On the quantification of energy dissipation in the impeller stream of a stirred vessel from fluctuating velocity gradient measurements

Abstract

The turbulence energy dissipation rate (ε) in the impeller stream of a vessel of diameter T=100mm stirred by a Rushton turbine of diameter D=T/3 was directly measured with particle image velocimetry (PIV). Both 2-D and 3-D PIV techniques were employed to measure the mean velocities, Reynolds stresses and ε in the vessel for Reynolds numbers of 15 000–40 000. ε was determined directly from measurements of the fluctuating velocity gradients by analysing the PIV images with a resolution of 100μm. The values of the normalised ensemble-averaged dissipation rate (ε/N3D2) in the impeller stream were in the range 5–10. The measured fluctuating velocity gradients compared well with similar data obtained using a four-channel laser anemometer. The results are also compared with those of earlier works employing non-direct methods to estimate ε and show that some of these methods yield comparable values, although the spread of the some of the data previously reported is significant. The present results show the feasibility of direct measurement of the ε distribution with PIV and provide useful information for the design of mixing processes as well as for its more accurate estimation in future work.