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S. S. Gopalakrishnan, B. Pier and A. Biesheuvel
Laboratoire de mécanique des fluides et d'acoustique, École centrale de Lyon – CNRS – Université Claude-Bernard Lyon 1 – INSA, 36 avenue Guy-de-Collongue, 69134 Écully cedex, France
Journal of Fluid Mechnanics 752, 90–106 (2014)
The global linear stability of steady axisymmetric flow through a model fusiform aneurysm is studied numerically. The aneurysm is modeled as an inflation of gaussian shape on a vessel of circular cross-section. The fluid is assumed to be Newtonian and the flow far upstream and downstream of the inflation is a Hagen-Poiseuille flow. The model aneurysm is characterized by a maximum height H and width W, made dimensionless by the upstream vessel diameter, and the steady flow is characterized by the Reynolds number of the upstream flow. The base flow through the model aneurysms is determined for non-dimensional heights and widths in the physiologically relevant ranges 0.1≤H≤1.0 and 0.25≤W≤2.0, and Reynolds numbers up to 7000, which corresponds to peak values recorded during pulsatile flows under physiological conditions. It is found that the base flow consists of a core of relatively fast moving fluid, surrounded by a slowly recirculating fluid that fills the inflation; for the larger values of the ratio H/W a secondary recirculation region is observed. The wall shear stress in the inflation is vanishingly small as compared to the wall shear stress in the straight vessels. The global linear stability of the base flows is analysed by determining the eigenfrequencies of a modal representation of small-amplitude perturbations and by looking at the energy transfer between the base flow and the perturbations. Relatively shallow aneurysms (of relatively large width) become unstable by the lift-up mechanism and have a perturbation flow which is characterized by stationary, growing modes. More localized aneurysms (with relatively small width) become unstable at larger Reynolds numbers, presumably by an elliptic instability mechanism; in this case the perturbation flow is characterized by oscillatory modes.
hal-01084523
2014c_gopalakrishnan_jfm.pdf