Dear Kurt, Thanks for your help. I use 20 Fourier modes. I attach the related files here. "cylinder2_1_Spherigon.xml" is the geometry file. "two period_condition.xml" is the condition file. "WomParams2_2.xml" is the Womersley condition file where contains 20 modes of Fourier coefficients. Best, Shan On Mon, Jun 17, 2019 at 7:17 PM Kurt Sansom <kayarre@gmail.com> wrote:
How many Fourier modes do you have? What does that file look like?
~Kurt
On Mon, Jun 17, 2019 at 1:10 PM Shanshan Luo <luoss@sas.upenn.edu> wrote:
Dear Professor Sherwin, and Kurt,
Thank you for your reply but I still have some questions.
I set my mesh and inflow parameters as follows: 1)The real radius of inlet boundary is *R_real = 1 cm*. The radius of inlet boundary shown in Gmsh is *R_Gmsh = 1*. Hence we calculate the characteristic length to be *L_scal = R_real / R_Gmsh = 1 cm. * * R_Gmsh *is the non-dimensional radius. 2) We define the characteristic flow velocity to be the maximum value of the flow velocity *U_scal = U_max = 23 cm/s. * * U/U_scal *is the non-dimensional flow velocity 3) Next we calculate the characteristic time to the divison of L_scal and U_scal, i.e. *T_scal = L_scal / U_scal = 0.044 s. * * T/T_scal *is the non-dimensional time. Since the whole period lasts for* 0.71 s, *the non-dimensional period is *0.71/0.044 = 16.14.* 4)Based on (1),(2) and (3), assume the flow density *rho = 1.05 g/cm^3, *fluid viscosity *mu = 0.04 g/(cm*s), w*e can get the Reynolds number *Re = rho * U_scal * L_scal / mu = 598 *and the non-dimensional kinematic viscosity *nu* *= 1/Re = 0.0017*
With the above parameters *"T = 16.14, R = 1, nu = 0.0017"* , we calculate womersley numbers *"alpha_n", *the fourier coefficients *"A"* of the non-dimensional flow velocity together with the transformed fourier coefficients "\*tilde{A}*" as the fomulas in the tutorial.
However, when I set radius=1 in womersley boundary condition, the result seems wrong. The simulation blow up in half way and here I visualize the result in earlier time step. The first figure shows the geometry with inflow velocity. The second figure visualize velocity by arrows. In this result, I believe the red part of figure 1 should be bigger to fill out the inlet, which means setting radius=1 may not big enough in womersley boundary condition. Also, we can see some flow in going back from inlet, which is wrong because the inflow in my case should always move into the geometry but not move out from the inlet. So my question is, if radius=1 is not right, then how can I set the radius of Wommersley boundary condition ? Or is there some other problem in the set up which may cause this mistake? Thank you for your help! [image: WechatIMG1438.png] Figure 1 [image: WechatIMG1471.png] Figure 2
Best, Shan
On Mon, Jun 17, 2019 at 3:18 AM Sherwin, Spencer J < s.sherwin@imperial.ac.uk> wrote:
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, s.sherwin@imperial.ac.uk South Kensington Campus, Phone: +44 (0)20 7594 5052 Imperial College London, Fax: +44 (0)20 7594 1974 London, SW7 2AZ, UK http://www.imperial.ac.uk/people/s.sherwin/
-- Kurt Sansom
