**3. High-fidelity analysis of flapping flight aerodynamics**

In previous sections, we presented the data acquisition methods developed to obtain the most realistic reconstruction from high-speed videos. The output is a high-fidelity 3D model with the wing and body motions encoded therein. In the following discussion, the motion and deformation metrics are not isolated to study their effect on flight performance; rather, the deformations are intrinsic and influence aerodynamic footprint of the insect. Naturally, the next step is to simulate the flapping locomotion and identify the associated wake structures. We use computational fluid dynamics (CFD) simulation to understand the relevant flow features of different insects in free flight.

#### **3.1. Dragonfly in takeoff turning flight**

**2.3. Numerical method**

and body template models [49].

8 Flight Physics - Models, Techniques and Technologies

Stokes equations, as written in the following equations.

<sup>∂</sup>*<sup>t</sup>* <sup>+</sup>

<sup>∂</sup> (*ui uj*) \_\_\_\_\_\_\_\_\_\_\_ ∂ *xj*

<sup>∂</sup> *<sup>u</sup>* \_\_\_\_\_\_\_\_*<sup>i</sup>*

the pressure, and *Re* is the Reynolds number.

<sup>∂</sup> *<sup>u</sup>* \_\_\_\_\_\_\_\_*<sup>i</sup>*

where *ui*

To study the aerodynamics of free-flight insects, the flow fields were generated by direct numerical simulations of the three-dimensional unsteady, viscous incompressible Navier-

**Figure 5.** Initial configuration of a dragonfly template mesh. (a) Dragonfly with marker points on its wings. (b) Wing

∂ *xi*

= − ∂ *p* \_\_\_\_\_\_\_\_ ∂ *xi* + \_\_\_1 *Re* \_\_\_∂ ∂ *xj*( ∂ *u* \_\_\_*<sup>i</sup>*

The above Navier-Strokes equations are discretized using a cell-centered, collocated (nonstaggered) arrangement, where the velocity components and pressure are located at the same physical location. The equations are then solved by using the fractional step method. The discretization of the convective terms and diffusion terms are achieved by using an Adams-Bashforth scheme and an implicit Crank-Nicolson scheme, respectively. The immersed boundary method is a computational method used to simulate fluid flow over bodies which are embedded within a Cartesian grid. It eliminates the need for the complicated re-meshing

**Figure 6.** Reconstructed wings at a time step where a large amount of twist and camber is present in multiple wings.

(*i* = 1, 2, 3) are the velocity components in the x-, y-, and z-directions, respectively, *p* is

= 0 (1)

<sup>∂</sup> *xj*) (2)

Dragonflies are aerial predators and feed on other flying insects. Unlike most other insects, such as flies, wasps, and cicadas, that have either reduced hindwings or functionally combined forewings and hindwings as a single pair, dragonflies have maintained two pairs of wings throughout their evolution [60]. Their neuromuscular systems allow them to individually change many aspects of wing motion in each single wing, including the angle of attack, stroke amplitude, and wing deviation, which gives them unique flying capabilities of flight control.

**Figure 8.** Snapshots of a dragonfly in takeoff turning flight from the front-view camera (left) and side-view camera (right).

In general, the flapping motion shown in **Figure 8** generates pronounced changes in the angle of attack between each side wings, especially for the forewings. During the downstroke, the magnitude of the angle of attack for the left forewing is 29 ± 3° , whereas the value for the right forewing is 43 ± 5° . During the upstroke, the variations of the angle of attack for the left and right forewings are 73 ± 5° and 49 ± 3° , respectively. The angle of attack of the left and right hindwings at the mid-downstroke is 36 ± 1° and 21 ± 3° , respectively. During the upstroke, the minimum value for the left hindwing is 23 ± 4° and for the right hindwing is 33 ± 4° . For both forewings and hindwings, the asymmetric wing motion results in a relatively large angle of attack on the left-side wings during the downstroke and a small one during the upstroke. This finding implies that compared to the right-side wings, the left-side wings might experience higher drag force during the downstroke and lower thrust force during the upstroke.

