This paper deals with a vibratory problem of fluid-structure interaction. It considers the two-dimensional case of a rigid, smooth and circular cylinder undergoing transverse sinusoidal oscillations and immersed in a viscous fluid otherwise at rest. Our work is focused on the in-line force acting on the cylinder in unsteady laminar flow. The aim is to understand the variations of the force with time according to the configuration of the physical system. For that the analysis will also use an energetic approach based on the power balance. The physical system can be characterized by two non-dimensional numbers: the Reynolds number (Re) compares the importance of the fluid viscosity to its inertia, and the Keulegan-Carpenter number (Kc) measures the amplitude of the cylinder displacement compared to its diameter. First the incompressible Navier-Stokes equations are solved numerically by means of a finite elements method. The flow structure is analyzed by determining the evolution with time and throughout the computational domain of flow quantities, such as pressure field, vorticity field or stream lines. We also calculate the values versus time of the different terms occurring in the mean force balance and power balance. We compare these results for several pairs (Kc, Re) of “extreme” values. Thus it appears three characteristic configurations: the inertial Euler case (Kc≪1 and inviscid fluid), the Stokes case (Kc≪1 and Re≫1) and the drag case (Kc≫1). For these three reference configurations the physical mechanisms operating in the system are identified. But in intermediate cases, particularly when Kc>1, every mechanisms interact. Consequently the evolution of the force acting on the cylinder versus time is more complex and its interpretation becomes less straightforward. That is why a quantitative energetic analysis is carried out. We define a measure of the dissipative energy present in the flow. Then we compare the values of that coefficient for different cases throughout the map (Kc, Re).

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