Measuring the full dissipation rate tensor in homogeneous turbulence

Abstract

Recent developments in dense Lagrangian Particle Tracking with Shake-The-Box (Schanz et al. 2016) and data assimilation techniques, like FlowFit (Gesemann et al. 2016), raises hope that for moderate Reynolds numbers the full (time-resolved) velocity gradient tensor might be capturedexperimentally at high-spatial resolution more accurately than in previous generic turbulence measurements by e.g. Tomo-PIV. Here we present measurements of the full velocity gradient and dissipation rate tensor based on dense fields of fluid particle trajectories in homogeneous turbulence at Re-lambda~270 and ~370 in a von Kármán flow between two counter-rotating propellers. Applying the Shake-The-Box (STB) particle tracking algorithm (Schanz et al. 2016) we are able to instantaneously track up to ~100,000 particles in a measurement volume of 40 x 40 x 15 mm³. The data assimilation scheme FlowFit (Gesemann et al. 2016) applies Navier-Stokes- constraints by imposing conservation of mass and momentum to interpolate the scattered velocity and acceleration data by continuous 3D B-Splines in a cubic grid of cells, enabling to recover (locally) the smallest flow scales in the center of tetrahedrons of particles in close proximity (r < 3-Eta for the time-resolved 3D velocity, acceleration and pressure fields. Measuring Aij and 3D pressure fields at full temporal- and spatial resolution in experimental fluid mechanics is a highly desired capability since its beginning. Based on such data many derived quantities of high importance for data driven developments of advanced CFD methods and related turbulence models can be delivered which in turn can enhance their applicability towards higher Reynolds numbers and full coupled FSI problems e.g. for innovative aircraft design purposes.