Shake-The-Box: A Lagrangian tracking method for turbulence characterization at high particle densities

Abstract

In order to increase the prediction capabilities of advanced numerical methods for turbulent (wall bounded) flows at relatively high Reynolds numbers, accurate experimental validation data-sets including the full Reynolds stress tensor at high spatial resolution are urgently required. In particular the influence of pressure gradients and wall curvatures up to flow separation and the development of related shear layers need to be investigated experimentally in order to provide reliable data for the validation process and also to validate scaling laws, sub-grid- and turbulence-models. Furthermore, for advanced unsteady flow simulation methods (LES, DES, DNS etc.), the integration times and domains which are necessary for resolving flow features with very low spatial or temporal frequencies (such as superstructures in high Reynolds number turbulent boundary layers or recirculation regions in separated flows) are often not sufficient for a fully converged solution. Consequently, the used experimental methods have to be able to resolve a large range of spatial and temporal scales to be useful for code validation. Recently, the Shake-The-Box (STB) technique has been developed, which is a 4D-PTV evaluation method for densely seeded flows capable of coping with ill-posed 3D particle reconstruction problems based on few camera projections by seizing the temporal information with predictive steps and applying an iterative particle reconstruction and image matching scheme (see Iterative Particle Reconstruction). Within the resulting dense Lagrangian tracks the STB technique uses temporal fitting functions based on optimal Wiener filtering along all found particle paths. The parameters of an optimal Wiener filter are determined from statistical properties of the Lagrangian position, velocity and acceleration fluctuations along the reconstructed 3D particle positions and tracks for all three components separately. This temporal filtering approach enables an accurate estimation of position, velocity and acceleration vectors and enhancing the DVR to values > 1:1000, when sufficient track lengths are provided. Therefore, STB is able to deliver accurate mean- and Reynolds stress values (and higher order statistics) by bin-averaging (down to sub-pixel spatial resolution) and additionally provide the complete time-resolved velocity gradient tensor at a relatively high spatial resolution (comparable to a very well resolved tomographic PIV measurement) by using a proper interpolation scheme given with the “Flow-Fit” algorithm that was recently developed. The STB method has been applied to wall bounded turbulence in air and water and to an m³-scale thermal plume experiment using Helium–Filled-Soap-Bubbles (HFSB) as tracers. The results will demonstrate that with STB valuable data for turbulence characterization with outstanding temporal and spatial resolution especially in (wall bounded) shear flow can be obtained.