Flapping Airfoil Analysis of Micro Air Vehicles using STAR-CD
D.Funda Kurtulus 1,2, Alain Farcy 1, Laurent David, Nafiz Alemdaroglu Ecole National Superieur de Mechanique et d’Aérotechnique, LEA, Poitiers, France Middle East Technical University, Ankara Turkey

The aim of the flapping airfoil analysis is to understand the aerodynamic phenomena and the vortex topology of this highly unsteady motion. Instead of the use of real insect/bird wing geometries and motions, which are highly complex and difficult to imitate by a exact modeling, a simplified model is used to understand the unsteady aerodynamics and vortex formation during the different phases of the flapping motion.

Flapping Motion Description Inspired from Birds and Insects Hummingbirds and several insects use normal hovering where the wings are moving through a large angle in an approximately horizontal plane making a figure-of-eight motion with a symmetrical half-strokes.

The flapping motion is divided into 4 regions with the first region corresponding to half of the downstroke where the leading edge is pointing in positive direction and second one to the half-upstroke. While the third and fourth regions, are the mirror images of these two regions, corresponding to the second half of upstroke and downstroke respectively. Figure 2 shows a detailed description of the flapping motion in one period. In order to use a simplified model, the symmetrical NACA 0012 airfoil is chosen for the present study. The nomenclature of the parameters is such thatα represents the angle of attack, c is the airfoil chord, V is the translational velocity, xα is the position of change of angle of attack, xv is the position of change of velocity. In the figure, the center of rotation (denoted by a) is at chord location of the airfoil. The motion is implemented into the program using the moving grid option and user defined subroutines of STAR-CD.

Parametrical Study with STAR-CD and Comparison with Experiments
A total of 216 cases were investigated numerically, by changing the parameters described in Figure 2. The vorticity contours at the half-amplitude location for different center of rotations are given in Figure 3 for α=30°, Re=1000, xv=2c, xa=2c. During this parametric study it is found that the most influential parameter for the aerodynamic force coefficients is the angle of attack and the second is the center of rotation.

Fig 2 Flapping motion definition.

During the beginning of 2nd and 4th re
gions of the flapping motion, the airfoil enters the trace of the leading edge vortex, translational vortex and rotational vortex that were generated before the return. At angles of attack higher than 30°, the effects of the downwash due to these vortices are stronger. For small angles, the lift coefficient has both negative and positive values, which give average force coefficients close to zero. As the angle of attack is increased to 30°, these negative peaks
disappear and at 45° positive peaks are observable.

Vortex identification by considering Q-criteria and first and second eigenvalues are visualized. The demonstrated results are obtained by using STAR-CD for a 2-D, unsteady, laminar flapping motion. High positive values of Q imply vortex regions where the rotation rate is dominant compared to the strain rate. The vorticity contours and pressure values are also represented for comparison to the different techniques. The streamlines are visualized in both inertial reference frame and body fixed
reference frame.

The whole computational domain is moving, with the motion imposed by user subroutines, defining the flapping motion angular and translational velocities. The motion of the grid domain close to the airfoil is shown in Fig.2. The whole domain is a 20c radius O-type computational grid. Macros were developed for the calculation of the second invariant of velocity gradient (also called as second invariant of the mean rate-of-displacement tensor) Eq.1 and eigenvalue of the sum (called the µ criteria):

The results are also compared with the experimental visualization techniques as Particle Image Velocimetry (PIV) and laser sheet visualizations (Figure 5). The numerical solutions are very satisfactory compared to experimental results although the problem is highly unsteady.

Conclusion
In this study, the flapping motion aerodynamics was considered for a symmetrical hovering case for use in future Micro Air Vehicle applications. MAV’s resembling insects and small birds with flapping wings. The complexity of the problem raises the necessity of a simplified model, so a two-dimensional model was investigated with a symmetrical airfoil with variable velocity and angular velocity laws. The analysis tools used for the description of the phenomena are the numerical simulations and the experimental investigations. The numerical simulations were performed with STAR-CD using the moving grid capability. STAR-CD was used for the parametrical study to get a first idea of the parameters which influence the flapping motion study. It was concluded that the most influencing parameter is the starting angle of attack. The second important parameter is the center of rotation. The other parameters as the change of position of the velocity and angle of attack and Re (or Reynolds number) were found to be less important.