model with a(1) = 1.0 better modeled the separated and adverse pressure gradient flows than the original modified Menter k-omega shear-stress transport turbulence model with a(1) = 0.31. Furthermore, in the absence of separation and adverse pressure gradient flows, the proposed and original modified Menter k-omega shear-stress transport turbulence models computed almost the same results. These observations suggest that the proposed data assimilation methodology effectively estimates the optimal parameter values of turbulence models and that the estimated a(1) (1.0) improves the performance of the modified Menter k-omega shear-stress transport turbulence model over the original value (i.e., 0.31).