Causing
a stir
Dr
Anupam Dewan brings to light the challenges faced in CFD simulation
of fluid mixing in stirred vessels
AFluid
mixing processes are widely encountered in chemical, food and mining
industries. Stirred vessels are often used for such mixing. The flow
in mixing vessels is agitated by single or multiple rotors (impellers).
The impeller is an important component of a stirred tank as it imparts
motion and shear to the fluid, thus leading to mixing. Impellers can
be of different shapes and sizes, depending on the application. Mixing
processes are quite complex and require not only an understanding of
the fluid behaviour, but also an understanding of the equipment’s
power requirements. A lack of understanding can result not only in unsatisfactory
product quality, but also large production costs.
In terms of geometry, mixing tanks can be classified as baffled and
un-baffled, whereas in terms of flow regimes, they can be characterised
as laminar and turbulent. Baffles are used in the vessel to break the
vortex and prevent the solid body rotation of the fluid, but does not
mix the fluid.
Sometimes, impellers are classified on the basis of axial flow or radial
flow characteristics. Radial flow impellers direct the liquid flow towards
the wall of the reactor, along the radius of the tank. On the other
hand, Axial flow impellers force the liquid flow downwards, towards
the base of the tank. While radial flow impellers are primarily used
for gas-liquid mixing and blending processes, axial flow impellers provide
gentle but efficient mixing and are used for reactions involving shear
sensitive cells and particles.
Power number and mixing time are two important parameters used to evaluate
the efficiency of an impeller. Power number Np is a dimensionless parameter
that measures the power requirements of an impeller. Np=P/(rN3D5), where
P is the power to impeller, D: the impeller diameter, N: the impeller
rotation speed and r: the fluid density. The power used by the fluid
is given as P = 2 p N t, where t is the torque. Correlations for Np
as a function of Reynolds number are available in the literature.
A good impeller is one which not only has a small mixing time, but also
a small power number.
Different types of impellers
|
|
|
|
| Radial
flow impeller: Rushton turbine with three blades. |
Radial
flow impeller: Rushton turbine with five blades. |
Axial
flow impeller: Propeller turbine |
The Challenge
The industry needs well designed mixing vessels
to facilitate efficiency in mixing and thereby reduce power consumption.
An important consideration in the design of any agitated vessel is the
power required to drive the impeller and the power used by the liquid
in mixing. The difference between the two should be small so that maximum
amount of energy is spent in actually mixing the liquid. Standard stirrers
used in the industry usually consume a large fraction of the input power
to stir the liquid (to cause a circular motion of fluid) and thus, only
a small part of power is used to actually mix the fluid. Research effort
should, therefore, be directed at designing improved mixers.
Computational fluid dynamics (CFD) is a cost effective design tool.
It is also an invaluable source of insight. CFD simulation of flow in
a stirred vessel is a challenging task, as it requires several considerations.
The flow within a stirred vessel is highly threedimensional and unsteady.
CFD requires that the computational grid match the shape of the vessel
and all its components, which are often geometrically complex. The grid
chosen should be fine enough to capture the smallest flow scales. A
very fine grid could result in higher computational requirements.Further,
the relative motion of the impeller with respect to stationary vessel
needs to be treated. This consideration influences the mesh generation
and the method of solution employed to solve the governing equations
in a CFD code.
There are three strategies to account for the motion of impeller: (1)
Rotating frame model (2) Multiple reference frame model and (3) Sliding
mesh model.
The first is the simplest and this steady approach solves the governing
equations for the entire domain in a rotating frame. The Coriolis force
is included in the governing equations. However, the approach can be
applied only to un-baffled tanks with smooth walls. In the second approach,
which is also steady in nature, more than one reference frame is used.
The impeller in the rotating frame is stationary and an exchange of
information at the interface of the two frames (one rotating frame surrounding
the impeller and the second stationary containing the vessel and its
components) is required during the solution procedure. The solution
of the flow field in the rotating frame in the region surrounding the
impeller imparts the effect of impeller rotation to the outside region
containing tank and baffles. However, the orientation of the impeller
with respect to baffles does not change during the solution procedure.
This...
....CONTD
