an experimental investigation on the asymmetric wake...

An Experimental Investigation on the Asymmetric Wake

Formation of an Oscillating Airfoil

Wei Ren1

Shanghai Jiao Tong University,Shanghai, PRC 200240

Hui Hu2

Iowa State Univeristy, Ames, IA 50011

and

Hong Liu3 and James C. Wu4

Shanghai Jiao Tong University,Shanghai, PRC 200240

Bio-inspired aerodynamic designs have been mutually promoted by the studies on

flapping wings in the past decades. Among the tons of researches topics, the wake

formation/structure of an oscillating airfoil is more attractive, and it results in the

development of both numerical methods and flow diagnostics techniques. In this paper,

wake formation behind a sinusoidally piching NACA 0012 has been studied with PIV

measurements. The evolution of wake structures with increasing Strouhal number was

reproduced successfully. With further experiments, the effect of Strouhal number, the

amplitude and mean value of AOA on the asymmetric wake formation were also investigated.

Results showed that the distance between vortex street became larger with increasing

amplitude, while mean strength of vortices declined. Besides, the asymmetric wake

formation was strongly dependent on the mean. Specifically, based on our experiments, the

direction of wake asymmetry was changed at a and .

Nomenclature

A = Peak to peak amplitude of the airfoil’s trailing edge

AoA = angle of attack

= amplitude/maximum value of AOA

= mean value of AOA c = chord length

f = oscillating frequency

k = reduced frequency, ⁄

= Air density

Re = Reynolds number based on the chord length, ⁄

St = Strouhal number, ⁄

= freestream velocity

= Cartesian coordinates

= phase angle

= spanwise (z) vorticity

1 Graduate Student, School of Aeronautics and Astronautics. Email: [email protected]. 2 Associate Professor, Department of Aerospace Engineering, AIAA Associate Fellow. Email: [email protected]. 3 Professor, School of Aeronautics and Astronautics. Email: [email protected]. 4 Chair Professor, School of Aeronautics and Astronautics, AIAA Associate Fellow. Email: [email protected].

51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition07 - 10 January 2013, Grapevine (Dallas/Ft. Worth Region), Texas

AIAA 2013-0794

Copyright © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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I. Introduction

IO-INSPIRED aerodynamic design and corresponding academic researches have been stimulated by the need

for Micro-Air-Vehicles (MAVs) in the past decade. Since fixed wings work less efficiently in the range of

Reynolds number in insect flight1 (about to ), two main wing motions are utilized in current MAV designs:

rotary- and flapping wings. Since It is regarded that the propulsive efficiency of an idealized flapping wing is greater

than that of a simplified propeller model because of the disadvantageous trailing vorte system generated by the

propeller2. Besides, flapping wing motion, as inspired by bird and insect flight, is much more attractive.

Flapping-wing systems generally involve the wing completing pitching, plunging, and sweeping components of motion over a flapping cycle3, and it creates swirling of air and generates aerodynamic forces that allow insects to

dart forward, to turn, and to hover, as reported by Wang4. Considering the intricacies behind them and lacking of

exact theory and accurate measuring techniques, it is quite challenging to completely understand the aerodynamics

of birds/insects wing flapping. Further details of bio-inspired aerodynamics developments can refer to

comprehensive reviews by Wang4 and Shy et al.5.

Although there are plenty of research insterests in this topic, wake pattern or wake formation investigation

attracts most attention. It is well known that flapping airfoils/wings generate thrust at certain combinations of

flapping frequency and amplitude. Koochesfahani6 studied the wake patterns of an oscillating airfoil pitching at

small amplitudes through the dye visualization and Laser Doppler Velocimetry (LDV), and it was observed that

wake patterns could be influenced by the frequency, amplitude and most important, the shape of the oscillation wave. Previous researches7-9 reported that optimum propulsion efficiency for a flapping airfoil/wing (defined as the ratio of

aerodynamic/hydrodynamics power output to mechanical power input) would be within the range of .

