branched pipe, appropriate BC at the outlets

kmgraju · August 11, 2014, 11:23

Dear all
I am trying to model branched artery having two branches from the main pipe. I also model a stenosis in the main pipe.The pipe branches after the stenosis. I am interested to see the pressure drop across the stenosis. I know the mass flow rate at the inlet. I know the pressure at the inlet. From this information one can easily find out inlet velocity .
How to model this kind of problem. Is there any way to calculate the mass flow rate through branches( two pipes are different in diameter and different in length). If I didn't choose inlet boundary condition as pressure then I must assign outlet boundary as pressure. What is the appropriate value of the pressure at the two outlets? Note that I am interested in pressure drop across the stenosis.

singer1812 · August 11, 2014, 11:43

This seems a more appropriate question for a literary search within your field. Unless you have data at the location of the outlet points, you essentially are "guessing" at what the outlet boundary conditions are (I am assuming they would be different).

One thing you could do is parametrically study the pressure drop across the stenosis as a function of mass flow rate out of the branches. Perhaps you can vary the set mass flow out of one branch from 0% to about 100% (do not set the other branch to a mass flow outlet as this can cause instability) and do a number of runs. You might find that the pressure varition across the stenosis is not a strong function of what goes on in the branches (then again, maybe it is, but you will have the data to scope it out).

kmgraju · August 11, 2014, 12:17

Quote:

Originally Posted by singer1812

This seems a more appropriate question for a literary search within your field. Unless you have data at the location of the outlet points, you essentially are "guessing" at what the outlet boundary conditions are (I am assuming they would be different).

One thing you could do is parametrically study the pressure drop across the stenosis as a function of mass flow rate out of the branches. Perhaps you can vary the set mass flow out of one branch from 0% to about 100% (do not set the other branch to a mass flow outlet as this can cause instability) and do a number of runs. You might find that the pressure varition across the stenosis is not a strong function of what goes on in the branches (then again, maybe it is, but you will have the data to scope it out).

Thank you Mr Singer

Why don't assume opening pressure boundary condition have constant pressure value which is same at both outlets?

singer1812 · August 11, 2014, 12:21

You could.

But, I tend to think that would not be appropriate.

WARNING: I am not in the medical field,

BUT I would think that those 2 different paths, with the amount of the path you have modeled, DO NOT have the same conditions.

If it were me, I would model out to were the boundary conditions are known, or, do as I said before and perform a sensitivity.

kmgraju · August 12, 2014, 03:22

Any other suggestion for this kind of problem

ghorrocks · August 12, 2014, 06:50

I do not understand what you are trying to model - your original post is ambiguous. You say you are only interested in the pressure drop across the stenosis, but then you also say you want to know the flow split between the two outlet branches. They are different questions and probably not tightly related.

Assuming you want the pressure drop over the stenosis, then remove the branch and put a pressure boundary in. Then a mass flow rate boundary at the other end and the simulation is straight forward.

If you want to know the flow split between the two branches then you need to know the pressure conditions in the two branches.

Dave442 · August 12, 2014, 07:26

Hi,

Are you considering a coronary artery? Outlet boundary conditions for the coronary vasculature are difficult to define since a large degree of resistance is introduced by the contraction of the heart. This results in a nonlinear and time-varying system. Many authors simply assume linearity and time-invariance and make some assumption with regards to the flow split. In certain papers, a three-element Windkessel function is specified at the outlet of each branch. The methods used to identify appropriate parameters for these functions are described in the literature. Other methods of approximating the outlet boundary conditions are also described in the literature.

Here are two recent papers that I am aware of:
http://www.ncbi.nlm.nih.gov/pubmed/20507966
http://www.ncbi.nlm.nih.gov/pubmed/23676893

There are probably many, many more if you go looking.

Good luck,
Dave

kmgraju · August 12, 2014, 13:23

Thank you for your kind information.
I have gone through some of the articles that they used velocity as the inlet and mass flow rate at the outlet using Murray's law.I don't know they claimed that the flow is realistic flow.

