Measuring the full velocity gradient tensor and all elements of the dissipation rate in homogeneous turbulence using Shake-The-Box and FlowFit

Abstract

We present measurements of the full velocity gradient and dissipation rate tensor based on dense fields of fluid particle trajectories in homogeneous turbulence at Rel~270 and ~350 in a von Kármán flow between two counter-rotating propellers. Applying the Shake-The-Box (STB) particle tracking algorithm, we are able to instantaneously track up to ~100.000 particles in a measurement volume of 50 x 50 x 15 mm³. The mean inter-particle distance is lower than 7 Kolmogorov lengths. The data assimilation scheme FlowFit with continuity and Navier-Stokes- constraints is used to interpolate the scattered velocity and acceleration data by continuous 3D B-Splines in a cubic grid, enabling to recover (locally) the smallest flow scales. In the presentation, we show Lagrangian velocity, acceleration and jolt statistics, as well as the Eulerian counterparts on velocity and pressure gradients with respective Q-R-diagrams, compute the energy dissipation rate directly by using local velocity gradient information gained by FlowFit at midpoints of particle tetrahedra in close proximity of a few Kolmogorov lengths and compare it to known indirect approaches.