Recovering turbulent flow field from local quantity measurement: turbulence modeling using ensemble-Kalman-filter-based data assimilation

This paper is focused on the recovery of the global flow field through data assimilation of local flow quantity measurement and Reynolds-averaged Navier–Stokes (RANS) modeling. Particular attention is given to the optimization of various RANS model constants using the ensemble Kalman filter (EnKF) approach. To this end, a free round jet at Reynolds number Re = 6000 is experimentally measured using particle image velocimetry (PIV), serving as the observation data and validation purpose. A total of four different RANS models are separately employed as system models in the data assimilation, i.e., the Spalart–Allmaras, \(k - \varepsilon\), \(k - \omega\), and shear stress transport models. The results convincingly demonstrate that all models with EnKF augmentation are considerably improved compared with their original counterparts. Among all models, the \(k - \varepsilon\) model with EnKF augmentation showed the best performance in predicating the time-averaged flow quantities. Subsequently, the \(k - \varepsilon\) model with EnKF augmentation is examined to demonstrate its robustness and sensitivity for different observational data. Three different selection strategies of observational data are documented here: the velocity distributions in a region, along a line, and at a single point. For all of these selections, the observational data in the jet transition region are shown to be the best candidate for flow field recovery.