Insects flip their wings around each stroke reversal and may enhance lift in the early stage of a half-stroke. The possible lift-enhancing mechanism of this rapid wing rotation and its strong connection with wake vortices are still underexplored, especially when unsteady leading-edge vortex (LEV) behaviours occur. Here, we numerically studied the lift generation and underlying vorticity dynamics during the rapid rotation of a low aspect ratio flapping wing at a Reynolds number ( ${\textit {Re}}$ ) of 1500. Our findings prove that when the outboard LEV breaks down, an advanced rotation can still enhance the lift in the early stage of a half-stroke, which originates from an interaction with the breakdown vortex in the outboard region. This interaction, named the breakdown-vortex jet mechanism, results in a jet and thus a higher pressure on the upwind surface, including a stronger wingtip suction force on the leeward surface. Although the stable LEV within the mid-span retains its growth and location during an advanced rotation, it can be detrimental to lift enhancement as it moves underneath the wing. Therefore, for a flapping wing at ${\textit {Re}}\sim 10^3$ , the interactions with stable and breakdown leading-edge vortices lead to the single-vortex suction and breakdown-vortex jet mechanisms, respectively. In other words, the contribution of wing–wake interaction depends on the spanwise location. The current work also implies the importance of wing kinematics to this wing–wake interaction in flapping wings, and provides an alternative perspective for understanding this complex flow phenomenon at ${\textit {Re}}\sim 10^3$ .

Due to adverse viscous effects, revolving wings suffer universally from low efficiency at low Reynolds number (Re). By reciprocating wing revolving motion, natural flyers flying at low Re successfully exploit unsteady effects to augment force production and efficiency. Here we investigate the aerodynamics of an alternative, i.e., a revolving wing with concomitant unsteady pitching and vertical flapping perturbations (a pitching-flapping-perturbed revolving wing). The current work builds upon a previous study on flapping-perturbed revolving wings (FP-RWs) and focuses on combined effects of pitching-flapping perturbation on force generation and vortex behaviors. The results show that, compared with a FR-RW, pitching motion further (1) reduces the external driving torque for rotating at 0° angle of attack (α₀) and (2) enhances lift and leads to a self-rotating equilibrium at α₀ = 20°. The power loading of a revolving wing at α₀ = 20° can be improved using pitching-flapping perturbations with large pitching amplitude but small Strouhal number. Additionally, an advanced pitching improves the reduction of external driving torque, whereas a delayed pitching weakens both the lift enhancement and the reduction of external driving torque. Further analysis shows that pitching effects can be mainly decomposed into the Leading-Edge-Vortex (LEV)-mediated pressure component and geometric projection component, together they determine the force performance. LEV circulation is found to be determined by the instantaneous effective angle of attack but could be affected asymmetrically between upstroke and downstroke depending on the nominal angle of attack. Pitching-flapping perturbation thus can potentially inspire novel mechanisms to improve the aerodynamic performance of rotary wing micro air vehicles.

The mechanisms of leading-edge vortex (LEV) formation and its stable attachment to revolving wings depend highly on Reynolds number ( $\textit {Re}$ ). In this study, using numerical methods, we examined the $\textit {Re}$ dependence of LEV formation dynamics and stability on revolving wings with $\textit {Re}$ ranging from 10 to 5000. Our results show that the duration of the LEV formation period and its steady-state intensity both reduce significantly as $\textit {Re}$ decreases from 1000 to 10. Moreover, the primary mechanisms contributing to LEV stability can vary at different $\textit {Re}$ levels. At $\textit {Re} <200$ , the LEV stability is mainly driven by viscous diffusion. At $200<\textit {Re} <1000$ , the LEV is maintained by two distinct vortex-tilting-based mechanisms, i.e. the planetary vorticity tilting and the radial–tangential vorticity balance. At $\textit {Re}>1000$ , the radial–tangential vorticity balance becomes the primary contributor to LEV stability, in addition to secondary contributions from tip-ward vorticity convection, vortex compression and planetary vorticity tilting. It is further shown that the regions of tip-ward vorticity convection and tip-ward pressure gradient almost overlap at high $\textit {Re}$ . In addition, the contribution of planetary vorticity tilting in LEV stability is $\textit {Re}$ -independent. This work provides novel insights into the various mechanisms, in particular those of vortex tilting, in driving the LEV formation and stability on low- $\textit {Re}$ revolving wings.

The flapping wings or fins in an in-line arrangement are a common scene in flocks and schools, as well as flying creatures with multiple pairs of wings, e.g., dragonflies. Conventional studies on these topics are underpinned by tandem plunging airfoils in either a vertical or a declined stroke plane. The former model mostly considers a symmetrical pitching motion, and the latter model fails to separate the effect of the asymmetric pitching from that of the declined incoming flow. However, our study focuses on the tandem airfoils with vertical plunging and asymmetric pitching in a horizontal freestream and, therefore, explains the effects of asymmetric pitching on tandem plunging airfoils. Using numerical methods, the aerodynamic performance and vortical structures of the tandem airfoils are examined, and the effects of the non-zero geometric angle of attack (α₀), phase angles in the plunging and pitching motion (φ and θ), and inter-foil spacing (G/c) are discussed. Our results show that the tandem arrangement is beneficial to enhance the propulsion thrust while retaining the lifting capacity of the airfoil at a non-zero α₀. The effects of φ and G/c are coupled since they both determine the interaction between the hind airfoil and the leading-edge vortex in the wake and the out-of-phase mode is suggested for the tandem airfoils at G/c = 1 to enhance both lift and thrust. For a tandem airfoil with in-phase mode, the optimal G/c is around 1.5 to 2. Moreover, the asymmetric pitching of the in-phase plunging airfoils should be synchronized to retain the enhanced performance.

The physics of leading-edge vortex (LEV) stability on flapping wings and autorotating seeds is still underexplored due to its complex dependency on Reynolds number ( $\textit {Re}$ ), aspect ratio (AR) and Rossby number (Ro). Our previous study observed an interesting dual-stage vortex tilting between radial and tangential components in a stable LEV. Here, the establishment of this novel mechanism, i.e. dual-stage radial–tangential vortex tilting (DS-VT $_{r-t}$ ), is investigated and explained in detail using numerical methods. The contributions of other tangential vorticity transport terms are also considered. It is shown that the stable LEV region coincides mostly with a constant ratio of tangential and radial vorticity components. The DS-VT $_{r-t}$ mechanism functions as a negative feedback loop for radial vorticity, thereby contributing to the LEV stability at $\textit {Re} > 500$ . Specifically, this mechanism involves a dual-stage vortex tilting starting from negative radial component to positive tangential component, and then back to positive radial component, thereby leading to a $180^{\circ }$ reversal of radial vorticity. The radial Coriolis acceleration can also assist the DS-VT $_{r-t}$ by enhancing the tangential vorticity component and the reduction of radial vorticity inside the LEV via the second stage of DS-VT $_{r-t}$ . The effects of $\textit {Re}$ , AR and Ro on the constant radial–tangential vorticity ratio and DS-VT $_{r-t}$ are then analysed. The coupled effects of AR and Ro are separated into rotational effects and those of tip and root vortices. Our results establish an evident relationship among the LEV stability, the constant radial–tangential vorticity ratio, and the DS-VT $_{r-t}$ , thereby deepening the understanding in the vorticity transport of LEV formation and stability.