Aerodynamics and flow features of a damselfly in takeoff flight

Damselflies (Hetaerina Americana) were caught outside during the summer of 2012 in Dayton, Ohio for experiments. Prior to the experiments, the caught damselflies' wings were dotted for tracking purposes (figure 1). The video footages were then recorded shortly after their capture in a quiescent environment of about room temperature (70 °F) in order to prevent inactivity during the time of experiments.

Zoom In Zoom Out Reset image size

The damselflies initiated flight autonomously in the shooting area. Their flight triggered a photogrammetry setup consisting of three orthogonally arranged and synchronized cameras shooting at 1000 frames per second (fps). After recording the flight, the wings were removed and morphological parameters were measured (see table 1). We selected one of the recorded footages for analysis. In this recording, the damselfly initiated flight from a pitch down body orientation and flew upward and forward thereafter. The dotted wings of the insect were tracked manually frame by frame in Autodesk Maya (Autodesk Inc.). Figure 1(b) shows a visual representation of the reconstructed insect placed on top of an image. Our surface reconstruction technique (shown in figure 1(c)) allows us to record and measure small deformations in the wing during flight (see section 2.2). We are capable of measuring wing twist and camber during flight. The accuracy of this reconstruction technique is discussed extensively in Koehler et al's work [33] and has been applied in the study of damselflies, dragonflies and cicadas [13, 34–37].

The wing kinematics and deformations were measured by defining a least-square reference plane (LSRP) generated based on the points on the reconstructed wing surface. The LSRP is the plane of least wing deformation. For details of how the LSRP was calculated, see the work of Koehler et al [33]. A mean stroke plane was also defined based on the average trajectory wing tip per stroke. The orientation of the wing in the stroke plane is described by three Euler angles; flap, deviation and pitch. Flapping motion is the revolution of the wing in a back and forth manner and is positive during the downstroke. The up and down rotations with respect to the stroke plane is expressed by the deviation angle as is positive when the wing is above the stroke plane. The wing pitch angle is characterized by the rotation of the wing about its pitching axis close to the leading edge. The pitch angle is measured clockwise from the intersection between the LSRP and the line defining the stroke plane hence varies between 0° and 180°. The geometric angle of attack (AoA_geom or $\alpha$), is defined as the angle between the normal to LSRP and the normal to the stroke plane and is equivalent to the wing pitch. The effective angle of attack (AoA_eff or ${{\alpha}_{\text{eff}}}$), is the angle between the wing and the incident flow upon it. For wing deformation metrics, the local twist angle is reported. The twist angle is the relative angle of the deformed wing chord line with a rigid plane of reference defined as the LSRP. Since the surface of the wing is deformed and twisted, the local angle of the chord line with LSRP varies along the wing span. Thus, we use the term 'local twist angle' to emphasize that the orientation of the wing surface relative to the rigid plane of reference is not constant and varies along the span. Visual representations of these definitions are rendered in figure 2.

Zoom In Zoom Out Reset image size

To elucidate the flow field around the damselfly in flight, we obtained the flow information from computational simulations. A high fidelity CFD solver based on the immersed boundary method was used in this study. We solved the incompressible viscous Navier–Stokes equation (equation (1)) using a finite difference method with 2nd order accuracy in space and a 2nd order fractional step methods for progressing in time. More details of this method and its application in studies on dragonflies and cicadas can be found in [33, 35, 38].

$$\begin{eqnarray}&&\nabla \centerdot \mathbf{u} ~\text{=} ~\text{0;}\,\,\,\,\frac{\partial \mathbf{u}}{\partial t}+\mathbf{u}\centerdot \nabla \mathbf{u}=-\frac{1}{\rho}\nabla p+\upsilon {{\nabla}^{2}}\mathbf{u}\,.\end{eqnarray} \tag{ 1 }$$

Here u is the velocity vector, $\rho$ is the density, $\upsilon$ is the kinematic viscosity and $p$ is the pressure.

