A computational fluid dynamic (CFD) modelling approach is used to study the unsteady aerodynamics of the flapping wing of a hovering hawkmoth. We use the geometry of a Manduca sexta-based robotic wing to define the shape of a three-dimensional 'virtual' wing model and 'hover' this wing, mimicking accurately the three-dimensional movements of the wing of a hovering hawkmoth. Our CFD analysis has established an overall understanding of the viscous and unsteady flow around the flapping wing and of the time course of instantaneous force production, which reveals that hovering flight is dominated by the unsteady aerodynamics of both the instantaneous dynamics and also the past history of the wing. <P> A coherent leading-edge vortex with axial flow was detected during translational motions of both the up- and downstrokes. The attached leading-edge vortex causes a negative pressure region and, hence, is responsible for enhancing lift production. The axial flow, which is derived from the spanwise pressure gradient, stabilises the vortex and gives it a characteristic spiral conical shape. <P> The leading-edge vortex created during previous translational motion remains attached during the rotational motions of pronation and supination. This vortex, however, is substantially deformed due to coupling between the translational and rotational motions, develops into a complex structure, and is eventually shed before the subsequent translational motion. <P> Estimation of the forces during one complete flapping cycle shows that lift is produced mainly during the downstroke and the latter half of the upstroke, with little force generated during pronation and supination. The stroke plane angle that satisfies the horizontal force balance of hovering is 23.6 degrees , which shows excellent agreement with observed angles of approximately 20-25 degrees . The time-averaged vertical force is 40 % greater than that needed to support the weight of the hawkmoth.
Tadpoles are unusual among vertebrates in having a globose body with a laterally compressed tail abruptly appended to it. Compared with most teleost fishes, tadpoles swim awkwardly, with waves of relatively high amplitude at both the snout and tail tip. In the present study, we analyze tadpole propulsion using a three-dimensional (3D) computational fluid dynamic (CFD) model of undulatory locomotion that simulates viscous and unsteady flow around an oscillating body of arbitrary 3D geometry. We first confirm results from a previous two-dimensional (2D) study, which suggested that the characteristic shape of tadpoles was closely matched to their unusual kinematics. Specifically, our 3D results reveal that the shape and kinematics of tadpoles collectively produce a small 'dead water' zone between the head-body and tail during swimming precisely where tadpoles can and do grow hind limbs--without those limbs obstructing flow. We next use our CFD model to show that 3D hydrodynamic effects (cross flows) are largely constrained to a small region along the edge of the tail fin. Although this 3D study confirms most of the results of the 2D study, it shows that propulsive (Froude) efficiency for tadpoles is overall lower than predicted from a 2D analysis. This low efficiency is not, however, a result of the high-amplitude undulations of the tadpole. This was demonstrated by forcing our 'virtual' tadpole to swim with fish-like kinematics, i.e. with lower-amplitude propulsive waves. That particular simulation yielded a much lower Froude efficiency, confirming that the large-amplitude lateral oscillations of the tadpole do, indeed, provide positive thrust. This, we believe, is the first time that the unsteady flow generated by an undulating vertebrate has been realistically modelled in three dimensions. Our study demonstrates the feasibility of using 3D CFD methods to model the locomotion of other undulatory organisms.
The hydrodynamics and undulating propulsion of tadpoles were studied using a newly developed two-dimensional computational fluid dynamics (CFD) modeling method. The mechanism of thrust generation associated with the flow patterns during swimming is discussed. Our CFD analysis shows that the kinematics of tadpoles is specifically matched to their special shape and produces a jet-stream propulsion with high propulsive efficiency, as high as that achieved by teleost fishes. Investigation of the effect of Reynolds number indicates that the Froude efficiency increases with increasing Reynolds number with no ceiling in generating the jet-stream propulsion. Further studies using tadpole- and fish-shaped models with hindlimbs added to their body profiles reveal that the tadpole shape ­ a globose head with a tapered tail and hindlimbs at the base of the tail ­ allows tadpoles, but not fish, to develop hindlimbs with very little handicap on propulsion. The shapes and kinematics of tadpoles appear to be specially adapted to the requirement of these organisms to transform into frogs.