experimental study of shock wave oscillation on …fliu.eng.uci.edu/publications/c127.pdfamerican...

American Institute of Aeronautics and Astronautics

1

Experimental Study of Shock Wave Oscillation on SC(2)-0714 Airfoil

Zijie Zhao1 Xudong Ren2, Chao Gao3

Northwestern Polytechnical University (NPU), Xi’an 710072, China

Juntao Xiong4, Feng Liu5, and Shijun Luo6 University of California, Irvine (UCI), CA 92697-3975

An experimental study executed in the NPU NF-6 transonic wind tunnel on shock oscillations over SC(2)-0714 airfoil is presented. Tests are conducted at freestream Mach number from 0.72 to 0.82, Reynolds number based on the airfoil chord change from approximating 3.0 million to 5.0 million with transition strip fixed at 28% chord length. Limited span wise pressure distributions are obtained to verify the two-dimensionality of the flow field. The unsteady pressures on upper surfaces are analyzed and transonic buffet onset points are given. The results show that the phenomenon is essentially two dimensional in the middle of the model. The effect of the Reynolds number is negligible when the difference is about 1 million. Finally Lee’s self-sustained shock oscillation model is examined.

Nomenclature b = airfoil model wing span, mm c = airfoil model chord length, mm Cp = mean pressure coefficient, (p-p∞)/q0 Cp(t) = time depend pressure coefficient Cprms = rms value of Cp(t) fluctuations |Cp|

2 = Cp(t) power spectrum f = frequency of unsteady flow oscillation, Hz k = reduced frequency, 2πfc/ U∞ U∞ = freestream velocity Pst = freestream stagnation pressure, Pa P∞ = freestream static pressure, Pa P = local static pressure, Pa q0 = freestream dynamic pressure, Pa M∞ = freestream Mach number Re = Reynolds number based on free stream condition and chord length rms = root mean square x, y, z = Cartesian coordinates, origin at wing root leading edge x = chord wise coordinate from wing leading edge towards downstream y = upward coordinate perpendicular to wing plane z = span wise coordinate from wing root plane towards wing port side = angle of attack τ = time delay

1 Ph.D. Student, Now exchange to Department of Mechanical Engineering, National University of Singapore. E-mail: [email protected] 2 Graduate Student, Department of Fluid Mechanics. 3 Professor and Associate Director, National Key Laboratory of Science and Technology on Aerodynamic Design and Research. 4 Postdoctoral Researcher, Department of Mechanical and Aerospace Engineering, Senior Member AIAA 5 Professor, Department of Mechanical and Aerospace Engineering. Associate Fellow AIAA. 6 Researcher, Department of Mechanical and Aerospace Engineering.

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

AIAA 2013-0537

Copyright © 2013 by The authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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I. Introduction t transonic flow condition, shock wave and boundary layer interaction with separation may induce large

scale flow oscillation over the surface, known as transonic buffet. The oscillations are self-sustained for a range of mean flow Mach numbers and angles of attack, during the oscillation the shock wave travels along the chord, and its strength varies. Meanwhile, the down-stream separation location and the thickness of the boundary layer fluctuate1.The shock motion and associated flow field oscillations can change the aerodynamics and moments of the aircraft. Dramatic change of the aerodynamic force will cause large-scale lift oscillations that can limit the flight envelope of aircraft. It also can provoke dangerous vibrations leading to the destruction of a wing or a turbo machine blade2. It is for these reasons that the shock-buffet phenomenon has been an important factor in the design, and has been studied in wind tunnel tests since the eighties3. For modern supercritical wing design with thick profiles, the shock-induced fluctuations are particularly severed and periodic shock motions with large amplitudes are observed at high subsonic Mach numbers.

