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BEM Flow Mixers
BEMflow is a boundary element simulation package for designing, optimizing, and analyzing polymer processes and equipment. The boundary-only approach of the boundary element method (BEM) makes it extremely attractive for modeling flows in extruders, mixing heads, extrusion dies, internal batch mixers, among others. The boundary element method is founded in rigorous mathematical theory that reduces the dimensionality of the problem and minimizes user interaction time.
For the first time optimization, in a realistic time frame on desk top computers, can be done on complex 3-dimensional geometries such as mixing devices. This program has been used as a consulting tool for several years. The Madison Group along with our European partner, M-Base Engineering + Software, are now in the processes of commercializing BEMflow to bring this new technology to the polymer processing industry. Please review our case studies and publications in this web page or contact us for information about our consulting services with BEMflow
Advantages
* Eliminates expensive and time consuming trial and error testing
* Allows easier optimization
* Boundary only discretization
* Minimum data input
* Low user interaction and set-up time
* High accuracy
* Fast computation times
Processes
* Single screw extruders
* Twin screw extruders
* Distributive mixers
* Dispersive mixers
* Static Mixers
* Extrusion dies
* Internal batch mixers
Capabilities
* 2-D and 3-D models
* Moving solid boundaries
* Moving free boundaries
* Particle tracking
* Residence time distributions
* Strain rate distributions
* Mixing quality assessment
* Pressure distributions
BEMflow has recently been used to help design and optimize a new mixing section for extrusion and a new static mixer. This is possibly the first time a simulation package has been used to completely design a new mixing section. BEMflow was used to optimize the shape of these two sections for dispersive and distributive mixing.
The CRD mixing section, developed by Chris Rauwendaal, was design to provide high dispersive mixing by assuring that the material has more than one pass through the high stress region. In the typical Maddock (LeRoy) or UC mixing section, the material goes over (sees) the high stress region only once with limited distributive mixing. The CRD provides the high stress region with a patented wedge shape that was developed using BEMflow. A patent has been issued for the CRD extrusion mixing section and is now in the process of being license by several screw manufacturers.
Recent Publications Using BEMflow:
Fogarty, Jim, Dave Fogarty, Chris Rauwendaal and Antoine Rios, "Turbo-Screw™, New Screw Design for Foam Extrusion", to be published in SPE ANTEC (2001).
Polymer Processing Simulation Trends, Tim Osswald and Paul Gramann, SAMPE, Erlangen, Germany, 2001
Rios, A.C., E. Santanach, P.J. Gramann, and C.J. Rauwendaal, "Extruder Breaker Plate Offers More Efficient Mixing", Plastics Additives & Compounding, Elsevier, p 30-33 (2000).
Rios, Antoine C., Maria del P. Noriega, Paul J. Gramann and Tim A. Osswald, "Experimental and Numerical Study of Rhomboidal Mixing Sections", Inter. Poly. Proc., 15, 1, p.12, (2000)
A New Dispersive Mixer for Single Screw Extruders, by Chris Rauwendaal, Tim Osswald, Paul Gramann and Bruce Davis.
The Boundary Element Method
When doing a fluid dynamics analysis the most time consuming portion is usually the creation of the finite difference grid or finite element mesh. This can easily take days for even simple geometries and with complex geometries make an analysis impractical. If moving boundaries are present typically only a few runs at select times can be simulated.
With the boundary element method a mesh is placed only on the surface of the geometry. With moving boundaries there is no remeshing required between time steps since the elements move right with the geometry. To simplify this point a two dimensional example of a banbury mixer with two rotating rotors is shown.
Finite Element Mesh
4921 nodes
1526 elements
9842 degrees of freedom
A mesh must be generated for each time step
Boundary Element Mesh
130 nodes
65 elements
260 degrees of freedom
No remeshing required
BEM Advantages
The advantages of the boundary element method allow for relatively easy optimization of complex 3-dimensional geometries. The example below shows the introduction of three pins to the channel of the single screw extruder shown above. It takes minutes to modify the original geometry and have a model ready to solve. The resulting mixing effect, flow rate, pressure distribution, etc. are quickly analyzed and the geometry can be quickly changed for optimization.
3-Dimensional Mesh
The elements are placed only on the surface of the model. Line drawings or surface models are easily meshed with the boundary element method.
438 elements needed for this model
Particle Tracking
Because interpolation functions are not used (exact velocities are calculated) particle tracking is easy and accurate. At every internal point for every time step the velocity, strain rates, mixing effect, etc. are calculated allowing for a complete analysis of the process. Streamlines and residence time distribution (RTD) or cumulative residence time distribution functions (CRTD) are accurately calculated.
