Numerical simulation of vortex-induced vibration of elastic cylinder

Study of the flow around a bluff body and its effect on the flow induced vibration is relevant to design of bridges, tall buildings and similar structures. The flow around bluff bodies, arranged in tandem where one of the bodies is in the wake region of the seconds one, was studied using numerical simulation. This phenomenon is related to the response of bluff bodies immersed in fluid flow and is known as Vortex Induced Vibration (VIV). Vortex energy extraction is of interest to this work. This paper presents the results of a 2D numerical simulation of the wake interaction of two circular cylinders at low Reynolds number using ANSYS Fluent Workbench. The upstream cylinder is stationary, while the downstream elastic cylinder can be affected by the vortices in the wake of the first cylinder. The paper reports the behaviour of the elastic cylinder through a CFD model, with a focus on harnessing the vortical energy. Also discussed is the theoretical maximum energy that can be harvested by this method. For validation purposes, the modelled amplitude of the oscillation is compared to published data in literature. The results show that the motion of elastic cylinder can be modelled as a simple mass spring damper model. Introduction Flow induced vibration is a phenomenon which is related to interaction of fluid forces and elastic forces in the structures [9]. These phenomena are related to the response of the structure which is immersed in fluid flow and are known as Vortex Induced Vibration (VIV). The vibration induced on structures by vortices is of importance because of its potentially destructive effect of structures. In these phenomena a non-stationary excitation force is exerted on the structures by vortices, which depending on the Reynolds number can be periodic. The vortex shedding behind a cylinder is known as a vortex street and the behaviour of the vortices in the wake of the structure is similar, regardless of the geometry of the structure. Blevins [6] showed that the vortex shedding in a steady subsonic flow is a function of the Reynolds number. Zdravkovich [11] presented the detailed information of the exerted forces on the stationary circular cylinder in different regimes. The results reveal that by increasing the Reynolds number from laminar to transitional regimes, Re=10-10, the lift force on the cylinder can increase significantly. Vortices energy can be harnessed and used as a renewable, friendly energy. A study of the flow around a pair of cylinders as a tandem body might a simple model to harness the vortices energy by downstream cylinder. This paper investigates numerically the flow interaction between two circular cylinders to explain a new concept of renewable generation energy due to VIV. In this model the upstream cylinder is stationary while the downstream has one degree of freedom and can oscillate freely in the normal to the mean flow direction. Mathematical model A simple schematic of the arrangement of two cylinders is shown in Figure 1. The moving rigid cylinder is mounted on an elastic base with one degree of freedom in y-direction. Therefore, the elastic cylinder is a simple mass-damper-spring system [4] and the equation of motion can be defined as . (1) In the equation above, is the total oscillating mass of system, y is the normal direction of flow, and are velocity and acceleration of cylinder, respectively, is damping coefficient, is spring stiffness and is the fluid force which is exerted on the cylinder boundary perpendicular to the flow. Figure 1. Schematic of two cylinders in cross flow, the upstream is rigidly mounted; the downstream is free to move In Equation (1), it is appropriate that non dimensional parameters such as mass ratio and damping factor are considered instead of mass and damping constant. The mass ratio can be defined as the total oscillating mass of system over the specific mass of fluid, ⁄ and damping factor is ζ= √ ⁄ . In former equation, is the fluid density, D is the diameter of cylinder and l is the length of the cylinder. In this research, the mass ratio and damping factor were and ζ= 0.007 based on the assumptions of Carmo [8] and the experiments of Assi [2] to validate the results. The Reynolds number, Re = ⁄ , is 1500 based on the diameter of the upstream cylinder D where is free stream velocity and is kinematic viscosity of fluid. For this Reynolds number, the nondimensionalised frequency which is defined as Strouhal number ⁄ ( is the vortex frequency). The Strouhal number for the selected Reynolds number is close to 0.2 [6]. For the system under investigation, vortex shedding in the wake of upstream cylinder exerts harmonic forces on the elastic downstream cylinder. The asymmetric distribution of pressure acts on the surface of elastic cylinder and generates the translational motion. This motion has been simulated using the ANSYS Fluent Workbench 14.0. To model the behaviour of elastic cylinder a User Define Function as a UDF file has been loaded in the Fluent and it has been coupled by a dynamic mesh setup. In this interaction the sinusoidal response of the cylinder causes the fluctuating transverse amplitude and force. Therefore, harmonic displacement, velocity and lift coefficient equations of the cylinder can be considered respectively as