Dynamics and Stability of Coaxial Cylindrical Shells Conveying Viscous Fluid

In this paper the dynamics and stability characteristics of coaxial cylindrical shells containing incompressible, viscous fluid flow are examined in contrast to previous studies where the fluid has been considered to be inviscid. Specifically, upstream pressurization of the flow (to overcome frictional pressure drop) and skin friction on the shell surfaces are taken into account, generating time-mean normal and tangential loading on the shells. Shell motions are described by Flu¨gge’s thin shell equations, suitably modified to incorporate the time-mean stress resultants arising from viscous effects. The fluctuating fluid forces, coupled to shell vibration, are determined entirely by means of linearized potential flow theory and formulated with the aid of generalized-force Fourier-transform techniques. It is found that the effect of viscosity in the annular flow generally tends to destabilize the system, vis-a`-vis inviscid flow, whereas viscous effects in the inner flow stabilize the system. These effects can be quantitatively very important, so that, generally, neglect of viscous effects cannot be justified.