BEM Capabilities
Since only the boundaries of the geometry need to be meshed the engineer's time is not wasted on creating the model, but analyzing the results. Flow rates, pressure losses, mixing quality, residence time distributions are only a few of the capabilities that the program is able to evaluate. The ability to allow the engineer to quickly analyze changes or ideas makes BEMflow a very powerful tool.
Twin Screw Extruder
Twin screw extruders have developed into the best available continuous mixing devices. In general, they can be classified as intermeshing or nonintermeshing, and co-rotating or counter-rotating twin screw extruders. The intermeshing twin screw extruder (shown here) renders a self-cleaning effect which evens-out the residence time of the polymer in the extruder. The main characteristic of this type of configuration is that the surfaces of the screws are sliding past each other, constantly removing the polymer that is stuck to the screw.
During the compounding of fiber filled polymers in the twin screw extruder, there is a great deal of fiber breakage that occurs. The attrition of fiber length can significantly reduce the favorably properties of the final product, i.e. strength and creep. The twin screw extruder is well known for its dispersive mixing capability, but the extent of fiber breakage in this extruder is not. To help understand the fiber breakage that occurs and the phenomena that governs it, the boundary element simulation program BEMflow was used. Using this program, the flow field, pressure distribution, type of flow (rotation, shear or elongation) and strain rate throughout the twin screw and a kneading block mixing section were calculated. With this information, the final Length/Diameter distribution of the fiber was predicted. More importantly, the influence of screw geometry, processing conditions and material properties on the final Length/Diameter was calculated.
Particle tracking through the twin screw extruder.
Pressure distribution in the twin screw extruder.
The twin screw extruder is commonly used for the processing of fiber filled polymers. The figures above show the calculated particle tracking and pressure distribution in the co-rotating twin screw extruder. The geometry of the kneading block and its calculated velocity distribution down the axis of the mixing section are shown below.
Solid model of the kneeding blocks.
Axial velocity distribution in the kneeding blocks.
Koch Static Mixer
During the comopounding or mixing of polymers, motionless or static-type mixers are commonly used. This is especially true when processing sensitive materials which cannot be exposed to a high degree of shear. The Koch SMX static mixer is commonly used for distributive mixing in many industries. The mixing capability of this system alon with no moving parts makes it attractive when contamination is of concern.
This mixer is mainly used for laminar flow mixing. As the fluid passes through the section, it is repeatedly divided and recombined, thus increasing the homogeneity of the mixture.
Using BEMflow, particles were tracked through the exact geometry of the mixing system and information on the type of flow (shear or elongation), stresses, pressure distribution, rates of deformation, and residence time distributions were calculated. From the analysis, the smallest droplet size that the mixer could produce was calculated - the mixing capability of the system was predicted.
Particle tracking through the SMX static mixer.
Pressure distribution in the SMX static mixer.
Here, the predicted particle tracking and pressure distribution, which were calculated with BEMflow, are shown. BEMFlow is being used to predict and optimize the overall mixing capability and pressure consumption of this device.
Since only the surfaces of the device need to be meshed with BEMflow, the meshing is relatively easy to do. In fact, meshing this device with finite elements would take several days, whereas, the one shown here took several hours with boundary elements.
LeRoy "UC" or Maddock Mixing Section
Dispersive mixing elements are often used to break up agglomerates or secondary fluid droplets during extrusion. This is of upmost importance during thin film extrusion, reactive extrusion, compounding, and pigmentation. The most commonly used dispersive mixing section contains flutes or splines along the section. In this type of mixer, one or more barrier flights are placed along the screw so that material must flow over the flight. The barrier flight clearance is chosen such that a high shear rate, and corresponding high shear stress, is generated by flow over the flight. A well known fluted mixing section is the Union Carbide (UC) mixing section invented by LeRoy. Maddock from Union Carbide published results of experiments popularlized its use.
Particle Tracking
This is one section of a repeated section around the screw. The "UC" mixing section is typically used as a dispersive mixer and is usually placed at the end of the extruder to disperse any solids that may be present before leaving the extruder . Here, the tracking of points show the recirculation pattern before crossing over the land region. The strain rate and type of flow at each point is accurately computed. This gives the engineer the ability to evaluate the mixing capability of the section.
260 elements needed for this model
Pressure Distribution
The pressure loss across the "UC" mixing section is easily computed. Changing the boundary element mesh to evaluate modifications to the geometry for increasing the mixing capability or decreasing pressure loss is very quick.
