Not yet, I'm working on it

I just skiped it here, for clarity. It's just a constant factor...

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

Not yet, I'm working on it

I just skiped it here, for clarity. It's just a constant factor...

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

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.

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.

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

womersley
 

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

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

Probably it has been a long time since you worked on this case, but maybe can you explain more detailed how you managed to implement the womersley profile and how octave-routine works?