[American Institute of Aeronautics and Astronautics 36th AIAA Fluid Dynamics Conference and Exhibit...

American Institute of Aeronautics and Astronautics

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A Parametrical Study with Laser Sheet Visualization for an Unsteady Flapping Motion

D. Funda Kurtulus* Aerospace Engineering Department Middle East Technical University, 06531 Ankara, Turkey

Laboratoire d’Etude d’Aérodynamique (CNRS UMR6609) Ecole Nationale Supérieure de Mécanique et d'Aérotechnique, Poitiers, France

Laurent David† Laboratoire d’Etude d’Aérodynamique (CNRS UMR6609) Université de Poitiers, Poitiers, France

Alain Farcy‡ Laboratoire d’Etude d’Aérodynamique (CNRS UMR6609) Ecole Nationale Supérieure de Mécanique et

d'Aérotechnique, Poitiers, France

Nafiz Alemdaroglu§ Aerospace Engineering Department Middle East Technical University, 06531 Ankara, Turkey

In order to better understand the vortex dynamics and evaluation of the flow structures during the unsteady flapping motion, experimental visualizations are considered. The visualizations are represented for the phenomenological analysis of the flow. The flow is assumed to be laminar with the Reynolds number of 1000. The evaluation of the complex flow topology is investigated instantaneously for the effect of the different parameters. The vortex identification is performed for the change of incidence position xa, the change of velocity position xv and the starting angle of attack α0.

Nomenclature c chord Re Reynolds number St Strouhal number t* non-dimensional time ta time corresponding to the xa location where the variation of the angle of attack occurs tv time corresponding to the xv location where the variation of the velocity occurs T period V instantaneous velocity of the flapping motion V0 constant velocity during the translational phase VP velocity input for the photo timing xa position at the beginning of angle of attack change xv position at the end of constant velocity region xT/4 maximum x location, half-amplitude α instantaneous angle of attack α0 constant angle of attack during the translational phase α& instantaneous angular velocity of the flapping motion ν kinematic viscosity

* Dr., Aerospace Eng. Dept., METU Ankara Turkey & LEA ENSMA Poitiers France, AIAA Member † Prof., LEA SP2MI Université de Poitiers, BP40109, avenue Clément Ader 86961 Futuroscope Chasseneuil France ‡ Dr. Ing., LEA ENSMA, BP40109, avenue Clément Ader 86961 Futuroscope Chasseneuil France § Prof., Aerospace Engineering Dept., METU 06531 Ankara Turkey, AIAA Member

36th AIAA Fluid Dynamics Conference and Exhibit5 - 8 June 2006, San Francisco, California

AIAA 2006-3917

Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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I. Introduction HE study of the wing motions of a variety of insects and calculation of the forces resulting from these motions are established by Maxworthy1 where the fluid dynamics of flapping forward flight and hovering flight is summarized. Hovering flight is explained in 4 categories which are the normal hovering, the clap-and-fling

mechanism, inclined wing stroke plane and vertical-stroke plane. Normal hovering is where the wing stroke is approximately horizontal. Hummingbirds and the majority of insects are included in this group. The inspiration from the bio-aerodynamics results an idea for the researches to have MAV’s resembling to insects and small birds such as hummingbird with flapping wings. Some reviews of these researches are given by Mueller2, DeLaurier3, Shy et al.4, Van den Berg and Ellington5, Ellington6, Dickinson and Götz7, Lai and Platzer8. Most resent developments in the literature on flapping wing concept are given by Platzer and Jones9. Large animals such as birds appear to operate in the lower frequency regime, while the smaller ones, such as insects in the higher frequency regime. Wang10 investigated especially the frequency selection in forward flight, the time scales associated with the shedding of the trailing and leading-edge vortices and the forces corresponding to them. Among the three parameters (Reynolds number Re=Uoc/ν, Strouhal number or advance ratio Sta=f a/Uo and reduced frequency parameter Stc=f c/Uo where a is amplitude and c is the chord) Re dependence is expected to be very low for sufficiently high Re (Re≥103). Dickinson11 observed by experimental results that four important parameters of stroke reversal influenced the generation of the force during the subsequent stroke. These are the position of the rotational axis, the speed of rotation, the angle of attack of the preceding stroke and the length of the preceding stroke. The motion of the wing profile was divided into three temporally distinct phases: the first translation (downstroke), wing rotation; the second translation in the opposite direction from the first (upstroke). The mean streamwise velocity field of the wake of a NACA 0012 airfoil oscillating in plunge at zero freestream velocity and at a zero angle of incidence was calculated by Lai and Platzer8. The vortical flow patterns in the wake of a NACA 0012 airfoil pitching at small amplitudes are studied by Koochesfahani12 in a low-speed water channel by considering the effect of both sinusoidal and non-sinusoidal shape of the waveform. In order to better understand the unsteady topology of the flapping motion, a 2D simplified model is investigated experimentally with NACA 0012 airfoil. The description of the prescribed flapping motion problem and experimental tools are represented. The influences of the position of the angle of attack change xa, the angle of attack α0 and the position of the velocity change xv are investigated experimentally.

