Why bother with viscosity models?
 

Howdy Foamers,

As I'm writing up my dissertation, I couldn't help but come to the conclusion that using viscosity models (power law, Carreau-Yasuda what have you) is simply the wrong way to model a shear thinning fluid in a CFD environment. Hear me out. You can much more accurately match an experimental shear rate - viscosity curve with something like a high order polynomial or a spline formulation than you can trying to force a particular model's parameters to match your data. This 'force fit' is typically done with some kind of least-squares approach.

I believe that these models are simply left over from pencil paper non-Newtonian pipe flow solutions. Don't get me wrong, I use these models all the time, I just feel there is a more intelligent way to go about this.

Any thoughts?

I do not know the background of the models that you mention, but I would think the most important thing is to get the viscosity-strain rate curve right. For the known models there is probably (correct me if I am wrong), physical argument for the parameters in the model. Parameters that have a real life meaning are in my opinion favourable. But if your fluid does not match the assumptions of the model, then it does not make sense to use them and I'd also rather use a correct fit with more parameters than a worse fit with the wrong physical meaning.

Hi,
What is your shear thinning fluid? I am asking this because in Macosko book ' Rheology: Principles, Measurements, and Applications ', you can see that many polymeric (shear thinning) fluids are described well using power law, Yasuda and many more. In my opinion, it is well proven in literature that many polymer systems follow this models. I am wondering if you have completely new system. However, by rheological measurements you can produce your own fit for viscosity and strain rates.
M K Singh

My fluid in particular is a Carreau-Yasuda type. These fluids are characterized by an upper shear rate viscosity plateau, a lower shear rate viscosity plateau, and a smooth transition between the two.

Looking at the viscosity profile it definitely follows this pattern but you still get a better fit if you scrap the model.

I feel that part of the problem is the curve representations on log-log axes. What looks like a great fit could actually be way off.

Have you had a look at the viscoelastic models in 1.6-ext? There is one called WhiteMetznerCarreauYasuda. Don't know if this is the one you're talking about ... the two extra names got me confused

Hi Bernhard,
I actually implemented a viscosity Carreau-Yasuda model myself. I believe the viscoelastic model you are referring to models the relaxation time lambda with a CY type curve.

Certainly "fitting" an experimental curve is easy and works in one specific case, but in my opinion makes little sense in a CFD context, because it removes the generality of the CFD approach.

Keep in mind that the purpose of physical models is to try to represent the actual physics of the problem, as a function of a set of parameters. This does not necessarily imply that you will match experiments in every case, because you might neglect certain aspects. The objective of the modeler is to make physical models more accurate and general, not to replace them with an empirical correlation that can be easily found by regression of experimental data ;-)

My two cents on the topic are to think about the physical significance of the models i.e. phenomenological vs. purely empirical. Sure, an purely empirical model may fit your data better (and I see the engineering significance of that) but there are reasons that models have certain terms appearing in them, having direct connection to experimental observation (phenomena).

But these are the questions that one asks while writing a dissertation, hence why people often speak very vaguely rather than definitive in a dissertation when talking about "models".

I like the discussion by the way.

Some entertaining links
http://levenspiel.com/octave/elephant.htm
http://demonstrations.wolfram.com/FittingAnElephant/

I can agree with both sides of the discussion. The past sixty years of debris flow models are a history of failure when it comes to viscosity models, because each model is only capable to reproduce experiments or test cases when it is calibrated by equal experiments, but fails when applied to other terrains and material compositions.
Never the less the dominating physical processes were more and more understood by the different trys of rheological modelling, so today the viscous effects of the fluid and the granular dynamics of the grains are now accounted for seperateley by most approaches, with two phase models or Eulerien-Lagrangian coupled simulations.
These models have to try to stay as simple as possible, because the aim is that an engineering office should be able to model a hillslope in reasonabole time without needing a super-cluster, they might have data of grainsize distribution and experience in water content of expected debris flows, but no experimental shear-viscosity relation for each site. Especially with debris flow material it is not trivial to get a shear-viscosity relation experimentally due to large grains.
I think here the long-term aim is, using viscosity models allows to convince the society of certain approaches that are then seen as valid and allow engineering protection design as well as hazard risk zoning and ensurance.