Comparison of specific energy dissipation rate calculation methodologies utilising 2D PIV velocity measurement

Abstract

It is critical to have an efficient energy budget in all the industrial process applications involving multiphase flow system where a significant amount of power is invested to achieve a desired outcome such as valuable particle collection and recovery in mineral flotation circuits. In order to achieve this aim there needs to be an ability to properly characterise the energy dissipation in the system; and from this knowledge to develop methodologies so that the supplied energy is distributed suitably among the eddies of different sizes which are responsible for enhancing different transport events such heat/mass transfer, mixing etc. The aim of the study was to obtain the 2D instantaneous velocity field in a homogeneous near isotropic turbulence field using particle image velocimetry (PIV) and then compute the space and time averaged specific energy dissipation rate from velocity field using four different methods, namely: (1) dimensional analysis, (2) velocity gradient, (3) structure function, and (4) energy spectrum. The system was studied in the Taylor Reynolds number range of 24–60, where it was found that the difference between the computed specific energy dissipation rates could be as much as 100 percent. Whilst it was found that there were uncertainties in all four methodologies, it is argued that the energy spectrum method is likely to give the most realistic quantification of the specific energy dissipation rate value since it was shown to satisfy the system energy balance which was not possible to do so for the other three methods. The energy spectrum method also had the added benefit of incorporating integral scale, Taylor microscale and Kolmogorov length scales in the quantification of the specific energy dissipation rate; whereas the other three methods are limited to either integral scale or Taylor microscale only. The limitation of the energy spectrum method, however, is the resolution of the energy spectrum down to the Kolmogorov length scale due to the noise in the measurement; and to resolve this problem a filter was applied to denoise in the dissipation range.