Blood and shear strain rate

Dave442 · July 26, 2012, 11:13

Hi all,

I am relatively new to cfd and I wish to conduct an analysis of blood flow. Blood, however, exhibits variable dynamic viscosity at shear rates below 100 s-1. To account for this I want to use the Carreau model to define the viscous behaviour of blood. I have found a paper in which material constants for modelling blood with the Carreau model are reported but the definition of the scalar shear strain rate seems different to that reported in the Ansys theory manual.

I was wondering if someone with a bit more expertise with cfd and non-newtonian fluids could comment on the difference between the definition of the scalar shear strain rate which is reported in the Ansys theory manual and that reported in the paper which I have linked. To my understanding, the scalar shear strain rate is defined as the square root of the second invariant of the strain-rate tensor. I'm just confused by the different definitions I keep encountering online and in the literature.

Many thanks!
Dave

ghorrocks · July 26, 2012, 20:32

The CFX non-newtonian model "Bird Carreau" is what you are looking for. This is exactly the model your literature article used so the parameters can just go straight in. Although I note they have a typo in the article because the specify n(0) twice and do not specify n(infinity), but you are going to have to sort out what they actually meant to write there.

Dave442 · July 27, 2012, 07:10

Hi Glenn,

Thank you for replying. As I understand it, blood is a shear-thinning fluid so its viscosity decreases as the shear rate increases. The n(0) and n(inf) terms are used to define the viscosity at very low and very high shear rates, respectively. So I think n(0) = 0.056 Pa.s and n(inf) = 0.00345 N Pa.s. Does that make sense?

What is really confusing me is the definition of the scalar shear strain rate. In the paper I linked, I think it is defined as follows:

sstrnr = sqrt[0.5*(SijSij)]

Whereas in the Ansys theory manual it is defined as follows:

sstrnr = sqrt[2*(del_ui/del_xj)(Sij)]

Here Sij is the rate of deformation (or strain-rate tensor). When I work out the math I wind up with a different forms of the scalar shear strain rate. I may be messing up the math somewhere though.

Any thoughts would be appreciated!
Dave

July 26, 2012, 11:13	Blood and shear strain rate	#1
Dave442 Member Dave Join Date: Aug 2011 Posts: 33 Rep Power: 15	Hi all, I am relatively new to cfd and I wish to conduct an analysis of blood flow. Blood, however, exhibits variable dynamic viscosity at shear rates below 100 s-1. To account for this I want to use the Carreau model to define the viscous behaviour of blood. I have found a paper in which material constants for modelling blood with the Carreau model are reported but the definition of the scalar shear strain rate seems different to that reported in the Ansys theory manual. I was wondering if someone with a bit more expertise with cfd and non-newtonian fluids could comment on the difference between the definition of the scalar shear strain rate which is reported in the Ansys theory manual and that reported in the paper which I have linked. To my understanding, the scalar shear strain rate is defined as the square root of the second invariant of the strain-rate tensor. I'm just confused by the different definitions I keep encountering online and in the literature. Many thanks! Dave

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July 26, 2012, 20:32		#2
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,870 Rep Power: 144	The CFX non-newtonian model "Bird Carreau" is what you are looking for. This is exactly the model your literature article used so the parameters can just go straight in. Although I note they have a typo in the article because the specify n(0) twice and do not specify n(infinity), but you are going to have to sort out what they actually meant to write there.

July 27, 2012, 07:10		#3
Dave442 Member Dave Join Date: Aug 2011 Posts: 33 Rep Power: 15	Hi Glenn, Thank you for replying. As I understand it, blood is a shear-thinning fluid so its viscosity decreases as the shear rate increases. The n(0) and n(inf) terms are used to define the viscosity at very low and very high shear rates, respectively. So I think n(0) = 0.056 Pa.s and n(inf) = 0.00345 N Pa.s. Does that make sense? What is really confusing me is the definition of the scalar shear strain rate. In the paper I linked, I think it is defined as follows: sstrnr = sqrt[0.5(SijSij)] Whereas in the Ansys theory manual it is defined as follows: sstrnr = sqrt[2(del_ui/del_xj)(Sij)] Here Sij is the rate of deformation (or strain-rate tensor). When I work out the math I wind up with a different forms of the scalar shear strain rate. I may be messing up the math somewhere though. Any thoughts would be appreciated! Dave