Numerical Studies of Viscous Flow Around Step Cylinders

Abstract

A step cylinder consists of a small diameter cylinder (d) attached coaxially to a large diameter cylinder (D). Structures with a similar shape as the step cylinder have been extensively used in many marine engineering ap- plications, for example, the underwater hull of a semi-submersible offshore platform, the supporting structures for a floating wind turbine, and the ma- rine riser with staggered buoyance elements. In recent years, there has been an increasing interest in the flow around step cylinders. Previous studies investigated dominating vortex cells in step cylinder wakes, the vortex in- teractions between them, and the force distributions on the surface of step cylinders. However, there has been little discussions about the formation mechanism and detailed process of vortex interactions, the diameter ratio (D/d) effects on the wake, and the vortex system around the step cylinder under a sub-critical Reynolds number (ReD). To focus on these aspects, in the present thesis, the flow around step cylinders with diameter ratios 2 ≤ D/d ≤ 3 at two Reynolds numbers ReD=150 and 3900 were investi- gated by directly solving the three-dimensional Navier-Stokes equations.

The new findings can be mainly divided into two parts. In the first part, we investigated the vortex interactions in the wake behind step cylin- ders with 2 ≤ D/d ≤ 3 at RD=150. Two types of N-cell cycles: the long N-cell cycle, and the fundamental N-cell cycle, were first identified beside the conventional N-cell cycle. Moreover, two newly observed vortex loop structures were observed to antisymmetrically or symmetrically appear in the neighboring N-cell cycles. After developing a reliable method that can be used to calculate the phase information of vortices, the vortex interac- tions, especially the vortex dislocations were analyzed in detail. A vortex dislocation mechanism, together with its effects in the newly identified sym- metric and antisymmetric vortex interactions, were described.

In the second part, the flow around a step cylinder with D/d=2 at ReD=3900 was investigated. Four horseshoe vortices were observed to form above the step surface in front of the upper small cylinder in the time-averaged flow. Their developments were analyzed. Moreover, a pair of base vortices and a backside horizontal vortex in the rear part of the step surface behind the small cylinder were captured. For the instantaneous flow, hairpin vortices were found to form between the horseshoe vortices. Furthermore, in the small cylinder wake, Kelvin-Helmholtz vortices were observed and analyzed.

The present thesis contributes a deeper and more complete physical understanding of the wake behind step cylinders.