Dense velocity reconstruction with VIC-based time-segment assimilation

Abstract

AbstractThe vortex-in-cell time-segment assimilation (VIC-TSA) method is introduced. A particle track is obtained from a finite number of successive time samples of the tracer’s position and velocity can be used for reconstruction on a Cartesian grid. Similar to the VIC + technique, the method makes use of the vortex-in-cell paradigm to produce estimates of the flow state at locations and times other than the measured ones. The working principle requires time-resolved measurements of the particles’ velocity during a finite time interval. The work investigates the effects of the assimilated length on the spatial resolution of the velocity field reconstruction. The working hypotheses of the VIC-TSA method are presented here along with the numerical algorithm for its application to particle tracks datasets. The novel parameter governing the reconstruction is the length of the time-segment chosen for the data assimilation. Three regimes of operation are identified, based on the track length and the geometrical distance between neighbouring tracks. The regime of adjacent tracks arguably provides the optimal trade-off between spatial resolution and computational effort. The VIC-TSA spatial resolution is evaluated first by a numerical exercise; a 3D sine wave lattice is reconstructed at different values of the particles concentration. The modulation appears to reduce (cut-off delay) when the time-segment length is increased. Large-scale PIV experiments in the wake of a circular cylinder at Red = 27,000 are used to evaluate the method’s suitability to real data, including noise and data outliers. Both primary vortex structures in the Kármán wake as well as interconnecting ribs are present in this complex flow field, with a typical diameter close to the average inter-particle distance. When the time-segment is increased to adjacent tracks and beyond, a more regular time dependence of local and Lagrangian properties is observed, confirming the suitability of the time-segment assimilation for accurate reconstruction of sparse velocity data. Graphical abstract