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

Abstract

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.