Finite Element Method - Application using Fastflo
Two-phase flow in a stirred tank
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 vessel considered 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 m/s. The Reynolds number of the
flow is Re = 118000, based on the tip velocity of the turbine blades and
the radius of the mixing tank.
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Computed velocity vectors (left) and temperature contours
(right). |
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:
- Two-fluid model to account for the two-phase flow.
- Models for interfacial drag, added virtual mass and interfacial
lifting forces.
RNG k-e model for turbulence
effect.
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. 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 the above figure. 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. Also shown
in the above figure are the temperature contours computed using Fastflo.
The Fastflo results have also been compared with experimental
data; good agreement has been observed for the radial air velocity
profiles.
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, 233-
249 (1996).
[2] Z. Zhu and A.N. Stokes, Simulation of two phase flows in a
stirred mixing tank, International Conference on CFD in
Mineral and Metal Processing and Power Generation, Melbourne, Australia
(1997).
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