Construction of the vortex-surface field from tomographic particle image velocimetry data of flow past a vortex generator

We extend the vortex-surface field (VSF), a Lagrangian-based flow diagnostic method, to experimental data of the tomographic particle image velocimetry (Tomo-PIV). The boundary-constraint method is applied to construct the VSF from the instantaneous Tomo-PIV velocity field in the wake flow of a ramp vortex generator (VG) at a moderate Reynolds number. Under finite experimental noises, the VSF construction has satisfactory errors, showing the applicability of the VSF to visualize Tomo-PIV data. From a Lagrangian viewpoint, the VSF is used to elucidate the formation and evolution of coherent structures in the VG wake. The initially planar vortex surfaces consisting of undisturbed vortex lines in the laminar boundary layer are first lifted as the flow past over the VG. Subsequently, the bulge-like outer vortex surfaces in the near wake of VG generate a strong shear layer, and the near-wall inner vortex surface downstream to VG is lifted by the streamwise vortices formed from the lateral VG edges. Further downstream, the outer vortex surfaces break up into arch- or hairpin-like structures due to the Kelvin--Helmholtz instability. The geometric deformation of vortex surfaces is quantified by conditional means of the VSF gradient.