# arterial wall

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April 28, 2013, 02:42
arterial wall
#1
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bitak
Join Date: Jul 2009
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Hello all.
I want to simulate arterial wall (free wall model) and so I should to define mass transfer condition in wall .( I need to have suction velocity=4e-8 m/s and diffusion coefficient= 5e-8 m^2/s)
my geometry is a cylinder.
my boundary condition:

At inlet I have specific concentration.
at outlet I have no change in concentration.
at wall my concentration comes from mass transfer equation.
How I can simulate this problem in CFX ?????????????
I really need to know
Attached Images
 Capture.JPG (13.3 KB, 16 views)

 April 28, 2013, 06:06 #2 Member   bitak Join Date: Jul 2009 Posts: 56 Rep Power: 9 I can not read your reply!!!!!!!!!!!!!!!!!!!!!!!!11

 April 28, 2013, 06:41 #3 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 12,704 Rep Power: 98 Don't worry about the spam which was posted here before - I have removed the post and banned the user. What an idiot. Now to answer your question.... First of all, you will need to define the X and Y directions and what the symbols in the equation mean. Without some definitions it is useless. But I can see two general approaches for modelling this mass transfer: 1) You can define a boundary condition and/or a source term at the arterial wall to model the mass flux through the artety wall. 2) You can put a solid domain around the blood domain to model the artery itself. You can then model diffusion in this as well, so the effect of the aretery wall is more directly modelled. Note that you will still need to specify a boundary condition on the outside face of the artery wall, it will just be a boundary condition more suited to the artery outside wall, which persumably means the interface to the intercellular region.

 April 28, 2013, 07:43 #4 Member   bitak Join Date: Jul 2009 Posts: 56 Rep Power: 9 Vw: suction velocity at wall D: diffusion coefficient C: concentration Co: inlet concentration Cw: wall concentration

 April 28, 2013, 07:50 #5 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 12,704 Rep Power: 98 In that case the equation appears to be defining the concentration along the artery as a whole. That is the whole cross section is lumped together and a 1D approach used to model the concentration. CFX is a 3D solver so cannot really model 1D effects. It models the 3D effects. So if you want to match the equation model in CFX I would set the inlet concentration to C0, the concentration at the walls at Cw and let CFX handle the rest.

 April 28, 2013, 08:08 #6 Senior Member   Lefteris Join Date: Oct 2011 Location: UK Posts: 199 Rep Power: 7 I don't know if it will be helpful but there is this paper: Coupled Fluid–Structure Interaction Hemodynamics in a Zero-Pressure State Corrected Arterial Geometry - Vavourakis, Papaharilaou, Ekaterinaris - Journal of Biomechanics, Volume 44, Issue 13, 2011 __________________ Lefteris

 July 1, 2013, 01:29 #7 New Member   zhouqishan Join Date: Jun 2013 Posts: 8 Rep Power: 5 hi， have you solve your problem? do you konew how apply the @ outlet flux = 0?

July 2, 2013, 09:01
#8
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zhouqishan
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Quote:
 Originally Posted by ghorrocks 1) You can define a boundary condition and/or a source term at the arterial wall to model the mass flux through the artety wall.
，could you please show us more about how set a source term? is there any example can follow? Thank you in advance.

 July 2, 2013, 18:50 #9 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 12,704 Rep Power: 98 The documentation describes source terms pretty well, have a read. I do not think the tutorials cover source terms so you might need to ask CFX support for an example. But this application looks straight forward. In fact you might not need a source term at all. Define your C as an additional variable, put a flux defined as your final equation at the wall and an outlet condition on the end. This will do it - but it will be modelling the concentration in 3D, not 2D as you equation suggests.

