The zero equation turbulence model gives approximate turbulence viscosity at a point as a function of velocity at that point and length scale. I haven't come across much literature on how to find the length scale.
The mixing length is typically the size of the shear layer making the turbulence. For a jet, or mixing layer, or wake, it is the half-width of the jet or mixing layer or wake. This means that the mixing length varies as you go along (streamwise) the jet,layer,wake. But does not vary across it.
Similarity analysis (math) or experiments tell you how fast the jet/layer/wake size will grow as a function of the distance downstream. Note that axisymmetric jets/wakes grow at different rates than planar ones.
A boundary layer is slightly different. The mixing length is "the distance to the wall".
Nobody uses one-equation models for the last 40 years because (1) the only situations it which they work is those in which you essentially know the answer already, and (2) inputting prescribed functions (like mixing length) into a computer code is a royal pain.
Spallart-Almaras is a one-equation model for boundary layers. It already has the assumption of mixing length = distance to the wall, incorporated into it. So you don't need to specify how to get it (it knows how). This model is still used widely for B.L. dominated flows (like airfoils).
In turbulence modeling, as in life, you get what you pay for.
If 50% of your problem physics results from turbulence. Maybe you should spend 50% of your effort on that physics. Cheap = useless.
I use Spallart-Allamaras model extensively for kind of flows over A/C wings. It works well for this type of airfoil flows. This I snot by coincident. The reason is that this model was designed using extensive experimental and empirical data on this type of flow and hence working well for this group is not surprising. However, it is not a guarantee that it will do the same for a different type of flows. Indeed, this is the holy grail for 1-eq models. they are only good for what they were designed for. Therefore, it is important to know which type of flow you want to apply the model for before you can select the appropriate model, and there are quite a few of them out there!
Hi Adil,
Thanks for your answer. I am looking forward to convert the Spalart Allmaras model to a zero equation turbulence model using user defined functions in FLUENT. My applications will mostly be coarse grid CFD for huge enclosure cooling purposes.
Hi Pratik, I think that unfortunately Dr. Blair Perot is correct in his doubts about using one-equation turbulence closures.
Look at an ideal eddy, the elementary particle of turbulence: there is a radius and a rotation rate (vorticity, or frequency). Yes, there are many such vortices forming a statistical ensemble. But these two features are crucial: an rms frequency and an rms radius. Turbulence is not a simple thing and many nobelists lost their nerves about it, so you really dont get it cheaper than for those two scales. However there is hope and good news: There is a solution now to this seemingly eternal issue. A primary paper you may find attached.
Article Universal equations and constants of turbulent motion
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