Abstract
In theoretical and experimental studies of flow instabilities in collapsible tubes, the loss of stability occurs in the form of non-axisymmetric motion of the tube walls with the partial or full collapse of the tube, while the axisymmetric perturbations of the tube are damped. However, for the case of non-Newtonian power law fluid, axisymmetric perturbations can grow for a small power law index n. An analysis of infinite-length tube shows that instability is possible only for power law index n<0.611, and absolute instability can occur only for n<1/3. This paper is devoted to investigation of flutter of finite length elastic tubes conveying power law fluid. For untensioned finite length tubes an analytical solution is obtained. The instability boundary coincides with the boundary of absolute instability for infinitely long tubes. For non-zero longitudinal tension N the problem is investigated numerically. It is shown that the region of instability becomes smaller with an increase of the longitudinal tension N.
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