Unsteady viscous effects on the annular-flow-induced instabilities of a rigid cylindrical body in a narrow duct

Abstract

The dynamics and stability of a rigid cylindrical body oscillating about a hinge in a coaxial cylindrical duct containing flowing fluid are considered in this paper. A previously developed analytical model, in which the fluid-dynamic forces exerted on the oscillating cylinder had been determined by means of inviscid flow theory, is extended to take into account the unsteady viscous effects of a real fluid flow, in an approximate manner. It is shown that there exists a critical location of the hinge: if the cylinder is supported upstream of that point, then it remains stable at all flow velocities; however, if it is supported downstream of that location, then negative-damping oscillatory instability is possible for flow velocities sufficiently large to overcome the positive restraining mechanical damping of the system. The critical location of the hinge depends on the relative width of the annular passage with respect to its mean radius. By comparing inviscid and viscous flow theory results, it is shown that inviscid theory generally underestimates stability, by a margin increasing with the narrowness of the annulus.