Such periodic shock motions have been reported over sixty years ago4. Lee5 presented a comprehensive review of shock-buffet studies, including physical models of the shock-buffet mechanism. He described the structure of the buffeting flow field and provided two empirical criteria to determine the buffet boundary. One criterion is based on a steady behavior of the separated boundary layer which was reported by Pearcey et al6. Another criterion is using unsteady pressure fluctuations to classify the type of shock boundary interaction which was first proposed by Mundell and Mabey7. Unsteady flow over fixed airfoil at transonic condition was reported by Humphreys8 firstly. After that transonic buffet on an 18% circular-arc airfoil at zero angle of attack has been investigated by McDevitt et al9. In transonic speed a series of supercritical airfoil at high incidence were studied10-14. Results show that there are some difference in the mechanisms of periodic shock motion between a lifting airfoil at incidence and a symmetrical one at zero incidences. Then special attention was given to the supercritical airfoils. A. Alshabu et al.15 found the existence of upstream-moving waves over BAC3-11 airfoil and they also believe wave generation is coupled with vortex generation in the boundary layer. L. Jacquin et al.2 described a new experiment executed in the ONERA S3Ch transonic wind tunnel on shock oscillations over the OAT15A supercritical profile and gave lots of details to develop an experimental database on transonic buffet. Meanwhile using CFD to predict buffet onset and boundary has been investigated by several authors, and some methods have been developed to resolved transonic buffet problem like Unsteady Reynolds-Averaged Navier-Stokes (URANS) 1, 16-18 zonal-DES19 and Large Eddy Simulation (LES) approach such as the work done by Garnier and Deck20. J. D. Crouch’s et al.21 studies showed that the origin of buffet onset is tied to a global instability and global instability analysis could provide good qualitative and quantitative descriptors for buffet onset. Although the buffet problem has been study for sixty years, the physical mechanism for buffet onset is still not fully understood.

The aim of present paper is to evaluate the test techniques, to constitute possible experiment data for transonic buffet over the supercritical airfoil and to study the process of buffet in a newly established transonic wind tunnel. The experiments were executed in the NPU NF-6 wind tunnel using a supercritical airfoil model profile. The result includes naphthalene film sublimation flow visualization over the airfoil and steady and unsteady pressure measurements. Finally conclusions are drawn.

II. Experimental Setup The present study was carried out in the continuous closed-circuit transonic wind tunnel NF-6 at the

Northwestern Polytechnical University, Xi’an China. The two-dimensional test section size is 0.8(high)×0.4(wide)×3(long) m. This facility is driven by a two-stage axial-flow compressor. The stagnation pressure of the tunnel air can be adjusted from 1.0 to 5.5 times of atmospheric pressure. The air was dried until the dew-point in the test section was reduced sufficiently to avoid condensation effects. The upper and lower walls are 6%-perforated with holes 60° inclined upstream. The flow uniformity in the test section was examined. The centerline Mach number distributions were calculated by centerline static pressures. The flow is uniform in the test section in Mach number between 0.20 and 1.00 from the entrance to the exit. The Mach number distributions along the centerline are shown in Fig. 1.

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Fig. 1 Mach number distributions along the centerline of the test section of the wind tunnel.

A. Model and Measurements The model is an SC(2)-0714 airfoil (see Fig. 2) with a relative thickness of 14%, a chord length c = 250mm, a

span of b=400mm (which gives the aspect ratio =1.6). The central region of the airfoil has is equipped with 54 static pressure orifices and 27 Kulite pressure transducers, the type of the Kulite sensor is XCQ-093. There are 20 static pressure orifices at z/c = 0.75 and z/c =- 0.5 on the upper surface in order to check the flow two dimensionality. Figure 3 is the upper and lower view of model surface, showing the positions of the pressure orifices and Kulite transducers. The model installed in the test section is shown in Fig. 4.

Fig. 2 Lateral view

(a) upper view (b) lower view

Fig. 3 Locations of the static pressure orifices and Kulite transducers

Fig. 4 SC(2)-0714 supercritical profile in the NF-6 transonic wind tunnel

X/C

Y/C

0

0

0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

1

1

-0.05 -0.05

0 0

0.05 0.05

0.1 0.1

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B. Test Conditions The test conditions are presented in Table 1. The freestream Mach numbers varied between 0.72 and 0.82, ΔM∞

=0.01, the angles of attack was set between 0° and 5°. The experiment was conducted in two times with different stagnation pressure and the Reynolds number based on the airfoil chord of 250 mm is approximately 3.7×106 and 5.0×106 separately. The boundary layer transition fixed at xtr/c=28%. In order to check the flow in the bounder-layer is laminar or not, the naphthalene film sublimation flow visualization method was used. In the turbulent region the temperature will elevate and the turbulence of the boundary layer will become high compared to the laminar region. Those characteristics will cause the naphthalene to increase its rate of sublimation. Figure 5(a) shows that the naphthalene film was fully attached the upper surface of the model, Fig. 5(b) shows the condition of the film after the experiment which taken at M∞ = 0.78, α= 0°, Re = 3.7×106. We can see the transition line is xtr/c =28%. The naphthalene film sublimation experiment was conducted in low Re, but the laminar region should keep a relative long distance at high Re without fixed transition.