The vortex structures were characterized by the Q-criterion [39] shown below.

$$\begin{eqnarray}&&Q=\frac{1}{2}\left[|\boldsymbol{\Omega }{{|}^{2}}-|\mathbf{S}{{|}^{2}}\right]>0.\end{eqnarray} \tag{ 2 }$$

Here $\mathbf{S} ~\text{=} ~ \frac{1}{2}\left[\nabla \mathbf{u}+{{\left(\nabla \mathbf{u}\right)}^{\text{T}}}\right]$ and $\boldsymbol{\Omega } ~\text{=} ~ \frac{1}{2}\left[\nabla \mathbf{u}-{{\left(\nabla \mathbf{u}\right)}^{\text{T}}}\right]$ are the strain rate and vorticity tensors respectively. More details on the flow visualization techniques are shown in Koehler et a's work [40].

The simulation was run on a non-uniform Cartesian grid. The computational domain size was about 50$\bar{c}$  ×  50$\bar{c}$  ×  50 $\bar{c}$ with about 13.8 million grid points in total. The high resolution uniform grids surround the insect in a volume of 14.5$\bar{c}$  ×  12$\bar{c}$  ×  13.5$\bar{c}$ with a spacing of about 0.06$\bar{c}$. This ensured sufficient resolution for capturing the 3D flow field. The stretching grids move in all three directions from the fine region to the outermost boundaries. The boundary conditions of the domain on all sides are zero gradient.

The Reynolds number for the flight is defined by $\operatorname{Re}=\frac{{{{\bar{U}}}_{\text{tip}}}\bar{c}}{\upsilon}$ and is 1220. It is measured based on the average wing tip speed (${{\bar{U}}_{\text{tip}}}=3.05\,\,\text{m}\,\,{{\text{s}}^{-\text{1}}}$), mid-chord length ($\bar{c}=0.006\,\,\text{m}$), kinematic viscosity of air at room temperature ($\upsilon =1.5\times {{10}^{-5}}\,\,{{\text{m}}^{2}}\,{{\text{s}}^{-1}}$). Validation for the flow solver can be found in recent works by Wan et al [38] and Li and Dong [36].

The current grid set-up was selected based on checks to ensure the grids are refined to preclude grid dependence of the simulation. Figure 3(b) shows the comparison of the lift coefficient history of the second flapping stroke in three grids (coarse, medium and fine). The difference of both the mean value and the peak value of lift between the medium-grid case (adopted in this paper) and the fine-grid case is about 2%, thereby, establishing that the aerodynamic force calculations in the current study were grid-independent.

Zoom In Zoom Out Reset image size

3.1.1. Body kinematics

To evaluate flight behavior during and after flight initiation, we studied the kinematics based on the reconstruction output. Figure 4(a), shows the body motion of the damselfly during the takeoff stage of flight. After being stationary for some time, the wings begin to slowly peel off during the preparatory stages before initiating takeoff. The preparatory stage lasted for 30 ms. During the preparatory stage, the insect adjusted both the stroke plane of the wings relative to the body and the pitch angle of the body. At the start of the takeoff, the body was at a pitch down orientation (about  −50°). Liftoff, defined as the time duration within which the legs of the insect leave the platform, starts with the wings moving downward in a steep stroke plane. The whole takeoff encompasses the up and downstroke of the wing during the first flapping stroke. Our observation suggests that legs do not play a significant role in pushing the body up. It takes less than a wingbeat for the insect to get airborne. This is a relatively short time among the insects which do not jump to initiate flight [8]. The peak vertical acceleration measured based on the center of mass motion during liftoff was about 3 g. The value was less than the vertical acceleration for fruit fly takeoff (6 g) [4] and butterfly takeoff (10 g) [24].

