Flow-number

The values of the discharge flow number and the circulation flow number are calculated for the different operative conditions. Values of the discharge flow and the circulation flow are gathered in Table 4.8. Fluid density and angular velocity are also recalled. Discharge and circulation flow are calculated as described in Appendix A.

Table 4.8: Discharge and circulation flow for the different simulations in the CE12500 reactor.

$Re$	Discharge flow	Circulation flow	Density	RPM
$-$	$[kg/s]$	$[kg/s]$	$[kg/m^3]$	$-$
30	3.126	4.76729	10	100
300	722.6	671.628	1000	50
3000	1.85	1.93949	1000	0.1
3000	1784	1907.58	1000	100
$2 \cdot 10^5$	1.65	1.89673	1.4	100
$3\cdot 10^6$	1430	1602.30	1000	100

Values of discharge flow number and circulation flow number are plotted against Reynolds number in Figure 4.25. The trend for the discharge flow number is similar for both the CE12500 and the laboratory reactor. The discharge flow number represents the pumping ability of the impeller and is independent from the vessel configuration (number and position of the baffles). Discharge flow numbers calculated for the laboratory vessel and the CE12500 can be compared to assess the scale-up possibility of the code. Figure 4.26 shows flow number values derived for the laboratory vessel and its industrial counterpart.

Figure 4.25: Discharge Flow number and Circulation Flow number versus Reynolds number: CE12500.

Figure 4.26: Verification of scale-up: flow number calculated for laboratory and industrial size vessel lie on the same curve.

Power number values and corresponding discharge flow number are also used to calculate the pumping efficiency of CE12500 in the different operating conditions. Figure 4.27 shows variation of pumping efficiency as a function of Reynolds number. For CE12500 pumping efficiency stabilizes around a value of 0.4 for Reynolds number larger than 2000. Comparison with Figure 4.14 obtained for the laboratory reactor shows that pumping efficiency is reduced for the industrial size CSTR. This is expected since, even if reactors are geometrically similar, the industrial vessel is equipped with two beaver tail baffles while the simulated laboratory vessel is equipped with a single beaver tail baffle. Since power consumption is proportionally larger for the industrial vessel, the same pumping capability obtained at a larger power expense results in a lower pumping efficiency.

Figure 4.27: Pumping efficiency versus Reynolds number: CE 12500.