Performance of a Proposed Micro-Aerial Vehicle Design

By: David Cooper

University of Alabama at Birmingham

As the name suggests, micro aerial vehicles (MAV) are simply small unmanned flying

machines. No precise definition of MAV based upon size yet exists but they are typically

dimensioned similarly to small birds or even large insects. Some current designs weigh less than

4g and have wing spans around 10cm.

MAV’s are further classified based upon the method they utilize to achieve flight.

Operational designs vary from the more conventional fixed and rotary wing configurations to the

much more complex and less understood flapping wing styles. Because of the impressive

combination of high speed, high maneuverability, and precise control observed in the flight of

insects, the amount of research being conducted into the mechanics of flapping wing flight and

its adaptation to MAVs is increasing.

As a capstone design project for engineering students at the University of Alabama at

Birmingham, (UAB) an MAV was developed during the 2010/2011 academic year. The final

design is depicted in figure 1. The vehicle is of the so-called, “X-wing,” configuration

popularized in 1985 by Frank Kiesler with his rubber band powered “canard flapper” (Jones,

Bradshaw, Papadopoulos, and Platzer, 2005). The X-wing configuration takes advantage of the

“clap and fling” aerodynamic mechanism, utilized in the flight mechanics of some insects.

The design incorporates two pair of flexible wings, spanning a total of 150mm, joined to

a central shaft and sharing a single axis of rotation. The wings cyclically rotate counter to one

another assuming a favorable pitch for thrust production as a result of their flexibility. As the

wings approach one another, the changing acceleration causes the flexible membrane to reverse

its pitch. At their closest point, the wing membranes press together, forcing air in the direction

of thrust, to complete the “clap” portion of the wing to wing interaction. The “fling” occurs as

the wings separate, leading edge first, drawing air in towards the wing leading edges. Three

wing-to-wing interactions occur during each flapping cycle. The interactions between wings are

thought to increase the thrust performance of the vehicle.

Simulations were conducted during the design process in order to optimize flight

parameters and determine performance characteristics. Parameters such as maximum pitch,

pitch timing, and flapping frequency, were adjusted in order to reach the target average thrust of

0.1N while minimizing the power required. Initially, in order to reduce simulation time, only

one wing from each connected pair was modeled and the resulting forces were doubled. Once an

acceptable parameter set was found, the other two wings were added and two more optimization

iterations were conducted.

SIMULATION SET-UP

In order to capture the large displacements undergone by the wing membrane material,

the wing motions were approximated using a rigid body assumption. The alternative would have

been to incorporate a secondary FEA solver capable of accounting for the large deformations of

the wing membrane. The rigid body approach was selected since the simulation was to be run on

a single processor and the rigid body motion would be less computationally expensive.

Although the function of the wings requires that they be flexible, the supporting rod positioned

across the membrane ensures the flexing resembles a semi rigid flap hinged at the leading edge

of the wing. Therefore, the rigid assumption is reasonable as long as the specified pitching

motion is realistic.

MESH

The morphing mesh functionality of STAR CCM+ lends itself well to the demands of

flapping wing simulations. However, there are certain restrictions placed upon the morphing

mesh that required consideration. Steps were taken to avoid errors resulting from the large

deformation of the mesh and the poor cell quality that results as well as to avoid the creation of

negative volume cells.

The original geometry was generated within a CAD package and imported into STAR

CCM+. As seen in figure 2, the wings were originally positioned in a way that was not seen

during the actual motion. Instead the wings were set so as to minimize their displacements from

the original position after the mesh was generated. Also, the centers of rotation were displaced

to allow for a minimum of 6mm between the wings at their closest points. The minimum

distance was necessary to reduce the ratio of maximum to minimum distance between the wings

in order to maximize cell quality. Once the polyhedral with prism layer mesh was generated, the

wings were moved into the proper starting positions with two iterations of the mesh morpher

solver with the morpher method set to rigid body. The first iteration was to set each wing to the

proper positions with respect to the flapping motion and the second was to set them to the proper

pitch. The resulting slightly deformed mesh is shown in figure 3. The size of the mesh was

limited due to the resources and time available. Plans are in place to utilize a distributed

environment for a future simulation with a much finer mesh.

MOTION SPECIFICATION

The motion was separated into two components, flapping and pitching, for each wing.

Attributes of the flapping motion were determined through analysis of the vehicle drive

mechanism, a simple 4-bar linkage for which a constant input speed was specified. For a

complete cycle, the angular position, and velocity, curves for each wing were defined.

The pitching motion was specified through careful consideration of the wing geometry

and the requirement that the wings remain a minimum distance from one another. The maximum

pitch and the point it could be reached were both specified for each wing and a cubic spline

curve was generated to fit the specifications. Two separate pitch curves were necessary to

account for all four wings since two of them experienced two wing to wing interactions. For the

two wing simulations, only one pitch curve was necessary. The data was tabulated and imported

into STAR-CCM+ as tab delimited tables.

The two components of the motion were then added vectorially and applied to each wing

with the use of field functions within STAR CCM+. This task was complicated by the pitching

rotation being about the wing leading edge. As such, its axis of rotation was a function of time

and needed to be calculated for each time step. Eleven total field functions were written in order

to define the motions. Three field functions simply interpolated the imported tables, four

calculated the pitch axes of rotation, and the last four combined the interpolated velocities and

axis information into the motion specific to each wing.