Zoom In Zoom Out Reset image size

The total takeoff duration is about 45 ms and the direction of motion is up and forward while the damselfly also turns slightly. Nevertheless, the translational displacement is significantly higher than the rotational displacement. The focus of our work is on the translational displacement. The mean body Euler angles during the first wing beat are  −5.5°, 46.6°, 8.4° and the maximum rotational velocities during the first wing beat 500° s⁻¹ and 200° s⁻¹ for roll, pitch and yaw respectively. The takeoff is slow and stable and no tumbling was observed [8]. The body was kept straight and no body deformations were obvious. We include two subsequent flapping strokes in our analysis to document latter events during flight. During the latter strokes, the damselfly ascends, travels further and attains a more horizontal posture as flight speed increases (figure 4(c)).

3.1.2. Wing kinematics and deformations

The average kinematics of the left and right wing measured in the stroke plane are shown in figure 4(b). The gray shading denotes the downstroke of the forewings. From the onset of flight, the motion of the fore and hind pairs of wings are offset by a slight phase difference that increases over time. The forewings (FW) lead the hind wings (HW) by about 26° in the initial stroke (takeoff stroke) and about 37° in the latter strokes (2nd and 3rd strokes) as shown in figure 4(b).

Averaged across the three flapping strokes, the wings sweep through a stroke plane that maintains an orientation of about 18.6  ±  5.3° for the forewings and 21.6  ±  6.1° for the hindwings, measured clockwise with respect to the longitudinal axis of the body. We will refer to this as the geometric stroke plane angle (${{\beta}_{\text{b}}}$). ${{\beta}_{\text{b}}}$ is measured based on the trajectory of the wing tips. Wing kinematics including the geometric stroke plane vary from one stroke to the next, which indicates constant adjustment of the wing kinematics by the insect [11]. In the global orientation, due to steep body angle, the stroke plane with respect to the horizon (${{\beta}_{\text{h}}}$) is heavily influenced. The fore and hind wings flap at a stroke plane angle of 49.8  ±  21.1° and 52.8  ±  21.4°, relative to the horizon, respectively, with the highest stroke plane inclination occurring in the takeoff stroke. At this instant, the stroke plane is titled steeply downwards while a less tilted stroke plane is utilized as the body becomes more horizontal in subsequent strokes. During the takeoff, ${{\beta}_{\text{h}}}$ are very similar both in up and downstroke with variations of a couple of degrees (1° for FW and 7° for HW), whereas the difference in other strokes is more obvious wherein downstroke stroke planes are more inclined than the upstroke (15° for FW and HW) due to a faster rate of change of body posture compared to ${{\beta}_{\text{b}}}$.

In the first wing beat, the wings flap with the highest stroke amplitude recorded throughout the flight (120° and 140° for FW and HW respectively). At all times, the hindwings flap with a higher stroke amplitude (figure 4(b)). As the wings flap, they are oriented at high pitch angles/AoA_geom. The instantaneous values are shown in figure 4(b). The half-stroke average AoA_geom during the first downstroke is 51° and 65° for the fore and hindwings respectively. Whereas, the half-stroke average AoA_geom is 71° and 81° during the upstroke fore and hindwings respectively. During takeoff, it is evident that the hindwings flap at higher pitch both in the upstroke and downstroke. Though, in subsequent strokes, the forewings flap with higher pitch during the downstrokes (figure 4(b)). In latter upstrokes, the average pitch of the fore and hindwings are similar even though the hindwings still flap with greater stroke amplitude. The upstroke AoA_geom in the takeoff stroke is about 20° higher than the downstroke. Comparing the initial upstroke with latter upstrokes, the average upstroke AoA_geom is about 30–35° greater. On the contrary, the stroke average downstroke AoA_geom only varies by at most 13°. At reversal, the wings rotate and experience the highest AoA. During this period, the wings may generate instantaneous AoA_geom in excess of 90°.

