Research Papers

Numerical Study of Purely Viscous Non-Newtonian Flow in an Abdominal Aortic Aneurysm

[+] Author and Article Information
Victor L. Marrero, John A. Tichy, Onkar Sahni

Scientific Computation Research Center
and Department of Mechanical,
Aerospace and Nuclear Engineering,
Rensselaer Polytechnic Institute,
Troy, NY 12180

Kenneth E. Jansen

Department of Aerospace Engineering Sciences,
University of Colorado,
Boulder, CO 80309

1Corresponding author.

Manuscript received October 26, 2012; final manuscript received April 11, 2014; accepted manuscript posted April 24, 2014; published online August 6, 2014. Assoc. Editor: Ender A. Finol.

J Biomech Eng 136(10), 101001 (Aug 06, 2014) (10 pages) Paper No: BIO-12-1517; doi: 10.1115/1.4027488 History: Received October 26, 2012; Revised April 11, 2014; Accepted April 24, 2014

It is well known that blood has non-Newtonian properties, but it is generally accepted that blood behaves as a Newtonian fluid at shear rates above 100 s−1. However, in transient conditions, there are times and locations where the shear rate is well below 100 s−1, and it is reasonable to infer that non-Newtonian effects could become important. In this study, purely viscous non-Newtonian (generalized Newtonian) properties of blood are incorporated into the simulation-based framework for cardiovascular surgery planning developed by Taylor et al. (1999, “Predictive Medicine: Computational Techniques in Therapeutic Decision Making,” Comput. Aided Surg., 4, pp. 231–247; 1998, “Finite Element Modeling of Blood Flow in Arteries,” Comput. Methods Appl. Mech. Eng., 158, pp. 155–196). Equations describing blood flow are solved in a patient-based abdominal aortic aneurysm model under steady and physiological flow conditions. Direct numerical simulation (DNS) is used, and the complex flow is found to be constantly transitioning between laminar and turbulent in both the spatial and temporal sense. It is found for the case simulated that using the non-Newtonian viscosity modifies the solution in subtle ways that yield a mesh-independent solution with fewer degrees of freedom than the Newtonian counterpart. It appears that in regions of separated flow, the lower shear rate produces higher viscosity with the non-Newtonian model, which reduces the associated resolution needs. When considering the real case of pulsatile flow, high shear layers lead to greater unsteadiness in the Newtonian case relative to the non-Newtonian case. This, in turn, results in a tendency for the non-Newtonian model to need fewer computational resources even though it has to perform additional calculations for the viscosity. It is also shown that both viscosity models predict comparable wall shear stress distribution. This work suggests that the use of a non-Newtonian viscosity models may be attractive to solve cardiovascular flows since it can provide simulation results that are presumably physically more realistic with at least comparable computational effort for a given level of accuracy.

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Fig. 1

Viscosity–shear rate curve for blood using Carreau–Yasuda model

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Fig. 2

Patient-specific AAA anatomical model of the lumen along with the locations of planes where the results are presented. The abdominal aneurism is in planes C through G, with healthy tissue at the inlet in planes A and B

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Fig. 3

Volumetric flow rate derived from imaging data [48] along with specific instants during the cardiac cycle where the results are presented. The plot is over an open interval of t ∈ [0,tp).

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Fig. 4

Comparison of the steady state speed between Newtonian (left column) and non-Newtonian (right column) models for Mesh A5 at locations shown in Fig. 2

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Fig. 5

(a) Instantaneous data for two cycles of a variable of interest. These data show the cycle-to-cycle variation. For illustration purposes, the same instant in the cardiac cycle is shown. (b) The second cycle (red) has been shifted by a period tp to overlap the first cycle (blue). The phase-locked average of the two cycles is shown by the dashed black line.

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Fig. 6

Comparison at (a) t/tp = 0.05 and (b) t/tp = 0.25 of the phase-locked average of the speed for eight cycles between Newtonian (left column) and non-Newtonian (right column) for Mesh A5 at locations shown in Fig. 2

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Fig. 7

Comparison at (a) t/tp = 0.55 and (b) t/tp = 0.75 of the phase-locked average of the speed for eight cycles between Newtonian (left column) and non-Newtonian (right column) for Mesh A5 at locations shown in Fig. 2

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Fig. 8

Comparison at (a) t/tp = 0.05, (b) t/tp = 0.25, (c) t/tp = 0.55, and (d) t/tp = 0.75 of the phase-locked average of the wall shear stress for eight cycles between Newtonian (left) and non-Newtonian (right) for Mesh A5




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