Hu et al.10 investigated the unsteady vortex structures in the wake of a root-fixed flapping wing ( ), which

revealed that 3-D flapping wing would be much more complicated compared with those in the wakes of 2-D

flapping airfoils. To simplify the problem without losing the generality, this paper will focus on the pitching motion

in 2-D.

For plunging case, qualitative and quantitative comparisons conducted by Jones et al.11 were excellent over a

broad range of reduced frequencies and Strouhal numbers. They reported that the formation and evolution of the

thrust-indicative wake structures were primarily inviscid phenomena and demonstrated asymmetric, deflected wake patterns came up at Stouhal numbers greater than about 0.1. Lai and Platzer12 and Young and Lai13 respectively

reported their results of an oscillating NACA 0012 airfoil at a Reynolds number of experimentally and

numerically. Both revealed a change from a von Karman vortex street to (1) multiple-vortex-per-half-cycle wake

patterns for drag-producing conditions, through (2) more complicated vortex structures as the neutral thrust

condition was approached, to (3) a reverse von Karman vortex street for thrust-producing conditions. Futher

experimental investigations on asymmetric wake were conducted with PIV measurements. It was shown that the

onset of wake asymmetry (amplitude ratio of 0.215) would occur in the Strouhal number range ,

and the direction of the wake deflection was established when the motion was initiated and remains unchanged14-15.

For pichting case, Yu et al.16-17 demonstrated the existence of three similar wake formation as that in plunging

case, and the deflected wake was found to appear at approximately Strouhal number 0.31 and reduced frequency

15.1 for the pitching amplitude . Besides, it was obtained that the reduce frequency would affect the strength of

the shedding vortices and further affected the formation of the asymmetric wake. In the numerical simulations, the

direction of deflection wake was determeined by the initial phase angle, which was consistence with the plunging

case. However, this result cannot be confirmed by the corresponding experiments.

In this paper, an experimental investigation on the asymmetric wake formation of an oscillating airfoil were

conducted with PIV measurements. The effect of Strouhal number, reduced frequency, mean AOA and amplitude on

the wake asymmetry were analyzed.

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II. Experimental Setup

The experiments were performed in a closed-circuit low-speed wind tunnel located in the Aerospace Engineering

Department of Iowa State University. The tunnel has a test section with a 1 × 1 ft (30 × 30 cm) cross section and all

the walls of the test section optically transparent. The wind tunnel has a contraction section upstream the test section

with honeycomb, screen structures and cooling system installed ahead of the contraction section to provide uniform

low turbulent incoming flow to enter the test section. A uniform freestream velocity of ⁄ is maintained in the

test section during the present study.

The airfoil used in the present laboratory was a NACA 0012 airfoil. The NACA 0012 had the maximum

thickness of 12% of the chord length. This airfoil was common symmetric airfoil in researches. The chord length of

the airfoil was 4 inch ( 101mm) and spanwise length of 11.5 inch ( 292.1mm). A linkage mechanism was used to

provide the sinusoidal piching motion ( ). Readers who were interested in the details may refer to

the conference paper by Yu et al.17.

Figure 1 shows the experimental setup used for the PIV measurement. During the experiment, the test airfoil was

installed in the middle of the test section. A PIV system was used to make flow velocity field measurements along

the chord at the middle span of the airfoils. The flow was seeded with 1~5 μm oil droplets. Illumination was

provided by a double-pulsed Nd:YAG laser (NewWave Research Solo) adjusted on the second harmonic and

emitting two pulses of 200 mJ at the wavelength of 532 nm with a repetition rate of 2 Hz. The laser beam was

shaped to a sheet by a set of mirrors, spherical and cylindrical lenses. The thickness of the laser sheet in the

measurement region is about 0.5mm. A high resolution 12-bit (1600 x 1200 pixel) CCD camera (PCO-1600, CookeCorp) was used for PIV image acquisition with the axis of the camera perpendicular to the laser sheet. The

CCD cameras and the double-pulsed Nd:YAG lasers were connected to a workstation (host computer) via a Digital

Delay Generator (DDG, Berkeley Nucleonics, Model 565), which controlled the timing of the laser illumination and

the image acquisition. For phase-lock measurement, the delay generator was connected to a digital pulse generator

to provide a trigger signal, which obtained from a tachometer.