II. Description of the Problem and Experimental Tools The model is simplified by use of a symmetrical airfoil (NACA 0012), so that the symmetry of the motion both during upstroke and downstroke is not lost (Fig. 1). The flapping motion is simulated with the superposition of a translational motion and a rotational motion around a center of rotation. During the translational phase, the airfoil translates with a constant velocity until the time tv and position xv, where a rotational motion around a point on the chordline is superposed to the translational motion at a predefined time ta and position xa. The translational velocity is zero (V = 0) at the end of the strokes. After the time ta and the position xa, the airfoil starts to rotate around the center of rotation where it reaches 90° angle of attack at the quarter period. The rotation is such that the leading edge stays as leading edge during all phases of the motion. A rectangular wing with a NACA 0012 airfoil section is displaced in a tank filled with water by associating a rotational and a translational motion. The experimental setup is a 1.5 m×1 m×1 m water tank. The wing is delimited by two rectangular plates made of epoxy with 50 cm×90 cm dimensions in order to obtain a 2D flow (Fig. 2). The wing is free to rotate relative to the plates. The chord length, c, of the wing is 6 cm and the span is 50 cm. The centre of rotation is at c/4 location of the airfoil. A laminar flow is generated with a Reynolds number of 1000 relative to the chord and the maximum translational velocity V0. The system consists of 2 step motors. The first motor is a high torque brushless motor associated with an endless screw allowing the translational motion with a maximum linear velocity of 4 cm/s. The second one, associated with 2 pulleys allows the rotation of the profile. The useful distance of the translational motion is 600 mm and that of the rotational is of 360°. The flapping motion is carried out in zero free-stream velocity. A laminar flow is generated with a Reynolds number of 1000 calculated with respect to the chord and the maximum velocity of the motion. The total displacement of the airfoil is fixed to 6c. The system is controlled with variable velocity in open loop using a computer with a real time data acquisition. The generated signal is also used for the synchronizations of image acquisition. The seeding is done by using micro-spherical hollow particles of glass silver plated on the surface with a

T


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mean diameter of 15 µm. The concentration of the particles in the whole volume of the water tank is approximately Vparticle/Vtank = 1.9·10−6. The camera used is a NIKON-MB-21, with model F4S. The lighting system chosen for this experiment is a continuous laser system with argon SPECTRA-PHYSICS of 10 W of maximum capacity. To obtain the laser sheet, two spherical lenses of focal distance 50 mm are followed by cylindrical lens of focal distance 25 mm and in order to obtain the direction of the luminous plan. The non-dimensional time is denoted by t* and defined in Eq.1.

c

tVt P ⋅=* (1)

where Vp = c/T and T is the average period found by repeating three times the experiment during 12 periods.

Fig. 1 Definition of the parameters

Fig. 2 Experimental setup

Table 1 compares calculated and experimentally measured period of the motion for the different cases investigated. The error of the period is due to the step motors which are not suitable for a sudden change from zero velocity to a positive value which is needed for the kinematics of the flapping motion prescribed. Non-dimensional time t* error is less than 1.7%. The results are compared with the velocities and periods in air by use of the similitude. Subscribe 1 corresponds to the air data and subscribe 2 corresponds to the water data of the experimental measurements.


