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.