The locomotion of a flapping flexible plate in a viscous incompressible stationary fluid is numerically studied by an immersed boundary-lattice Boltzmann method for the fluid and a finite element method for the plate. When the leading-edge of the flexible plate is forced to heave sinusoidally, the entire plate starts to move freely as a result of the fluid-structure interaction. Mechanisms underlying the dynamics of the plate are elucidated. Three distinct states of the plate motion are identified and can be described as forward, backward, and irregular. Which state to occur depends mainly on the heaving amplitude and the bending rigidity of the plate. In the forward motion regime, analysis of the dynamic behaviors of the flapping flexible plate indicates that a suitable degree of flexibility can improve the propulsive performance. Moreover, there exist two kinds of vortex streets in the downstream of the plate which are normal and deflected wake. Further the forward motion is compared with the flapping-based locomotion of swimming and flying animals. The results obtained in the present study are found to be consistent with the relevant observations and measurements and can provide some physical insights into the understanding of the propulsive mechanisms of swimming and flying animals.

The dynamics of viscous fluid flow over a circular flexible plate are studied numerically by an immersed boundary-lattice Boltzmann method for the fluid flow and a finite-element method for the plate motion. When the plate is clamped at its centre and placed in a uniform flow, it deforms by the flow-induced forces exerted on its surface. A series of distinct deformation modes of the plate are found in terms of the azimuthal fold number from axial symmetry to multifold deformation patterns. The developing process of deformation modes is analysed and both steady and unsteady states of the fluid-structure system are identified. The drag reduction due to the plate deformation and the elastic potential energy of the flexible plate are investigated. Theoretical analysis is performed to elucidate the deformation characteristics. The results obtained in this study provide physical insight into the understanding of the mechanisms on the dynamics of the fluid-structure system.

Fluid-structure-interaction problems are ubiquitous, complicated, and not yet well understood. In this paper we investigate the interaction of a leading rigid circular cylinder and a trailing compliant filament and analyze the dynamic responses of the filament in the wake of the cylinder. It is revealed that there exist two flapping states of the filament depending on the cylinder-filament separation distance and the relevant critical distance distinguishing the two states is associated with the Reynolds number and the filament length. It is also found that the drag coefficient of the cylinder is reduced but that of the filament may be increased or decreased depending on its length. Compared with a single filament in a uniform flow, the filament of the same mechanical properties flapping in the wake of the cylinder has a lower frequency and a greater amplitude.

In this paper, the interaction between an elastic plate and viscous fluids is numerically studied through a coupling lattice Boltzmann method with a finite element method. In simulations, the plate, which has a clamped trailing edge, is immersed in a linear shear flow of relatively low Reynolds numbers (Re). The dynamical analysis has been conducted in terms of aspect ratio (H), Reynolds number (Re), stiffness coefficient (K), and attack angle (β). Four generic modes for the plate motion or deformation are identified, and the respective characteristics are shown. Three maps of mode distributions depending on K, H, Re, and β are given definitely. Three routes for the plate to reach the deflected mode have been found. The elastic potential energy under different K numbers and aspect ratios H is compared. It is indicated that the larger aspect ratio would result in larger efficiency of energy transformation. It is also found that the flapping mode can only occur when the attack angle β ≥ 0°, i.e., if β < 0°, the plate merely remains in the deflected or straight mode. The vortex structures and the pressure distributions are shown clearly for flapping and deflected modes of the plate. The present results can provide useful information to the physical understanding of the dynamics for the plate motion in shear flows and can also offer additional knowledge about a flexible plate using energy from ambient fluids.