For the post processing, each phase lock result is averaged from 150 frames while time averaged results from

1035 frames. The PIV velocity vectors were obtained by using a frame-to-frame cross-coorelation technique in an

interrogation windown of pixels with an effective overlap of of the interrogation windows. The

vorticity was computed from the velocity fields.

Figure 1 Experimental setup for the PIV measurements

III. Results and Discussions

For the results reported here, the free-stream velocity was approximately ⁄ , resulting in a chord

Reynolds number of 3,500 and Strouhal number within for different mean AOA. Figure 2 depicted all

the experiments conducted. It was shown that our study reproduced evolution of the wake formation behind an

oscillating NACA 0012 airfoil by Yu et al.16-17. Besides, with further investigation, more interesting results had been obtained. In this section Experimental results on wake structures/formation from PIV measurements will be

discussed.

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(a) (b)

Figure 2 (a) Strouhal number vs reduced frequency. (b) Strouhal number vs mean angle of attack

Points mark the experiments conducted by the authers.

(Square & Cross: ; Delta: ; Circle: )

A. Effect of Strouhal number

In section A, the effect of Strouhal number on the wake formation of an oscillating airfoil is discussed. In Figure

2, all the experiments are divided into four regions based on the specific wake formation from our PIV results. The

four regions can be referred to:

(A) drag-type, momentum deficit: ,

(B) neutral-type: ,

(C) thrust-type, momentum surplus: , and

(D) thrust/lift-type: . Figure 3-7 display the wake transition processes from the drag-type to the thrust/lift-type. Each figure represents

one of the wake structures, and provides the phase-lock results at . The corresponding

velocity vectors for each phase are also plotted in these figures. For simplicity of reading, the vectors are given here

on every other node. (Skip = 2 in both X and Y direction) In the meantime, only the tail of NACA 0012 is shown,

and the max AOA is with a zero mean AOA. Note that all the phase-lock results are plotted in a translated

coordinate for convenience. ( ⁄ ) ⁄ .

It is clearly shown that in Figure 3 negative vorticity is over the positive one in the vortex street, which resulting

in a momentum deficit10,17. Figure 4 indicates a neutral-type wake and Figure 5 shows a thrust-type wake, which

characterized by positive vorticity staying on the top of the vortex street. During our experiments, neautral-type wake is difficult to obtain since very little disturbance can make the wake into either drag-type or thrust-type. Also,

one can justify this from Figure 2, the region B, which refers to neutral type, is narrow indeed.

Onset of the aysmmetric wake occurs at a Strouhal number of 0.32, which is consistent with the conclusion by

Yu et al.17. Although the deflection angle is quite small, from Figure 8, it is shown that the peak of velocity profile

inclines to lower , indicating the whole vortex street is asymmetric. The same phenomenon, but much more clearly,

can be found when . And at a larger Strouhal number, the deflection angle is larger. In our results, only a

stable bottom-side deflection wake is obtained, while a top-side deflection wake can be found at the start of wind

tunnel.

With Strouhal number increasing, the vortex strength (characterized by vorticity) becomes stronger. Comparing

Figure 5 with Figure 6, it can be found that the latter one has larger high-vorticity region. In the meantime,

comparing Figure 6 with Figure 7, from vorticity contour, vortex pairs are more likely to stay close at .

That means the oscillating airfoils can gain more momentum from the flowfields with larger Strouhal number. Once

the momentum obtained exceeds a critical value, the wake formation will change.

In Ref. 17, the question “can the deflective direction of the wake be changed?” is discussed, here, two more

factors will be investigated: the amplitude and mean value of AOA.

