Wall-Fluid Instabilites in Compliant Channels Conveying Developing Flows
Abstract
A collapsed lung airway or flexible tube is modelled as a two-dimensional channel of infinite length. We consider the linear stability of this system conveying a developing flow profile, which is approximated with a uniform profile and perturbation of the Blasius profile for flow over a flat plate. Exact and asymptotic solutions are found for the uniform profile. For the perturbation profile an analytical solution is found for long waves and a numerical shooting solution for arbitrary wave lengths. Results for the uniform and perturbation profiles are found to be generally in qualitative agreement, though the perturbation profile is less stable. For the perturbation profile we find a long wave instability which is absent for uniform flow and hence has not been seen in previous channel studies. This is stabilized by increasing the elastance of the wall, but other wall properties do not affect the critical flow speed except in correction terms. Increasing the channel width decreases the critical flow speed for the instability, but increases the critical flow rate. We hypothesize that this is related to the tube collapse that is seen in this type of system prior to the appearance of an oscillatory (flutter) instability. The finite wave length (flutter) instability is destabilized by decreasing wall damping, increasing wall inertia, decreasing wall elastance or flexural rigidity, and decreasing channel width, and may appear independent of or simultaneously with the long wave instability. Comparisons with experimental investigations of air flow in flexible tubes shows that the theoretically predicted flutter frequencies are in good agreement with those observed experimentally, but that there are difficulties in comparing the predicted critical flow speeds, due to the tube geometry introduced by the tube collapse that precedes flutter. We investigate the possible effect of this geometry using finite elements software to model flow in the collapsed tube cross-section. c
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1994
- Accession Number
- ADA356810
Entities
People
- Peter G. Larose
Organizations
- Northwestern University