Integrating along a streamline

JPBodner · October 28, 2011, 09:27

Damage to red blood cells in a flow is often evaluated by an equation like this:

damage=a*(shear stress)^b * (time)^c where a,b,c are constants.

Here, time is the time of exposure at the local value of shear stress. In other words, the idea is to integrate this along a streamline to determine how a particular red blood cell would be damaged.

Anyone know how to integrate an expression like this along a streamline in STAR-CCM+?

JB

RobertB · October 29, 2011, 10:09

Had you considered doing it as a source term. To find out flight time I think you put in a source term of density (it's in one of the examples). Thus you can see how long it takes to get from the inlet to a point.

You should be able to generate a source term which will essentially be the damage incurred while in that cell and the code will integrate it for you.

You can also see where the most damage is done purely by plotting up the source term (you may need to normalize by volume).

The other option is to run tracks, get the track file format from CD, dump the other data you need and write a program to do it externally.

ping · November 7, 2011, 05:57

on a quick think about this, I dont think you need streamlines or the 'age of flow via density' technique mentioned by robertb as used to measure age of air in buildings. you say the damage is time at a certain shear stress, so it would seem to me that you just need a field function which works out the damage during the current timestep = shear stress * dtime (with your constants included of course). then you need to add this to the current sum of damage to get the new total damage locally everywhere in the field. do the sum using a field monitor of type sum. plot this scalar field function. seems simple to me?

RobertB · November 7, 2011, 07:49

This would only provide total damage in the domain. It is likely that to design better parts you will need to attribute local damage to specific features which I do not believe this technique will do.

ping · November 8, 2011, 03:14

shear-tracking.jpg
...it is not the total sum (that is a simple sum report) but the sum in each cell - this is why field monitors are such wonderful tools. however on second thoughts this is not what you want - it would tell you where the worst cells for creating damage are in fluctuating flow.
Whereas you need the transported damage summed, so you should be using a passive scalar for this: create the field function for your damage variable; add a passive scalar; add a region source for this scalar and use the damage field function as the source for the scalar. to get the units correct your might need to think about it a bit. i did this in a little test and the results are in the image - you can see the local shear stress at the top and the passive scalar below, with high values in the recirculation zone behind as one would expect.

JPBodner · November 8, 2011, 17:57

Yes, Ping. I think you have the idea that I came upon independently. (Actually, see "Fast three-dimensional numerical hemolysis approximation" by Garon and Farinas, Artificial organs, 2004.) Some people use the streamline approach, but the problem is that it only gives you an answer along the streamlines you happen to select. Also, in order to calculate the residence time, you need to use cell size and the velocity field, and this can be sketchy near the no-slip walls.

So, the preferred approach is to use a passive scalar and then use a source term to generate local damaged protein and then it can convect downstream to other parts of the flow. It's an Eulerian approach vs a Lagrangian approach.

Now the trick of the implementation is to come up with a representative shear stress (tau) for each finite volume cell. The paper suggests a von Mises type of approach. Does anyone know how to extract the stress tensor components in STAR-CCM+? They're not standard outputs.

Thanks for the input!

Quote:

Originally Posted by ping

Attachment 9910
...it is not the total sum (that is a simple sum report) but the sum in each cell - this is why field monitors are such wonderful tools. however on second thoughts this is not what you want - it would tell you where the worst cells for creating damage are in fluctuating flow.
Whereas you need the transported damage summed, so you should be using a passive scalar for this: create the field function for your damage variable; add a passive scalar; add a region source for this scalar and use the damage field function as the source for the scalar. to get the units correct your might need to think about it a bit. i did this in a little test and the results are in the image - you can see the local shear stress at the top and the passive scalar below, with high values in the recirculation zone behind as one would expect.

JPBodner · November 8, 2011, 18:05

Now that I think about it, the only problem with the above approach is the conservation of red blood cells/proteins. You can generate an amount that exceeds what comes in potentially. I think I might also define another passive scalar representing the undamaged concentration and link the two such that the total damaged concentration cannot exceed the supply of undamaged entering the system.

ping · November 8, 2011, 18:44

glad it is looking feasible now. here is a shear stress field function i have used in the past (turn on 'temporary storage retained' in solver):

sqrt( mag2($$U_VelocityGrad) + mag2($$V_VelocityGrad) + mag2($$W_VelocityGrad) ) * $DynamicViscosity

kastarkas · October 14, 2016, 03:35

Greeetings to all,

Thanks a lot for this above discussion.
PLease excuse me to join this conservation here to seek some continuity of my previous thread

http://www.cfd-online.com/Forums/cfx...searching.html

I too work on the same problem for my thesis.
The eulerian approach has been discussed above. The alternate solution to find the exposure time and trajectory of each blood cell is via a Lagrangian Approach.

So for that I have doubt on "whether a variable with the value of an expression, can be integrated along the pathlines" using some functions in CFX ??

By doing Length Integral over the pathlines, will that be right ?

Can someone please explain how to implement it in CFX ?

