The validity of axisymmetric assumptions when investigating pulsatile biological flows

Abstract

Computational fluid simulations of biological flows is increasingly popular due to its inexpense and ability to define the flow throughout the entire domain---both common limiting factors for experimental work. A common assumption has been that both the geometry and the flow field through an aneurysm is axisymmetric; however, investigations into non-biological flows have seen that even with an axisymmetric geometry, non-axisymmetric flow may develop. Idealised geometries are used to investigate these biological flows as it simplifies the model to enable an improved understanding of the effect geometry has on the flow. Additionally this simplification allows the implementation of a computationally cheaper axisymmetric code. We test this axisymmetric assumption by applying Floquet stability analysis to investigate the stability of the flow and thus determine when an axisymmetric aneurysmal flow is unstable to non-axisymmetric instabilities. Dimensions of the model are selected to be consistent with a high risk aneurysm in the human abdominal aorta and Reynolds numbers relevant to aneurysms in large arteries are examined. The presence of three dimensional instabilities has a significant impact on the validity of the assumption of axisymmetry. The maximum streamwise vorticity in the perturbation fields is found to occur at the downstream section of the aneurysm, implying that it is in these areas that the results of axisymmetric simulations differ the most from fully three dimensional flow.