Flow-induced Instabilities of Cylindrical Structures

Abstract

A kaleidoscopic view of the many diverse and interesting instabilities are presented, to which cylindrical structures are susceptible when in contact with flowing fluids. The physical mechanisms involved are discussed in each case, to the extent that they are understood, and the degree of success of available mathematical models is assessed. Four classes of problems are dealt with, according to the disposition of the flow vis-a`-vis the cylindrical structures: (a) instabilities induced by internal flows in tubular structures; (b) instabilities of solitary or clustered cylinders due to external axial flow; (c) annular-flow-induced instabilities of coaxial beams and shells; (d) instabilities of arrays of cylinders subject to cross-flow. In the first class of problems, the stability of straight tubular beams and cylindrical shells conveying fluid is discussed first, followed by the stability of curved pipes containing flow. In the second class of problems, the instabilities of solitary and clustered cylinders subjected to an external axial flow are treated, and their dynamical behavior is compared to that of systems with internal flow. The third class of problems involves annular flow in coaxial systems of beams and/or shells. Cross-flow-induced instabilities of clustered cylinders, in the form of arrays of different geometrical patterns, are the last class of problems considered; they are fundamentally distinct from the foregoing in terms of the fluid mechanics of the problem, for in this case the flow field is not irrotational—not even approximately.