Global and local energy dissipation in a turbulent Von Kármán flow

etc15 Tracking Number 171

We use PIV measurements to study local and global energy transfer in a Von Kármán flow. First, we use a Large Eddy Simulation (LES) approximation to model and compute the injected and dissipated power. This procedure involves a free parameter that is calibrated using angular momentum balance. We then estimate the local and global mean injected and dissipated power for several types of impellers, for various Reynolds numbers and for various flow topologies. These PIV-estimates are then compared with direct injected power estimates, provided by torque measurements at the impellers. The agreement between PIV-estimates and direct measurements depends on the flow topology. In symmetric situations, our estimates capture 30 to 70% of the actual energy dissipation. However, our results become increasingly inaccurate as the shear layer responsible for most of the dissipation is approaching one of the impeller, where it cannot be resolved by our PIV set-up. Finally, we show that a very good agreement between PIV-estimates and direct estimates of the dissipated power is obtained using a new method based on the work of Duchon and Robert that generalizes Kármán-Horwath equation to non-isotropic, non homogeneous flows. This method provides parameter-free estimates of the energy dissipation as long as the smallest resolved scale lies in the inertial range.