**Figure 9** shows the time sequence of the 3D flow field, which is identified by plotting the iso-surface of the Q-criterion [61]. To illustrate the development of the vortical structures, six snapshots from the flapping motion are shown. For each wing, a leading-edge vortex (LEV) is developed and grows stronger, remaining stably attached to the wing during the downstroke. As the wing sweeps, the LEV, the tip vortex (TV), and the shed trailing-edge vortex (TEV) connect and form a vortex loop. Because of the phase relationship between the forewings and hindwings, when the forewings reach the end of their downstroke, the hindwings have already started to move upward. As the hindwings flap upward, distinct fully developed vortex rings are gradually shed into the flow field from the trailing edge of the wings. At the same

**Figure 9.** 3D vortex structures in the flow for a dragonfly in takeoff turning flight. The vortex structure is visualized using the iso-surface of the Q-criterion.

time, the upward-moving hindwings interact with the vortex loop formed by the forewings. This flow feature has been termed forewing-hindwing interaction in previous 2D and 3D tandem-wing studies [38, 62]. In addition to the forewing-hindwing interaction, during the upstroke, the wings catch their own wakes from the preceding downstroke, which disrupts the vortex loop structures through the wing-wake interaction and forms a stronger TV and TEV. During the maneuver, distinct asymmetric vortex formation also occurs between the left and right sides. This asymmetric phenomenon also makes the shed vortex rings tilted and distorted. By interacting with the vortex loops formed by other wings as well as previously shed vortex loops, the wake becomes more complicated. Due to the viscous dissipation effect and wing-wake interactions, only the LEV and TV in the near wake are still distinguishable in the flow field. The key features observed here are the presence of vortex loop structures in the near wake around the wings.

#### **3.2. Butterfly in vertical takeoff**

**Figure 9.** 3D vortex structures in the flow for a dragonfly in takeoff turning flight. The vortex structure is visualized

In general, the flapping motion shown in **Figure 8** generates pronounced changes in the angle of attack between each side wings, especially for the forewings. During the downstroke,

**Figure 8.** Snapshots of a dragonfly in takeoff turning flight from the front-view camera (left) and side-view camera

and 21 ± 3°

forewings and hindwings, the asymmetric wing motion results in a relatively large angle of attack on the left-side wings during the downstroke and a small one during the upstroke. This finding implies that compared to the right-side wings, the left-side wings might experience

**Figure 9** shows the time sequence of the 3D flow field, which is identified by plotting the iso-surface of the Q-criterion [61]. To illustrate the development of the vortical structures, six snapshots from the flapping motion are shown. For each wing, a leading-edge vortex (LEV) is developed and grows stronger, remaining stably attached to the wing during the downstroke. As the wing sweeps, the LEV, the tip vortex (TV), and the shed trailing-edge vortex (TEV) connect and form a vortex loop. Because of the phase relationship between the forewings and hindwings, when the forewings reach the end of their downstroke, the hindwings have already started to move upward. As the hindwings flap upward, distinct fully developed vortex rings are gradually shed into the flow field from the trailing edge of the wings. At the same

higher drag force during the downstroke and lower thrust force during the upstroke.

. During the upstroke, the variations of the angle of attack for the left

, respectively. The angle of attack of the left and right

and for the right hindwing is 33 ± 4°

, respectively. During the upstroke, the

, whereas the value for the

. For both

the magnitude of the angle of attack for the left forewing is 29 ± 3°

and 49 ± 3°

using the iso-surface of the Q-criterion.

right forewing is 43 ± 5°

(right).

and right forewings are 73 ± 5°

hindwings at the mid-downstroke is 36 ± 1°

10 Flight Physics - Models, Techniques and Technologies

minimum value for the left hindwing is 23 ± 4°

The flapping motion of a monarch butterfly (*Danaus plexippus*) in vertical takeoff flight is present in **Figure 10**. The butterfly's body and wing were then reconstructed with extraordinary details. Direct numerical simulation was then carried out in order to understand the vortex formation during the takeoff motion.

The vortex structures of the flow field are shown in **Figure 11**. Several thin swirling vortices start from each wing tip as the wings flap downward. The thin swirling vortices twist immediately after the separation from each wing tip and form a tip vortex (TV) during the downstroke. As the butterfly left upward, the thin vortices are merged by the viscosity into a coherent vortex under the insect body. The TV during downstroke generates lift as the reaction of inducing the downward flow. Wingtip vortices during upstroke are also made by the vorticities of the wings aligned close to the negative and positive vertical directions. Trailingedge vortices released at the transitions from downstroke to upstrokes are barely visible in the wake of butterfly flapping motion.

