Through the advent of enhanced medical imaging computational modelling can now be applied to anatomically correct arterial geometries. However many flow feautures under physiological and pathological flow paraemeters, even in idealised problems, are relatively poorly understood. A commonly studied idealisation of an arterial blockage or stenosis, potentially generated by atherosclerosis, is a sinusoidally varying constricted tube. Although most physiological flow conditions are typically laminar, in this configuration turbulent flow states can arise due to the local increase in sectional Reynolds number. To examine the onset of turbulence in this geometry, under a simple non-reversing pulsatile flows, we have applied Floquet stability analysis and direct
As illustrated in the above figure, a period-doubling absolute instability mode associated with alternating tilting of the vortex rings that are ejected out of the stenosis/constriction during each pulse. This primary instability occurs for relatively large reduced velocities associated with long pulse periods (or low Womersley numbers). For lower reduced velocities the primary instability typically manifests itself as azimuthal waves (Widnall instability modes) of low wavenumber that grow on each vortex ring. We have also observed the shear layer of the steady axisymmetric flow is convectively unstable at still shorter temporal periods.
In this presentation we shall outline the challenges of modelling vascular flow problems with a particular focus on idealised stenotic flow. After briefly outlining the numerical analysis methods we shall discuss the flow investigations outlined above and their relation to more classical vortex instabilities.
- Computational Mathematics and Applications Seminar