Hierarchy of hybrid unsteady-flow simulations integrating time-resolved PTV with DNS and their data-assimilation capabilities

Data-assimilation capabilities of hybrid-type simulations integrating time-resolved particle image velocimetry with unsteady computational fluid dynamics (CFD) are characterized, and a series of algorithms developed previously are evaluated in terms of four criteria: (i) compatibility with the governing equations; (ii) completeness of a set of flow quantities; (iii) temporal and spatial filtering functions; and (iv) spatial resolution. This study specifically introduces a hierarchy of three hybrid simulations combining time-resolved particle tracking velocimetry (PTV) and direct numerical simulation (DNS) from low to high fidelities: the proper orthogonal decomposition-Galerkin-projection approach with proportional feedback of PTV data, the DNS solver with similar feedback, and the DNS solver with the extended Kalman filter. By solving a planar-jet problem at Re approximate to 2000, we demonstrate that the resultant hybrid flow fields essentially (i) satisfy the governing equations spatially and approximately temporally, and (ii) can provide instantaneous pressure fields (iii) with the noise levels substantially lower than those of the original PTV data and (iv) the resolution comparable to CFD. The results show that increasing the feedback gain improves replicability, i.e. the agreement between the simulation and the data; however, it degrades temporal compatibility and filtering functions. On the other hand, the fidelity enhances both replicability and spatial filtering, but increases computational cost.