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B. Effect of amplitude

In this section B, the dependency of the deflective direction of the asymmetric wake on the amplitude of AoA is

examined. Figure 2 (a) shows region A, C and D are investigated in this paper. All the cases in this section are at a

zero mean AOA.

In Figure 9, it is depicted that with amplitude increasing the distance between vortex street becomes larger, and

unit vortex strength goes weeker. For , the extrema of vorticity is around , while for , the

extrema can reach over . Figure 9 (b) plots the mean velocity profiles of all three cases at ⁄ . It can be

found that, the peak of velocity delines as increasing amplitude, which indicates that the vortex interactions become

weaker and the area of each one is ∫ ( )

, respectively. This result means that larger

amplitude may cause slightly lower ability of obtaining momemtum from surrounding flowfields. Hence, it can be

deduced that the onset of asymmetric wake occurs later at a larger amplitude.

C. Effect of mean AOA

In this section C, the dependency of the deflective direction of the asymmetric wake on the mean value of AoA

is examined. Figure 2 (b) shows region A, C and D are investigated in this paper. All the cases in this section are at a

amplitude of and a Strouhal number of ( corresponding reduced frequency is ).

Interestingly, it is shown that the direction of wak asymmetry can be eliminated or reversed as mean AOA

increasing. Specifically, comparing case and , the deflection angle becomes smaller. When , the asymmetric wake is eliminated, and in the downstream the wake is more likely to incline to the upper side.

At negative mean AOA, a curve of negative vorticity (in blue) on the upper side is obvious. This flow structure

can be referred to the Kelvin-Helmholtz instability. With the mean AOA decreasing, the strength of the upper side

negative vorticity becomes stronger, while the lower side one goes weaker.

Hence, it is clear that the wake formation is strongly dependent on the mean value of AOA.

IV. Conclusion

Bio-inspired aerodynamic designs have been mutually promoted by the studies on flapping wings in the past

decades. Among the tons of researches topics, the wake formation/structure of an oscillating airfoil is more

attractive, and it results in the development of both numerical methods and flow diagnostics techniques. In the

previous work, wake strucutres behind a sinusoidally pitching NACA 0012 have been studied with both

experimental and numerical approaches. It was reported that Strouhal number was considered to be a vital element

to form the asymmetric wake, and the direction of wake symmetry was sensitive to the alignment of the wind tunnel.

In this paper, an experimental investigation on the asymmetric wake formation was studied. Firstly, the evolution

of wake structures with increasing Strouhal number was reproduced successfully with PIV measurements. It was confirmed that the wake would experienced four modes: (a) drag-type; (b) neutral-type; (c) thrust-type; and (d)

thrust/lift-type. In the meantime, the oscillating airfoils can gain more momentum from the flowfields with larger

Strouhal number.

Secondly, with further experiments, the effect of Strouhal number, the amplitude and mean value of AOA on the

asymmetric wake formation had been investigated. Results showed that the distance between vortex street became

larger with increasing amplitude, while mean strength of vortices declined. Besides, it can be deduced that the onset

of asymmetric wake occurred later at a larger amplitude.

Thirdly, it was clear that the wake formation was strongly dependent on the mean value of AOA. Specifically,

based on our experiments, the direction of wake asymmetry changed at a and . On the other hand,

at negative mean AOA, to the Kelvin-Helmholtz instability was obvious on the upper side. With the mean AOA decreasing, the strength of the upper side negative vorticity became stronger, while the lower side one went weaker.

Futher work will focus on the theoretical analysis and numerical simulation of the current results and

conclusions.

Acknowledgments

The authors also want to thank Mr. Bill Rickard of Iowa State University for his help in conducting the wind

tunnel experiments. The support of J. C. Wu Foundation for Aerodynamics is gratefully acknowledged.

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References

[1] Hanson, Perry H., “Science and Technology of Low Speed and Motorless Flight,” NASA CP-2085, 1979.

[2] Kuchemann, D. and Weber, J., “Aerodynamic Propulsion in Nature,” Aerodynamics of Propulsion, McGraw-Hill, New York, 1953, pp. 248-260.