 July 3, 2013, 02:18 #10 New Member   zhouqishan Join Date: Jun 2013 Posts: 8 Rep Power: 5 Thanks for your reply, I will read the source terms in the documentation carefully. Beginning of the simulation, I have the same idea as you. I defined volumetric additional variable. Although I could find the answer in "http://www.cfd-online.com/Forums/cfx/103928-outlet-boundary-condition-additional-variable.html" for the outlet, I was puzzled by the boundary condition of unit concentration on the wall. In the mass transfer equation for the wall, cw is the concentration on the wall, note vw is the water infiltration velocity but the solute, D the kinematic diffusivity, ∂C/∂n the concentration gradient normal to the wall. cw is relationship with the∂C/∂n. And I am no idea about how to set the ∂C/∂n, maybe the source terms will work. To be honest, I can finish the simulation in the fluent. In fluent, the diffusive flux is approximated in two parts: primary gradient and secondary gradient (this equal contains cw and∂C/∂n ). Then I get a new equal without ∂C/∂n. And the two macros in fluent are available to enable me to the necessary geometrical variables of the cell and calculates the secondary gradient term in equation respectively. The problem is that I failure to find the similar macros as the fluent. Any suggestion? Thanks!

 July 3, 2013, 07:22 #11 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 12,704 Rep Power: 98 In your equation I presume Cw is the concentration of the wall. What is Vw?

July 3, 2013, 09:16
#12
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zhouqishan
Join Date: Jun 2013
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Quote:
 Originally Posted by ghorrocks In your equation I presume Cw is the concentration of the wall. What is Vw?
oh,there are so many parameters. here vw is the water infiltration velocity but the solute.

 July 3, 2013, 19:10 #13 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 12,704 Rep Power: 98 Does that means the walls are porous and liquid is flowing through them?

July 3, 2013, 21:29
#14
New Member

zhouqishan
Join Date: Jun 2013
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Quote:
 Originally Posted by ghorrocks Does that means the walls are porous and liquid is flowing through them?
yes, but it is without porous.

 July 4, 2013, 07:17 #15 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 12,704 Rep Power: 98 So how are you modelling the infiltration velocity if you do not have a porous domain?

 July 4, 2013, 09:13 #16 New Member   zhouqishan Join Date: Jun 2013 Posts: 8 Rep Power: 5 well, in our simulation the vw is too small to induce the change of the velocity. So, it is logical to take this way. The problem is how to express ∂C/∂n in the cfx.

 July 4, 2013, 16:28 #17 Member   bitak Join Date: Jul 2009 Posts: 56 Rep Power: 9 I think we should define additional variabel and the Vw is velocity for transport of paticles in the wall in the wall BC for additional variable the transfer coefficient is true and (density*Vw) is mass flux in this option and value is zero. what is your oponion?????

 July 4, 2013, 20:06 #18 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 12,704 Rep Power: 98 So what defines Vw, if you are not modelling it directly?

July 4, 2013, 22:20
#19
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zhouqishan
Join Date: Jun 2013
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Hi, bitak. In my opinion you make some mistake. The completely equation is in the attached thumbnail.
Note vw is the water infiltration velocity, Kw a permeability coefficient of the solute;
The paper ' Stagnant Film Model for Concentration Polarization in Membrane Systems' will help you.

The kw is too small for the vw, so the kw can be assumed to be 0, and then we obtain the simpler equation as your attached thumbnails.
(cw is the concentration on the wall,
D the kinematic diffusivity,
∂C/∂n the concentration gradient normal to the wall. )

Quote:
 Originally Posted by ghorrocks So what defines Vw, if you are not modelling it directly?
Thanks for your reply, Glenn. I have no idea in the cfx. But in the fluent, I can solve the simple equation for the wall with Taylor series (showed in the attached). In the two equation, there are two parts is uncertain: cw and ∂C/∂. So I can get the cw without a porous domain.
Attached Images
 equation.png (29.5 KB, 7 views)

 July 5, 2013, 07:34 #20 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 12,704 Rep Power: 98 CFX has a variable for the wall normal vector. This should help you get the normal gradient.

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