Recent studies have shown that by utilizing the interactions among median fins (the dorsal, anal, and caudal fins), fishes can achieve higher propulsion performance at the caudal fin. This work aims at a systematic study of the effects of dorsal/anal fin shape and flapping phase on the hydrodynamic performance due to median-fin interactions (MFI) in underwater propulsion using a three-dimensional bluegill sunfish model. Flow simulations were conducted on stationary Cartesian grids using an immersed-boundary-method-based incompressible Navier-Stokes flow solver. The results showed that, due to the collision between the posterior body vortices (PBVs) and caudal fin leading edge vortices (LEVs), the latter is strengthened. As a result, the thrust and efficiency of the caudal fin are improved simultaneously, by 25.6% and 29.2%, respectively. Increases in the dorsal/anal fin area result in stronger caudal fin LEVs, and thus further caudal fin performance enhancement. On the other hand, changing the dorsal/anal fin flapping phase affects the collision time between the PBVs and the LEVs, and results in caudal fin performance changes. Phase-leading dorsal and anal fins are found to improve caudal fin efficiency, whereas phase-lag dorsal and anal fins maintain caudal fin thrust at a higher level. Compared to trunk-synchronized dorsal and anal fins, 60° phase-leading dorsal and anal fins increase the propulsive efficiency of the caudal fin from 77.9% to 90.1%. In addition, it is found that the presence of the dorsal and anal fins greatly reduces drag on the fish body by preventing the PBVs from crossing the body midline and debilitating interactions between the left- and right-stroke PBVs. Results of this work improve our understanding of MFI in fishlike swimming and demonstrate the benefits of optimal MFI for the design of high-performance bioinspired underwater vehicles.

Hydrodynamics of median-fin interactions in fish-like locomotion: Effects of fin shape and movement

The effect of hawkmoth-like flexibility on the aerodynamic hovering performance of wings at a Reynolds number of 400 has been assessed by conducting fluid structure interaction simulations incorporating a finite difference based immersed boundary method coupled with a finite-element based structure solver. The stiffness distribution of a hawkmoth forewing was mapped onto three wing shapes (r¯1 = 0.43, 0.53, and 0.63) defined by the radius of the first moment of wing area each with aspect ratios, AR = 1.5, 2.96, 4.5, and 6.0 using elliptic mesh generation, the Jacobi method for iterations, and the concept of the barycentric coordinate system. The results show that there is a dominant chordwise deformation at AR = 1.5, and the wings also deform in the spanwise direction and their tips deviate from the horizontal stroke plane as AR increases. At AR = 1.5, 2.96, and 4.5, flexibility increases the mean lift (up to 39%, 18%, and 17.6%, respectively) for all wing shapes. At AR = 6.0, the r1¯ = 0.53 and 0.63 flexible wings give lesser lift than the rigid equivalents because of negative lift or small positive lift during the early stroke as the vortical structures remain on the bottom surface. This is attributed to the rapid pitch-down rotation, lesser stroke angular velocity than the rigid wing, and upward motion of the wingtip, away from the horizontal stroke plane. From the design perspective, the anisotropic flexible wings (except r1¯ = 0.53 and 0.63 with AR = 6.0) can be used in micro aerial vehicles for high lift requirements, such as for a high payload. Results here show that in nature, the hawkmoth wings with r1¯ and AR of 0.43-0.44 and 2.73-2.92, respectively, appear to have a combination of the shape, AR, and flexibility that optimizes power economy.

Effects of hawkmoth-like flexibility on the aerodynamic performance of flapping wings with different shapes and aspect ratios

In nature, creatures such as birds, insects, and fish have excellent flight and mobility capabilities. The prominent flight performance of many creatures employing flapping wings has attracted researchers to study the aerodynamics of bionic flapping wings, which has potential application in designing micro air vehicles and autonomous underwater vehicles. Bionic movements usually have to adapt to the low Reynolds number environment. It is noteworthy that the flow field of a flapping wing at low Reynolds numbers flow state is closely related to the complex non-linear shedding and viscous phenomenon, especially in a three-dimensional (3D) flapping wing. In order to observe the influence of the viscous phenomenon on flapping wing propulsive performance at low Reynolds numbers, the flow field characteristics of the 3D flapping wing under different Reynolds numbers are discussed using the immersed boundary-lattice Boltzmann method with the Chinese supercomputer TianHe-II in this paper. The influence of kinematic parameters on the flow characteristics at low Reynolds number is particularly emphasized, considering that the biological movement involves many kinematic parameters, the unsteady flow field and vortex structure around the flapping wing are analyzed in detail. This study reports that the law of the flapping wing propulsive performance strongly depends on kinematic parameters that affect the vortex changes. The underlying flow mechanism behind flapping wing performance at low Reynolds numbers has been explored, which will make it possible to apply superior kinematic parameters to improve the propulsive performance of a flapping-like new airplane.

