A SECOND METHOD TO MESH THE VAT
The meshing technic
Considering the problem
of dealing with high number of faces to impose boundary conditions, we
tried a "direct strategy" : we built directly the 3-D vat, without building
quarters first. Therefore we have a limited number of faces and can easily
impose the boundary conditions. We define the mesh on each face separately,
and then we ask Gambit to mesh the volume, taking in account the defined
faces' mesh. There is no choice for the volume meshing technic : only an
unstructured mesh is avalaible. The following picture shows this new geometry
Direct building of the vat.
This way to build the
geometry is easier than the one previously developped, however it does
not allow to control the meshing technic as well : it 's not possible to
choose the volume mesh type, and it's not easy to refine the mesh where
it is necessary. The user has to find a compromise between the two technics.
As the mesh generator Gambit is developped by Fluent, the mesh can be directly used to make simulations with Fluent.
However it's important to be careful when defining the reference frame : in fact, the fact that the agitator is rotating must be taken in account. There should be possible to define a moving mesh for this agitator, and to solve the equations in the galilean laboratory frame; nevertheless, as the exterior wall present a rotation symmetry, it's better to solve the equations in the rotating frame. Therefore, the blade are fix in this frame, and the wall is rotating in the opposite direction of the agitator movement in the laboratory frame. Fluent allows to process this case by selectionning Motion Type "Moving reference Frame" in Define -> Boundary conditions -> Fluid :
Fluent simulations results
Below are few results
we got when we made simulations with FLUENT.
This results were obtained with glycerin (very high viscosity) and for a Reynolds number equal to 10.
This is the closest situation we could imagine to simulate a visco-elastic fluid which is the kind of fluid that will be mixed in this type of vat.
Velocity magnitude in the laboratory frame (velocity is zero at the wall).
We can see on this plot
that in the lab frame, the velocity on the wall is zero and the velocity
at the edge of the blades follows a linear law: V ~ w*r.
Velocity magnitude in the moving frame (velocity is zero on the blade).
In the blade frame, the
velocity is zero on the blades and equal to w*R on the wall.
in the blades plan.
Tangential velocity in the moving frame.
This picture shows the
tangential velocity in the blades' frame. We can clearly see that there
is a recirculation : the red area has a positive tangential velocity, whereas
the other areas have a negative tangential velocity. This recirculation
phenomena can be observed on the following picture, showing the velocity
vectors in a cross-section :
Velocity vectors in a cross-section of the reactor.
This final picture shows the pressure field in a cross-section. The blades are rotating with a positive angle in the lab frame, we can verify that the pressure is higher in front of the blades (red areas) and lower behind them (blue areas).
Pressure field in a cross-section of the reactor.