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July 26, 2012, 10:13 
Blood and shear strain rate

#1 
Member
Dave
Join Date: Aug 2011
Posts: 33
Rep Power: 7 
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 s1. 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 nonnewtonian 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 strainrate tensor. I'm just confused by the different definitions I keep encountering online and in the literature. Many thanks! Dave 

July 26, 2012, 19:32 

#2 
Super Moderator
Glenn Horrocks
Join Date: Mar 2009
Location: Sydney, Australia
Posts: 12,638
Rep Power: 98 
The CFX nonnewtonian 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, 06:10 

#3 
Member
Dave
Join Date: Aug 2011
Posts: 33
Rep Power: 7 
Hi Glenn,
Thank you for replying. As I understand it, blood is a shearthinning 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 strainrate 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 

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