The effect of Dean, Reynolds, and Womersley number on the flow in a spherical cavity on a curved round pipe. Part 1. Fluid mechanics in the cavity as a canonical flow representing intracranial aneurysms.

Flow in side-wall cerebral aneurysms can be ideally modelled as the combination of flow over a spherical cavity and flow in a curved circular pipe, two canonical flows. Flow in a curved pipe is known to depend on the Dean number De, combining the effects of Reynolds number, Re, and of the curvature along the pipe centreline, κ. Pulsatility in the flow introduces a dependency on the Womersley number Wo. Using stereo PIV measurements, this study investigated the effect of these three key non-dimensional parameters, by modifying pipe curvature (De), flow-rate (Re), and pulsatility frequency (Wo), on the flow patterns in a spherical cavity. A single counter-rotating vortex was observed in the cavity for all values of pipe curvature κ and Re, for both steady and pulsatile inflow conditions. Increasing the pipe curvature impacted both the flow patterns in the pipe and the cavity, by shifting the velocity profile towards the cavity opening and increasing the flow rate into the cavity. The circulation in the cavity was found to collapse well with only the Dean number, for both steady and pulsatile inflows. For pulsatile inflow, the counter-rotating vortex was unstable and the location of its centre over time was impacted by the curvature of the pipe, as well as the Re and the Wo in the freestream. The circulation in the cavity was higher for steady inflow than for the equivalent average Reynolds and Dean number pulsatile inflow, with very limited impact of the Womersley in the range studied.