The active synchronous deformation in the arc length of an airfoil employed in a flapping wing can improve its energy extraction efficiency. The present study seeks to understand the underlying physics of this energy extraction by conducting transient numerical simulations of a novel arc-deformable flapping foil design based on dynamic mesh technology and a relative heaving motion reference system. The influence of the flapping frequency and the pitching amplitude on the energy extraction efficiency of the flapping foil modeled under a constant arc length is investigated. The effects of the deformation magnitude β and the position of the deformation center on the energy extraction efficiency are also examined at a constant flapping frequency and pitching amplitude. The results show that active synchronous arc deformation can greatly improve the energy extraction efficiency of a flapping foil compared to the efficiency of a conventional non-deformable flapping foil design. In addition, the results provide sets of optimal flapping frequencies and pitching amplitudes for the deformable flapping foil design with fixed deformation parameters and the non-deformable foil design that obtains the highest energy extraction efficiencies. A single high efficiency zone is obtained for the deformable foil design at a relatively high flapping frequency. In contrast, relatively high efficiency zones are obtained for the non-deformable foil design at both a relatively low flapping frequency and a high flapping frequency. The energy extraction efficiency of the deformable flapping foil first increases with increasing β up to a maximum value of β = 0.25 and then decreases with a further increase in β. The energy extraction efficiency of the deformable flapping foil is also demonstrated to increase as the deformation center moves from the leading edge of the foil to the trailing edge, attaining a maximum value when the deformation center coincides with the center of the pitching axis, and then decreases.

Flapping wing devices have attracted considerable attention as a new means of power extraction. The present study applies transient numerical calculations based on the dynamic mesh technique to investigate the influences of leading edge, trailing edge, or overall circular arc airfoil deformations on the power extraction efficiencies of a flapping wing device under the condition of maintaining a constant arc length along the mean camber line of the foil. The results indicate that airfoil deformations can improve the power extraction efficiency of the flapping wing device. The primary reason is that the active synchronised deformation of the foil increases the effective curvature and the velocity circulation around the foil. In addition, the performance curve of the flapping wing device exhibits two frequency ranges with relative high efficiency. In the low frequency region, if the leading edge vortex (LEV) detaches from the trailing edge just as the foil reverses its heaving direction, the foil will gain much more energy due to the positive power extraction of the pitching moment. In the high frequency region, a small steady body‐attached vortex (BAV) maintains a high lift, and, thus, the device extracts more power due to the enhanced heaving force.

Previous work has shown that the employment of a gap drainage impeller in a centrifugal pump can improve the pump's hydraulic performance and cavitation resistance. However, during experiments, an unconventional cavitation phenomenon has been observed in the form of a staggered pair of fixed impeller flow tunnels. For the purpose of understanding the factors involved with this unconventional phenomenon, the present study analyzes the cavitation formation and evolution processes using numerical and experimental methods. A scalable detached eddy simulation (SDES) method was employed to address unsteady turbulent flow. First, the method was validated by comparing the performance data and liquid water velocity distributions obtained by calculation and experiment in the absence of cavitation. Then, numerical simulations of the cavitation flow field were conducted under a flow discharge condition one-half that of the optimum value. Within a particular range of cavitation numbers, the calculated results are found to reproduce the unconventional cavitation phenomenon observed in the experiments. The formation mechanism involves a combination of many factors such as impeller geometry, inflow discharge condition, and cavitation number. As for a certain geometry, the formation and evolution processes can generally be analyzed and explained according to the influence of the attack angle, which is affected by variations in the allocated flow discharge and cavitation volume in each impeller tunnel. The jet flow through the gap between the main and vice blades also contributes to the formation of this phenomenon.

To facilitate the smooth transition of operational modes in self-sustaining micro-thrusters, this study focuses on a device employing semi-passive flapping wings. Transient numerical methods are used to analyze the variation of flap energy acquisition and propulsion characteristics with pitching frequency, and the relationship between the dominant vortex structure and the force characteristics is analyzed by using the integral momentum theorem and the dynamic mode decomposition (DMD) method. The results indicate that, under the investigated operational conditions, with an increase in the pitching frequency, distinct wake evolution characteristics were observed. In the energy harvesting operational regime, the wake patterns manifest as 2P + mS, 2S + mS, and mS types. During the transitional phase from energy harvesting to propulsion, the wake patterns shift from 2S + mS to 2S transitional types, eventually leading to the manifestation of a reverse Karman vortex street (2S RBVK). In the propulsion operational regime, the wake patterns consist of a reverse Karman vortex street and asymmetric reverse Karman vortex street phenomena. Simultaneously, it was observed that the transition of flapping-wing performance from energy harvesting to propulsion conditions delays behind the transformation of vortex street structures. This delay is attributed to the necessity for the flapping-wing device to overcome its own resistance before generating a net effective propulsive force. The contributions of unsteady wake to thrust primarily encompass vortex thrust, thrust due to localized fluid acceleration, induced momentum force, and induced pressure force. As the pitching frequency increases, the influence of wake vortices on propulsion also intensifies. The contribution of wake vortices to flapping-wing propulsion is determined by the spatial distribution of Lamb vectors and localized fluid accelerations. The conclusions drawn from the dynamic modal analysis and reconstructed flow field analysis of wake vortices align with the findings of the investigation of wake vortices based on the integral momentum theorem.

Flapping-wing devices working in an energy-harvesting mode have the advantage of environmental adaptation. To analyze the energy-extraction characteristics of a flapping wing with the free-surface effect, transient-numerical studies were carried out based on the homogeneous two-phase volume-of-flow model, the shear stress transport k–ω turbulence model, and dynamic-grid technology. These studies took into consideration the influences of the dimensionless submergence depth $S_d$ along with the Froude number Fr. The following results were obtained. (1) In the subcritical condition of Fr < 1, there was a critical hydrofoil submergence depth. When it was greater than this critical value, the existence of the free surface was able to promote the energy-extraction efficiency. On the contrary, the closer the flapping wing was to the free surface, the lower its energy-harvesting efficiency was. (2) When the hydrofoil submergence depth was small, the energy-harvesting efficiency first increased and then decreased with the increase in Fr. Furthermore, the smaller $S_d$ was, the faster the energy-extraction efficiency of the flapping wing decreased. While $S_d$ was large, for example $S_d$ > 9, the energy-extraction efficiency first increased and then gradually approached the unbounded-flow condition as Fr increased, but it was always lower than the unbounded-flow case. (3) Compared with the case of unbounded flow, the existence of the free surface affected the motion of the leading-edge vortex, thereby changing the magnitude and direction of the lift force and pitch moment. The relative position of the free-surface wave crest to the wing also affected the pressure distribution around the flapping-wing surface, which in turn affected the energy-harvesting properties. Additionally, Fr affected the formation and shedding of the vortex around the flapping wing, and the movement synchronization between the leading-edge vortex and the flapping wing was extremely important to the energy-harvesting performance.