Dissipation effect on local and global stability of fluid-conveying pipes

In this article, the effect of dissipation on local and global stability of fluid conveying pipes is analyzed. The local approach refers to an infinite medium and uses wave propagation analyses without taking boundary conditions into account. The global approach refers to the same medium, but with finite length and associated with a given set of boundary conditions. The finite length system is generally studied by calculating its eigenmodes and eigenfrequencies. Criteria for local instability are derived in the first part of this paper, and dissipation is found to significantly affect local stability. Moreover, dissipation is found to have a stabilizing or destabilizing effect, depending on the other parameters. Next, numerical computations are presented for finite-length systems and results are analyzed and compared with local stability properties of the corresponding media. When the system is sufficiently long, it is found that critical velocity for global instability tends to a local criterion which can be that of local stability of the damped medium or a local transition criterion of the undamped medium, which is not necessarily the local instability criterion. Finally, a reasoning based on lengthscale ratios is developed. It allows to know which criterion is able to predict the global stability for long systems.