Numerical simulation in vortex-induced vibrations at low mass-damping

Abstract

In this paper, we present some numerical results from a study of the dynamics and fluid forcing on an elastically mounted rigid cylinder with low mass-damping, constrained to oscillate transversely to a free stream. The vortex shedding around the cylinder is investigated numerically by the incompressible two-dimensional ReynoldsNavier-Stokes equations. These equations are written in a primitive formulation in which the Cartesian velocity components and pressure share the same location at the center of the control volume. The numerical method uses a consistent physical reconstruction for the mass and momemtum fluxes: the so-called CPI (Consistent Physical Interpolation) approach in a conservative discretization using structured finite volumes. The numerical results are compared to experimental results. In the experiment, the Reynolds number is in the range 900-15000, the reduced velocity is including between 1.0 and 17.0. The mass ratio is 2.4 and the mass-damping is 0.013. The simulations predict correctly the maximum amplitude. On the other hand, the numerical results don't match the upper branch as found experimentally. However, these results are encouraging because, no simulations have yet predicted a so high amplitude of vibration. INTRODUCTION Vortex shedding behind bluff bodies arises in many fields of engineering, such as heat exchanger tubes, marine cables, flexible riser in petroleum productions and other marine applications, bridges, chimneys stracks. These examples are only a few of a large number of problems where vortex-induced vibrations are important. The practical significance of vortex-induced vibrations has led to a large number of fundamental studies." The case of an elastically mounted cylinder vibrating as a result of fluid forcing is one of the most basic and revealing cases in the general subject of vortex-induced bluff-body fluidstructure interactions. Consequently, determination of the unsteady forces on the cylinder is of central importance to the dynamics of such interactions. Despite the extensive Copyright ©2001 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. force measurements for a cylinder undergoing transverse forced vibration, there have appeared no direct lift-force measurements in the literature for an elastically mounted arrangement. Sarpkaya recently presented a set of drag measurements for a cylinder which can oscillate both inline and transverse to the flow. We should also note that Hover et a/. have developed a novel feedback control system to study free motions. Khalak and Williamson have presented new force measurements of lift and drag for a hydroelastic cylinder of very low mass and damping. Consequently, comparisons of forces between numerical results and experimental data are difficult because of the lack of measurements. Vortex-induced vibration is generally associated with the so-called "lock-in" phenomenon where the motion of the structure is believed to dominate the shedding process, thus synchronizing the shedding frequency. Lock-in is characterized by a shifting of the vortex shedding frequency (/s) to the system natural frequency (/n) (/s ~ /n). Lock-in can also refer to the coalescence of the shedding, the cylinder oscillation and natural frequency (/s ~ / ~ A). Numerous studies in vortex-induced vibration literature support the existence of lock-in." However, Gharib have noted an abscence of lock-in behavior from almost all these experimental studies even for small mass ratios [m*=(oscillatingmass)/(displaced fluid mass)]. In almost all the literature, the problem of vortexinduced vibration of a cylinder with a large mass ratio has been well studied. However, there remain some rather basic questions concerning vibration phenomena under the conditions of very low mass and damping and for which there are few laboratory investigations. As one reduces the mass ratio to 1% of the value used in the classical study of Feng, it is of significant and fundamental interest to know what is the dominant response frequency during excitation, what is the range of normalized velocity for significant oscillations or lock-in, and what is the amplitude of response as a function of normalized velocity? Recently, Khalak and Williamson published a review for these phenomena. Theirs experiments show that there exists two distinct types of response for the transverse OSAMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.