[3] Maxworthy, T., “The Fluid Dynamics of Insect Flight,” Annual Review of Fluid Mechanics, Vol. 13, 1981, pp. 329-350.

[4] Wang, Z. Jane, “Dissecting Insect Flight,” Annual Review of Fluid Mechanics, Vol. 37, 2005, pp. 183-210.

[5] Shyy, W., Aono, H., Chimakurthi, S. K., Trizila, P., Kang, C.-K., Cesnik, C. E. S. and Liu, H., “Recent Process in

Flapping Wing Aerodynamics and Aeroelasticity,” Progress in Aerospace Sciences, Vol. 46, 2010, pp. 284-327.

[6] Koochesfahani, M. M., “Vortical Patterns in the Wake of an Oscillating Airfoil,” AIAA Journal, Vol. 27, 1989, pp. 1200-1205.

[7] Anderson, J. M., Streitlien, K., Barrett, D. S. and Triantafyllou, M. S., “Oscillating Foils of High Propulsive Efficiency,”

Journal of Fluid Mechanics, Vol. 360, No. 41, 1998, pp. 41-72.

[8] Wang, Z. Jane, “Vortex Shedding and Frequency selection in Flapping Flight,” Journal of Fluid Mechanics, Vol. 410, 2000, pp. 323-341.

[9] Platzer, M. F., Jones, K. D. and Lai, J. C. S., “Flapping-wing Aerodynamics: Progress and Challenges,” AIAA Journal,

Vol. 46, No. 9, 2008, pp. 2136-2149.

[10] Hu, H., Clemons, L. and Igarashi, H., “An Experimental Study of the Unsteady Vortex Structures in the Wake of a Root-Fixed Flapping wing,” Experiments in Fluids, Vol. 51, No. 2, 2011, pp. 347-359.

[11] Jones, K. D., Dohring, C. M. and Platzer, M. F., “Experimental and Computational Investigation of the Knoller-Betz Effect,” AIAA Journal, Vol. 36, No. 7, 1998, pp. 1240-1246.

[12] Lai, J. C. S. and Platzer, M. F., “Jet Characteristics of a Plunging Airfoil,” AIAA Journal, Vol. 37, No. 12, 1999, pp.

1529-1537.

[13] Young, J. and Lai, J. C. S., “Oscillating Frequency and Amplitude Effects on the Wake of a Plunging Airfoil,” AIAA Journal, Vol. 42, No. 10, 2004, pp. 2042-2052.

[14] von Ellenrieder, K. D. and Pothos, S., “PIV measurement of the asymmetric wake of a two dimensional heaving

hydrofoil,” Experiments in Fluids, Vol. 43, No. 5, 2007.

[15] Von Ellenrieder, K. D., Parker, K. and Soria, J., “Fluid Mechanics of Flapping Wings,” Experimental Thermal and Fluid Science, Vol. 32, 2008, pp. 1578-1589.

[16] Yu, M. L., Hu, H. and Wang, Z. J., “A Numberical Study of Vortex-Dominated Flow around an Oscillating Airfoil

with High-Order Spectral Difference Method,” AIAA Paper 2010-0726.

[17] Yu, M. L., Hu, H. and Wang, Z. J., “Experimental and Numerical Investigations on the Asymmetric Wake Vortex Structures around an Oscillating Airfoil,” AIAA Paper 2012-0299.

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Figure 3 Phase lock results in the contour of dimensionless vorticity ( , )

𝜙 𝜙

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Figure 8 Mean velocity profiles at ⁄ . Green dash lines plot the peak at different location

( Left: , , Right: , )

(a)

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(b) (c)

Figure 9 Time averaged results at with different amplitude .

(a) Plot in the contour of dimensionless vorticity. (b) Velocity profile at ⁄ . (c) Velocity profile at

⁄ and .

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Figure 10 Time averaged results with different mean angle of attack . Plot in the contour of dimensionless

vorticity ( , )

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an experimental investigation on the asymmetric wake...

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