Power number

Power consumption is evaluated at pseudo-steady state by integration of the distribution of total forces over the impeller, as described in Appendix A. Since the full transient simulation starts from still fluid, achievement of convergence to the pseudo-steady state is to be assessed during the calculations. Convergence is achieved when the upflow curve, the power consumption and the azimuthal momentum are stable in time, as described in Appendix A. Figure 4.8 shows the distribution of total forces (pressure and shear forces) acting on the impeller and on the vessel wall at pseudo-steady state for simulation S1. A maximum for the total force is found where the discharge flow impinges the vessel wall. Figure 4.9 shows the distribution of forces on the impeller: the force acting on the front of blades (due to the pressure) is smaller than that acting behind blades (due to higher shear). In this region, vortices generated by the upper and lower profiles of the blades merge.

Table 4.3 summarizes the values of power consumption obtained for the simulations.

Table 4.3: Power consumption calculated for different simulations. Values are in Watt.

S1	S2	S3	S4	S5	S6
0.727	8.72	0.366	4.097	0.310	4.840

Figure 4.8: Total force distribution on vessel wall and impeller.

Figure 4.9: Total force distribution on impeller.

These values are used to derive the curve of power number versus Reynolds number, shown in Figure 4.10.

Figure: Power number versus Reynolds number: computed results ($\circ$) and empirical correlations [equations from B.13 to B.15].

Figure 4.11: Power number versus Reynolds number: experimental data.

Calculated points are shown together with power characteristics derived from Nagata (1975), as discussed in Appendix B. Since the laboratory reactor belongs to the same class and is geometrically similar to CE12500, we compared our results against data supplied by Tycon $-$ Technoglass (Sassetto and Artusi, 2000). These data are referred to as reference curve. Power number values calculated by simulations lie on the reference curve. This curve is slightly higher than the single baffle curve, in green in Figure 4.10. This indicates that simulations overestimate power consumption. In Figure 4.11, power number data obtained from experiments are plotted on the same curves (reference curve and single baffle curve). It can be observed that also experimental points lie between the 1 baffle and the reference curve, and agreement with the power characteristic for the single baffle curve is better in the high Reynolds range.

In Figure 4.12, power numbers calculated from the simulations (y axis) are directly compared with experimental data (x axis). Power number values are in good agreement for simulation S2, S3 and S4, while computer simulations tend to overestimate simulations S1, S5 and S6.

Figure 4.12: Comparison between computer simulations and experimental data. Computer simulations tend to overestimate data at low and high $Ne$.