It would be really blissful if someone can help me out.

ping · October 15, 2016, 03:53

you had better convert to STAR-CCM+, or find a CFX forum

kastarkas · October 15, 2016, 05:18

Witty one dear ping.
I never found anything in CFX forum.
But can you please confirm the logic ?

October 28, 2011, 09:27	Integrating along a streamline	#1
JPBodner New Member Jeff Join Date: Aug 2010 Posts: 11 Rep Power: 15	Damage to red blood cells in a flow is often evaluated by an equation like this: damage=a(shear stress)^b (time)^c where a,b,c are constants. Here, time is the time of exposure at the local value of shear stress. In other words, the idea is to integrate this along a streamline to determine how a particular red blood cell would be damaged. Anyone know how to integrate an expression like this along a streamline in STAR-CCM+? JB

November 8, 2011, 18:44		#8
ping Senior Member Ping Join Date: Mar 2009 Posts: 556 Rep Power: 20	glad it is looking feasible now. here is a shear stress field function i have used in the past (turn on 'temporary storage retained' in solver): sqrt( mag2($$U_VelocityGrad) + mag2($$V_VelocityGrad) + mag2($$W_VelocityGrad) ) * $DynamicViscosity bluebase likes this.

October 14, 2016, 03:35		#9
kastarkas Member kastarkas Join Date: Aug 2016 Posts: 45 Rep Power: 9	Greeetings to all, Thanks a lot for this above discussion. PLease excuse me to join this conservation here to seek some continuity of my previous thread http://www.cfd-online.com/Forums/cfx...searching.html I too work on the same problem for my thesis. The eulerian approach has been discussed above. The alternate solution to find the exposure time and trajectory of each blood cell is via a Lagrangian Approach. So for that I have doubt on "whether a variable with the value of an expression, can be integrated along the pathlines" using some functions in CFX ?? By doing Length Integral over the pathlines, will that be right ? Can someone please explain how to implement it in CFX ? It would be really blissful if someone can help me out. Last edited by kastarkas; October 15, 2016 at 00:21.

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October 29, 2011, 10:09		#2
RobertB Senior Member Robert Join Date: Jun 2010 Posts: 117 Rep Power: 16	Had you considered doing it as a source term. To find out flight time I think you put in a source term of density (it's in one of the examples). Thus you can see how long it takes to get from the inlet to a point. You should be able to generate a source term which will essentially be the damage incurred while in that cell and the code will integrate it for you. You can also see where the most damage is done purely by plotting up the source term (you may need to normalize by volume). The other option is to run tracks, get the track file format from CD, dump the other data you need and write a program to do it externally.

November 7, 2011, 05:57		#3
ping Senior Member Ping Join Date: Mar 2009 Posts: 556 Rep Power: 20	on a quick think about this, I dont think you need streamlines or the 'age of flow via density' technique mentioned by robertb as used to measure age of air in buildings. you say the damage is time at a certain shear stress, so it would seem to me that you just need a field function which works out the damage during the current timestep = shear stress * dtime (with your constants included of course). then you need to add this to the current sum of damage to get the new total damage locally everywhere in the field. do the sum using a field monitor of type sum. plot this scalar field function. seems simple to me?

November 7, 2011, 07:49		#4
RobertB Senior Member Robert Join Date: Jun 2010 Posts: 117 Rep Power: 16	This would only provide total damage in the domain. It is likely that to design better parts you will need to attribute local damage to specific features which I do not believe this technique will do.

November 8, 2011, 03:14		#5
ping Senior Member Ping Join Date: Mar 2009 Posts: 556 Rep Power: 20	shear-tracking.jpg ...it is not the total sum (that is a simple sum report) but the sum in each cell - this is why field monitors are such wonderful tools. however on second thoughts this is not what you want - it would tell you where the worst cells for creating damage are in fluctuating flow. Whereas you need the transported damage summed, so you should be using a passive scalar for this: create the field function for your damage variable; add a passive scalar; add a region source for this scalar and use the damage field function as the source for the scalar. to get the units correct your might need to think about it a bit. i did this in a little test and the results are in the image - you can see the local shear stress at the top and the passive scalar below, with high values in the recirculation zone behind as one would expect.

November 8, 2011, 18:05		#7
JPBodner New Member Jeff Join Date: Aug 2010 Posts: 11 Rep Power: 15	Now that I think about it, the only problem with the above approach is the conservation of red blood cells/proteins. You can generate an amount that exceeds what comes in potentially. I think I might also define another passive scalar representing the undamaged concentration and link the two such that the total damaged concentration cannot exceed the supply of undamaged entering the system.

October 15, 2016, 03:53		#10
ping Senior Member Ping Join Date: Mar 2009 Posts: 556 Rep Power: 20	you had better convert to STAR-CCM+, or find a CFX forum

October 15, 2016, 05:18		#11
kastarkas Member kastarkas Join Date: Aug 2016 Posts: 45 Rep Power: 9	Witty one dear ping. I never found anything in CFX forum. But can you please confirm the logic ?