Figure 8. Time variation of
vorticity
fields by TR-PIV measurement on the sampling plane of
P45.
To have an overall view of the vortex distributions, we visualize the
vortex structures in the whole vessel by LES predictions. Several
methods for vortex structure visualization have been proposed in the
published references, e.g. stream lines, iso-surfaces of vorticity,
complex eigenvalues of the velocity gradient tensor, swirl strength andQ -criterion25,26.
In this work, the Q criterion, which is one of the most popular
criteria, is used to visualize the vortex distributions27. TheQ -criterion represents the local balance between strain rates and
vorticities, and the vorticity in the impeller region is higher than
that in the bulk region28,29.
The Q is defined by
(1)
where, S is the
rate-of-strain tensor and Ω is the vorticity tensor.
Figure 9 provides a qualitative comparison of the turbulent vorticities
colored by the vorticity magnitude in two cases of N = 90 rpm andN = 120 rpm. One can see that the vorticity is uniformly
distributed in the tank. Moreover, increasing the rotating speed from 90
rpm to 120 rpm, the vorticities near the tank becomes richer, implying
that the radial discharge by the composite blade might play an important
role in the mixing intensification in the whole tank.