Subcritical flutter in collapsible tube flow: a model of expiratory flow in the trachea.
Using an axisymmetric geometry that retains certain qualitative features of the trachea, we extend one-dimensional modeling of flow in collapsible tubes to include both curved shell effects and, for untethered tubes, wall inertia. A systematic scaling of the finite deformation membrane equations leads to an approximate set which is consistent with the one-dimensional fluid model; axial and normal wall variables are coupled elastically, but only axial inertia is retained. Transverse curvature causes elastic coupling that can give rise to axial wall motion and a flutter instability. The source of instability is the product of a nonzero reference axial curvature with axial tension variation due to axial stretching. The numerical results suggest that this mechanism may be significant even in processes which cannot be assumed one-dimensional.
Walsh
C
C
Institute for Aerospace Studies, University of Toronto, Ontario, Canada.
Sullivan
P A
PA
Hansen
J S
JS
D001696:Biomechanical Phenomena; D008448:Maximal Expiratory Flow Rate; D008954:Models, Biological; D012123:Pulmonary Ventilation / Q000502:physiology*; D013314:Stress, Mechanical; D014132:Trachea / Q000502:physiology*