Without pressure condition how did they model? Please share your ideas and thoughts

singer1812 · August 12, 2014, 14:01

Dave gave you a series of articles related to this. It is a complicated area that most people outside of your field have no experience in.

Once again, if you have nothing else to go on, I would suggest you run this as a parametric and see if the drop is even sensitive to the branch.

kmgraju · August 13, 2014, 12:34

Quote:

Originally Posted by singer1812

Dave gave you a series of articles related to this. It is a complicated area that most people outside of your field have no experience in.

Once again, if you have nothing else to go on, I would suggest you run this as a parametric and see if the drop is even sensitive to the branch.

Hi all
I use velocity as inlet.
since I don't know the pressure at the outlet, can I use the boundary condition at he outlet as areaAve(Pressure)@outlet by setting pressure value (assume 86 mmHg) as a domain initial condition. Is it stress free boundary condition?

shall I introduce 0 pa both at outlets?

I found some article and they use CFX they mentioned stress free boundary condition at the outlet? what does it mean?. In some other cases, they specified as zero pressure gradient. what is zero pressure gradient?
Kindly tell me how to use these conditions in cfx

kmgraju · August 15, 2014, 02:42

Quote:

Originally Posted by singer1812

This seems a more appropriate question for a literary search within your field. Unless you have data at the location of the outlet points, you essentially are "guessing" at what the outlet boundary conditions are (I am assuming they would be different).

One thing you could do is parametrically study the pressure drop across the stenosis as a function of mass flow rate out of the branches. Perhaps you can vary the set mass flow out of one branch from 0% to about 100% (do not set the other branch to a mass flow outlet as this can cause instability) and do a number of runs. You might find that the pressure varition across the stenosis is not a strong function of what goes on in the branches (then again, maybe it is, but you will have the data to scope it out).

Yes
It is a good assumption I can start .

If I set inlet as a pressure boundary and one of the branch as mass flow rate What is the the other branch outlet boundary condition?
You mentioned that
("do not set the other branch to a mass flow outlet as this can cause instability") what does it mean?
Thank you

singer1812 · August 18, 2014, 10:46

You can set 2 branches to mass flow rate (the inlet and one outlet). The one outlet mass flow will some percentage of the inlet mass flow (this is your parametric).

Put another pressure BC on the other branch. Mass flow out of this branch will be determined via continuity. If you set this as a mass flow or velocity you probably will not converge or cause instability.

Run this over a series of flow mass flow rates on the branch outlet to get the sensitivity of the stenosis (at least for a steady state condition).

But as Dave said, the real conidition is very complicated, and what I suggest may be an over simplication.

August 11, 2014, 11:23	branched pipe, appropriate BC at the outlets	#1
kmgraju Senior Member Govindaraju Join Date: Apr 2010 Posts: 209 Rep Power: 17	Dear all I am trying to model branched artery having two branches from the main pipe. I also model a stenosis in the main pipe.The pipe branches after the stenosis. I am interested to see the pressure drop across the stenosis. I know the mass flow rate at the inlet. I know the pressure at the inlet. From this information one can easily find out inlet velocity . How to model this kind of problem. Is there any way to calculate the mass flow rate through branches( two pipes are different in diameter and different in length). If I didn't choose inlet boundary condition as pressure then I must assign outlet boundary as pressure. What is the appropriate value of the pressure at the two outlets? Note that I am interested in pressure drop across the stenosis.

