Instability onset for submerged cylinders

Abstract

This paper describes how the global stability of a circular cylinder is affected when submerged in a two-phase gravitational flow. The flow behavior is governed by both the Reynolds and the Froude number, while the depth of the cylinder has been varied to create different scenarios for the stability analysis. The baseflow obtained by the numerical solution of the 2D Navier-Stokes equations has been analyzed, and the first bifurcation (i.e. Hopf type) has been explored for different depths, Reynolds and Froude numbers. In addition to the typical vortex shedding instabilities associated to isolated cylinders, the presence of an interface between fluids creates new instabilities associated with the free surface that present more complex and deformed structures. According to the region of the parameter space studied here, two main causes of instabilities have been found: the ones provoked by vortex shedding on the cylinder wake (wake instabilities) at low Froude numbers and the ones produced by the free surface deformation (free surface instabilities) at high Froude numbers. When instabilities are related to vortex shedding, the critical Reynolds number and the frequency of the most unstable mode are comparable to the classical solution without free surface and gravity effects. In all cases, the shape of the most unstable mode is deformed and distorted according to the free surface location, while the critical Reynolds numbers and the frequency associated to the perturbation are both affected by the gravity and the free surface presence.