The wings of damselflies are flexible, deforming and twisting as they flap through the air. The effective angle of attack (${{\alpha}_{\text{eff}}}$) measured at 0.5R is reported here, although ${{\alpha}_{\text{eff}}}$ is not sigificantly different at 0.7R and 0.9R (see figure 5(b)). The half-stroke average ${{\alpha}_{\text{eff}}}$ during the 1st downstroke is 44° and 45° for the fore and hindwings respectively. In the upstroke, half-stroke average ${{\alpha}_{\text{eff}}}$ and 45° and 51° for the fore and hindwings respectively. During the downstroke, the ${{\alpha}_{\text{eff}}}$ for the pair of wings is very similar, whereas in the upstroke, slight differences are evident with the hindwings having a slightly higher ${{\alpha}_{\text{eff}}}$. Comparing the initial upstroke with latter upstrokes, the average upstroke ${{\alpha}_{\text{eff}}}$ is about 15° and 23° greater for the fore and hindwings respectively. On the contrary, the downstroke ${{\alpha}_{\text{eff}}}$ only varies by at most 6° and 11° for the fore and hindwings respectively. The effective angles of attack during this flight are higher than previously reported values. Sato et al [12] recorded a maximum ${{\alpha}_{\text{eff}}}$ of 15° for majority of the downstroke during forward flight of damselflies.

Zoom In Zoom Out Reset image size

Figure 5(a) shows the local twist along the wing. Three cross sections are chosen for display; 0.5R, 0.7R, 0.9R. Similar to the wing kinematics, the twist profiles of the wings are averaged between the left and right wings. The measured twist angle across the cross-sections is at most 20° and occurs at the cross-sections nearest to the wing tip (0.9R). The maximum twist recorded occurred during the mid-stroke with the forewings deforming more than the hindwings. The upstroke twist are also more significant than the downstroke's. The mid-chord of the wing (0.5R) has minimal twist.

3.2.1. 3D flow structures

Having quantified the wing motions and deformations, here, we present the three-dimensional (3D) flow phenomena based on the CFD simulation to study how the wing motions and corresponding deformations influence the aerodynamic mechanisms responsible for force generation. Figure 6 shows the evolution of the wake structures in the takeoff stroke. The start, mid and end of the downstrokes and upstrokes are shown on the left and right columns respectively. The snapshots are selected based on the timing of the hindwings. This way, we can capture the details of both pairs of wings since the forewings lead by a small phase difference. The left wings are shown, however, the same flow phenomena occur on the right wings. The vortex structures are visualized by plotting the iso-surface of the Q-criterion. Two iso-surface values (Q  =  3% and 6% of maximum Q) are chosen to identify the wake structures. The flow structures evident on both pairs of wings are mainly characterized by tip vortices (TV) and an LEV.

Zoom In Zoom Out Reset image size

At the onset of the downstroke, a starting vortex sheet (SV) sheds from the trailing edge of the wing surface. Simultaneously, an LEV is formed due to wing translation both on the fore and hindwings. The vortex rapidly grows in size and strength as the wing flaps at high AoAs. The LEV remains attached to the wing surface till wing reversal when it is shed and another LEV develops for the first upstroke only, on the anatomical lower surface of the wing which has become the aerodynamic upper surface (figure 6(d)). We do not observe multiple LEVs rather a single LEV across the wing surface. The excess vorticity is concentrated near the tip and sheds into a strong trailing vortex. During the upstroke, an LEV develops immediately after completion of the downstroke in the first stroke only (figures 6(c) and (d)). The LEV actually forms first at the distal part of the wing where the combination of high wing pitch and velocity, consequently leads to high ${{\alpha}_{\text{eff}}}$, and causes flow separation. At about mid-stroke, an LEV covering the wing surface is observed (figure 6(e)). The LEV is similar in size to the first downstroke's LEV (figure 6(b)) at this instant. Therefore, the magnitude of circulation and thus the lift production capacity of the wing surface should be similar. The LEV remains attached to the surface and sheds during rotation.

3.2.1.1. A comparison of first and subsequent strokes

To understand the flow structures observed in the takeoff stroke, we compared the findings to the second flapping stroke. Figure 7 shows selected snapshots of the evolution of the near wake in the first two wing beats. These snapshots are taken at both the fore (top row) and hindwing (bottom row) mid-strokes.

