Computational Fractal Fluid Dynamics

[Conceptual]

Doing a google search only leads to a few dead links, and this paper...

http://markjstock.com/computation_fract ... daries.pdf

Does anyone here mind explaining how fractals are integrated into the CFD process to predict turbulent flows? And is this where most of the divergence of outcomes arise between Computation and Windtunnel?

:Looking forward to some very deep and explitative responses:

Thanks for your willingness to educate as always!

[syguy]

... how fractals are integrated into the CFD process to predict turbulent flows?

Turbulence is fractal in nature, i.e., the turbulent structures (instantaneous velocity fields) are similar at different spacial resolutions, until you reach the molecular scale. To accurately model a turbulent flow you need to resolve all these turbulent length scales (Direct Numerical Simulation), but it is extremely resource intensive (massive element counts) and impractical for all but the simplest problems.

Most practical CFD approaches use Reynolds-Average Navier-Stokes (RANS) with turbulence models to represent the turbulence indirectly and avoid resolving all the fractal turbulence length scales. In recent times Large Eddy Simulation (LES) has become practical for some flows (typically requires large element counts) by representing larger (though still small) turbulent eddies directly and modeling smaller eddies.

For more on RANS try: http://www.symscape.com/reynolds-averag ... -equations

So in answer to your question the turbulence model is the primary means by which the fractal nature of turbulence is addressed.

And is this where most of the divergence of outcomes arise between Computation and Windtunnel?

Yes, the turbulence model is a primary determiner of accuracy for simulating a flow - there are numerous models tuned for various types of flows.

The other primary concern is the mesh resolution - turbulence models still require relatively fine mesh elements along walls to resolve boundary layers in order to capture viscous effects, such as flow separation and skin friction. Without a well resolved model the best turbulence model won't provide accurate results.

Hope this helps.

[Conceptual]

Thanks for the info!

As always tho, it leads to more questions...

Do you know of any work being done to move away from the RANS estimates to true fractal equasions? The fractal equasions that I have seen in this new area of research (for me) so far seem to be rather simple, but I can see how the process intensity can arise with the exponential nature of them.

And about mesh smoothness... Do you use the "tasselation" effect on models to make them smoother? From what I have seen from the ATI demos for their Stream processors, the meshes become VERY high in cell count.

About the Tasselation: http://www.amd.com/us/Documents/Catmull ... ePaper.pdf

PM me if you want any of the info that I have compiled.

Thanks again!

[syguy]

Do you know of any work being done to move away from the RANS estimates to true fractal equations?

Can't say I do. LES is closer to representing the fractal nature of turbulence down to a certain length scale, but it doesn't explicitly deal in fractal equations.

Do you use the "tessellation" effect on models to make them smoother?

I presume you are referring to the near real-time hardware support for tessellation on the latest graphics cards. I don't have any experience in exploiting this, though it looks interesting.

The surface mesh tools (Quadrilateral and Triangle) I've developed evaluate and place points on the true analytic geometry (e.g., NURBS) - which means higher resolutions will approach the true geometry - similar in principle to the GPU tessellation process, i.e., different resolutions of the same geometry. Some CFD tools mesh a faceted tessellation that represents the original analytic geometry, so they don't approach the original analytic geometry with higher mesh resolutions.

More differences:

• For CFD the quality (shape) of the mesh elements is important, whereas in visualization it's a minor issue and therefore the visualization algorithms are typically tuned for generation speed.
• For RANS and LES simulations you need a volume mesh, not just a surface mesh, so resolution changes need to be carried over in to the volume elements which is an order of magnitude more difficult algorithmically than surface meshing.

the meshes become VERY high in cell count

I think the high cell count is just to highlight the rendering speed of their graphics cards. It appears that real-time tessellation is best used in reducing cell counts when the viewer is far from an object and incrementally adding detail as the object gets closer to the viewer. This is known as Level Of Detail (LOD) modeling. You kind of use this approach more explicitly (manual control) in CFD where you mesh certain areas at higher resolution (e.g., airfoils) than others (e.g., outer boundaries).

I've probably gone on too much...

[Conceptual]

Another big thank you for your info!

Do you think that there would be a market for true fractal turbulence models?

[syguy]

Do you think that there would be a market for true fractal turbulence models?

If a fractal turbulence model could be accurate over a wide range of flow regimes, but require less resources (CPU + memory) than existing models then absolutely there would be market for it. Even if it was generally applicable with some resource overheads that could be valuable too - without having to resort to LES.

There are turbulence models, such as Reynolds Stress Models (RSM), for RANS that are more widely applicable, but they haven't proved attractive due to their resource overheads compared to specifically tuned turbulence models, such as Spalart Allmaras for external aerodynamics.

[Conceptual]

Thanks again!

[mstock]

Hi! I was drawn here because of the link to my paper on turbulence and fractals. I am sorry it wasn't more useful.

There has been some research in using fractal statistics to model the subgrid scales (SGS) in Large-Eddy Simulation (LES). The work was done by my advisor Werner Dahm and a fellow grad student Greg Burton a few years ago. Here is a link to part 1 of their paper:

Multifractal subgrid-scale modeling for large-eddy simulation. I. Model development and a priori testing.
http://adsabs.harvard.edu/abs/2005PhFl...17g5111B

If I recall correctly, the method was an improvement on even the multi-level subgrid scale models in use at the time. But since that work, Dr. Burton has moved on to a different method for SGS modeling, one that doesn't seem to involve fractals: http://www.stanford.edu/group/ctr/semin ... 090508.pdf

I hope that helps.

[jddh1]

Hi! I was drawn here because of the link to my paper on turbulence and fractals. I am sorry it wasn't more useful.

There has been some research in using fractal statistics to model the subgrid scales (SGS) in Large-Eddy Simulation (LES). The work was done by my advisor Werner Dahm and a fellow grad student Greg Burton a few years ago. Here is a link to part 1 of their paper:

Multifractal subgrid-scale modeling for large-eddy simulation. I. Model development and a priori testing.
http://adsabs.harvard.edu/abs/2005PhFl...17g5111B

If I recall correctly, the method was an improvement on even the multi-level subgrid scale models in use at the time. But since that work, Dr. Burton has moved on to a different method for SGS modeling, one that doesn't seem to involve fractals: http://www.stanford.edu/group/ctr/semin ... 090508.pdf

I hope that helps.

Nice to see another michigan man on here.

Is Dahm's hair still "frozen" in the upright position?

[santhip]

Hi..

Does anyone know what the strength and weakness of fractal modeling of turbulence is ? Is there any university where there is research in this area ?

Thanks,