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 bitak April 28, 2013 02:42

arterial wall

1 Attachment(s)
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

 bitak April 28, 2013 06:06

 ghorrocks April 28, 2013 06:41

Don't worry about the spam which was posted here before - I have removed the post and banned the user. What an idiot.

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.

 bitak April 28, 2013 07:43

Vw: suction velocity at wall
D: diffusion coefficient
C: concentration
Co: inlet concentration
Cw: wall concentration

 ghorrocks April 28, 2013 07:50

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.

 Aeronautics El. K. April 28, 2013 08:08

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

 zhouqi July 1, 2013 01:29

hi，
have you solve your problem? do you konew how apply the @ outlet flux = 0?

 zhouqi July 2, 2013 09:01

Quote:
 Originally Posted by ghorrocks (Post 423602) 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.

 ghorrocks July 2, 2013 18:50

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.

 zhouqi July 3, 2013 02:18

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!

 ghorrocks July 3, 2013 07:22

In your equation I presume Cw is the concentration of the wall. What is Vw?

 zhouqi July 3, 2013 09:16

Quote:
 Originally Posted by ghorrocks (Post 437539) 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.:)

 ghorrocks July 3, 2013 19:10

Does that means the walls are porous and liquid is flowing through them?

 zhouqi July 3, 2013 21:29

Quote:
 Originally Posted by ghorrocks (Post 437665) Does that means the walls are porous and liquid is flowing through them?
yes, but it is without porous.

 ghorrocks July 4, 2013 07:17

So how are you modelling the infiltration velocity if you do not have a porous domain?

 zhouqi July 4, 2013 09:13

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.

 bitak July 4, 2013 16:28

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.

 ghorrocks July 4, 2013 20:06

So what defines Vw, if you are not modelling it directly?

 zhouqi July 4, 2013 22:20

1 Attachment(s)
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 (Post 437888) 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.

 ghorrocks July 5, 2013 07:34

CFX has a variable for the wall normal vector. This should help you get the normal gradient.

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