Measurements of the energy dissipation rate in homogeneous turbulence using dense 3D Lagrangian Particle Tracking and FlowFit

Abstract

We present measurements of the full velocity gradient tensor and all volumetric dissipation rate elements based on dense fields of fluid particle trajectories in homogeneous turbulence at Re ~270 and ~370 in a Kármán flow between two counter-rotating disks with impellers. Applying the Shake-The-Box (STB) Lagrangian Particle Tracking (LPT) algorithm, we are able to instantaneously track up to 80.000 particles in a volume of 40 x 40 x 15 mm³. The mean interparticle distance is lower than 7 Kolmogorov lengths for the Re_lambda ~270 case. A data assimilation scheme (FlowFit) with continuity and Navier-Stokes- constraints is used to interpolate the scattered velocity and acceleration data by a continuous 3D B-Spline representation, enabling to recover (locally) the smallest flow scales. In the presentation, we show Lagrangian velocity and acceleration statistics, as well as the Eulerian counterparts on velocity gradients and pressure fields. We compute the energy dissipation rate directly by making use of quadruples of particle trajectories in close proximity (r < 3 eta) and compare it to indirect approaches using second-order velocity- and velocityacceleration structure functions in the inertial subrange.