Numerical simulation of vibration of horizontal cylinder induced by progressive waves

Abstract

Maritime structures often comprise cylinders of small diameter relative to the prevailing wave length. This paper describes the direct forcing immersed boundary simulation of the hydroelastic behaviour of a rigid, horizontal circular cylinder in regular progressive waves. Fluid motions are numerically solved by the full Navier–Stokes equations, and the free surface by the volume-of-fluid method. The Reynolds number Re = 110, Keulegan–Carpenter number KC = 10, Froude number Fr = 0.69 and Ursell number U rs ≈ 12. A single-degree-of-freedom model is used for the elastically mounted cylinder. Velocity profiles for the stationary cylinder case have been successfully validated using experimental results. The frequency response for reduced velocities $4.5\lt {U}_{R}^{*}\lt 5.3$ have been compared with theoretical data. Three transverse vibration regimes are identified: lower beating ($4\lt {U}_{R}^{*}\lt 4.5$); lock-in ($4.7\lt {U}_{R}^{*}\lt 4.8$); and upper beating ($5\lt {U}_{R}^{*}\lt 10$) modes. The lower and upper beating regimes exhibit varying amplitude response. The lock-in mode represents the region of fixed and maximum response. The lower beating and lock-in modes have peaks at a common vibration to wave frequency ratio ${f}_{{\rm{w}}}^{*}$ = 2. For the upper beating mode, ${f}_{{\rm{w}}}^{*}$ = 1, except for ${U}_{R}^{*}=10$ when ${f}_{{\rm{w}}}^{*}$ = 2.