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In five years, we’re going to reach an interesting centennial milestone in the field of Fluid Dynamics.  It was back in 1920 when the term “Rheology” was first introduced by Eugene C. Bingham.  As the story goes, Bingham and his colleague, Markus Reiner, drew their inspiration from an ancient Greek phrase, “Panta Rhei”, literarily meaning “Everything Flows” ... and the rest as they say, is history! Another phrase I personally like to associate with the now broad field of rheology is “Deceptively Simple”.  Vexing memories of my Master’s Thesis, where I literally watched paint dry in an experimental study of the drainage of a viscoelastic suspension down a glass plate, are still very vivid. Despite, or more precisely because of this experience, my interest in the processing of materials with unusual characteristics has remained with me and I am thrilled to share with you that we have added a new discipline, Computational Rheology, to STAR-CCM+ v10.06. 

Multiple extrudate cases showing the extrudate surface colored by displacement from the original die cross section.

Before getting into the details of the capability, let’s start by putting the material properties that Computational Rheology is designed to work with into perspective. Cooking oils are about 100X more viscous than water and honey is about 100X more viscous again.  These materials are what we call newtonian: their viscosity is the same no matter what shear we apply to them.  Polymers, when they are being processed in their molten state, can be up to a million times more viscous than water and the viscosity of asphalt (or bitumen), relative to polymers, goes up by another 5 orders of magnitude.  And polymers are where the material behavior starts to get very interesting as they can exhibit both a viscous and an elastic response to shear.  They can also exhibit a time dependence with respect to how they are being sheared or stretched.  In short, time scales matter for these materials, as evidenced by one of the key dimensionless groups in rheology, the Deborah Number, which is a ratio of the material relaxation time to the observation time.  

Accurate prediction of the response of an industrially relevant, rheologically interesting material, subject to processing conditions, can be a challenge … even the “deceptively simple” extrusional flow through a die with an annular cross section may exhibit unusual and sometimes counter-intuitive end results depending on the material you’re working with.  

To model extrusion and internal flows of highly viscous materials, with the potential for significant heat generation, we’ve incorporated some of the most widely used and highly regarded viscoelastic constitutive equations (Oldroyd-B, Giesekus-Leonov and Phan Tien-Tanner) in STAR-CCM+ v10.06.  But that’s only part of what you’ll need to succeed here! To be able to accurately and robustly converge the strongly coupled velocity, pressure, stress and free surface variables, we’re using our recently introduced Finite Element solver. It is truly the right tool for the right job.  We have also added several novel stabilization methods that will get you to fully converged solutions far more rapidly compared to other methods and tools.  

There is some overlap in functionality with our Finite Volume solver.  Specifically, it is possible to solve problems using any of the generalized newtonian models that we support (Power Law, Cross and Carreau-Yasuda models) using either solver technology. However, the overlap is quickly resolved using the simple guideline of identifying what your dominant physics are.  If your flow is characterized by highly viscous materials and if your material exhibits strong viscoelastic effects, and/or significant viscous heating is expected, then Computational Rheology using the Finite Element solver is your choice. If on the other hand, radiation, turbulence, multiphase, or moving parts (including overset methods) need to be accounted for, then the Finite Volume solver, for now, is recommended.  Looking down the road slightly, we will be broadening the capabilities of Computational Rheology, and adding functionality to capture the strengths of both solvers to address problems with increasingly complex physics.


Non-Newtonian flow in a Caterpillar Micromixer, with cutaway view to show how Normal Stress Differences increases with increasing rheological model relaxation time, λ

So far, I’ve focused on what’s new so let’s review what stays the same.  Setting up a computational rheology flow/energy problem uses the same tools and processes you’re already familiar with.  The steps of CAD import, mesh generation, model selection, boundary condition specifications, solver setup and data analysis all happen within the same familiar integrated environment.  And, Computational Rheology, just like Computational Solid Mechanics, is included with STAR-CCM+ with no additional licensing costs.  The Computational Rheology feature is making its debut in the STAR-CCM+ v10.06 production release.  We’ve got a lot more planned and as always, we welcome your feedback to help us mature this technology to best fit your needs. 


 Single Jet Cavity Fill of a Highly Viscous Fluid

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Matthew Godo
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