Details of Insect Wing Design and Deformation Enhance Aerodynamic Function and Flight Efficiency

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Science  18 Sep 2009:
Vol. 325, Issue 5947, pp. 1549-1552
DOI: 10.1126/science.1175928


Insect wings are complex structures that deform dramatically in flight. We analyzed the aerodynamic consequences of wing deformation in locusts using a three-dimensional computational fluid dynamics simulation based on detailed wing kinematics. We validated the simulation against smoke visualizations and digital particle image velocimetry on real locusts. We then used the validated model to explore the effects of wing topography and deformation, first by removing camber while keeping the same time-varying twist distribution, and second by removing camber and spanwise twist. The full-fidelity model achieved greater power economy than the uncambered model, which performed better than the untwisted model, showing that the details of insect wing topography and deformation are important aerodynamically. Such details are likely to be important in engineering applications of flapping flight.

Insects achieve remarkable flight performance with a diverse range of complex wing designs (1, 2). Computational fluid dynamics (CFD) offers an opportunity to identify the features underpinning the aerodynamic performance of insect wings. By comparing numerical simulations of different designs, it is possible to test the effects of modifications that may be outside the natural range of variation. Unfortunately, a lack of detailed measurements of insect wing kinematics has limited previous numerical studies of insect flight to two-dimensional (2D) models (36) or to 3D models in which the wings are modeled as rigid flat plates (711) or as rigid sections with constant camber and twist (12). Such simplifications can dramatically change the conclusions drawn about flow structure (13), and no model has yet been validated experimentally against flow visualizations from a real insect. We used the most detailed set of insect wing kinematics published to date (2) to develop the first 3D CFD model of an insect with deforming wings. We validated the results of our CFD simulations against qualitative and quantitative flow visualizations of real locusts. We then used progressive simplifications of the wing kinematics to analyze the aerodynamic consequences of the measured twist and camber.

We modeled a typical wingbeat of the desert locust Schistocerca gregaria (14) by averaging the kinematics of four consecutive wingbeats from one of the individuals described in (2). These kinematics were obtained by using four high-speed digital video cameras to track more than 100 natural features and marked points on the wings, which were then used to reconstruct the deforming surface topography of the wings with a mean spatial error of 0.11 mm (15). We fitted cubic splines to the wing outline and veins, and we interpolated these spatially to give the surface mesh for the CFD simulations, which we then interpolated temporally to give up to 800 time steps per wingbeat (14). We gave the modeled wings a nominal constant thickness of 0.05 mm based on published cross-sections of the wing veins and membrane (16). We did not attempt to model variations in thickness due to wing venation. Folding of the hindwing against the thorax could not be modeled exactly, and we instead modeled the hindwing as if it were joined to the thorax along its chord (14).

We solved the unsteady incompressible Navier-Stokes equations assuming laminar flow using a commercial CFD package (14). We constructed the CFD grid for the locust kinematics in multiple parts by using commercial software, and we incorporated the wing motions via a look-up table prescribing the kinematics (14). The wings and body were meshed with a triangular surface grid and surrounded with a thin boundary-layer grid to provide adequate resolution of velocity gradients normal to the surface. These were then surrounded with stationary outer regions representing the wind tunnel, and a deforming inner region in which the wings and boundary layer grids moved. A symmetry plane running through the sagittal plane of the insect was used. Aerodynamic forces on the wings and body were calculated by integrating pressure and viscous shear stress over the surfaces. Starting transients in the calculated aerodynamic forces vanished rapidly within the first wingbeat, with very close agreement between wingbeats thereafter, so we allowed the simulation to run for four repeated wingbeats. Aerodynamic power requirements were calculated by integrating the inner product of the local pressure and viscous forces with the local wing surface velocity in a coordinate system fixed to the insect’s body.

