Abstract
We examine the effect of wall inertia on the onset of highfrequency selfexcited oscillations in flow through an elasticwalled tube. The previous asymptotic model of Whittaker et al. (Proc. Roy. Soc. A466, 2010), for a longwavelength highfrequency instability in a Starlingresistor setup, neglected inertia in the tube wall. Here, we extend this model by modifying the ‘tubelaw’ 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 oomphlib framework.
Original language  English 

Pages (fromto)  4777 
Number of pages  31 
Journal  Quarterly Journal of Mechanics and Applied Mathematics 
Volume  71 
Issue number  1 
Early online date  15 Nov 2017 
DOIs  
Publication status  Published  1 Feb 2018 
Profiles

Robert Whittaker
 School of Mathematics  Lecturer in Applied Mathematics
 Fluid and Solid Mechanics  Member
Person: Research Group Member, Academic, Teaching & Research