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August 11, 2014, 11:43		#2
singer1812 Senior Member Edmund Singer P.E. Join Date: Aug 2010 Location: Minneapolis, MN Posts: 511 Rep Power: 21	This seems a more appropriate question for a literary search within your field. Unless you have data at the location of the outlet points, you essentially are "guessing" at what the outlet boundary conditions are (I am assuming they would be different). One thing you could do is parametrically study the pressure drop across the stenosis as a function of mass flow rate out of the branches. Perhaps you can vary the set mass flow out of one branch from 0% to about 100% (do not set the other branch to a mass flow outlet as this can cause instability) and do a number of runs. You might find that the pressure varition across the stenosis is not a strong function of what goes on in the branches (then again, maybe it is, but you will have the data to scope it out).

August 11, 2014, 12:21		#4
singer1812 Senior Member Edmund Singer P.E. Join Date: Aug 2010 Location: Minneapolis, MN Posts: 511 Rep Power: 21	You could. But, I tend to think that would not be appropriate. WARNING: I am not in the medical field, BUT I would think that those 2 different paths, with the amount of the path you have modeled, DO NOT have the same conditions. If it were me, I would model out to were the boundary conditions are known, or, do as I said before and perform a sensitivity.

August 12, 2014, 03:22		#5
kmgraju Senior Member Govindaraju Join Date: Apr 2010 Posts: 209 Rep Power: 17	Any other suggestion for this kind of problem

August 12, 2014, 06:50		#6
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,871 Rep Power: 144	I do not understand what you are trying to model - your original post is ambiguous. You say you are only interested in the pressure drop across the stenosis, but then you also say you want to know the flow split between the two outlet branches. They are different questions and probably not tightly related. Assuming you want the pressure drop over the stenosis, then remove the branch and put a pressure boundary in. Then a mass flow rate boundary at the other end and the simulation is straight forward. If you want to know the flow split between the two branches then you need to know the pressure conditions in the two branches.

August 12, 2014, 07:26		#7
Dave442 Member Dave Join Date: Aug 2011 Posts: 33 Rep Power: 15	Hi, Are you considering a coronary artery? Outlet boundary conditions for the coronary vasculature are difficult to define since a large degree of resistance is introduced by the contraction of the heart. This results in a nonlinear and time-varying system. Many authors simply assume linearity and time-invariance and make some assumption with regards to the flow split. In certain papers, a three-element Windkessel function is specified at the outlet of each branch. The methods used to identify appropriate parameters for these functions are described in the literature. Other methods of approximating the outlet boundary conditions are also described in the literature. Here are two recent papers that I am aware of: http://www.ncbi.nlm.nih.gov/pubmed/20507966 http://www.ncbi.nlm.nih.gov/pubmed/23676893 There are probably many, many more if you go looking. Good luck, Dave

August 12, 2014, 13:23		#8
kmgraju Senior Member Govindaraju Join Date: Apr 2010 Posts: 209 Rep Power: 17	Thank you for your kind information. I have gone through some of the articles that they used velocity as the inlet and mass flow rate at the outlet using Murray's law.I don't know they claimed that the flow is realistic flow. Without pressure condition how did they model? Please share your ideas and thoughts

August 12, 2014, 14:01		#9
singer1812 Senior Member Edmund Singer P.E. Join Date: Aug 2010 Location: Minneapolis, MN Posts: 511 Rep Power: 21	Dave gave you a series of articles related to this. It is a complicated area that most people outside of your field have no experience in. Once again, if you have nothing else to go on, I would suggest you run this as a parametric and see if the drop is even sensitive to the branch.

August 18, 2014, 10:46		#12
singer1812 Senior Member Edmund Singer P.E. Join Date: Aug 2010 Location: Minneapolis, MN Posts: 511 Rep Power: 21	You can set 2 branches to mass flow rate (the inlet and one outlet). The one outlet mass flow will some percentage of the inlet mass flow (this is your parametric). Put another pressure BC on the other branch. Mass flow out of this branch will be determined via continuity. If you set this as a mass flow or velocity you probably will not converge or cause instability. Run this over a series of flow mass flow rates on the branch outlet to get the sensitivity of the stenosis (at least for a steady state condition). But as Dave said, the real conidition is very complicated, and what I suggest may be an over simplication.