A comparison of dissipation estimation methods in a stirred tank using Particle Image Velocimetry (PIV)

Particle Image Velocimetry (PIV) measurements have been acquired in a cylindrical tank stirred by a Rushton turbine. Since the six-bladed Rushton turbine is symmetric with respet to each blade, phase-averaged velocity fields in the r-z plane were required at intervals of 10 degrees within one sextant. Two datasets were acquired, with magnifications of 0.26 and 0.56 respetively. Five mean square gradients are computed from the PIV data and turbulent dissipation is estimated directly using these quantities. Four estimates of dissipation are presented, each based on certain assumptions about the turbulent flow. The first estimate is based only on the measured component υ_1,1², the second estimate uses all of the available measured components and applies isotropic assumptions for the unknown components. The third and fourth estimates assume that the turbulence is statistically axisymmetric, and assumptions of axisymmetry around two axes are compared. The estimates which assume statistical axisymmetry around the z-axis and the estimate which uses all known components and isotropic assumptions for the unknown components are consistent and appear useful as a lower bound. The estimate which relies only on the measured component u_1,1² appears to be a higher bound.