Lagrangian and Eulerian dynamics of coherent structures in turbulent flow over periodic hills using time-resolved tomo PIV and “Shake-the-box”

Kurzfassung

In the present work two advanced optical measurement techniques, time-resolved tomographic PIV and the newly developed 4D-PTV technique “Shake-The-Box” (STB), show its ability of delivering important and complementing field data of fluid mechanical significance within an experimental study of a generic turbulent periodic hill flow (ERCOFTAC test case 81) on the basis of the same series of particle images. The experiment was carried out at the periodic hill water tunnel at the TU Munich using six 4 Mpx CMOS cameras and a high-repetition pulse laser for volume illumination of tracers within the EC funded frame work project AFDAR. While the first technique is well known to deliver Eulerian velocity data on a regular 3D grid in a robust way and thus the full time-dependent velocity gradient tensor with a relatively high, but limited spatial resolution, the newly developed STB technique opens the door to a fully Lagrangian point of view of a (the same) densely seeded flow and at the same time nearly completely solving the ghost particle problem. This two-fold approach – with the additional possibility of interpolating the irregular Lagrangian track data from the STB evaluation onto a regular grid - enabling combined analyses of the interaction of fluid-elements and coherent flow structures e.g. its local topologies. Two-point-space-time correlations and conditional averaging as well as spatio-temporal tracking of flow events are possible for the first time in cross-talk of both frames of reference with highly accurate time–resolved 3D data from experiments. Furthermore, the huge amount of Lagrangian track data is used for spatially high-resolved global statistics using bin-averaging. This approach is delivering e.g. accurate velocity profiles of all components (also for strong shear flow), corresponding RMS-fields and all components of the Reynolds stress tensor. PDFs of Lagrangian velocity and acceleration or spectra without the limits of the low-pass filtering of an interrogation window can be derived easily if statistical convergence can be reached. The dense Lagrangian acceleration data can be used as well for the determination of time-resolved 3D pressure fields via integration of the Poisson equation. In this study only a small portion of the possibilities can be shown or indicated due to statistical limits of the present data-set and some missing post-processing tools for the relatively rare and experimentally new field of an Eulerian and Lagrangian cross-analysis.