Galloping instability of a cross-flow pendulum

The dynamics of a T-shaped body mounted at the free end of a frictionless pendulum, free to oscillate in a plane perpendicular to an incoming air flow, is investigated experimentally. The T-shaped body consists of a thin square plate facing the flow at normal incidence and fitted with a splitter plate downstream of the square plate, in the middle of the square. Two main parameters are explored, namely the length of the splitter plate, ranging from 0.33 to 1.22 times the side of the square plate, and the amplitude of the reduced velocity, ranging from 20 to 89. The one degree of freedom motion of this pendulum is shown to be prone to the galloping instability, due to the presence of the splitter plate. Using a quasi-steady description of the aerodynamic force coefficient, the onset and the saturation of the galloping are shown to be readily predicted by a nonlinear dynamic model. Under specific approximations, we show that the nonlinear model can be further simplified as a Van der Pol oscillator, allowing us to predict the saturated state from only two parameters of the quasi-steady aerodynamic force coefficient (specifically the slope at zero yaw angle and the first root coefficient). Finally, pressure measurements over the splitter-plate surfaces provide a precise estimation of the instantaneous force. The quasi-steady approximation is shown to be not strictly valid, even for reduced velocity of the order of 20, commonly considered the lowest limit for its accuracy in textbooks. The unsteadiness is very similar to dynamic stall and is found to be driven by a delay in the response of the separated near wake. However, the aerodynamic power, averaged over one oscillation cycle, is satisfactorily described by the quasi-steady evolution of the aerodynamic force coefficient. Since the time scale for the energy exchange between the flow and the pendulum is at least one order of magnitude slower than the pendular dynamics, the quasi-steady approximation correctly captures the dynamics of the galloping oscillations.