Hi Shan,

Sorry I have not used this routine for a while. I attach some old notes I had on the derivation but perhaps Kurt is better placed to answer your email.

I would guess that

- alpha should indeed mean alpha_n.

- R is the radius of the Gmsh boundary

- T is the time period of the oscillation

It is possibly confusing to refer to them as non-dimensional since this depends on how you have set up your mesh and inflow parameters.

Cheers,

Spencer.

On 15 Jun 2019, at 22:33, Shanshan Luo <luoss@sas.upenn.edu> wrote:

Dear all,

I'm confused about description of womersley number on Page 150 of user-guide-4.4.1. Can anyone give me some suggestions?

On Page 150, for the formulas below:

<Screen Shot 2019-06-15 at 5.20.02 PM.png>

<Screen Shot 2019-06-15 at 5.20.11 PM.png>

How can I calculate 'alpha'? Or it is a typo and should be 'alpha_n'?

Also for the formula :

<Screen Shot 2019-06-15 at 5.23.19 PM.png>,

what does R and T represent?

Does R mean RADIUS (the non-dimensional radius of the boundary in Gmsh) or the real radius (with dimension) of the object?

Does T mean Period (the non-dimensional cycle time period)?

Thank you very much!

Best,

Shan

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Spencer Sherwin FREng, FRAeS
Head, Aerodynamics,
Director of Research Computing Service,
Professor of Computational Fluid Mechanics,
Department of Aeronautics,
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