Four motions were then created in order to apply the calculated values to each wing. The

origins for each motion were offset to account for the original accommodations made during

mesh generation. The motions were then assigned to the appropriate wing within the fluid region

after the morpher method was set to “motion.”

POST PROCESSING

The overriding goal of each simulation was to extract the thrust and power information

for each input parameter set. Therefore, the aerodynamic forces acting on each wing were

computed via the report and monitor functionalities within Star CCM+. Thrust was defined as

the resultant force acting on the wings in the direction of flight, in this case the positive z

direction. Also, the moments about the flapping axis of rotation were calculated in order to

quantify the resistance to the flapping motion. From the extracted moment the power required

could be calculated, by simply taking its product with the rotational speed.

The pressure distribution over the wings served as a qualitative check of the feasibility of

the specified pitching motion. Since the actual wings rely on their flexibility to achieve a

favorable pitch, the pitching motion would tend to be in the direction of decreasing pressure until

the maximum pitch is reached. Therefore, if the wings were seen to be “fighting” the pressure

gradient, the pitch timing was adjusted until a more “realistic” motion was found. The pressure

distribution was monitored visually, throughout the simulation with the use of a scalar displayer.

Finally, a streamline displayer aided in the visualization of the complex flow field.

RESULTS

An implicit unsteady, laminar, segregated flow, ideal gas simulation was conducted for

each parameter set on a single dual core AMD 2.2GHz processor with 2GB of RAM over a total

solver elapsed time of roughly 36 hours per flapping cycle. Each flapping cycle consisted of 200

time steps.

Several combinations of maximum pitch angle and flapping frequency were investigated

as well as the effects of delaying or advancing the pitch timing with respect to flapping position.

The resulting performance information from each simulation is presented in table 1. A general

trend of increasing performance with increasing pitch angle was observed. However, reason

would indicate that a maximum possible pitch angle exists based upon the material and flapping

frequency. 45° was selected somewhat arbitrarily as the maximum feasible angle and will be

updated after testing of the actual vehicle takes place.

Earlier simulations indicated that no appreciable hysteresis effects occurred from one

cycle to the next. Therefore, the performance information could be deduced from a single

flapping cycle. The resulting thrust and moment plots for one cycle during the final 23Hz

simulation are shown in figure 5. For the same simulation, scenes displaying the pressure

distribution over the wings and streamline plots are presented in figures 6 through 8. Vortices

shed during the previous wing to wing interaction are the most evident flow feature in each scene

presented. The speed with which these vortices separate from the immediate vicinity of the

wings partially explains the observed lack of hysteresis effects. It appears that the flapping

frequencies are too low for one cycle to affect the next.

CONCLUSIONS

Due to the large number of approximations and assumptions made in the conduct of these

simulations, a large uncertainty exists with respect to the resulting predictions. However, the

predicted frequencies and power requirements are reasonably close to measured values from

similarly dimensioned vehicles such as those made by the team at the Ohio center of excellence

for micro air vehicle research at Wright State University (2010). Their measured thrust values

during wind tunnel tests of 0.15N at 18Hz and requiring an input power of around 1.5W are

reasonably close to those predicted. Although, a one to one comparison is not appropriate due to

the different wing geometries, the measurements lend validity to the predictions allowing design

decisions to be made with much more confidence.

The power required to achieve flight is likely within a 0.3 to 0.6W range and will require

a flapping frequency of approximately 20Hz. Using these values, a gear ratio and motor were

selected and testing will occur by the end of April 2011.

Jones, K.D. Bradshaw, C.J. Papadopoulos,J. Platzer, M.F. (2005, Aug). Bio-inspired design of

flapping-wing micro air vehicles. The Aeronautical Journal , pp. 385-393.

Wright State University. (2005). Research projects. retrieved on 3/20/2011 from

http://www.engineering.wright.edu/mav/research/projects.shtml#wind-tunnel

Figure 1: Vehicle upon which the simulations were based. The vehicle has a wing span of

150mm and weighs less than 10g requiring 0.1N to hover.

Figure 2: Wing geometry with the wings labeled. The direction of flight is towards the lower

left as depicted.

1

2

3

4

150mm

Figure 3: Polyhedral mesh at the starting positions. The mesh was “pre-morphed” to

accommodate the relatively high displacements required during the simulation.

Figure 4: Motion specification curves defined over one flapping cycle. The 1 interaction pitch

motion was applied to wings 1 and 4 while the 2 interaction pitch was applied to wings 2 and 3.

Figure 5: Thrust (left) and Moments (right) acting on the wings over one cycle.

Figure 6: Streamline and pressure distribution. The largest flow feature is the vortex shed

during the previous wing to wing interaction at the 12 o’clock position. The vortex separation

prior to the next 12 o’clock interaction partially explains the lack of hysteresis effects.

Figure 7: Streamline and pressure distribution. The highly chaotic nature of the flow field is

evident as the wings are advancing towards another 12 o’clock interaction.

Figure 8: Streamline and pressure distribution. The vortices being shed have almost completely

vacated the region in which they were originated.

Table 1: Parametric study results

Frequency (Hz) Maximum Pitch (deg) Avg Thrust (N) Avg Power (W)

30* 30* 0.08* 0.65*

35* 30* 0.11* 1.02*

35* 45* 0.15* 0.79*

28* 45* 0.09* 0.33*

28 45 0.14 1.05

23 45 0.09 0.56

*Simulations conducted using only two wings and assuming symmetry.

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