In this paper, the vortex-induced vibration (VIV) of a main cylinder with two symmetrically arranged control rods at Reynolds number of 500 is numerically simulated. The control rods and the main cylinder are connected rigidly and can move synchronously, which is modeled as a spring oscillator with double degree of freedom. Seven gap ratios ( G/D = 0.1 ∼2) and sixteen angles ( α = 15° ∼165°) are used to model the cylinder system. Thirteen flow patterns are identified, and the VIV of the cylinder system in every flow pattern is discussed separately. It is found that the characteristics of the VIV of the cylinder system are similar in the same flow pattern, which may give a way to understand the VIV of the multiple cylinders further. Based on the classification in previous researches, some advanced insights into the passive control are achieved. The control rods located in the boundary layer ( G/D = 0.1) can change the VIV of the main cylinder most effectively, and the effect decreases with increasing gap ratio. The control rods immerged in the wake of the main cylinder may result in sub-harmonic resonance, while the control rods located centrally in front of the main cylinder does not obviously affect the VIV of the main cylinder. As G/D = 0.1 ∼0.7, overall, the control rods located nearly side-by-side with main cylinder can amplify the VIV, while the control rods located downstream of the main cylinder can suppress the VIV. As G/D = 1 ∼2, the control rods can suppress the VIV slightly, and the effect increases with increasing gap ratio and decreasing angle. For G/D = 0.1 & α = 105°, the VIV is magnified for maximum effect, and the peak amplitude is about twice that of the single cylinder. For G/D = 0.2 & α = 45°, the VIV is suppressed for maximum effect, and the peak amplitude is about 0.88% of that of the single cylinder.

The flow-induced vibration (FIV) of a cylinder cluster is often observed in subsea pipelines and marine risers. The motion of the cylinder clusters was often modeled as the equation of motion of a particle, which has ignored the torsion freedom. Hence, the answers to the following questions are still unavailable—what are the impacts of torsion on the FIV of a cylinder cluster? Does torsional freedom facilitate the development of new features in FIV? In the present work, the FIV of a two-tandem cylinder system was numerically studied under the consideration of torsional freedom. It was found that six well-defined regimes were formed in the FIV of the cylinder system with the increase in the reduced velocity. The formation of different regimes mainly occurred by the accouplement of two frequencies—the vortex shedding frequency and the natural frequency of the cylinder system. A quirky low frequency dominated the cross-flow vibration at some reduced velocities, significantly magnifying the cross-flow vibration and the torsional vibration. The two cylinders acted as two feet treading water alternatively, enabling the cylinder system to move further on one side at such low frequencies. The characteristics of the amplitudes and frequency responses vs U_r^* were qualitatively similar when the stiffness ratio k* was in the range of 10 ≤ k^* ≤ 50, where U_r^* was the torsional reduced velocity which was defined by the uniform velocity U divided torsional natural frequency f_rn and diameter of the cylinder D.

For both real fish and bionic fish, a rigid anterior portion is necessary for certain functions. How does the rigid anterior portion affect the locomotion of the flexible plate? Is it true that the rigid portion is redundant? It is lack of clear cognition on these questions. In this paper, the self-propulsion of the rigid-flexible composite plate is studied numerically. We suppose that the forces are exerted on the junction point to maintain a given pitch motion of the rigid portion, the deformation of the flexible portion is consequent. The ratio between the lengths of the flexible portion and the rigid portion is changed to model the composite plate, and the effect of the stiffness of the flexible plate is investigated. It is found that the propulsive velocity and the Froude efficiency actually decrease following the increasing proportion of the rigid plate. However, the conclusion is different as the elastic energy stored in the flexible plate is considered. We find that the case with larger flexible portion is efficient for the ultra-soft posterior plate, while the case with smaller flexible portion is efficient for the stiff posterior plate. It happens to coincide with the swimming behavior of live fish. The hydrodynamic force at the tail is hindering the propulsion of the plate, which means that the motion of the tail plays a decisive role on the force distribution on the plate, rather than the thrust only produced at the tail. We think that the short ultra-soft membrane at the tail of the real fish is an important feature to improve its swimming behavior. It is expected that the study in this paper will give a further insight into the mechanism of the locomotion of fish and give some implications for the design of the soft bionic fish.

To understand fish swimming behavior in unsteady flows, this paper introduces the Kármán gait model to numerically investigate the hydrodynamics of fish-like swimming in an asymmetric vortex environment, specifically the P + S mode (a pair of vortices are shed from one side of the cylinder and a single vortex from the other side during one oscillation period) created by an oscillating cylinder. The immersed boundary method is employed to model both the fish-like airfoil and the vibrating cylinder. Through simulations across a broad range of controlling parameters, we analyze the advancement efficiency of the airfoil in the P + S mode, the force coefficients, Fourier spectra of hydrodynamic forces, and the interactions between the airfoil and vortices. Our findings reveal that the fundamental phase Φ0 is crucial, as it directly influences the airfoil's position relative to the vortex and affects the forces exerted. Other parameters play a secondary role, primarily reinforcing the effect of the fundamental phase on airfoil–vortex interactions. Furthermore, the vortex pair boosting effect, unique to the P + S mode, enhances the airfoil's thrust and swimming efficiency. The wake environment behind the airfoil is also vital for maximizing benefits from the P + S mode. When the fundamental mode fs, indicative of the airfoil's ability to extract energy from vortices, dominates the Fourier spectra of hydrodynamic forces, it supports the airfoil's motion in the P + S mode. Conversely, when the first harmonic mode 2fs dominates the drag spectrum, it hinders propulsion by reducing the airfoil's thrust in the swimming direction.

The fish can be driven by the sarcomere at different locations of the body. To study the hydrodynamic performance of the fish in this process, the self-propulsion of a composite plate driving on two points was investigated. It is supposed that the forces were exerted on the junction point to maintain a given pitch motion of the rigid portion, and an additional external moment was exerted at a point on the flexible plate. The ratio between the lengths of the rigid portion and the flexible portion was fixed as 1/9, which was reasonable for a real fish. The acting point and phase angle of the additional external moment was varying to study the cooperation of the forces on different points. It was found that the additional external moment was not always promoting the propulsion velocity and efficiency of the composite plate. The additional external moment near the joint point was most suitable for improve the propulsive velocity and efficiency of the composite plate. The anti-phase additional external moment was prejudicing the propulsion of the plate. The additional external moment could change the vibration shape of the flexible plate and the flow structure around it. As ϕ = π , the amplitude and the gradient of the deformation was largely reduced, and the wake became long and narrow. The hydrodynamic forces at the head and tail portion of the flexible plate were hindering the propulsion of the plate, while the thrust was mainly produced on the intermediate portion. It was expected that our investigation can be helpful for the design of the soft robotic fish.