Symmetry-breaking response of a flexible splitter plate attached to a circular cylinder in uniform flow

Static and dynamic fluid-structure interaction of a flexible plate behind a stationary cylinder in uniform flow is explored for a body-to-fluid mass ratio of 10. Steady flow-structure computations for Re = 150, based on the diameter of cylinder and free-stream speed, reveal four regimes with respect to increasing flexibility of the plate. The plate does not undergo any lateral deflection in regime 1 beyond which it undergoes a symmetry-breaking bifurcation causing it to spontaneously deflect laterally. The curvature is of the same sign along the entire length of plate in regime 2 while it changes sign along the plate in regime 3. The lateral deflection, however, is still maximum at the plate tip. The location of maximum deflection moves away from the plate tip in regime 4. The evolution of flow structures including the strength of various standing vortices, with flexibility, is studied. The role of reattachment of flow on the surface of the plate and the modification of the pressure distribution is explored. The critical Re, beyond which the splitter plate spontaneously achieves a deflected shape, decreases with increase in flexibility. It is estimated to be Re = 122.33 for the limiting case of an infinitely flexible plate. Computations for dynamic fluid-structure interaction reveal several regimes of lock-in with different natural vibration modes of the plate and related hysteresis. No lateral bias in the time-averaged deflection is found during lock-in; it occurs in the desynchronization regime that precedes the lock-in regime with second mode. For the mass ratio considered, the bias in the static and dynamic simulations start at the same flexibility.