Mixing in Tween Screw Extruders
Said GHALIMI (mfn06)
We simulate the 2-D rotation of transient flow reproduced by the rigid rotation of two cams in a batch mixer. It is essentiel to maitain a communication between the all fluid zones for all angular positions, i.e. the size of the elements near external boundary is linked to the minimum gap between the barrel and the cams.
If no communication exists between some fluid zones, the pressure level becomes entirely determined by the compressibility factor.
Ones evaluates the flow every 4 degrees of the cams rotation. the total time of simulation corresponds to 180 degrees of rotation (45 steps). The fluid is Newtonian and isothermal. the mesh superposition technique is used to simplify th mesh generation of the flow domain.
Fig. 1 - 3D view of cams.
To select the the proper model of a fluid is one of the most important aspects in the simulation of a flow. one must always considers the couple (Fluid - Liquid). a constitutive equation is valid for a given fluid in a given flow.
Most of fluids are characterized by shear -thinning and non-quadratic first normal stress difference. There are serveral viscosity functions which depend on the shear-rate and the time relaxation such as :
Power law :
eta = K (gamma)^(n-1)
Carreau law :
eta = (eta0 - etaINF)(1 + (lamda gamma)^2)^((n-1)/2)
It is important to mention that the power law dependence on should be avoided for the relaxation time, as it leads to high relaxation times for low shear rates ! the selection of the Carreau behavior is certainly better, indeed, it yields a constant relaxation time at low shear-rates. and usually makes the use of an evolution strategy successful.
Despite it's interssting features from a viscometric viewpoint, those models may exhibit a strange numerical behavior at high shear - rates and lead to spurious oscillations in the solution. this strange behavior finds its origin in intrinsic properties of the model.
Because, the problem is time - depending , we use the mesh superposition technique both to simplify the mesh generation and to avoid any remeshing technique. We mesh each part, the barrel and the two cams. the two cams are initially located outside the barrel. During the Polydata session, we will use define an initial translation to position them at the correct location in the flow domain.
Fig. 1 - Initial mesh of the barrel and the two cams.
In order to calculate the flow, we solve the Navier - Stokes equations modified by addition of a penality term which imposes the velocity of the cams at the nodes of the flow domain included in the solid regions.
Fig. 1- mesh of the barrel and the two cams after few time-steps.
Constant viscosity :
In the figure above, we can see the velocity field for four succecive positions, the saving time step correspond to a full rouud of the cams.
We show the pressure at step 15 : we observe - as expected - a pressure increase in front of the moving cams, and a pressure drop at the back of them.
Power law :