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Table 1 Experimental periods and cases investigated for Re=1000 Air Water

α0 xv xa V1 [m/s] T1 [s] V2 [m/s] T2 [s] (calculated)

T [s] (experimental)

VP [m/s] (camera)

30° 45° 60°

2c

1c 1.5c 2c

2.5c

1.454 0.098 0.0167 51.42 50.71 0.0118

30° 45° 60°

2.5c

1c 1.5c 2c

2.5c

1.454 0.090 0.0167 47.31 46.72 0.0128

The photos are taken with constant time increments ∆t* for xv=2c and xv=2.5c cases with different xa and α0. There is a time delay (62 ms) of the camera opening before starting to take photos. The exposure time for Nikon F4 is adjusted such that each photo can be taken within the same intervals ∆t* (Fig. 3).

Fig. 3 Visualization adjustments for camera to have same time intervals ∆t*

The velocity and angle of attack distribution corresponding to four different xa parameters at each time for α0=45°, xv=2c case are given in Fig. 4. The values on the graph represent the velocity and angle of attack data at each visualization instants.

Fig. 4 Instantaneous velocity and angle of attack distributions of the experimental data at xa=1c, 1.5c, 2c and 2.5c for α0=45°, xv=2c case. The black lines correspond to the exact prescribed motion


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The influence of the parameters as the position of the angle of attack change xa, the angle of attack α0, the position of the velocity change xv, are investigated to understand the physics of the vortex topology. The instantaneous visualizations are compared to see the effect of these parameters on the vortex formation and on the trace of the vortices from the previous stroke which results different downwash effects on the airfoil in return throughout the flow field.

III. Results The flow topology and the trajectories are investigated during a whole period of the flapping motion for different parameters. The visualizations are obtained with an exposure time of 500ms. The displacement of the particles during this time interval draws a part of trajectory giving an idea of the flow topology in the inertial reference frame for this specific experimental visualization. All the results are given for the 7th stroke of the flapping motion. At this time interval, the influence of the impulsive start is negligible and all the vortices observed at the time t*= 1.00 (representing the beginning of the 8th period) are also similarly visible at the time t*= 0 (representing the beginning of the 7th period). The topology for a reference configuration has been performed previously and three types of vortices are distinguished during the flapping motion study13 namely the leading edge vortex (LEV), translational vortex (TV) and the rotational stopping vortex (RSV). The blue colors represent the clockwise vortices and the red colors represent the counter-clockwise vortices. The vortices with yellow color represent the trace from the previous stroke. In this study, the same vortex topology is observed for different parameters with some change in the size of vortices and positions of the vortex cores depending on the parameter. The influence of these parameters on the formation and the growth of the vortices are worth to investigate in order to understand the physical principal behind this unsteady motion. The numerical results14 reveal that after 30° starting angle of attack, the instantaneous lift coefficient is positive throughout the period. The PIV measurements15 of the flow field show the similarity of the numerical simulations with the experimental data.

A. Effect of the xa location The instantaneous vortex topology near the airfoil at t*=0.10 are represented in Fig. 5 for different xa parameters. The time corresponds to the instant just before the constant velocity translational phase starts. For xa=1c, the airfoil rotates from 90° to α0 value in 2c distance, however for xa=2.5c, the airfoil has to rotate to the same angle α0 in a shorter distance (0.5c). The angle of attack, angular velocity and translational velocities at the given time are represented in Table 2 for different xa parameters. At the given instant, it is noted that the airfoil is in pure translation without any rotational velocity only for xa=2.5c case. Until the constant velocity translational phase, there is a formation of a counter-clockwise leading edge vortex (LEV1) which detaches very quickly from the surface of the airfoil, leaving its place to a newly generated leading edge vortex LEV2. LEV1 is clearly observable with closed streamlines for small xa values. The trace of the LEV1 disappears very quickly for high xa values. LEV2 stays attached to the airfoil until the mid-amplitude location (Fig. 6).