We validated our CFD method against an independent CFD algorithm (17) by using our method to replicate published force computations for a simple model of a flapping dragonfly wing in hover (11, 14). The predicted instantaneous vertical force coefficients from the two algorithms were in excellent agreement, with a linear correlation coefficient of 0.99 over the course of the wingbeat. To verify the grid-independence of the CFD simulations, we performed computations with several levels of grid and time-step refinement of the locust kinematics data (14). The baseline grid consisted of 1.12 × 106 volume cells and used 200 time steps per wingbeat. We compared our baseline results with a refined grid consisting of 4.11 × 106 volume cells (14) and with the baseline grid using 400 or 800 time steps per wingbeat. We found no significant variation in force and power results as the grid was refined or the number of time steps was increased, and we therefore used the baseline grid with 200 time steps per wingbeat for the remainder of our simulations.

We also validated the results of the CFD simulation against flow visualization data from real locusts by comparing the predicted flow structures with qualitative smoke visualizations and quantitative digital particle image velocimetry (DPIV) measurements at the same position mid-wing (14, 18). The CFD simulation captures the overall structure of the flow field with remarkably high fidelity throughout the wingbeat (Fig. 1). The CFD also shows a reasonably close quantitative fit to the DPIV data, although because each of the three different techniques was applied to a different individual, we do not expect to see an exact match. The main difference between the results of the three techniques is in the presence of smaller-scale flow features in the DPIV and smoke visualizations. In particular, the roll-up of the shear layer trailing the wing is not particularly well matched by the CFD: The shear layer is present in the simulation, but the grid is apparently not fine enough to capture the detail of wake instabilities behind the trailing edge. Further DPIV flow visualizations showing the consistency of the measured flowfield between different wingbeats are shown in fig. S4.

Fig. 1

Validation of CFD simulation using full-fidelity wing kinematics (left column: 3.3 m/s free stream, 9° body angle), against DPIV measurements (middle column: 3.5 m/s free stream, 7° body angle) and smoke visualizations (right column: 3.3 m/s free stream, 9° body angle). Data are shown at four consecutive stages (A to D) of the wingbeat, beginning with the start of the downstroke, for the vertical plane that intercepts the hindwing at the mid-wing position when the wing is horizontal. The CFD and DPIV figures plot flow velocity vectors in a body-fixed reference frame and are colored according to the vertical downwash speed. For clarity, only every fifth vector is plotted in the DPIV figures. Further replicates of the DPIV data are available in fig. S4. Overall, the numerical simulation captures the empirical structure of the flow field with remarkably high fidelity. Figure S5 shows the equivalent CFD simulations for the two simplified wing kinematics models, which do not capture the empirical structure of the flow field with such fidelity.

DPIV also offers the opportunity for a detailed quantitative validation of the computed flow field. We compared a published downwash distribution measured using DPIV (18) with the results of our CFD model at the same stage mid-downstroke (Fig. 2). The CFD model closely captures the shape and magnitude of the measured downwash distribution at the position shown, which is approximately one chord length behind the hindwings. Once again, we do not expect an exact match, because the DPIV measurements (18) were made on an individual different from the one on which the kinematics measurements that we used for the CFD simulation were made (2).

Fig. 2

Computed downwash distribution (solid line) from the CFD simulation using full-fidelity wing kinematics, validated against published DPIV measurements (crosses) of the downwash (18). The measurements are made approximately one mean chord length behind the trailing edge of the hindwing. The data represent the stage mid-downstroke shown in Fig. 1B, and the three different data points at each spanwise station represent measurements made on different wingbeats from one individual. The simulation accurately captures the measured turning points in the downwash distribution at about one-third and two-thirds of wing length and also the crossing to upwash near the wingtip.

To investigate the effect of detailed wing shape and kinematics, we reran the CFD simulation with two progressively simplified sets of wing kinematics (Fig. 3). In the first simplified model, termed “uncambered,” we removed the corrugation and camber of the wings while retaining the same local instantaneous twist and angle of attack along the wing. We did this by replacing the cambered chord with a straight line connecting the leading and trailing edge (rear wing) or a straight line at the same mean incidence (forewing). In this simplified model, the wings undergo the same torsional deformation along the span as the real wing does.

