Estimation of the turbulent kinetic energy dissipation in a culture cell stirred tank bioreactor

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.