By coupling the Donnell–Mushtari shell equations to an analytical inviscid fluid solution, the linear dynamics of a rotating cylindrical shell with a corotating axial fluid flow is studied. Previously discovered mathematical singularities in the flow solution are explained here by the physical phenomenon of blocking. From a reference frame moving with the traveling waves in the shell wall, the flow is identical to the flow in a rigid varicose tube. When the ratio of rotation rate to flow velocity approaches a critical value, the phenomenon of blocking creates a stagnation region between the humps of the wall. Since the linear model cannot account for this phenomenon, the solution blows up.
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Blocking in the Rotating Axial Flow in a Corotating Flexible Shell
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Gosselin, F., and Païdoussis, M. P. (October 23, 2008). "Blocking in the Rotating Axial Flow in a Corotating Flexible Shell." ASME. J. Appl. Mech. January 2009; 76(1): 011001. https://doi.org/10.1115/1.2998486
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