a) xa=1c b) xa=1.5c c) xa=2c d) xa=2.5c

Fig. 5 Experimental visualization of flapping motion for different xa values with α0=45°, xv=2c at t*=0.10 It is observed that the line joining the core of the Translational Vortex TV1 generated during the current stroke and Translational Vortex TV3 generated during the previous stroke form different angles with respect to the vertical


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axis (Table 2). The core of the vortex TV3 is closest to the TV1 as the xa parameter increases. In the same time, the radius of the vortex diminishes with an increase in xa parameter. The trace of the counter-clockwise vortex TV3 rotates around the clockwise translational vortex TV1 (Fig. 6). TV3 is influenced first by the translating airfoil which pushes it downwards and second by clockwise translational vortex TV1 which causes it to rotate in clockwise direction around its center.

Table 2 Parameters for different xa values with α0=45°, xv=2c at t*=0.10

Case α(t*) α& (t*) [rad/s] V(t*) [m/s] TV1 and TV3 position relative to vertical axis (Fig. 5)

xa=1c 51.18° 0.072 0.0164 26° xa=1.5c 47.30° 0.049 0.0164 63° xa=2c 45.08° 0.007 0.0164 38° xa=2.5c 45.00° 0.000 0.0164 -3°

At t*=0.15, the trace of the LEV2 from the previous stroke is more dominant also for high xa values. The airfoil translates and enters to the trace of this vortex and pushes it toward downwards (Fig. 6). The newly generated vortex TV2 causes TV1 to separate from the airfoil surface. It is noted that TV1 separates quicker for high xa values as can be seen in Fig. 6 for xa=2.5c case. The newly formed translational vortex TV2 seems to be like a trace of the TV1 at the wake of the airfoil. The leading edge vortex LEV3 forms causing LEV2 to separate from the airfoil surface at t*=0.20 (Fig. 7). TV2 is observed in closed streamline form only for xa=1c. For other xa values, it is observed as the continuation of the TV1 in inertial frame of reference. It is noted that the formation of the LEV3 is quicker for small xa values. Although, LEV3 is already formed for xa=1c, 1.5c and 2c cases at t*=0.20, it is not visible for xa=2.5c case at this time instant yet.

a) xa=1c b) xa=1.5c

c) xa=2c d) xa=2.5c

Fig.6 Experimental visualization of flapping motion for different xa values with α0=45°, xv=2c at t*=0.15


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Fig.7 Experimental visualization of flapping motion for different xa values with α0=45°, xv=2c at t*=0.20 (top) and t*=0.25 (bottom)

The separation of TV2 wait for a while for xa=1c and 1.5c cases (Fig. 8) however, at t*=0.25, the TV3 is already formed for xa=2c and 2.5c cases with a separation of TV2. At t*=0.25, the airfoil is just at the mid location of the flapping motion domain. The LEV1 does not separate completely from the wake of the airfoil at the leading edge for xa=1c and 1.5c cases. The counter-clockwise leading edge vortex LEV2 stretches before the complete separation due to the translation of the airfoil, the formation of LEV3 and the effect of clockwise translational vortices TV2 and TV3. Its effect is dominant over the whole upper surface of the airfoil at t*=0.30.


Fig.8 Experimental visualization of flapping motion for different xa values with α0=45°, xv=2c at t*=0.30 The leading edge vortex LEV3 stays attached to the airfoil surface until the end of the translational phase where new LEV4 and LEV5 vortices are formed during rotation. These lastly formed leading edge vortices are pushed upwards by the return of the airfoil and disappear after a while. The translational vortex TV3 detaches from the airfoil surface just before the return of the airfoil where a rotational stopping vortex RSV1 is formed. The RSV1 is formed earlier and have sufficient time to grow for small xa.


