An Experimental Study of the Stability of Cantilevered Coaxial Cylindrical Shells Conveying Fluid

Abstract

This paper presents an experimental study on the stability of a cantilevered cylindrical flexible (silicone rubber) shell, concentrically located within a rigid cylinder and subjected to air flow in either the annular region or inside the shell. Measurements were made of (i) the critical flow velocities of the shell for various (shell length)/radius and (annular gap)/radius ratios, and (ii) frequencies of oscillation of the shell at different subcritical flow velocities. In the case of annular flow, both divergence and flutter were observed, while only flutter was observed for internal flow. The experimental results were compared with those obtained with the two theoretical models previously developed by the authors; in the first, the unsteady shell-motion-induced fluid forces are evaluated by inviscid flow theory, while the steady ones by viscous flow theory (this model is called "Theory 1" for short); in the second, both are calculated by viscous flow theory, with the unsteady forces being obtained from a CFD solution of the linearized, unsteady Navier-Stokes equations (this model is termed "Theory 2"). Theory 1 agrees quantitatively reasonably well with experimental data for annular flow, both in terms of frequencies of oscillation and critical flow velocities, although experimental values of the critical flow velocities are somewhat lower than the theoretical ones; on the other hand, the critical flow velocities as predicted by Theory 2 were found to agree with experimental data far better, in fact extremely well. In case of internal flow, critical flow velocities predicted by Theory 1 are higher than experimental values, but still in fairly good agreement with them.