**Figure 10.** Snapshots of a butterfly in takeoff flight from the front-view camera (left) and side-view camera (right).

**Figure 11.** 3D vortex structures in the flow for a butterfly in takeoff flight. The vortex structure is visualized using the iso-surface of the Q-criterion.

#### **3.3. Damselfly in yaw turn**

Here, a damselfly (*Calopteryx maculata*) is involved in performing a yaw turn maneuver during which it also ascends for about three body lengths (**Figure 12**). To perform a turning maneuver, the wings must generate aerodynamic forces to sustain body weight while simultaneously producing turning moments to rotate the body around its center of mass (CoM) while remaining almost-stationary or moving forward. During a yaw turn, the horizontal component of the aerodynamic force is oriented toward the center of curvature. This force reorientation produces lateral forces for rotation around the center of mass. In addition, an asymmetry in wing kinematics between the wings on the outside of the turn (left wings) and right wings on the inside of the turn is necessary to create a yaw torque differential. Insights into how the damselfly flight forces can be gleaned from the flow field data. To generate forces for flight, the damselfly used an unsteady mechanism such as a leading-edge vortex on its wings which feeds into a tip vortex (**Figure 13**). Although the wake structure is quite complex, an asymmetric flow structure with a stronger flow field oriented toward the right wing is observed, which indicates that the inner wings may be playing a substantial role in executing the turn by creating large force/yaw torque differences between the contralateral wing pairs.

**Figure 12.** Snapshots of a damselfly in yaw turn from the top-view camera (left) and side-view camera (right).

Learning from Nature: Unsteady Flow Physics in Bioinspired Flapping Flight http://dx.doi.org/10.5772/intechopen.73091 13

**Figure 13.** 3D vortex structures in the flow for a damselfly in yaw turn. The vortex structure is visualized using the isosurface of the Q-criterion.

#### **3.4. Cicada in turning maneuver**

**3.3. Damselfly in yaw turn**

12 Flight Physics - Models, Techniques and Technologies

iso-surface of the Q-criterion.

wing pairs.

Here, a damselfly (*Calopteryx maculata*) is involved in performing a yaw turn maneuver during which it also ascends for about three body lengths (**Figure 12**). To perform a turning maneuver, the wings must generate aerodynamic forces to sustain body weight while simultaneously producing turning moments to rotate the body around its center of mass (CoM) while remaining almost-stationary or moving forward. During a yaw turn, the horizontal component of the aerodynamic force is oriented toward the center of curvature. This force reorientation produces lateral forces for rotation around the center of mass. In addition, an asymmetry in wing kinematics between the wings on the outside of the turn (left wings) and right wings on the inside of the turn is necessary to create a yaw torque differential. Insights into how the damselfly flight forces can be gleaned from the flow field data. To generate forces for flight, the damselfly used an unsteady mechanism such as a leading-edge vortex on its wings which feeds into a tip vortex (**Figure 13**). Although the wake structure is quite complex, an asymmetric flow structure with a stronger flow field oriented toward the right wing is observed, which indicates that the inner wings may be playing a substantial role in executing the turn by creating large force/yaw torque differences between the contralateral

**Figure 11.** 3D vortex structures in the flow for a butterfly in takeoff flight. The vortex structure is visualized using the

**Figure 12.** Snapshots of a damselfly in yaw turn from the top-view camera (left) and side-view camera (right).

Here, the flight of a cicada which initiates flight and immediately executes a banked turn is recorded. Unlike the yaw turn scenario of the damselfly where the wings do the majority of the force reorientation, and the roll motion of the body is minimal, banked turns are distinct but more commonly found in nature. During banked turns, the animal reorients the total aerodynamic force vector toward the center of the turn by simply rotating the body around its longitudinal axis. This is evident in **Figure 14** wherein the cicada rolls its body by about 90° to reorient the force vector into the center of curvature like an airplane. During this flight, the cicada still utilizes unsteady mechanism such as a LEV (**Figure 15**) to help maintain a strong enough component to sustain weight. The asymmetry in flow features on the left and right sides indicates a force difference necessary to induce a roll torque for the turn.

**Figure 14.** Snapshots of a cicada in takeoff turning flight from the front-view camera (left) and side-view camera (right).

**Figure 15.** 3D vortex structures in the flow for a cicada in takeoff turning flight. The vortex structure is visualized using the iso-surface of the Q-criterion.
