# Pulsatile Womersley velocity profile

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August 22, 2011, 07:31
#21
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Daniel
Join Date: Nov 2009
Posts: 10
Rep Power: 9
Quote:
 Originally Posted by liguifan Did you successfully implement the Womersley pulsatile inlet flow using u(r,t) = exp(z*t) * (1 - J0(z*r) / J0(z) ) where z is complex number?
Not yet, I'm working on it

Quote:
 Originally Posted by liguifan I am working on the same thing as well. Where is the A/z*rho*w term gone?
I just skiped it here, for clarity. It's just a constant factor...

Quote:
 Originally Posted by liguifan They use womersley inlet condition with womersley number 7... I got a parabolic velocity profile pulse with time. But the velocity profile seem to be symmetrical, which like a sin function across 1s ( time period )...
The Womersley Solution is for oscillatory flow, not pulsatile...
The pressure ansatz is harmonic, and so is the velocity...
For systolic wave forms you might find something helpful in the papers from METTE OLUFSEN...

Cheers
Daniel

August 22, 2011, 07:33
#22
New Member

Daniel
Join Date: Nov 2009
Posts: 10
Rep Power: 9
Quote:
 Originally Posted by liguifan Did you successfully implement the Womersley pulsatile inlet flow using u(r,t) = exp(z*t) * (1 - J0(z*r) / J0(z) ) where z is complex number?
Not yet, I'm working on it

Quote:
 Originally Posted by liguifan I am working on the same thing as well. Where is the A/z*rho*w term gone?
I just skiped it here, for clarity. It's just a constant factor...

Quote:
 Originally Posted by liguifan They use womersley inlet condition with womersley number 7... I got a parabolic velocity profile pulse with time. But the velocity profile seem to be symmetrical, which like a sin function across 1s ( time period )...
The Womersley Solution is for oscillatory flow, not pulsatile...
The pressure ansatz is harmonic, and so is the velocity...
For systolic wave forms you might find something helpful in the papers from METTE OLUFSEN...

Cheers
Daniel

 October 11, 2011, 08:00 #23 New Member   Michael Stiehm Join Date: Sep 2010 Posts: 13 Rep Power: 9 Hallo, I am very interested in oscillating and pulsatile inletBC, so this is a great thread...thanks for that. But I have two questions: 1: Where did you get the Womersley Solution for the real part (post 16 and 17)? 2: When you have got this solution, is there still an need to solve the basic womersley solution with bessel function for complex numbers? Because the real part solution looks very nice!! Thanks a lot Michael Last edited by miael; October 12, 2011 at 10:14.

November 14, 2011, 05:09
#24
Member

Join Date: Apr 2010
Posts: 53
Rep Power: 9
Quote:
 Originally Posted by miael Hallo, I am very interested in oscillating and pulsatile inletBC, so this is a great thread...thanks for that. But I have two questions: 1: Where did you get the Womersley Solution for the real part (post 16 and 17)? 2: When you have got this solution, is there still an need to solve the basic womersley solution with bessel function for complex numbers? Because the real part solution looks very nice!! Thanks a lot Michael
Hi Michael,
the shown equation is derived for a 2D channel and not for a 3D pipe. Although, you have nice pulsatile effects the flow rate is a sinus if you integrate it. to get a flow rate which composes of multiple sinus and cosinus functions, the complex womersley equation is necessary.

 March 11, 2012, 15:37 #25 New Member   juanjo rivera Join Date: Jan 2010 Posts: 3 Rep Power: 9 Nihil, Are you finished the implementation of the Womersley BC for velocity?. Can you show one example? I am interesting to implement it but in function of flow rate, not pressure gradient.

 March 19, 2012, 09:13 #26 New Member   Michael Stiehm Join Date: Sep 2010 Posts: 13 Rep Power: 9 Hello Juanjo, perhabs I can help you with your womersley-problem. I used an octave-routine to calculate the womersley-profile. There you have no problem with komplex bessel functions. So you can calculate your velocity field for every time step you wanna use. Additional you have to create a points file (see tutorial) and then use the BC timeVaryingMappedFixedValue. I got good results with that. Hope I could help. Michael

June 23, 2012, 22:42
womersley
#27
Member

Guifan Li
Join Date: Apr 2011
Location: New York City, U.S.
Posts: 96
Rep Power: 8
Quote:
 Originally Posted by miael Hello Juanjo, perhabs I can help you with your womersley-problem. I used an octave-routine to calculate the womersley-profile. There you have no problem with komplex bessel functions. So you can calculate your velocity field for every time step you wanna use. Additional you have to create a points file (see tutorial) and then use the BC timeVaryingMappedFixedValue. I got good results with that. Hope I could help. Michael
Hi Michael,

I am working on the Womersley-problem for a while and I still didn't work out a good solution.

It sounds like you put the Womersley equation with complex bessel function into octave which is quite amazing. But how do you store the data ( velocity at different location for a 3D case)?

Btw, did you use the same equation below?

Thanks
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 June 25, 2012, 04:10 #28 New Member   Michael Stiehm Join Date: Sep 2010 Posts: 13 Rep Power: 9 Hello, yes this is the equation I use. If you want to calculate the womersley-profile in octave you need the function besselj(0,...) for the complex bessel-function. So you get the womersley-profile u(r,t) for a 2D case. Because of axis-symmetric condition you can use the relationship r=sqrt(x^2+y^2) to calculate the 3D velocity field. As inlet BC I use timeVaryingMappedFixedValue therefore a file called points is required which contains the coordinates and for every time step you need a velocity file which contains the velocity field regarding to the "point" file. Regards Michael

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