Fig. 3

Computed surface pressure maps from the CFD simulations using full-fidelity kinematics (A), uncambered kinematics (B), and untwisted kinematics (C). The same four consecutive stages of the wingbeat are shown as in Fig. 1, beginning with the start of the downstroke. There is an extensive area of low pressure over the hindwing in the untwisted model, indicative of leading-edge separation. A more limited separation is visible near the root of the hindwing in the uncambered model. There is no clear evidence of separation with the full-fidelity kinematics. The plots at the bottom of the figure show the corresponding 2D flow fields for the stage of the downstroke when the hindwing is horizontal, for the same vertical plane as in Fig. 1. The variation in flow separation between the three kinematics models is demonstrated in these images by the reversed flow over the top surface of the uncambered and untwisted wings, even though the hindwing angle of attack is identical in all three simulations in these sections. The reduction in the extent of flow separation between the uncambered and untwisted wing must be due to wing twist and associated 3D flow effects. The lack of reversed flows with the full-fidelity kinematics is presumably due to the curvature of the wing section and the reduced local angle of attack at the leading edge. Figure S5 shows the effects on the computed 2D flow field through the wingbeat.

In the second simplified model, termed “untwisted,” we also removed torsional deformation along the span, by replacing the forewing with a flat plate of the same instantaneous projected area and same instantaneous angle of attack at the mid-wing position. The hindwing was replaced with two flat plates of the same total instantaneous projected area, joined along a line running from the axilla to a point midway between the fourth and fifth anal veins at the trailing edge. This allowed us to match the mid-wing angle of attack while avoiding unrealistic motions at the wing root. In this simplified model, the wings undergo the same wholesale rotation about their base as the real wing does, but the modeled wings undergo no torsional deformation.

Both simplified kinematics models preserve the gross changes in projected and wetted wing area that result from corrugation and folding of the hindwing (2). The wetted area of the hindwing in the full-fidelity model varies by as much as 14%, which reflects folding of the wing against the thorax. The wetted area of the hindwing in the untwisted model varies by as much as 19%, and the 5% difference here reflects the fact that the untwisted wing does not corrugate, because it is modeled as a flat plate.

The computed surface pressure field for the full-fidelity model shows no evidence of leading-edge separation, with the locally varying camber ensuring that the leading edge is well aligned with the oncoming flow at all times (Fig. 3A). In contrast, the untwisted kinematic model shows massive separation on the hindwing mid-downstroke, when the downward velocity of the wing is maximal, as evidenced by a low-pressure region extending over much of the wing’s upper surface at this time (Fig. 3C). The uncambered model also shows evidence of separation, but with the low-pressure region confined to the basal part of the hindwing (Fig. 3B). The 2D flow fields plotted in the bottom row of Fig. 3 confirm that flow separation is present in the two simplified models. Flow reversal is clearly visible over the hindwing for both the uncambered (Fig. 3B) and untwisted (Fig. 3C) models, but there is no evidence of flow reversal with the full-fidelity kinematics (Fig. 3A). This difference is present despite the hindwing angle of attack being identical among simulations in the 2D plane shown in Fig. 3, and it must therefore result from a combination of 3D effects and camber.

We compared the computed aerodynamic forces and aerodynamic power requirement for the full-fidelity, uncambered, and untwisted kinematics models (Fig. 4). The aerodynamic force is resolved into a lift component normal to the free stream and a thrust component parallel to it. The uncambered wings generate less lift and thrust during the downstroke than the full-fidelity wings do, because of the absence of the positive camber present on the real wings. The uncambered wings generate a similar amount of lift to the full-fidelity wings through most of the upstroke, however, which is presumably because the real wings flatten and feather on the upstroke and are therefore better approximated by the uncambered model. The same features are reflected in the aerodynamic power requirement, with the uncambered wings requiring slightly less power than the full-fidelity wings on the downstroke but needing similar aerodynamic power on the upstroke. The pattern is more complicated for the untwisted wings, which nevertheless produce less lift and thrust than the full-fidelity model does and require greater aerodynamic power to do so.

