Biological flapping flight has always inspired human's imagination of flight. However, compared to the remarkable development of modern fixed-wing aircraft, our understanding of flapping flight is still limited due to the complexity of highly unsteady separated flows generated by flapping wings. Low-Reynolds-number flapping flight has recently attracted considerable attention in the aeronautical community due to the need to develop biologically inspired micro air vehicles (MAVs), and some success of building flapping MAVs has been achieved. Study of natural flyers is still a feasible way to improve the flight performance of MAVs, and therefore considerable efforts have been made on the flapping flight of insects, birds and bats [1–11].
Bats are the only flying mammals that are comparable to small birds in terms of the flight characteristics. However, bats have some unique features that are significantly different from birds, including the special skeletal anatomical structure with more degrees of freedom, highly deformable wing-membrane skin and more complicated wing kinematics [12–14]. Bats are more manoeuvrable and capable in slow flight [14–18]. Compared with a large body of literature on the flight of birds and insects, the results on flying bats are relatively limited. The studies of bat flight began from quantitative measurements of bat wing kinematics by using multiple cameras when a trained bat flies in a wind tunnel or a flight cage. Then, the major kinematical quantities of the flapping wing are extracted, including the wingbeat frequency, wingbeat amplitude, stroke plane angle, wing twist, local angle of attack (AoA) and camber. Based on these quantities, the bat wing surface can be reconstructed for experimental and computational analysis. Detailed measurements of the wing kinematics of a lesser dog-faced fruit bat (Cynopterus brachyotis) flying a cage were conducted by Tian et al. , and the trajectories of the wingtip and several digital points and the Strouhal numbers were presented. Further measurements of the wing kinematics of a lesser dog-faced fruit bat were conducted in a wind tunnel by Hubel et al.[20,21]. The complex kinematics of the bat wings was reconstructed by Riskin et al.  using the proper orthogonal decomposition from time-resolved measurements of targets on the wings. The more complete kinematical data of a Pallas' long-tongued bat (Glossophaga soricina) were presented by Wolf et al. .
To understand the flow structures generated by the bat wings and their relationship with the aerodynamic performance, particle image velocimetry (PIV) measurements synchronized with the wing kinematical measurements have been conducted. Wake velocity fields on the Trefftz plane behind a dog-faced fruit bat were obtained by Tian et al. , showing the organized tip vortices. Refined PIV measurements in the wake of a Pallas' long-tongued bat were conducted by Hedenstrom et al. , revealing that a vortex loop was generated by each wing in one cycle and the wake structure was much more complex than that of a flying bird. Further, Hubel et al.[20,21] reconstructed the three-dimensional wake structure and estimated the circulation that is responsible for the lift. PIV measurements by Muijres et al.  at several spanwise sections near the upper wing surface of a slow-flying bat revealed the formation of the leading-edge vortices (LEVs) that significantly increase the lift in slow-flying bats. In general, bats have the distinct aerodynamic performance associated with unique flow structures [14,18,26–28].
In contrast to insects and birds, bats have more than 10 joints on a wing to actively control the complex wing morphology and kinematics. The dynamically changing wingspan is one of the important kinematical aspects in bat flapping flight especially at low speeds. For example, the minimum wingspan of a slow-flying Pallas' long-tongued bat can be as low as about 60% of the maximum one . It is well known that the wingspan (or wing aspect ratio) has a significant effect on the aerodynamic force of a fixed wing by changing the distance between the tip vortices and the induced downwash velocity . In flapping flight where the LEV contributes considerably to lift, it is reported that the finite wingspan could be helpful to stabilize the LEV [30–32]. However, fixed-span flapping wings are considered in most studies on the effects of the aspect ratio, and the effect of the dynamically changing wingspan on lift generation is rarely discussed.
This work focuses on the effect of the dynamically changing wingspan on lift generation of a slow-flying bat. It is noted that the dynamically changing wingspan of bat wings changes not only the wing aspect ratio but also the wing area, which is significantly different from insect wings. This paper is organized as follows. First, the geometrical and kinematical model of a slow-flying bat is reconstructed based on the measurement data provided by Wolf et al. , and the corresponding bat model with a fixed wingspan is proposed as a reference for comparison. The numerical method and settings are briefly described. Then, the unsteady flow fields for the two models are obtained in direct numerical simulations (DNS) by solving the incompressible Navier–Stokes (NS) equations. The distinct flow structures, particularly the LEVs, are identified and their connection to lift generation is discussed. The results indicate that the dynamically changing wingspan can significantly enhance lift. Furthermore, based on a decomposition of lift into vortex lift and the fluid-acceleration term, it is shown that the elevated vortex lift corresponds to the LEVs intensified by the dynamically changing wingspan. Finally, the conclusions are drawn, indicating that lift enhancement is related to not only the geometrical effect of changing the lifting-surface area but also the nonlinear effect of the altered vortex structures (e.g. the LEVs) by the dynamically changing wingspan.