Numerical analysis of the flow-induced vibrations in the laminar wake behind a blunt body with rear flexible cavities

Abstract

We present a numerical study on the fluid–structure interaction of an incompressible laminar flow around a slender blunt-based body implementing a rear cavity of flexible plates. The study focuses on the use of this type of device to control the wake dynamics and the aerodynamic forces acting on the body, as well as to harvest energy from the flow. To that aim, the effects on the plates flow-induced vibrations (FIV) and on the dynamics of the flow of three control parameters, namely the reduced velocity, 0 ≤ U^∗ < 12, the mass ratio, m^∗ = [500, 1000] and the cavity height h_c , are evaluated at Reynolds number Re = 500. Four different branches are identified in terms of dynamic response, as U^∗ increases, regardless of the values of hc and m^∗. At low values of U^∗, an initial branch with a local peak of moderate amplitude response is observed, where the plates oscillate in counter-phase, in a varicose mode, with a frequency f_p that is synchronized with the second harmonic of the vortex shedding frequency, 2 f_{vs}, and similar to the natural frequency of the solid, f_n ≃ f_{1,n}. For intermediate values of U^∗, a transition towards a sinuous mode of oscillation occurs, where the plate frequency is synchronized with the vortex shedding frequency, f_p = f_{vs}. Initially, after such transition, the oscillation frequency is lower than the natural frequency of the plates f_p < f_{1,n}, so that a weak response defines a lower branch in the amplitude response curve. When U_∗ increases, a lock-in regime develops with f_p = f_{vs} = f_{1,n}, that is characterized by a response amplification, giving rise to the emergence of the upper branch, where the FIV amplitude of plates is the highest. Finally, a fourth desynchronization branch of moderate amplitude appears for larger values of U^∗, where the plates present a complex, multi-mode regime, characterized by the vibration at multiple frequencies within the range 5 f_{1,n} < f_p < 6.5 f_{1,n}. The analysis of the plates deformation through POD analysis reveals that they mainly oscillate following the first Euler–Bernoulli mode for the first three branches, and a combination of the second and first Euler–Bernoulli modes for the desynchronization branch. The effect of increasing the mass ratio is to mitigate the response at higher values of U^∗, while reducing the cavity height h_c leads to the fostering of oscillations within the upper and desynchronization branches. In general, the FIV response of plates alters the wake dynamics and the force coefficient, especially within the lock-in regime, where the drag is strongly amplified, although the fluctuations of the lift are attenuated (nearly a 40% reduction). Besides, reductions of the drag of approximately 2% are obtained within the initial and lower branches. Finally, a simple quantification of the energy transfer from the plates, through a linearized Euler–Bernoulli