Reduced-order Kalman-filtered hybrid simulation combining particle tracking velocimetry and direct numerical simulation

The capability of state-of-the-art techniques integrating experimental and computational fluid dynamics has been expanding recently. In our previous study, we have developed a hybrid unsteady-flow simulation technique combining particle tracking velocimetry (PTV) and direct numerical simulation (DNS) and demonstrated its capability at low Reynolds numbers. Similar approaches have also been proposed by a few groups; however, applying algorithms of this type generally becomes more challenging with increasing Reynolds number because the time interval of the frame rate for particle image velocimetry (PIV) becomes much greater than the required computational time step, and the PIV/PTV resolution tends to be lower than that necessary for computational fluid dynamics. To extend the applicability to noisy time-resolved PIV/PTV data, the proposed algorithm optimizes the data input temporally and spatially by introducing a reduced-order Kalman filter. This study establishes a framework of the Kalman-filtered hybrid simulation and proves the concept by tackling a planar-jet flow at $\mathit{Re}\approx 2000$ as an example. We evaluate the filtering functions as well as convergence of the proposed algorithm by comparing with the existing PTV–DNS hybrid simulation, and show some techniques available to hybrid velocity fields by analysing vortical motion in the shear layers of the jet.