The aerodynamic advantages of the full-fidelity wing kinematics are clearly revealed by comparing the total power economy of the different models, defined as the ratio of time-averaged total force to time-averaged total power. The total power economies in the uncambered (0.98 N W−1) and untwisted (0.84 N W−1) models are 7% and 15% lower, respectively, than the total power economy of the full-fidelity model (1.06 N W−1). This lower efficiency of momentum transfer is attributable partly to the leading-edge separation that occurs on the hindwings in the simplified models. In addition, the simplified wing kinematics cause the resultant force to have a less favorable direction, as can be seen from the large decrements in lift and thrust in Fig. 4. This results in an even greater reduction in lift power economy, defined as the ratio of time-averaged lift to time-averaged total power: The lift power economy of the uncambered wings (0.78 N W−1) is 12% lower than that of the full-fidelity model (0.88 N W−1), whereas the lift power economy of the untwisted wings (0.51 N W−1) is 35% lower. In summary, wing deformation in locusts is important both in enhancing the efficiency of momentum transfer to the wake and in directing the aerodynamic force vector appropriately for flight.

Fig. 4

Instantaneous lift-generated, thrust-generated, and aerodynamic power required in the CFD simulations using full-fidelity kinematics (A), uncambered kinematics (B), and untwisted kinematics (C). Solid and dashed lines denote the lift or power components for the hindwing and forewing, respectively. The wingbeat shown begins at the start of the hindwing downstroke and ends at the point denoted by the vertical line. For the lift and thrust plots, the shading shows the decrement (red) or increment (green) in instantaneous force for the simplified kinematics as compared to the full-fidelity model. For the power plots, the shading shows the equivalent increment (red) or decrement (green) in instantaneous power required.

The high-lift aerodynamics of insect flight are typically associated with massive flow separation and large leading-edge vortices (1921). However, when high lift is not required, attached-flow aerodynamics can offer greater efficiency. The aerodynamic power efficiency of locusts appears to derive from their ability to reduce flow separation and the associated loss of energy as vortical motion in the wake. Simple heaving or flapping flat plates can generate high lift with stable leading-edge vortices (21, 22), but designing robust lightweight wings that can also support efficient attached flow aerodynamics is likely to be much more difficult. Our results show that the secret to doing so lies in building a wing that undergoes appropriate aeroelastic deformation through the course of the wingbeat. We have shown previously that the shape and structure of a locust’s hindwing are tuned so that it twists appropriately to maintain a constant angle of attack across the wing during the downstroke (2). Our CFD simulations demonstrate furthermore that time-varying wing twist and camber are essential to the maintenance of attached flow. Implementing such tailored deformations in an engineered system is a difficult problem and may demand an evolutionarily optimized solution in order even to approach the elegance of an insect.

Supporting Online Material

Materials and Methods

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Figs. S1 to S5


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References and Notes

  1. Materials and methods are available as supporting material on Science Online.
  2. The research leading to these results has received funding from the Engineering and Physical Sciences Research Council (EPSRC) under grant GR/S23049/01 to A.L.R.T. and from the European Research Council (ERC) under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 204513 to G.K.T. J.Y. was supported by the Merit Allocation Scheme on the National Facility of the Australian National Computing Infrastructure (NCI-NF) and gratefully acknowledges the Rector of the University of New South Wales at the Australian Defense Force Academy for the award of a sabbatical scholarship to perform this work. R.J.B. holds an EPSRC Career Acceleration Fellowship. G.K.T. is a Research Councils UK Academic Fellow and Royal Society University Research Fellow. We gratefully acknowledge the EPSRC Instrument Loan Pool and thank N. J. Lawson for advice and the loan of equipment for the DPIV measurements.
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