The vortical structures and turbulence statistics in the near wake of rectangular, trapezoidal, triangular and ellipsoidal tabs were experimentally studied in a refractive-index-matching channel. The tabs share the same bulk dimensions, including a 17 mm height, a 28 mm base width and a $24.5^{\circ }$ inclination angle. Measurements were performed at two Reynolds numbers based on the tab height, $Re_{h}\simeq 2000$ (laminar incoming flow) and 13 000 (turbulent incoming flow). Three-dimensional, three-component particle image velocimetry (PIV) was used to study the mean flow distribution and dominant large-scale vortices, while complementary high-spatial-resolution planar PIV measurements were used to quantify high-order statistics. Instantaneous three-dimensional fields revealed the coexistence of a coherent counter-rotating vortex pair (CVP) and hairpin structures. The CVP and hairpin vortices (the primary structures) exhibit distinctive characteristics and strength across $Re_{h}$ and tab geometries. The CVP is coherently present in the mean flow field and grows in strength over a significantly longer distance at the low $Re_{h}$ due to the lower turbulence levels and the delayed shedding of the hairpin vortices. These features at the low $Re_{h}$ are associated with the presence of Kelvin–Helmholtz instability that develops over three tab heights downstream of the trailing edge. Moreover, a secondary CVP with an opposite sense of rotation resides below the primary one for the four tabs at the low $Re_{h}$ . The interaction between the hairpin structures and the primary CVP is experimentally measured in three dimensions and shows complex coexistence. Although the CVP undergoes deformation and splitting at times, it maintains its presence and leads to significant mean spanwise and wall-normal flows.

Dandelion seeds can stably diffuse owing to the dominant drag rather than the lift-based mechanism of the streamlined leaves of the plant, where this is known to favor their long-distance dispersal with the steady vortex attached. However, the generation mechanism of the vortex and the aerodynamic force exerted on the seeds through multiple filaments remain unknown. Clarifying these subjects may help realize the optimal performance of porous structures under different flight conditions. This study conducts numerical simulations to illuminate the influence of gaps and the Reynolds number (Re) on the wake structures and consequent drag force of dandelion seeds. We fabricate the seeds into circular disks composed of evenly distributed square cylinders placed in a vertical flow field with Re of 100 and 400, with the porosity of the pappus (ε) ranging from 0.887 to 0.964. We explain the geometric properties of the attached, steady vortex rings and clarify their generation mechanism, i.e., the base bleed and convection effects competed with vorticity generation, based on which the gaps are confirmed to delay chaotic vortices from occurring compared with the solid case. The weakened leeward pressure is critical for the increase in the drag coefficient to reach the peak level. The enhanced drag coefficient is several times higher than that in the solid case, endowing the seeds with a high loading capacity, and the porosity corresponding to its peak is beneficial for the structural design. These conclusions provide positive insights into the design of ventilated aircrafts with optimal long-distance dispersal performance.

In order to solve the inevitable instability problem of dandelion-like unpowered aircraft, transient simulations are carried out for the transition to turbulence of the wake from stable to unstable stage under different Reynolds numbers, and the vortex mode characteristics presented by the vortex structure as the Reynolds number increases are identified. Furthermore, by monitoring the velocity and lift and drag coefficients at different positions in dandelion flow field, the spectral characteristics of flow velocity and aerodynamic coefficients in the turbulent phase triggered by extreme aerodynamic environment are revealed. Compared with solid disk, it is found that the bandgap structure is more conducive to expanding the stable flight threshold of the dandelion-like aircraft, that is, the canopy configuration has weakening effect on airflow fluctuations. In addition, an evaluation method for unsteady boundary Reynolds number and load capacity of a dandelion-like aircraft is presented. The proposed method aims to plan a reasonable number of filaments (or porosity) for further designing dandelion-like aircraft with flight stability and high load capacity under aerodynamic conditions at different Reynolds numbers.

In this paper, we propose an improved nonsingular terminal sliding mode control method, to achieve finite-time trajectory tracking of a quadrotor unmanned aerial vehicle in the presence of external and mismatched disturbances. This method is combined with finite-time disturbance observers, which are employed to estimate these two types of disturbances, and it also ensures that disturbance estimation errors can converge to zero within a finite time. To counteract the effects of external disturbances, the control law incorporates their estimation. Additionally, we modify the sliding mode surface to include the estimation of mismatched disturbances, which helps to mitigate their impact. Then, we demonstrate the stability of the system using a Lyapunov function, showing that the tracking error will converge to zero within a finite time. Finally, simulation results indicate that the proposed control method can effectively suppress both types of disturbances.