Effects of kinematic parameters on three-dimensional flapping wing at low Reynolds number

Three-dimensional effects on the aerodynamic performance of flapping wings in tandem configuration

This paper reports results of an experimental investigation into ground effect on the aerodynamics of a two-dimensional elliptic airfoil undergoing simple harmonic translation and rotational motion. Ground clearance (D) ranging from 1c to 5c (where c is the airfoil chord length) was investigated for three rotational amplitudes (α
 m) of 30°, 45° and 60° (which respectively translate to mid-stroke angle of attack of 60°, 45° and 30°). For the lowest rotational amplitude of 30°, results show that an airfoil approaching a ground plane experiences a gradual decrease in cycle-averaged lift and drag coefficients until it reaches D ≈ 2.0c, below which they increase rapidly. Corresponding DPIV measurement indicates that the initial force reduction is associated with the formation of a weaker leading edge vortex and the subsequent force increase below D ≈ 2.0c may be attributed to stronger wake capture effect. Furthermore, an airfoil oscillating at higher amplitude lessens the initial force reduction when approaching the ground and this subsequently leads to lift distribution that bears striking resemblance to the ground effect on a conventional fixed wing in steady translation.

Ground effect on the aerodynamics of a two-dimensional oscillating airfoil

This paper reports a fundamental investigation on the aerodynamics of two-dimensional flapping wings in tandem configuration in forward flight. Of particular interest are the effects of phase angle (φ) and center-to-center distance (L) between the front wing and the rear wing on the aerodynamic force generation at a Reynolds number of 5000. Both experimental and numerical methods were employed. A force sensor was used to measure the time-history aerodynamic forces experienced by the two wings and digital particle image velocimetry was utilized to obtain the corresponding flow structures. Both the front wing and the rear wing executed the same simple harmonic motions with φ ranging from −180° to 180° and four values of L, i.e., 1.5c, 2c, 3c, and 4c (c is the wing chord length). Results show that at fixed L = 2c, tandem wings perform better than the sum of two single wings that flap independently in terms of thrust for phase angle approximately from −90° to 90°. The maximum thrust on the rear wing occurs du...

Aerodynamics of two-dimensional flapping wings in tandem configuration

This paper reports on a fundamental investigation of the effects of pitching phase angle (ϕ) and pitching amplitude (αA) on the aerodynamics of a two-dimensional (2D) flapping wing executing simple harmonic motion in hovering mode. A force sensor and digital particle image velocimetry were employed to obtain the time-dependent aerodynamic forces acting on the wing and the associated flow structures, respectively. Pitching phase angle ranging from 0° to 360° at three different pitching amplitudes, that is, 30°, 45° and 60°, was studied. Our experimental results revealed that the largest lift and lift/drag ratio were achieved under the condition of advanced pitching (ϕ > 90°). However, further increasing ϕ beyond a certain value would not enhance the average lift any more. In contrast, the delayed pitching (ϕ < 90°) would cause the average lift to decrease and generally the averaged drag to increase, compared to the normal pitching (ϕ = 90°), overall reducing the lift/drag ratio greatly. Our experimental results also supported the findings of Lua et al. (J Exp Fluids 51:177–195, 2011) that there are two kinds of wing–wake interactions, and they can either enhance or reduce lift on the wing depending on the wing motion and the timing of the reverse stroke. Our results show that wing–wake interaction of the first kind normally has an adverse effect on lift generation when the wing is undergoing delayed pitching but has a positive effect on the lift when the wing is undergoing advanced pitching motion. When the ϕ became larger, the second kind of wing–wake interaction, that is, sliding of the leading edge vortex under the wing, will cause the concurrent fall in lift and drag.

Effects of pitching phase angle and amplitude on a two-dimensional flapping wing in hovering mode

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.

https://www.worldscientific.com/doi/pdf/10.1142/S2010194514603846

Experimental study of ground effect on three-dimensional insect-like flapping motion *

A constitutive model of freeze–thaw damage to transversely isotropic rock masses and its preliminary application

This paper reports a fundamental investigation on the effect of phase difference (φ) between the flapping motion of forewing and hindwing on the lift and thrust generation of two-dimensional (2D) tandem wings in a forward flight condition at a Reynolds number of 5,000. Force sensor was used to measure time-dependent aerodynamic forces acting on the two wings, and digital particle image velocimetry (DPIV) technique was employed to obtain the associated vorticity field and flow structures. Three cases of phase difference were studied, namely 0 (in-phase), 90 and 180 (anti-phase). The results reveal that: (a) the cycleaveraged lift and thrust coefficient of the forewing are higher than the corresponding values of a single flapping wing for all the three cases; (b) the cycle-averaged lift coefficient of the hindwing is approximately the same as that of the single wing and is relatively independent of the phase difference; (c) the thrust coefficient of the hindwing decreases with increasing phase difference, and except for the case of φ = 180, they are higher than that of the single wing; (d) the maximum thrust coefficient that occurs on the hindwing during in-phase stroking is 85.4% higher than that of a single wing case. Also, it is found that when the leading edge of the hindwing interacted with the wake structures of the forewing, the thrust increased rapidly. In the absence of such interaction, especially for the case of φ = 180, the leading edge vortex (LEV) on the hindwing interacted destructively with the wake structures of the forewing, leading to a reduction in force generation compared to that of a single flapping wing. This finding supports previous computational modeling studies that the timing of vortex-vortex interaction plays a crucial role in the overall force generation of the hindwing.

Xiaohu Zhang

Papers

Aerodynamics of two-dimensional flapping wings in tandem configuration

Effects of pitching phase angle and amplitude on a two-dimensional flapping wing in hovering mode

Experimental study of ground effect on three-dimensional insect-like flapping motion *

A constitutive model of freeze–thaw damage to transversely isotropic rock masses and its preliminary application

Experimental study of two-dimensional flapping wings in tandem configuration