Non-axisymmetric flow development in pulsatile blood flow through an aneurysm

Computational fluid dynamics modelling of an abdominal aortic aneurysm is commonly simplified to consider a two-dimensional axisymmetric problem. To determine the validity of this assumption, a Floquet stability analysis was employed to predict the conditions under which an axisymmetric aneurysmal flow is unstable to non-axisymmetric instabilities. Dimensions of the model were selected to be consistent with a high-risk aneurysm in the human abdominal aorta. In particular, the model consisted of an elliptical bulge defining the aneurysm, and both upstream and downstream artery sections. A sinusoidal time-varying parabolic velocity profile was input upstream, with Womersley number a = 16.9 (representing a heart rate of 70 beats per minute when artery diameter D = 22.7 mm and kinematic viscosity ν = 3.3×10 ^-6 m ² / s). A Reynolds number range relevant to aneurysms in large arteries was examined, with the critical Reynolds number for non-axisymmetric transition and the corresponding azimuthal wavelength found to be Re _CRIT = 610 and λ = π (azimuthal mode number m = 2). The maximum vorticity at the vessel wall was found to occur at the distal end of the aneurysm bulge. The pulsatile flow frequency was also varied, with the frequency dependence on Re _CRIT and λ being established.