Calculations of Added Mass and Damping Coefficients for Hexagonal Cylinders in a Confined Viscous Fluid

A finite element model is formulated and computations performed for the hydrodynamic reactions of harmonically oscillating hexagonal cylinders in an incompressible, viscous fluid. Regular hexagonal cylinders pack closely together, increasing the hydrodynamic coupling effect. The formulation is based on a velocity and pressure approach assuming the amplitude of the motion is sufficiently small to allow linearization of the Navier-Stokes equations. The equations of motion are discretized through a Galerkin process with a six-node triangular finite element mesh. C°-type elements and mixed interpolation functions are used with quadratic functions for velocity and linear functions for pressure. The hydrodynamic reactions, in terms of added mass and damping coefficients, of an hexagonal cylinder oscillating in a confined circular cylinder and an array of seven hexagonal cylinders in a confined domain are computed. The effects of the size of the gap between adjacent cylinders and the frequency of oscillation are studied.