Zoom In Zoom Out Reset image size

The vortex structures on the wing during the downstrokes are similar. A well attached LEV is present on the wing surface and excess vorticity feeds into a TV. The upstroke is quite different, however. In comparison to the first stroke, an LEV is not observed during the translation of the wing in the second upstroke which indicates that the wing does not dynamically stall (figures 7(c) and (d)). However, an LEV appears for a short duration during the wing pronation due to rotation effects where the angle of attack increases rapidly as the wing rotates (figure 7(d)). The appearance of the LEV is for a short duration and cannot compensate for the inability of the wing to generate substantial lift during the translational part of the stroke. Due to the absence of an LEV, no excess vorticity spirals toward the tip. The wing simply translates with attached flows on its surface which is not visible with the Q-criterion. The vortical structures around the hindwings in (figure 7(d)), are the remnants of the shed LEV during the downstroke reversal of the second stroke originating from the anatomical dorsal surface of the wing.

Having identified the vortex structures, the time history of the LEV circulation of the left wings presented in figure 8(c), is calculated at the mid-span of the wings shown in figure 7. The circulation is calculated by measuring the flux of the vorticity. To do so, at every time step of the numerical simulation, a 2D plane normal to the axis of LEV is constructed. A vorticity threshold is set (typical of Eulerian vortex identification methods) to capture the vortex boundaries. The circulation is calculated using equation (3).

$$\begin{eqnarray}&&{{ \Gamma }_{\text{LEV}}}={{\iint }_{S}}\omega \centerdot \text{d}S\end{eqnarray} \tag{ 3 }$$

where $\omega$ is the vorticity. The area of integration (dS) is bound by the vorticity threshold and the circulation is non-dimensionalized by ${{\bar{U}}_{\text{tip}}}$ and $\bar{c}$ (figures 8(a)–(c)). The circulation curves lag behind the wing kinematics a bit due to the delay in vortex formation at the onset of flapping. A discontinuity in the curve exists around wing reversal because of the deterioration of one vortex and the emergence of another on opposite surfaces on the wing. The circulation grows from inception of flapping, attains a maximum around the mid-stroke region and begins to attenuate as reversal approaches. This is an indication of the evolution and strength of the vortex over time. Negative LEV circulation indicates clockwise rotation of vorticity and occurs during the downstroke. The reverse happens in upstroke.

Zoom In Zoom Out Reset image size

The total circulation as well as the fore and hind wing circulation in the 1st downstroke and upstroke are similar with the only difference being the rotational direction of the LEV. In subsequent strokes, another pattern emerges. The DS circulation is much higher than the US circulation. The hindwings, in general, have a higher circulation than the forewings over the course of the flight.

Since our method of calculating vorticity cannot distinguish between a vortex and the underlying shear layer, both on the wing surface and in between the vortices, we can attribute the circulation observed in the 2nd and 3rd US to the shear layer/attached flow or a very tiny and weak LEV in the subsequent upstrokes (see figures 7(c) and (d)).

To probe further into how the flow structures affect the force distribution on the wing surface, the distribution of the pressure difference between the top and bottom surface of the left wings is shown in figure 8(d). We show the pressure distributions at exactly the same snapshot as figure 7. The pressure difference is projected onto a top view image of the wings for clarity. Moreover, the forewing mid-strokes are superimposed on the hindwing mid-strokes. The same range of contours is plotted for the 1st and 2nd stroke only for ease of comparison. The pressure is non-dimensionalized as ${{C}_{p}}=\left(p-{{p}_{\infty}}\right)/0.5\rho \bar{U}_{\text{tip}}^{2}$. The pressure difference distribution indicates what part of the wing produces the greatest velocity difference or circulation. The greatest pressure difference is generated on the distal part of the wing toward the wing tip in both US and DS. At this point, the tip speed is greatest.

