Pulsatile Boundary Condition

a.sarami · December 11, 2013, 02:16

Dear Friends.

I would like to model blood flow in an artery, say an straight tube, with a pressure wave as the inlet Boundary condition. moreover, I would like to be sure that the flow enters the boundary with a parabolic profile, fully developed I mean. See, If I would like to assign flow or velocity at inlet, it was easy to create a parabolic velocity profile at inlet, but I am assigning pressure at inlet!

The only way, I think, is to extrude inlet for some length and estimate pressure drop over that additional length using poiseuille law then add it to the pressure wave and then simulate. Now, we can say that at the real inlet we would have the wanted flow with that wanted pressure this time in parabolic form. But the problem is here, I think if we have pulsatile inlet, we can not be sure that poiseuille's law is correct at the extruded length, I mean it may depend on the down stream of the pipe where the artery is located.

would you please help me creating a parabolic profile while specifying the pressure at BC?

Best
Ali

a.sarami · December 11, 2013, 02:40

My main question is that, how we can ensure that inlet velocity profile is parabolic when both inlet and outlet BCs are pressures?

I checked it out it 1m length 0.5cm diameter straight tube, the velocity at inlet was parabolic but the max velocity was a little bit different with what is expected from poiseuille but after passing 10-20 cm in the tube it gets better.
say max vel must be 100cm/sec, it is 95 cm/sec at inlet and 98-99 cm/sec after passing 10-20 cm in the tube.

ghorrocks · December 11, 2013, 05:18

You cannot specify both the velocity and pressure at a point. That is over specifying the flow. And, as you found out, if you specify the pressure some distance away and let the flow develop it will not exactly form the steady state parabolic profile - because your flow is not steady so it will not settle to a parabolic profile.

You cannot have a defined pressure and a perfect parabolic profile for all time no matter how to do it. You are going to have to allow variations in the pressure or velocity.

Your 10-20cm result sounds close enough to what you are looking for, so why not use that?

a.sarami · December 11, 2013, 10:27

Dear Friend, Thank you so much for your advice. It was of course very informative. But actually my problem is that by extruding my inlet boundary for about 20 cm, then I have a new inlet with a new pressure wave BC. You know I have the pressure BC at the real inlet not on this new artificial inlet after extruding. It seems that I need to have an exact sense of pressure drop over extruded length and add it to my pressure wave so that I can be sure that at real inlet I have my favorite pressure wave. But it seems not possible to have such an exact estimation.
Would you please advise
Thank alot

ghorrocks · December 11, 2013, 16:14

I think you missed my point. It is not possible to define the velocity AND pressure at any point in the flow at all times by any method. Anything you do will be an approximation of velocity or pressure, and that includes extending inlet conditions.

a.sarami · December 11, 2013, 16:25

Dear Friend, Thanks for your response. Of course I know it is not possible to specify both pressure and velocity. I would like to specify pressure at inlet, not velocity; but I would like CFX to calculate inlet velocity as a parabolic profile. So extention would be a good idea. But my question is this; again emphasizing that I am specifying pressure at inlet, If I extrude inlet, then my pressure BC does not works any more for this new inlet because we have a pressure drop over the extention. Of Course I may ignore the pressure drop over the extention and put simply my pressure BC at this new inlet, but is it reasonable to ignore a pressure drop in our calculations?
Thank you

ghorrocks · December 11, 2013, 16:32

Whether it is valid to ignore the pressure drop is entirely up to you. It will introduce an error, but whether the error is acceptable depends on your accuracy requirement and what you are trying to achieve with the model.

Note that in transient flow, even with an incompressible fluid, you will not get the inlet pressure minus a pressure drop at the end of the extension. The transient flow will introduce its own pressure variations to change the pressure profile.

