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The stability of flight by flapping wings is investigated by using the immersed boundary-lattice Boltzmann method (IB-LBM). First, the rotational motion with an initial small disturbance is computed, and it is found that the rotational motion is unstable for high Reynolds numbers. Second, we show simple ways to control the rotational and translational motion by bending or flapping the tip of the wing.

The application of a flapping wing mechanism offers a vast range of development possibilities for unmanned aerial vehicles (UAVs) and autonomous underwater vehicles (AUVs). The influence of wake transitions on flapping wing mechanism’s capabilities is not fully understood particularly at low Reynolds numbers. The numerical investigation of a symmetric airfoil performing sinusoidal heaving oscillations is performed to explore the wake transitions. The influence of heaving parameters on wake transitions when exposed to a constant velocity flow is investigated. The existence of reverse von Karman vortex street, deflected wake and chaotic wake is observed. The wake deflection is found to switch its direction before transforming into a chaotic wake. The coherent structures and its evolution with the flow are presented using proper orthogonal decomposition (POD). The underlying structures and their interactions for different wake situations are identified. Correlations for the nondimensional maximum velocity in the wake in terms of frequency and amplitude is proposed. The wake dynamics is found to depend significantly on the leading edge vortices. The time-varying velocity fluctuations in the flow field are presented and discussed in detail. The velocity fluctuation contours are used to identify the regions of momentum transfer. The transient nature of the flow field is studied using the phase plot. A transition route from the periodic to chaotic regime though a quasi-periodic regime is established using time series analysis. The wake transitions are observed to be more sensitive towards heaving frequency than the heaving amplitude.

The flapping kinematics have revealed a new paradigm of locomotion which is highly maneuverable and efficient compared to traditional propulsion systems. This work numerically investigates a three-dimensional wing undergoing pitching oscillations using Large eddy simulation (LES). The wake structure is presented using the $Q$-function, and the influence of pitching frequency on the structure of the wake is discussed. The vortices appear to travel as interconnected vortex rings in the bifurcated wake and are completely different from the two-dimensional investigations. The increase in pitching frequency $({\mathrm{\text{St}}}_D)$ generates the interlinking structures between the two limbs of the bifurcated wake. The interlinking between the two limbs increases with ${\mathrm{\text{St}}}_D$ and will get disrupted at sufficiently high ${\mathrm{\text{St}}}_D$. The increase in ${\mathrm{\text{St}}}_D$ increased the force generated by the pitching wing, and the periodic dynamics between the force coefficients slowly transformed to quasi-periodic dynamics. The transition to quasi-periodic dynamics has not reduced the force generation of the pitching wing. The disruption of interlinking structures between the two limbs enhanced the lift generated by the pitching wing. The present investigation shows that the wake vortex structure strongly depends on ${\mathrm{\text{St}}}_D$. The generation of a jet in the wake is visible in the mean velocity profile indicating the thrust developed by the wing. The formation of multiple peak profiles indicated the formation of multiple jets, which resulted in enhanced thrust production. The Reynolds stress field generated from the velocity fluctuations appears to be influenced by both the pitching oscillations and vortex interactions. This study can guide the selection of better kinematic parameters to enhance the propulsive performance.

In this study, models for the wake capture lift and drag force coefficients of a hovering flapping wing were presented using numerical fluid dynamics simulation to improve the blade element theory. The investigated wing is inspired by the fruit fly and has combined flapping and pitching movements. The effect of changing the wing acceleration time at the start ($\mathrm{\Delta }{\tau }_A$) and end of the half cycle ($\mathrm{\Delta }{\tau }_D$), as well as the Reynolds numbers in the range of 136–6800, on wake capture using the Taguchi orthogonal array test design, is investigated using the numerical fluid dynamics method, and the values of average lift and drag coefficients due to wake capture are obtained. These force coefficients were applied to linear and nonlinear regression methods to obtain the mathematical model, and a model for its changes was extracted. Finally, to obtain the instantaneous coefficients, the extracted models were placed in the normal distribution function, and the final instantaneous model was obtained. Examining the verification cases of the application of these wake capture relationships with the blade element theory, as well as the effects of translational force, rotational force and added mass force, revealed that this developed theory is capable of correctly predicting the wake capture force’s initial peak. The force coefficient trend in the final quasi-steady model with wake capture is similar to the computational fluid dynamics (CFD) results, according to a qualitative examination of the lift and drag force coefficients in a half cycle. This demonstrates a significant result: this theory, which is divided into four parts: transnational, rotational, added mass and wake capture, adequately covers the general physics of these complex movements.

