We present a detailed analysis of the voluntary take-off procedure of a dragonfly. The motions of the body and wings are recorded using two high-speed cameras at Beihang University. The experimental results show that the dragonfly becomes airborne after approximately one wingbeat and then leaves the ground. During this process, the maximum vertical acceleration could reach 20 m/s². Evidence also shows that acceleration is generated only by the aerodynamic force induced by the flapping of wings. The dragonfly voluntary take-off procedure is divided into four phases with distinctive features. The variation in phase difference between the forewing and hindwing and angle of attack in the down-stroke are calculated to explain the different features of the four phases. In terms of the key parameters of flapping, the phase difference increases from approximately 0 to 110 degrees; the angle of attack in down-stroke reaches the maximum at first and then decreases in the following take-off procedure. Due to experimental limitations, 2-D simulations are conducted using the immersed boundary method. The results indicate that the phase difference and the angle of attack are highly correlated with the unsteady fluid field around the dragonfly’s wings and body, which determines the generation of aerodynamic forces.

Dragonflies possess two pairs of wings and the interactions between forewing (FW) and hindwing (HW) play an important role in dragonfly flight. The effects of tandem-wing (TW) interactions on the aerodynamic performance of dragonfly hovering have been investigated. Numerical simulations of single-wing hovering without interactions and TW hovering with interactions are conducted and compared. It is found that the TW interactions reduce the lift coefficient of FW and HW by 7.36% and 20.25% and also decrease the aerodynamic power and efficiency. The above effects are mainly caused by the interaction between the vortex structures of the FW and the HW, which makes the pressure of the wing surface and the flow field near the wings change. During the observations of dragonfly flight, it is found that the phase difference ( γ ) is not fixed. To explore the influence of phase difference on aerodynamic performance, TW hovering with different phase differences is studied. The results show that at γ = 22.5°, dragonflies produce the maximum lift which is more than 20% of the body weight with high efficiency; at γ = 180°, dragonflies generate the same lift as the body weight.

A new non-intrusive reduced-order modeling method based on space-time parameter decoupling for parametrized time-dependent problems is proposed. This method requires the preparation of a database comprising high-fidelity solutions. The spatial bases are extracted from the database through first-level proper orthogonal decomposition (POD). The algebraic relationship between the time trajectory/parameter positions and the projection coefficient is described by the linear superposition of the second-level POD bases (temporal bases) and the second-level projection coefficients (parameter-dependent coefficients). This decomposition strategy decouples the space-time parameter effects, providing a stable foundation for fast predictions of parametrized time-dependent problems. The mappings between the parameter locations and the parameter-dependent coefficients are approximated as Gaussian process regression (GPR) models. The accuracy and efficiency of the PPOD-ROM are demonstrated through two numerical examples: flows past a cylinder and turbine flows with a clocking effect.