When we compare the mid-upstrokes of both the 1st and 2nd strokes, we find drastic differences in the pressure distribution. Figure 8(d), shows the pressure difference contours with the darker shade (dark blue) contours indicating regions of low pressure difference. An observation of figure 8(d) indicates lower pressure difference distribution on the wing during the 2nd upstroke as compared to the 1st. Comparing the flap velocities of the wing in these two phases of flight (see figure 4(b)), we find their velocities to be similar with the 2nd upstroke's slightly higher. The major difference is in the pitch angle and ${{\alpha}_{\text{eff}}}$. In the second stroke, the instantaneous ${{\alpha}_{\text{eff}}}$ is as low as 7° and 11° for the fore and hindwings during translation, which means the flow, did not stall. Conversely, the instantaneous ${{\alpha}_{\text{eff}}}$ is as low as 29° and 46° for the fore and hindwings in the first upstroke, indicating flow separation at the leading edge of the wing. Figure 7, shows the presence of an LEV in the 1st upstroke and its absence in the 2nd upstroke. The presence of an LEV should cause a higher pressure difference between the top and bottom surface of the wing. The 220% boost in the maximum pressure difference measured ($\Delta {{C}_{{{p}_{\max}}}}=1.6$ in 1st upstroke and $\Delta {{C}_{{{p}_{\max}}}}=0.5$ in 2nd upstroke) on the wing surface is attributed to the presence of the LEV which generates a low pressure region on the wing top surface. We also showed the pressure iso-surface around the wing and found that the regions of low pressure correspond to the regions where the leading edge vortex was present (figure 8(e)). Consistent with the conclusion based on the iso-surface of the Q-criterion as well as the pressure difference on the wing surface, we observe no low pressure bubble on the wing surface in the 2nd US.

The damselfly in this study did not use the clap and fling to boost force production. Figure 4(a) shows that at rest (−30 ms) the wings are clasped together. However, before flight, the wings had slowly separated from each other indicating no extra vorticity to help in lift production due to peeling is present. At the end of the 1st upstroke, the wings do not touch. The same was observed in the subsequent strokes. Since takeoff also occurred on a thin platform, ground effect is ignored. Therefore, only the flow structures and pressure distribution on and around the wing influence force generation.

The forces on the damselfly's wings were computed by the integration of the surface pressure and viscous shear stress. The force history is rendered in figures 9(a) and (b). FW and HW indicate the sums of the forces from the left and right forewings and hindwings respectively. For ease of visualization, the average force vectors during each half-stroke are shown in figure 9(c) for both the fore and hindwings. The colors of the force vectors in figure 9(c) correspond to the lines in figure 9(c). The vectors show the relative magnitude and direction of the forces on a half-stroke basis.

Zoom In Zoom Out Reset image size

During the 1st WB, the insect generates substantial forces in the up and down strokes. The downstroke is primarily for weight support. The maximum lift forces occurred around the mid-down stroke region with magnitudes ranging between 2–2.5 mN (3–3.5 times the body weight). It is during the first downstroke peak that the damselfly leaves the takeoff platform (18 ms). In the subsequent strokes, the downstroke lift forces supersede the initial lift forces but generate no lift in the upstroke. However, for thrust production, it appears that both the down and upstrokes are responsible. The maximum thrust generated during the entirety of flight occurs in the first upstroke. The thrust force is as great at the lift generated in the 1st downstroke.

In the takeoff stroke, the fore and hind wings share the burden of force generation evenly. However, in following strokes, it is obvious that the hindwings generate more force than the forewings (figure 9(b)). Overall, the damselfly generates about twice the amount of total force of the 2nd and 3rd WB during the 1st WB indicating that the takeoff stroke was the most energetically demanding for an insect during this flight. The aerodynamic power has the same trend as the resultant force generation and peak power consumption occurs in the first stroke. However, unlike the subsequent strokes, in the initial stroke, the total forces are evenly split for both lift and thrust generation (figure 9(b)). The damselfly only produces half of the total forces as of the 1st stroke in subsequent strokes with the entirety consolidated for force generation in the downstroke. This indicates that the damselfly can actively use its upstroke to generate extra forces in demanding flight conditions such as takeoff.

