Towards Turbulence Modeling Enhancement via the Correction of Boussinesq's Hypothesis - A Data-Driven Approach

The accuracy of the Reynolds-Averaged Navier-Stokes (RANS) equations coupled with linear eddy-viscosity turbulence models still represents a limitation nowadays. In this article, we present the current state of a new methodology to reconstruct the mean flow for the NASA wall-mounted hump problem. The RANS equations enclosed with the negative Spalart-Allmaras (S-A) turbulence model are corrected by introducing a viscous flux term, which allows to escape the stringent Boussinesq's hypothesis. This is compared against a second correction strategy where flow assimilation is performed by a corrective field in the S-A turbulence model. The numerical results provide evidences that by a Boussinesq's hypothesis reformulation, the assimilated mean flow attains almost an exact agreement with the high-fidelity wall-resolved large eddy simulations results. In contrast, the correction on the eddy-viscosity variable only allows for relatively limited corrections. In this article, we address the quality of the reconstructed results by investigating different types of assimilation cost functional; the first one relies on the reconstruction using solely wall information, the pressure and skin friction distributions over the hump surface, whereas the second one assimilates the conservative variables over an entire domain of interest. A study on the wall information assimilation demonstrates that it is not possible to accurately reconstruct flow data that was not used in the assimilation procedure. In comparison the second approach improves the overall accuracy of the solution, resulting in a more robust and reliable data-assimilation process.