. The Reynolds number of the flow is 
, based on the
tip velocity of the turbine blades and the radius of the mixing tank.
(Case Study 8, May 1997)
The problem
Liquid in a cylindrical mixing tank is stirred by a Rushton turbine, and gas is released into the tank through a sparger mounted along the axis below the turbine. There are baffles mounted on the cylindrical wall of the tank. At normal working conditions, the two-phase flow in the mixing tank is highly turbulent.
In this case, the liquid-water flow pattern is simulated numerically.
The distributions of the gas volume fraction and velocity are also
predicted. The schematic of this mixing tank is shown in Figure 1.
The vessel is an Applicon 151. The rotating speed of the turbine is
360 RPM, and the speed at which air is released into the liquid is 1.7
ms. The Reynolds number of the flow is , based on the
tip velocity of the turbine blades and the radius of the mixing tank.
Figure 1: Schematic of a mixing tank
Computations
The two-phase turbulent flow inside the mixing tank is modelled as axisymmetric. The tangential velocity in the region covered by the turbine blades is assumed to be that of a rotating solid body, the axial and radial velocity components are determined by the momentum Navier-Stokes equations for all fluid regions including the region occupied by the turbine blades and the baffles. An extra viscous term is added to the momentum equations in the baffle region.
A hybrid method based on a SIMPLE-type algorithm and artificial compressibility is used to solve for the liquid velocity and pressure. The gas velocity is solved using a two-step convection-diffusion operator-splitting method. The following models are used in the simulation:
model for turbulence effect.
 Figure 2: Mesh and water velocity arrows |
|
As the flow is axisymmetric, only half of the cross-section needs to be resolved. This half cross-section is discretized with 2000 linear triangle elements, as shown in the left half cross-section of Figure 2. The liquid phase flow converges within the first 120 iterations, while 600 iterations are needed to reach a converged solution for the gas phase flow. On a DEC 3000 Alpha workstation, the simulation of the two-phase flow takes 16 hours in CPU time.
Results
The computed velocity vector arrows of the liquid are shown in the right half cross-section of Figure 2. The velocity arrows illustrate the complex nature of the liquid flow inside the agitated mixing tank. The impeller blades push the liquid radially toward the outer wall. As a result, two large recirculating regions are formed.
The computed results are also compared with experimental data. In Figure 3, the computed air velocity in the radial direction is plotted against experimental data at the vertical location where impeller blades are mounted. The radial air velocity agrees well with experimental data (Figure 4).
Figure 4: Radial air velocity at axial location H = 0.94D
Benefits of Fastflo for this problem
References
[1] K E Morud and B H Hjertager, "LDA measurements and CFD modelling of gas-liquid flow in a stirred vessel", Chemical Engineering Sciences 51 (1996), 233-249.
[2] Zili Zhu and Nick Stokes, "Simulation of two-phase flows in a stirred mixing tank", Int. Conf. on CFD in Mineral and Metal Processing and Power Generation, Melbourne, Australia (1997).