Bifurcation analysis of flow over a rotatable cylinder with a splitter plate

A rotatable cylinder-splitter plate body submerged in a uniform flow is treated as a dynamical system. A finite-difference method is employed to solve the two-dimensional incompressible unsteady Navier-Stokes equations on a moving curvilinear coordinate system that is numerically generated and boundary-fitted. Fluid-structure interaction is considered by simultaneously solving the flow field and rotational dynamics of the body. At subcritical Reynolds numbers the splitter plate aligns itself with the line of symmetry, and greater numbers induce a bifurcation in which the splitter plate moves to a stable off-axis position. Calculations also show that higher Reynolds numbers create an unsteady flow and the body undergoes finite-amplitude limit-cycle oscillations related to a Hopf bifurcation. The oscillation spectra exhibit subharmonics when the number is increased above a higher critical level. The separation process behind the body is shown to be responsible for the offsetting of the plate.