Table 1 Test conditions for steady pressure and unsteady pressure measurement

M∞ α(°)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 6 0.72 × × × × × × × × × × × 0.73 × × × × × × × × × × 0.74 × × × × × × × × × × 0.75 × × × × × × × × × × 0.76 × × × × × × × × × × 0.77 × × × × × × × × × × 0.78 × × × × × × × × × × 0.79 × × × × × × × × × × 0.80 × × × × × × × × × × 0.81 × × × × × × × × × × 0.82 × × × × × × ×

(a) With naphthalene film (b) Fixed transition

Fig. 5 Naphthalene film sublimation at M∞ = 0.78, α= 0°, Re = 3.69×106.

III. Results and Discussion

A. Two Dimensionality Examine

Harris22 measured the static pressures over a SC(2)-0714 airfoil in NASA Langley 8ft transonic wind tunnel. Its measured pressure data may be considered of free air and used to find the wall interference corrections of the present wind tunnel. For the present supercritical airfoil, based on the technique discussed in Ref. 23, the boundary layer transition was fixed along the 28-percent chord line on the upper and lower surfaces of the model in an attempt to provide the same relative trailing edge boundary layer displacement thickness at model scale as would exist at full-scale flight conditions around Reynolds number of 40 million. It is noted that the simulation technique, which requires that laminar flow be maintained ahead at the transition trip, is limited to those test conditions in which

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shock waves or steep adverse pressure gradients occur behind the point of fixed transition so that the flow is not tripped prematurely. Figure 6 shows the distribution of the model surface pressure coefficient Cp measured at M∞ = 0.78 in different incidence angles. A supercritical profile is characterized by a pressure plateau compensated by compression induced by a pronounced camber on the rear part of the airfoil. When the angle of attack is 3 and 3.5deg, the shock wave is located at x/c=0.55 approximately. Comparisons of steady pressure measurements at two different span wise stations could reflect two dimensional flow of the wind tunnel, the comparisons of various angles of attack at M∞ =0.78 and Re ≈ 5.0×106 are made in Fig. 6. When the angle of attack (AOA) is low (α=0°, 3°, 3.5°), the steady pressure coefficient at the center have a good consistency with those off the center even at downstream portion of the model, the only appreciable deviation occurred nearest the wall for the data in Fig. 6(a) and Fig. 6(b). The shock positions have big difference among them when the AOA is 4 . According to these figures, these data indicate that the flows were essentially two-dimensional flow. Figure 7 puts the pressure distribution Cp at four different AOA (α=0°, 3°, 3.5°, 4°) together. At α=0°, 3° the shock remains steady (no buffet), when AOA increase to 3.5° the shock star to oscillate. We also notice that the position is forward at α=3.5° than that at α=3°, and pressure decrease at the trailing edge simultaneously. Figure 8 shows mean surface pressure coefficient at different Reynolds number, the shock wave position is forward at Re=5.0×106 than Re=3.7×106 coursed by different thickness of the boundary-layer24.

a) α=0° b) α=3°

c) α=3.5° d) α=4° Fig. 6 Comparisons of steady pressure measurements, M∞ =0.78, Re≈5.0×106

