This study focuses on the use of model and data fusion for improving the Spalart-Allmaras (SA) closure model for Reynolds-averaged Navier-Stokes solutions of separated flows. In particular, our goal is to develop of models that not-only assimilate sparse experimental data to improve performance in computational models, but also generalize to unseen cases by recovering classical SA behavior. We achieve our goals using data assimilation, namely the Ensemble Kalman Filtering approach (EnKF), to calibrate the coefficients of the SA model for separated flows. A holistic calibration strategy is implemented via a parameterization of the production, diffusion, and destruction terms. This calibration relies on the assimilation of experimental data collected velocity profiles, skin friction, and pressure coefficients for separated flows. Despite using of 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 2D-bump and modified BFS. Significant improvement is observed in the quantities of interest, i.e., skin friction coefficient ($C_f$) and pressure coefficient ($C_p$) for each flow tested. Finally, it is also demonstrated that the newly proposed model recovers SA proficiency for external, unseparated flows, such as flow around a NACA-0012 airfoil without any danger of extrapolation, and that the individually calibrated terms in the SA model are targeted towards specific flow-physics wherein the calibrated production term improves the re-circulation zone while destruction improves the recovery zone.

翻译：本研究聚焦于通过模型与数据融合改进Spalart-Allmaras（SA）封闭模型，以求解分离流的雷诺平均Navier-Stokes方程。具体目标为开发既能通过同化稀疏实验数据提升计算模型性能，又能恢复经典SA行为以实现对未见过算例泛化能力的模型。我们采用数据同化方法（即集合卡尔曼滤波法EnKF）标定SA模型针对分离流的系数，通过生产项、扩散项和破坏项的参数化实现整体标定策略。该标定基于同化分离流的速度剖面、壁面摩擦系数和压力系数实验数据。尽管仅使用单个流动条件（后向台阶BFS）的观测数据，重新标定的SA模型展现出对其它分离流（包括二维凸包和修正BFS等算例）的泛化能力。在所有测试流动中，关键物理量（壁面摩擦系数$C_f$和压力系数$C_p$）均得到显著改善。最后证实，新模型能恢复SA模型对外部非分离流（如NACA-0012翼型绕流）的预测能力，且无外推风险；SA模型中各单独标定项针对特定物理机制：标定后的生产项改善再循环区，而破坏项改进恢复区。