Lastly, we investigated the role of WWI. In dragonfly flight, it has been previously reported that the FW experience inwash due to the HW and the HW are affected by the downwash from the FW with benefits occurring if the phase relationship between the wings are chosen appropriately [41–45]. Experiments on hovering kinematics have shown that maximum lift for both pairs of wings is generated when the HW lead by a quarter of the cycle (90°) and the distance between the wings is closest [41]. By leading the FW, the hindwing avoids the downwash from the forewings. However, the case may be quite different for damselflies because unlike dragonflies the forewings lead the hindwings (see section 3.1.2) [12]. Experiments using dynamically scaled robots showed that when the forewings lead by a quarter stroke cycle, hindwing lift decreases by 40% [46]. In similar vein, numerical simulations of dragonfly-like wings at different advance ratios and phase differences showed that when the forewings lead the hindwings, the hindwing lift can decrease by 20–60% simply because the HW cannot avoid the FW downwash which alters the HW AoA_eff subsequently reducing the force production capability of the HW [44, 46].

To quantify the effect of WWI, we ran three sets of simulations using the same amount of computational mesh grids; forewings only (FO), hindwings only (HO), and all the wings together (ALL). In the ALL simulation the wings are separated by real spacing between the wings of this species at the wing root which is 0.465$\bar{c}$ (see figure 1). The results for the effect on interaction are shown in table 2 and figure 10.

Zoom In Zoom Out Reset image size

Table 2 summarizes the average force produced by each pair of the wings with and without WWI, during the takeoff stroke. Our simulation results show that WWI is beneficial to the aerodynamic performance of the forewings in DS and US. Whereas, the hindwings benefit from WWI only in US. The effect of WWI on force production of the hindwings is detrimental in DS, which is consistent with results found in a previous numerical investigation [44].

In subsequent strokes, when the insect began to fly forward, the forewing continued to experience increase in both vertical (12% in 2nd DS and 16% in 3rd DS) and horizontal forces (5% in 2nd DS and 15% 3rd DS) due to interaction. This is unlike the results in a previous numerical simulation on the dragonfly wings which reported little variation in the force produced by an isolated forewing and one flapping in the presence of a hindwing [44]. However, the results were sampled at intervals of 45° phase shift. Experimental results at smaller phase shift increments (8°) have shown that when the forewings leads by small phase shifts (0–55°), similar to our numerical simulation phase shift here (26–37°), FW forces can be increased (especially around 28°) [46]. The damselfly's HW also experienced a 2.4% increase in vertical force production and 10.7% increase in thrust in the 2nd DS. In the 3rd DS, both vertical and horizontal forces are attenuated by 3%. However, it is quite obvious that during peak force production, slightly after the mid-strokes, the HW was negatively affected by interaction (figure 10).

To probe how the WWI influences the aerodynamic performance of the wings, we plotted the vorticity contours (figure 11), superimposed by the velocity vector field, for the ALL case as well as the FO and HO cases, at the instants where the maximum force enhancement/reduction was observed during takeoff. Figure 11 compares vorticity and velocity vector fields of the ALL, FO, and HO cases, during DS (a)–(c) and US (d)–(f). The close proximity of the wings, during both DS and US, is beneficial to the aerodynamic performance of the forewings due to the favorable distortion of the forewing's downwash caused by the interaction between the hindwing's LEV and the forewing's trailing edge vortex (TEV). The upward jet (which is downward in US) induced between this vortex pair reduces forewing's downwash. This effect is known as the wall or ground effect [46, 47]. On the other hand, in DS, the hindwing is in the wake of the forewing and is therefore negatively affected by the forewing's downwash. During the upstroke, the relative spacing of the wings and the direction of their motions is in such way that the hindwing is no longer directly in the wake of forewing and therefore the adverse influence of the forewing's downwash is minimal. In addition, the hindwing benefits now from a similar wall effect as the forewing and its performance is enhanced.

Zoom In Zoom Out Reset image size

The vertical forces were not substantial in the upstroke phase but the horizontal forces were. We found that both the FW (8.8% decrease in 2nd US, 40% decrease in 3rd US) and HW (14.6% decrease in 2nd US, 7.3% decrease in 3rd US) horizontal forces were negatively affected by interaction.