A THEORETICAL-STUDY OF THE STABILITY OF CANTILEVERED COAXIAL CYLINDRICAL-SHELLS CONVEYING FLUID

This is a theoretical study of the stability of cantilevered coaxial cylindrical shells conveying incompressible fluid in the annular space in between and within the inner shell. The viscous effects of the mean flow are taken into account, but the perturbations of the equilibrium state on the basis of which stability is assessed is carried out by means of potential flow theory, thus neglecting unsteady viscous effects which might well become important for narrow annular flows. Shell displacements are described by Fliigge's equations of motion. Solution of the coupled fluid-structure equations is carried out by means of the Fourier Transform Method. Preliminary checks into various aspects of the solution are carried out, notably on the choice of the so-called "out-flow models", which determine the downstream boundary conditions on the fluid flow beyond the free end, and on the numerical aspects of the solution; these give confidence in the solution method, which is then used to obtain results for the problem at hand. The main finding of this research is that stability is lost by flutter for internal flow, according to both the inviscid and viscous variants of the theory; for annular flow, however, whereas inviscid theory predicts loss of stability by flutter, viscous theory (with dissipative effects included) predicts that the shell loses stability by divergence and then, at appreciably higher flow, by flutter. Reduction of the annular gap generally destabilizes the system; while increased steady viscous effects slightly stabilize the system for internal flow, they strongly destabilize it for annular flow. Increasing the length of the shell destabilizes the system for both internal and annular flows. The presence of internal flow in addition to annular flow tends to stabilize the system vis a-vis the case of annular flow, but only at low flow velocities, having the opposite effect at higher flows; the same effects arise when the main flow is internal and an annular flow added to the system. © 1991 Academic Press Limited.