Flapping foils are studied to achieve an efficient propeller. The performance of the flapping foil is influenced by many factors such as oncoming vortices, heaving amplitude, and geometrical parameters. In this paper, investigations are performed on flapping foils to assess its performance in the wake of a D-section cylinder located half a diameter in front of the foil. The effects of heaving amplitude and foil thickness are examined. The results indicate that oncoming vortices facilitate the flapping motion. Although the thrust increases with the increasing heaving amplitude, the propelling efficiency decreases with it. Moreover, increasing thickness results in higher efficiency. The highest propelling efficiency is achieved when the heaving amplitude equals ten percent of the chord length with a symmetric foil type of NACA0050 foil. When the heaving amplitude is small, the influence of the thickness tends to be more remarkable. The propelling efficiency exceeds 100% and the heaving amplitude is 10% of the chord length when the commonly used equation is adopted. This result demonstrates that the flapping motion extracts some energy from the oncoming vortices. Based on the numerical results, a new parameter, the energy transforming ratio (R_ET), is applied to explicate the energy transforming procedure. The R_ET represents that the flapping foil is driven by the engine or both the engines and the oncoming vortices with the range of R_ET being (0, Infini) and (−1, 0), respectively. With what has been discussed in this paper, the oncoming wake of the D-section cylinder benefits the flapping motion which indicates that the macro underwater vehicle performs better following a bluff body.

The present work employs the immersed boundary method to perform direct simulations of flow-induced vibrations in a tandem cylinder at laminar flows, where only the upstream cylinder (UC) is allowed to vibrate. The primary focus is to elucidate the vibration response of the UC and the underlying hydrodynamic mechanisms when a fixed downstream cylinder (DC) is introduced. The results indicate that varying spacing ratios (L/D) and reduced velocities (U*) leads to both self-limiting galloping and lock-in instabilities in the UC. The resonance regions for the UC can be categorized into different regimes, such as lock-in, harmonic lock-in (HLN), upper branch, and lower branch regimes, based on various mechanisms. Notably, the vibrations in the HLN regime are distinct from the traditional lock-in observed in a bare cylinder, with the oscillation frequency locking onto the higher-order fluid force frequency and the occurrence of larger amplitudes. Regarding the interference galloping instability, we show that the self-limiting amplitude is related to the vortex shedding points on either side of the DC. The introduction of a fixed DC results in the observation of six vortex shedding modes: C(2S), 2S, P+T, 2T, 2P, and Aperiodic. Among these, weak vortices in the 2P mode are found to suppress the vibration amplitude. The asymmetrical and aperiodic evolution of the wake flow generates even-order fluid forces. Furthermore, an analysis of the energy transfer indicates that the tandem cylinders exhibit high fluid kinetic energy conversion ability over a wide range of U*−L/D.