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B. Effect of the angle of attack α0 The vortex topologies at the beginning and at the end of the translational phase are represented in Fig. 9 for

different α0 values. The results are represented for xv=2c, xa=2c case. The trace of the previous stroke is dominant in the flow field for α0=45° and α0=60°. The LEV2 (cw) is the biggest for α0=60° (Fig. 9a). It is observed that for 30°, the mid-amplitude location of the domain is more stable and traces of the vortices are weaker.

a) t*=0.10 b) t*=0.45

Fig. 9 Experimental visualization of flapping motion for α0=30°, 45° and 60° at t*=0.10 (left column) and t*=0.45 (right column)

For α0=30°, the leading edge vortex LEV2 and the translational vortex TV2 stay attached to the surface of the

airfoil during the whole translational phase and the rotational stopping vortex RSV1 grows very quickly during the rotation (Fig. 9b). It is noted that, for α0=30°, the angular velocity is very high compared to higher α0 values in order to reach 90° at the end of the stroke in the same time interval. This high angular velocity results a growth in rotational stopping vortex (RSV1). During the return, TV1 is in contact with the RSV1 for 30° angle of attack motion. For higher angles of attack, the RSV1 is pushed toward downwards by the airfoil during the return and TV1 coincides with TV3 of the previous stroke instead of RSV1. The radius of the translational vortex TV3 increases as the angle of attack increases from 45° to 60°. The increase the constant angle of attack α0 however diminishes the radius of the RSV1.

At the beginning of the translational phase for all the angles of attack, the LEV1, LEV2 and TV1 formation are

visible. The translational vortex TV1 is separated from the airfoil trailing edge just before the formation of TV2 during translation and its effect is always dominant at the left and right edges of the flow domain. The position of the core of clockwise TV1 also shifts towards right with the increase of α0.

The instantaneous vortex topology for α0=60°, xv=2c and xa=2c case is represented in Fig. 10. The radius of the TV3 and LEV2 are found to be highly big compared to smaller α0 values at the given time instants. The LEV2 formed on the upper surface of the airfoil dominates strongly the downwash at the mid-amplitude of the flow domain. TV3 has also a dominant effect during the return of the airfoil. TV1 detaches from the airfoil trailing edge after t*=0.20.


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Fig. 10 Instantaneous experimental visualization of flapping motion for α0=60°, xv=2c and xa=2c

For α0=60°, the formation of the leading edge vortex LEV4 is visible with the separation of the LEV3 from the

airfoil surface at t*=0.35. At t*=0.45, a new LEV5 is formed. The trace of the vortices LEV3, LEV4 and LEV5 mix during the return of the airfoil and they interact with the lower surface of the airfoil after the rotation. New clockwise leading edge vortex LEV1 and counterclockwise translational vortex TV1 are formed at t*=0.55. The trace of clockwise vortex TV1 stays approximately at the same location during all instances of the motion.

C. Effect of the xv location The position of the variation of the velocity from the constant V0 value is also considered as a parameter of influence to the topology of the flapping motion study. Figure 11 shows instantaneous comparison of the xv=2c and xv=2.5c cases for a constant angle of attack α0 of 45° and the position of the change of angle of attack xa being 2c. Similar topology is observed for two cases. The trace of the translational vortex TV1 is found to be more insisting for xv=2.5c case. The trace of TV3 at t*=0.20 is found to be pushed more downwards as the velocity variation starts close to the end of the stroke domain (xv=2.5c case). Its trace is visible until t*=0.25 for xv=2c after a while it dissipates inside the trace of TV1.

The radius of the translational vortex TV3 at t*=0.45 is found to be bigger for high xv value. The trace of the

leading edge vortex LEV2 is more dominant for xv=2.5c case shown in Fig. 11 at t*=0.55. RSV1 for xv=2.5c is pushed by the airfoil return at t*=0.55 earlier than the xv=2c case.


