Figure 12. 3D contour plots of the dimensionless mean axial velocity (a) and absolute radial velocity (b) at different axial positions.
Effective mass exchange in the axial and radial directions can be further evaluated by the flow rates, which are calculated from the axial flow rates by integrating the radial profiles of the time-averaged mean axial velocity. Detailed information could be found in our previous work19. In this work, the time-averaged axial flow rate per unit area cross the horizontal as a function of z /T and time-averaged radial flow rate per unit area as a function of r /R are calculated and plotted in Figure 13, respectively. It is seen that there are two humps atz /T = 0.2 and z /T = 1.1 on the curves of the axial flow rates, where the lower short blades and upper short blades are located, respectively. In addition, the axial flow rate decreases gradually from the maximum value at z /T = 0.2 to a minimum value at z /T = 0.6, where the connected blades are located. This provides a further proof that part of the up-flow is gradually discharged to the radial flow along the axial direction. Similar trends are found when z /T decreases from 1.1 to 0.6, corresponding to the gradually discharging of the down-flow to the radial flow from the top. The profiles of the flow rate per unit areavs. r /R , as shown in Figure 13b, have obvious maximum values at r /R = 0.4-0.5 where the up-flow and down-flow meet with intensive interaction, implying that effective axial mass exchange between the upper and lower parts of the tank can be achieved.