Reactor BE12500

Reactor BE12500 is a vessel with torospherical bottom, equipped with a turbofoil turbine. Nominal capacity of the vessel is 12450 kg. Differently from model CE12500, design of the vessel for BE12500 is one-piece construction without the agitator entry port on the top cover. The agitator is a split hub design which is introduced through the manhole for assembly inside. In the configuration simulated, the agitator, a turbofoil turbine, is in the curved part of the tank, near the bottom. Two beaver-tail baffles are placed near the wall of the tank (angular position $\theta=0$ and $\theta=165^o$) to improve the circulation. The dimensions of the reactor are reported in Table 4.9.

Table 4.9: Geometrical dimensions of the industrial vessel BE12500.

Vessel diameter	D	2.348 m
Vessel height	H	3.133 m
Baffle width	$B_w$	0.17 m
Number of baffles	$n_B$	2
Impeller diameter	d	1.20 m
Blade width	b	$0.265-0.476~m$
Number of blades	$n_b$	4

Figure 4.28 shows a complete view of the computational domain defined for the BE12500. The computational domain is made of 308464 finite volumes.

Figure 4.28: BE12500 equipped with turbofoil turbine.

Figures 4.29 and 4.30 show the computational grid adopted. A regular meshing is used for the discretization of the cylindrical body of the tank. Distortion of the grid is locally produced to simulate accurately the shape of the baffles, as shown in Figure 4.30, A distorted grid is used also for the round bottom of the vessel (red part in Figure 4.29) to reproduce the curvature and to model the shape of the impeller. A very fine grid is used in the bottom region for the detailed modeling of the turbofoil turbine. Figure 4.31 shows the grid accurately shaped to reproduce the variable curvature of the blades. Constant thickness (equal to $2.5~cm$) is assumed for the blades. Impeller rotation is counter-clockwise.

Figure 4.29: Turbofoil Turbine: front view.

Figure 4.30: Turbofoil Turbine: top view.

Figure 4.31: Turbofoil Turbine.

Figure 4.32: Turbofoil Turbine: front view.

Simulations made on this model are aimed at evaluating the different performances of the turbofoil turbine with respect to the retreated curved blade impeller. Performances of the two agitators are evaluated with respect to power consumption and pumping capability. For this reason, a number of simulations is required to characterize the behavior of BE12500 in the same operative conditions for which characterization of the CE12500 is available. Simulations made are gathered in Table 4.10.

Table 4.10: Simulations made for BE12500.

Ref	Density $[kg/m^3]$	Viscosity $[Pa \cdot s]$	RPM
S1	1000.	20.	50
S2	1000.	1.	50
S3	1000.	0.1	50
S4	1000.	0.001	50

For BE12500, simulations at different Reynolds number are made changing the fluid viscosity only. Density and angular velocity are set to $1000~kg/m^3$ and $50~RPM$ and are kept constant for all the simulations. Reynolds numbers in the range $[60:1.2 \cdot 10^6]$ have been explored.

Simulation S1 is made with a very viscous fluid ( $\mu=20~Pa \cdot s$) to evaluate the effects of high viscosity on the flow field distribution. Simulation S4 is made with water. Conditions selected for simulation S3 and S4 are used to verify independency of power consumption from fluid viscosity in the fully turbulent range ( $Ne=\mbox{cost}$). Numerical simulations are made with the full transient approach (see Appendix A for details) starting from fluid at rest in the tank. The sliding mesh approach is used to account for the relative motion of impeller and vessel. The portion of the domain containing the turbofoil in which conservation equations are solved in a rotating frame of reference is shown in red in Figure 4.29. The sliding boundary (in red in Figure 4.33) is shown together with the other boundary conditions used for the simulation in Figure 4.33. No slip condition is used for the wall of the vessel ($\bf {v}=0$) and for the surface of the turbofoil turbine ( $v_{\theta}(r)=\omega r$). Free shear condition is used at the top of the vessel to simulate a flat free surface.

Figure 4.33: Boundary conditions for the simulations.