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a) xv=2c b) xv=2.5c

Fig. 11 Instantaneous experimental visualization of flapping motion for α0=45°, xa=2c

IV. Conclusion Experimental visualizations with laser sheet are performed for unsteady flapping motion study. The experiments

are done for different parameters and the effects of these parameters on the vortices generated are discussed. The flow topology shows similarities for different parameters. For α0=30°, the vortices are found to be more attached to the airfoil surface with less effect of the trace of vortices from previous strokes. The rotational stopping vortex is found to be bigger for small α0 and small xa values. The location of the angle of attack change (xa) is found to be important for the position of the formation of the vortices. As the xa parameter increases, the leading edge vortex LEV2 grows more while attached to the airfoil, before the formation of the LEV3. The translational vortex TV3


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forms earlier also dependent to late angular rotation of the airfoil. For high α0 values (45°, 60°) and high xv value of 2.5c, the trace of leading edge vortex LEV2 is found to be dominant in the mid-amplitude location of the domain. This is very strong especially for α0=60° where the radius of the vortices generated as LEV2 and TV3 are highly big compared to other cases. The trace of the vortex formation for different parameters is important for the understanding of the positive lift generation after α0=30° where the vortices are still attached to the airfoil during the translational phase and the high lift values for α0=45° and 60° due to the dominant influence of the vortex traces from previous stroke. This downwash velocity induced by LEV2, TV1 and TV3 and the location and the magnitude of these vortices is an important parameter for the understanding of the mechanism and will be used as an input for the analytical model developed14.

Acknowledgments This work was supported by ENSMA, METU, TUBITAK, CNRS and French Embassy in Turkey. Their supports are greatly acknowledged. Miss. Funda Kurtulus thanks also to Zonta International Foundation (USA) to select her as an Amelia Earhart Fellow of 2005.

References 1Maxworthy, T., “The Fluid Dynamics of Insect Flight,” Ann. Rev. Fluid. Mech., 198, 13, 329-50, 1981 2Mueller, T. J. “Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications,” AIAA Progress in

Astronautics and Aeronautics 195, AIAA Education Series, AIAA, Reston, VA, 2001 3DeLaurier, J. D., “An Aerodynamic Model for Flapping-Wing Flight,” Aeronautical Journal 1853, 125-130, 1993. 4Shy, W., Berg, M. and Ljungqvist, D., “Flapping and Flexible Wings for Biological and Micro Air Vehicles,” Progress in

Aerospace Sciences 35, 455-505, 1999 5Van den Berg, C., Ellington, C. P., “The three-dimensional leading-edge vortex of a 'hovering' model hawkmoth,” Phil.

Trans. R. Soc. Lond. 352, 329-340, 1997 6Ellington, C. P., “The Novel Aerodynamics of Insect Flight: Applications to Micro Air Vehicles,” J. Exp. Biol. 202, 3439-

3448, 1999 7Dickinson, M. H., Götz, K. G., “Unsteady Aerodynamic Performance of Model Wings at Low Reynolds Numbers,” J. Exp.

Biol. 174, 45-64, 1993. 8Lai, J. C. S., Platzer, M. F. “Characteristics of a Plunging Airfoil at Zero Freestream Velocity,” AIAA Journal, Vol. 39,

No.3, 531-534, 2002 9Platzer, M. F., Jones, K. D., “Flapping Wing Aerodynamics - Progress and Challenges,” AIAA-2006-0500, Jan. 2006, Reno,

Nevada, 2006 10Wang, Z. J., “Vortex Shedding and Frequency Selection in Flapping Flight,” Journal of Fluid Mechanics, 410, 323, 2000 11Dickinson, M. H., “The Effects of Wing Rotation on Unsteady Aerodynamics Performance at Low Reynolds Numbers,”

Journal of Experimental Biology, Vol. 192, Issue 1 179-206, 1994 12Koochesfahani, M. M., “Vortical Patterns in the Wake of an Oscillating Airfoil,” AIAA Journal Vol.27, No.9, Sept. 1989 13Kurtulus D. F., David L, Farcy A., Alemdaroglu N., “Laser Sheet Visualization for Flapping Motion in Hover,” AIAA-

2006-0254, 44rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, USA, 9 - 12 Jan 2006 14Kurtulus, D. F., Farcy, A., Alemdaroglu, N., “Unsteady Aerodynamics of Flapping Airfoil in Hovering Flight at Low

Reynolds Numbers” , AIAA-2005-1356, 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 10 - 13 Jan. 2005. 15Kurtulus, D. F., David, L., Farcy, A., Alemdaroglu N., “Aerodynamic Characteristics of Flapping Motion in Hover,” 13th

Int Symp on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 26-29 June 2006

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