Paper No. IJOPE NP-36 Saltara 1 Numerical Simulation of the Flow around an Elastically Mounted Cylinder F. Saltara , J. R. Meneghini and R. A. Fregonesi Department of Mechanical Engineering, University of São Paulo São Paulo, São Paulo, Brazil ABSTRACT The flow around a single cylinder free to vibrate in the transverse direction is investigated employing the 2D Discrete Vortex Method. The simulations are carried out for a mass parameter and Reynolds number that are typical of the flow around an oil extraction riser. Results of amplitude of induced vibration as a function of reduced velocity are compared with experimental data from Khalak and Williamson (1996). It is found that the maximum calculated amplitudes of vibration are lower than the experimental ones, but the simulations with the 2D Discrete Vortex Method proved to be inexpensive and well suited for qualitative studies and the development of strip-theory solvers capable of simulating long marine riser installed in ultra deep waters. KEY WORDS: vortex shedding ; vortex-induced vibration ; elastic cylinder ; riser ; CFD. INTRODUCTION In the last years, the need to improve technologies in the field of deep water oil extraction has lead to an increase in the interest in studies about the vortex-induced vibration (VIV) phenomenon. Some challenging VIV problems became common in particular engineering areas. One of those is present in the field of deep-water oil extraction. Recently, offshore oil platforms have been installed in water depths of over 2,000m. Flexible pipes named risers are used to link the seabed to the offshore platform for oil production. Risers are cylindrical bodies subjected to vibration due to vortex shedding, and one of the main effects of this vibration is to shorten their durability. Therefore, there is great interest in the development of tools to estimate the characteristics of VIV, and to evaluate its effect on fatigue of structures and their life expectancy. In order to calculate the cylinder response to the flow, one needs to solve the flow around the body. In the last years, researches were concentrated in solving the unsteady Navier-Stokes equation through finite-element or finite-volume methods. Through the flow solution at a given time it is possible to have the pressure and viscous tension distribution around he cylinder. Consequently, one can evaluate drag and lift forces on the body. The forces are then used to solve the motion of the cylinder. In this way, it is possible to obtain time histories of the drag, lift and position of the cylinder. This approach has a major drawback: finite-element and finite- volume methods are grid-dependent solving methods. They are well suited for the solution of the flow around a single free vibrating cylinder, but they are cumbersome when we seek the solution of the flow around more than one free cylinder. In this case, fixed meshes can not be used. In order to develop a more flexible solver, we decided to use the Lagrangian Discrete Vortex Method. This method of flow solution employs a moving grid composed of vorticity-carrying particles, the discrete vortices, and the vorticity transport equation can be solved simply by tracking the movement of these particles. As there is no fixed mesh, the method is well suited for the simulation of the flow around multiple moving bodies. It is also a simpler method when compared to finite-element and finite-volume methods. Although our objective is to solve the flow around a single cylinder, we assume that the development of a tool that can be easily used to simulate the flow around multiple moving cylinders is desirable in order to expand further researches. Flow-Induced Vibration Vibrations induced by vortex shedding have been a main subject of research in the field of fluid-structure interactions. These vibrations are usually modeled through a spring-mass-damper system. If the cylinder is free to vibrate only in the transverse direction in relation to the flow stream, as in Fig. 1, the movement of the cylinder is given by the equation: y F y k y c y m = + + ! ! ! (1) ijope NP-36 09-03-2002