Estimation of the turbulent kinetic energy dissipation rate from 2D-PIV measurements in a vessel stirred by an axial Mixel TTP impeller

The turbulent dissipation rate is a key parameter in stirred tanks and its local values may have a strong influence on the performance of many processes. However, the local dissipation rate estimation is far from easy in a stirred tank, especially near the impeller discharge where maximum values are encountered. The aim of this work is to estimate the dissipation rate in a vessel used for animal-cell cultures and stirred with a down-pumping axial impeller (Mixel TTP) from velocity fields measured by 2D-PIV. Special attention is paid to the assumptions necessary to estimate the dissipation rate from 2D measurements and to the influence of measurement spatial resolution on the estimated values. The analysis of isotropy ratios measured on vertical, horizontal and tangential planes shows that the turbulence in the impeller discharge is far from isotropic. Isotropy assumptions classically used to estimate the dissipation rate from 2D measurements may thus lead to erroneous values. Based on the measured isotropy ratios, a new relationship is proposed to estimate the dissipation rate in the impeller discharge. This relationship is then used to estimate the dissipation rate on a vertical plane located in the impeller discharge zone. In order to analyze the influence of the measurement spatial resolution on the estimated values of the dissipation, a total of 12 spatial resolutions are tested. Results show that if the spatial resolution is divided by a factor 2, the dissipation rate increases by 220%. For the smallest spatial resolution value used, the maximum dissipation rate estimated is 50 times higher than the mean overall dissipation rate and the corresponding minimum value of the Kolmogorov scale is nearly 3 times smaller than the Kolmogorov scale computed from the mean overall dissipation rate.