x/c

Cp

0

0

0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

1

1-2.4 -2.4

-2 -2

-1.6 -1.6

-1.2 -1.2

-0.8 -0.8

-0.4 -0.4

0 0

0.4 0.4

0.8 0.8

1.2 1.2

M=0.78,=0,upper surfaceM=0.78,=0,lower surfaceCp*

z/c=-0.5z/c=0.75

x/c

Cp

0

0

0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

1

1-2.4 -2.4

-2 -2

-1.6 -1.6

-1.2 -1.2

-0.8 -0.8

-0.4 -0.4

0 0

0.4 0.4

0.8 0.8

1.2 1.2

M=0.78,=3.5,upper surfaceM=0.78,=3.5,lower surfaceCp*

z/c=-0.5z/c=0.75

x/c

Cp

0

0

0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

1

1-2.4 -2.4

-2 -2

-1.6 -1.6

-1.2 -1.2

-0.8 -0.8

-0.4 -0.4

0 0

0.4 0.4

0.8 0.8

1.2 1.2


z/c=-0.5z/c=0.75

x/c

Cp

0

0

0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

1

1-2.4 -2.4

-2 -2

-1.6 -1.6

-1.2 -1.2

-0.8 -0.8

-0.4 -0.4

0 0

0.4 0.4

0.8 0.8

1.2 1.2


z/c=-0.5z/c=0.75

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Fig. 7 Mean surface pressure coefficient at different

AOA, M∞ =0.78, Re≈5.0×106

Fig 8. Mean surface pressure coefficient at different Re, M∞ =0.78, α=3.5°

B. Unsteady pressure analysis One of the earliest methods to determine buffet onset is described by Pearcey25 and Pearcey and Holder26 who

considered only airfoils encountering bubble separation. Buffet onset is determined by the Mach number or incidence when the bubble reaches the trailing edge and bursts. This can be obtained quite readily from the divergence of the trailing edge pressure. Other methods using unsteady forces or pressure measurements are described by Polentz et al.27 and Mabey28. In this experiment we can directly get the unsteady pressure on the airfoil surface. So the rms values of the Cp(t) at different position alone the chord wise were used to define the buffet boundary.

Both the continuous and fluctuating parts of the pressure signals provided by Kulite transduce. For the fluctuations, the sampling rate was set to 20 kHz and low-pass filtered at 2000 Hz. The sample length was fixed to 2s. The rms value of the Cp(t) fluctuation on the airfoil upper surface at different M∞ are plotted in Fig. 9 . From Fig. 9(a) shows that the buffet onset at α=5° at M∞=0.76, before buffeting, the fluctuation amplitudes remain weak. When the AOA beyond 5° buffet is established and strong fluctuation are detected at x/c=0.4. When the M∞ increase to 0.78, a big fluctuation amplitudes is measured at α=3.5°, the maximum being located at x/c=0.4 and the pressure fluctuation localized around x/c=0.3 to x/c=1. Compare Fig. 9(a) to Fig. 9(d), we can see the buffet onset AOA decrease from α=5° to α=1° when the M∞ increase from 0.76 to 0.82. It was noted that the oscillation occurred in a wide range of M∞ and AOA. Figure 10 shows the buffet boundary at different Reynolds number for this airfoil. The onset points of shock oscillations were observed from the unsteady pressure. From these pictures we see that the AOA decrease with March number increase at the onset point of the buffeting but the buffet boundary only have little difference between two Reynolds number.

a) M∞=0.76, b) M∞=0.78

x/c

Cp

0

0

0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

1

1-2.4 -2.4

-2 -2

-1.6 -1.6

-1.2 -1.2

-0.8 -0.8

-0.4 -0.4

0 0

0.4 0.4

0.8 0.8

1.2 1.2

=0 M=0.78=3 M=0.78=3.5 M=0.78=4 M=0.78

x/c

Cp

0

0

0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

1

1

-2 -2

-1.5 -1.5

-1 -1

-0.5 -0.5

0 0

0.5 0.5

1 1

M=0.78, =3.5, Re=5.0106

M=0.78, =3.5, Re=3.7106

x/c

Cpr

ms

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

α=0°α=0.5°α=1°α=1.5°α=2°α=2.5°α=3°α=3.5°α=4°α=5°

x/c

Cpr

ms

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

α=0°α=0.5°α=1°α=1.5°α=2°α=2.5°α=3°α=3.5°α=4°α=5°

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c) M∞=0.80 d) M∞=0.82

Fig. 9 Influence of incidence on the chord wise distribution of the Cp(t) rms Re≈5.0×106.

