Two-dimensional simulation of laminar flow around four two-degree-of-freedom cylindrical cylinders in a rectangular arrangement using random vortex-boundary element method

Flow-induced vibration is the effective factor in mechanical destruction of structures that are exposed to fluid flow. In this study, random vortex- boundary element methods (RVM-BEM), is used to simulate two-dimensional laminar fluid flow around four one/two-degrees-of-freedom cylindrical cylinders in a rectangular arrangemen. Hydrodynamic force coefficients, streamlines and cylinder displacements were plotted. The vorticity distribution is separated into blob-vortexes and its changes are studied by tracking these vortexes in the Lagrangian approach by considering two mechanisms of convection and diffusion in each time step. Satisfying no-slip boundary condition, vortex sheets were created on boundary. The cylinder vibrations were modeled as a system of mass, spring, and damper. The results showed that for 1 and 2DoF compared to the stationary cylinder, the average drag coefficient changes are 0.84 and 0.97, respectively. The rear cylinders vibrations amplitude were less than in the front cylinders. The y-amplitude was three times larger than x-amplitude. The maximum x-amplitude vibration of 1DoF cylinders was 1.51 times larger than 2DoF ones. Solving flow over 2DoF single cylinder by BEM(no need for homodis mapping or considering the vortexe images) with a similar solution in Ansys-Fluent software, showed 25% reduction in runtime and 2.3% increase in calculations accuracy.