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The effect of Dean, Reynolds and Womersley numbers 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

Published online by Cambridge University Press:  31 March 2021

Fanette Chassagne Open the ORCID record for Fanette Chassagne [Opens in a new window] ,
Michael C. Barbour Open the ORCID record for Michael C. Barbour [Opens in a new window] ,
Venkat K. Chivukula Open the ORCID record for Venkat K. Chivukula [Opens in a new window] ,
Nathanael Machicoane Open the ORCID record for Nathanael Machicoane [Opens in a new window] ,
Louis J. Kim Open the ORCID record for Louis J. Kim [Opens in a new window] ,
Michael R. Levitt Open the ORCID record for Michael R. Levitt [Opens in a new window]  and
Alberto Aliseda Open the ORCID record for Alberto Aliseda [Opens in a new window]
Fanette Chassagne*
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA98105, USA
Michael C. Barbour
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA98105, USA
Venkat K. Chivukula
Affiliation:
Biomedical and Chemical Engineering and Sciences, Florida Institute of Technology, Melbourne, FL32901, USA
Nathanael Machicoane
Affiliation:
University Grenoble Alpes, CNRS, Grenoble-INP, LEGI, 38000Grenoble, France
Louis J. Kim
Affiliation:
Department of Neurological Surgery, University of Washington, Seattle, WA98107, USA Department of Radiology, University of Washington, Seattle, WA98107, USA
Michael R. Levitt
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA98105, USA Department of Neurological Surgery, University of Washington, Seattle, WA98107, USA Department of Radiology, University of Washington, Seattle, WA98107, USA
Alberto Aliseda
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA98105, USA Department of Neurological Surgery, University of Washington, Seattle, WA98107, USA
*
†Email address for correspondence: fchassag@u.washington.edu
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Abstract

Flow in sidewall 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 $\textit {Re}$ and of the curvature along the pipe centreline, $\kappa$. Pulsatility in the flow introduces a dependence on the Womersley number $Wo$. Using stereo particle image velocimetry 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 $\kappa$ and Reynolds number $\textit {Re}$, for both steady and pulsatile inflow conditions. Increasing the pipe curvature impacted the flow patterns in both the pipe and the cavity, by shifting the velocity profile towards the cavity opening and increasing the flow rate in to 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 $\textit {Re}$ and $Wo$ in the free stream. The circulation in the cavity was higher for steady inflow than for the equivalent average Reynolds number and Dean number pulsatile inflow, with very limited impact of the Womersley number in the range studied. A second part of this study, that focuses on the changes in fluid dynamics when the intracranial aneurysm is treated with a flow-diverting stent, can be found in this issue (Barbour et al., J. Fluid Mech., vol. 915, 2021, A124).

JFM classification

Biological Fluid Dynamics: Biomedical flows Biological Fluid Dynamics: Blood flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A123
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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