a) Re≈5.0×106 b) Re≈4.0×106

Fig. 10 Onset point of shock oscillation Figure 11 shows the results of Fourier analysis of different AOA at M∞=0.78. At α=3° the fluctuation

amplitudes of all Kulite transducers remain weak the pressure is still steady. As the AOA increasing to 3.5°, the shock wave located between x/c=0.45 to 0.7 transducers and the signal is fully periodic meanwhile buffet is established. Figure 12 shows comparisons of different x/c positions pressure coefficient power spectrum results at α=3.5°, a prominent spectral peak corresponding to 70 Hz is seen from x/c= 0.45 to 0.7 with the largest amplitude at x/c= 0.55. This phenomenon is also observed at AOA is 4° and 5°; however, the spectral peak decreases in amplitude meanwhile increases the buffet frequency. For α=4°, a prominent spectral peak corresponding to 84 Hz is seen from x/c= 0.45 to 0.7 with the largest amplitude at x/c= 0.55 but the maximal amplitude is only almost half of condition. Figure 13 shows pressure coefficient power spectrum results at Re=3.7×106, M∞=0.78 and α=3.5°. Comparing this figure to Fig. 11(c), the region of buffeting looks the same but the amplification is bigger at Re=3.7×106 than Re=5.0×106.

Figure 14 shows the results of Fourier analysis of x/c=0.55 at M∞=0.78 in different incidence. Table 3 shows the buffet frequencies of different angles of attack, where the reduce frequency is defined as k=2πfc/ U∞. These results demonstrate that the buffet phenomenon is sensitive to the incidence.

From spectrum graph (Fig. 11, 12, 13 & 14), we notice that there are some low frequency oscillation appears. It may be caused by background turbulence and unsmooth of the model surface. In order to protect the Kulite sensor we used the PTEF (Polytetrafluoroethylene) to wrap around the transducer and then install the whole thing into the model. The diameter of the hole is 3.5mm at the model surface. So there is circle area is flat at the head of the Kulite transducer. We try our best to make the head of the Kulite sensor parallel to the model surface but there still have a little unsmoothed of the profile.

x/c

Cpr

ms

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

α=0°α=0.5°α=1°α=1.5°α=2°α=2.5°α=3°α=3.5°α=4°α=5°

x/c

Cpr

ms

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

α=0°α=0.5°α=1°α=1.5°α=2°α=2.5°α=3°

Mexp

α(°

)

0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.840

1

2

3

4

5

6

7

buffet boundary

no buffet

shock oscillation

Mexp

α(°

)

0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.840

1

2

3

4

5

6

7

buffet boundary

no buffet

shock oscillation

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a) α=0° b) α=3°

c) α=3.5° d) α=4°

Fig. 11 Influence of incidence on the power spectrum at M∞ =0.78 and Re≈5.0×106

Fig. 12 Comparisons of several Kulite transducers results at M∞=0.78, Re≈5.0×106, α=3.5°

Fig. 13 Pressure coefficient spectrum M∞ =0.78,

α=3.5° Re≈3.7×106

Fig. 14 Pressure coefficient spectrum of x/c=0.55 at M∞ =0.78 and Re≈5.0×106

f(Hz)

0

50

100

150

200

x/c

00.10.20.30.40.50.60.70.8

|cp|2

(Hz-2

)

0

0.0002

0.0004

0.0006

0.0008

0.001

f(Hz)

0

50

100

150

200

x/c

00.10.20.30.40.50.60.70.8

|cp|2

(Hz-2

)

0

0.0002

0.0004

0.0006

0.0008

0.001

f(Hz)

0

50

100

150

200

x/c

00.10.20.30.40.50.60.70.8

|cp|2

(Hz-2

)

0

0.0002

0.0004

0.0006

0.0008

0.001

f(Hz)

0

50

100

150

200

x/c

00.10.20.30.40.50.60.70.8

|cp|2

(Hz-2

)

0

0.0002

0.0004

0.0006

0.0008

0.001

f(Hz)

|CP|2

(Hz-2

)

50

50

100

100

150

150

200

200

0

0.0002

0.0004

0.0006

0.0008

0.001

x/c=0.45x/c=0.55x/c=0.65x/c=0.7

∧

70Hz

f(Hz)

0

50

100

150

200

x/c

00.10.20.30.40.50.60.70.8

|cp|

2(H

z-2)