This paper presents a fluid–structure interaction (FSI) solution technique in which the incompressible fluid dynamics involving moving boundaries is solved with the deforming-spatial-domain/stabilized space–time (DSD/SST) method and the structural dynamics is solved with the finite difference (FD) method. The DSD/SST and FD solvers are coupled by an implicit partitioned coupling strategy based on staggered subiterations. Three types of relaxation are applied on the FSI surface velocity and hydrodynamic force. The first one is applied to delay the coupling conditions at the beginning of each simulation; the second one is applied to relax the increment during each subiteration; and the third one is applied to filter high frequency oscillations between each time step. A pitching plate in a uniform flow is calculated to validate the FSI technique. The present results are in good agreement with data predicted by other methods. In addition, two problems are calculated to demonstrate the capability of this solver: an orbital flow over flapping foil propulsion and energy harvesting and a flexible plate in a cavity excited by an external force.

The modified immersed boundary method is introduced and applied to study the propulsive mechanism of a tandem flapping wings system. The effects of tandem wings distance and phase lag between the two flapping wings are investigated. Thrust force of the upstream wing is nearly constant and close to the magnitude of single flapping wing system. Thrust force of second wing is influenced by the distance and phase lag. With specific parameters, the second wing can obtain a maximum thrust which is larger than the one of first wing. The flow structures of the wake flow are classified into three different formations, and they are correlated to the trends of thrust force. The effects of distance and phase lag are coupled other than isolated. It is possible to lower down the power consumption of this tandem flapping wings system and enhance the total thrust force of the system at the same time.

In this study, we numerically examine the effect of wing flexibility on the lift force generated by a modeled flapping wing that simulates an insect flight in hover mode. The flow field around the flapping wing is assumed to be two-dimensional (2D), and the flow equations are formulated with the notion of “immersed boundary” for easy handling of the moving-boundary problem. In the 2D framework, the wing chord is treated as an elastic filament. To account for the large deformation in the wing, the motion of the filament is modeled using a geometrically nonlinear equation for bending beams. Both sets of equations are then solved according to the fluid–structure interaction concept using appropriate numerical schemes. Time variation of lift force on the wing is calculated for different values of wing flexural rigidity. Effects of elastic deformation of the wing and interactions between the bending wing and vortical flow structure are discussed. Flexural rigidity that gives the highest average lift force on the wing is sought. This study affirms that the flexibility of wing and the vortex-pair capture phenomenon are crucial to the lift force generation in the flapping-wing mechanics.

This paper focuses on an experimental investigation aimed at evaluating the aerodynamics force characteristics of three-dimensional (3D) insect-like flapping motion in the vicinity of ground. The purpose is to establish whether flapping wing insects can derive aerodynamic benefit from ground effect similar to that experienced by a fixed wing aircraft. To evaluate this, force measurements were conducted in a large water tank using a 3D flapping mechanism capable of executing various insect flapping motions. Here, we focus on three types of flapping motions, namely simple harmonic flapping motion, hawkmoth-like hovering motion and fruitfly-like hovering motion, and two types of wing planforms (i.e. hawkmoth-like wing and fruitfly-like wing). Results show that hawkmoth-like wing executing simple harmonic flapping motion produces average lift to drag ratio similar to that of fruitfly wing executing the same motion. In both cases, they are relatively independent of the wing distance from the ground. On the other hand, a hawkmoth wing executing hawkmoth flapping motion produces characteristic different from that of fruitfly wing executing fruitfly motion. While the value of the former is a function of the wing distance from the ground, the latter is minimally affected by ground effect. Unlike fixed wing aerodynamics, all the flapping wing cases considered here do not show a monotonic increase in with decreasing wing distance from the ground.