December 11, 2013, 02:16	Pulsatile Boundary Condition	#1
a.sarami Member Ali Sarami Join Date: Jun 2010 Posts: 34 Rep Power: 15	Dear Friends. I would like to model blood flow in an artery, say an straight tube, with a pressure wave as the inlet Boundary condition. moreover, I would like to be sure that the flow enters the boundary with a parabolic profile, fully developed I mean. See, If I would like to assign flow or velocity at inlet, it was easy to create a parabolic velocity profile at inlet, but I am assigning pressure at inlet! The only way, I think, is to extrude inlet for some length and estimate pressure drop over that additional length using poiseuille law then add it to the pressure wave and then simulate. Now, we can say that at the real inlet we would have the wanted flow with that wanted pressure this time in parabolic form. But the problem is here, I think if we have pulsatile inlet, we can not be sure that poiseuille's law is correct at the extruded length, I mean it may depend on the down stream of the pipe where the artery is located. would you please help me creating a parabolic profile while specifying the pressure at BC? Best Ali

December 11, 2013, 02:40	Clarifying	#2
a.sarami Member Ali Sarami Join Date: Jun 2010 Posts: 34 Rep Power: 15	My main question is that, how we can ensure that inlet velocity profile is parabolic when both inlet and outlet BCs are pressures? I checked it out it 1m length 0.5cm diameter straight tube, the velocity at inlet was parabolic but the max velocity was a little bit different with what is expected from poiseuille but after passing 10-20 cm in the tube it gets better. say max vel must be 100cm/sec, it is 95 cm/sec at inlet and 98-99 cm/sec after passing 10-20 cm in the tube.

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December 11, 2013, 05:18		#3
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,703 Rep Power: 143	You cannot specify both the velocity and pressure at a point. That is over specifying the flow. And, as you found out, if you specify the pressure some distance away and let the flow develop it will not exactly form the steady state parabolic profile - because your flow is not steady so it will not settle to a parabolic profile. You cannot have a defined pressure and a perfect parabolic profile for all time no matter how to do it. You are going to have to allow variations in the pressure or velocity. Your 10-20cm result sounds close enough to what you are looking for, so why not use that?

December 11, 2013, 10:27		#4
a.sarami Member Ali Sarami Join Date: Jun 2010 Posts: 34 Rep Power: 15	Dear Friend, Thank you so much for your advice. It was of course very informative. But actually my problem is that by extruding my inlet boundary for about 20 cm, then I have a new inlet with a new pressure wave BC. You know I have the pressure BC at the real inlet not on this new artificial inlet after extruding. It seems that I need to have an exact sense of pressure drop over extruded length and add it to my pressure wave so that I can be sure that at real inlet I have my favorite pressure wave. But it seems not possible to have such an exact estimation. Would you please advise Thank alot

December 11, 2013, 16:14		#5
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,703 Rep Power: 143	I think you missed my point. It is not possible to define the velocity AND pressure at any point in the flow at all times by any method. Anything you do will be an approximation of velocity or pressure, and that includes extending inlet conditions.

December 11, 2013, 16:25		#6
a.sarami Member Ali Sarami Join Date: Jun 2010 Posts: 34 Rep Power: 15	Dear Friend, Thanks for your response. Of course I know it is not possible to specify both pressure and velocity. I would like to specify pressure at inlet, not velocity; but I would like CFX to calculate inlet velocity as a parabolic profile. So extention would be a good idea. But my question is this; again emphasizing that I am specifying pressure at inlet, If I extrude inlet, then my pressure BC does not works any more for this new inlet because we have a pressure drop over the extention. Of Course I may ignore the pressure drop over the extention and put simply my pressure BC at this new inlet, but is it reasonable to ignore a pressure drop in our calculations? Thank you

December 11, 2013, 16:32		#7
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,703 Rep Power: 143	Whether it is valid to ignore the pressure drop is entirely up to you. It will introduce an error, but whether the error is acceptable depends on your accuracy requirement and what you are trying to achieve with the model. Note that in transient flow, even with an incompressible fluid, you will not get the inlet pressure minus a pressure drop at the end of the extension. The transient flow will introduce its own pressure variations to change the pressure profile.