New estimations of the added mass and damping of two cylinders vibrating in a viscous fluid, from theoretical and numerical approaches

International audienceThis paper deals with the small oscillations of two circular cylinders immersed in a viscous stagnant uid. A new theoretical approach based on an Helmholtz expansion and a bipolar coordinate system is presented to estimate the uid forces acting on the two bodies. We show that these forces are linear combinations of the cylinders accelerations and velocities, through viscous uid added coecients. The self-added mass and damping coecients are shown to decrease with both the Stokes number and the separation distance. The cross-added mass and damping coecients tend to increase with the Stokes number and the separation distance. Compared to the inviscid results, the eect of viscosity is to add a correction term which scales as Sk −1/2. When the separation distance is suciently large, the two cylinders behave as if they were independent and the Stokes predictions for an isolated cylinder are recovered. Compared to previous works, the present theory oers a simple and exible alternative for an easy determination of the uid forces and related added coecients. To our knowledge, this is also the rst time that a numerical approach based on a penalization method is presented in the context of uid-structure interactions for relatively small Stokes numbers, and successfully compared to theoretical predictions