The Effect of Wall Inertia on High-Frequency Instabilities of Flow Through an Elastic-Walled Tube

Walters, Martin C., Heil, Matthias and Whittaker, Robert J. (2018) The Effect of Wall Inertia on High-Frequency Instabilities of Flow Through an Elastic-Walled Tube. Quarterly Journal of Mechanics and Applied Mathematics, 71 (1). pp. 47-77. ISSN 0033-5614

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We examine the effect of wall inertia on the onset of high-frequency self-excited oscillations in flow through an elastic-walled tube. The previous asymptotic model of Whittaker et al. (Proc. Roy. Soc. A466, 2010), for a long-wavelength high-frequency instability in a Starling-resistor set-up, neglected inertia in the tube wall. Here, we extend this model by modifying the ‘tube-law’ for the wall mechanics to include inertial effects. The resulting coupled model for the fluid and solid mechanics is solved to find the normal modes of oscillation for the system, together with their frequencies and growth rates. In the system and parameter regime considered, the addition of wall inertia reduces the oscillation frequency of each mode, however its effect on the stability of the system is not as straightforward. Increasing wall inertia lowers the mean flow rate required for the onset of instability, and is therefore destabilising. However, at higher flow rates the instability growth rate is decreased, and so wall inertia is stabilising here. Overall, the addition of wall inertia decreases the sensitivity of the system to the mean axial flow rate. The theoretical results show good qualitative and reasonable quantitative agreement with direct numerical simulations performed using the oomph-lib framework.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
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Depositing User: Pure Connector
Date Deposited: 25 Aug 2017 05:05
Last Modified: 12 Jun 2021 08:30
DOI: 10.1093/qjmam/hbx024

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