0

0.0002

0.0004

0.0006

0.0008

0.001

∧

f(Hz)

0

50

100

150

200

()

01

23

45

6

|cp|2

(Hz-2

)

0.0002

0.0004

0.0006

0.0008

0.001

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Table 3 Buffet frequencies of different angles of attack at M∞ =0.78, Re≈5.0×106

α(°) 3.5 4 5

Reduced frequency k 0.44 0.53 0.63

C. Self-sustained shock oscillation feedback model Lee29, 30 proposed a possible mechanism of self-sustained shock oscillation during transonic buffeting. In this

close loop model the frequency of oscillation can be calculated. In Fig. 15, the shock wave is shown to oscillate on the upper surface at a mean position (xs) and a pressure wave is generated simultaneously. This pressure wave propagated downstream in the separated flow region at a velocity ap. On reaching the trailing edge; the disturbances generate upstream-moving waves at velocity au in the region outside the separated flow as a result of satisfying the unsteady “Kutta” condition. These two kinds of waves will interact with the shock wave and impart energy to maintain its oscillation. The loop is then completed. The period of the shock oscillation is the time it takes for a disturbance to propagate from the shock to the trailing edge plus the duration for an upstream wave to reach the shock from the trailing edge via the region outside the separation flow. The total time it takes for a complete loop is given by the following relation:

(1)

1/ 1/ (2)

au = (1-Mloc ) × aloc (3)

Mloc = R× [Mloc (at the surface)-M∞] +M∞ (4)

Tp is the total time it takes for a complete loop. Tp1 and ap are the time and speed for downstream pressure wave propagation; Tp2 and au are the time and speed for the upstream wave, xs is the time-mean shock location. Eq. (1) can get the frequency of the feedback loop which f = 1/Tp is then determined.

From xs/c=0.55 to x/c=1.00, we total have 14 pressure orifices. The local March number Mloc can be calculated from the local static pressure Pi and freestream stagnation pressure Pst. The relaxation factor R varies between 0 and 1 in this study we use R=0.77. The second part of Eq (2) part 2 can be written as:

Mloc (at the surface)= 1 (5)

∑ 1// .

/ (6)

The equals to 0.011s.

Fig. 15 Model of self-sustained shock oscillation

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In order to calculate the ap, two-point cross correlation of the unsteady pressure is used to determine the propagation direction and speed of the pressure fluctuations along a given path. A cross-correlation coefficient

),,x( yR for two variables x and y with time delay τ can be defined as

22 )(')('

)-(')('),,(

tytx

tytxyxR

(7)

Where x and y are the pressure fluctuations at the two points, and )(' tx and )(' ty are the fluctuating parts of x and y,

respectively. The over bar stands for time averaging, for example,

T

T dttxT

x0

)()1

(lim (8)

Thus, we have

)(')( txxtx , )(')( tyyty (9)

The result of M∞ =0.78 and α=3.5° is discussed in detail. Because the largest amplitude of pressure coefficient power spectrum occurs at x/c=0.55, The Kulite sensor at this position is used as the reference point. The cross-correlation analysis is conducted for the Kulite sensors locate at x/c=0.45, x/c=0.55, x/c=0.65, x/c=0.7 along the upper airfoil surface, for easy showing in Fig. 16 consider they are point a, ref, b, c separately. The local propagation speed of the pressure disturbances can be calculated by dividing the spatial distances between the neighboring points by the time delays between the peaks of the corresponding cross correlations shown in Fig.16. The time delay τ0 corresponding to Maximum values of correlation coefficient of the pressure fluctuations are shown in Table 4. As seen in Fig. 17, one finds on the upper side behind the shock pressure fluctuations propagating upstream with a negative velocity of about 0.156 U∞ within the separated region, for U∞ =261m/s, the wave transmit velocity ap is 40.7m/s. So the equals to 0.0027s.

The total time 0.0137 , so the buffet frequency is approximately 73Hz, which agrees well with the result measured by Kulite transducer.

Table 4 Time delay 0 corresponding to Maximum values of correlation coefficient

Location of Kulite sensor x/c=0.45(a) x/c=0.55(ref) x/c=0.65(b) x/c=0.7(c) Time delay τ0 (s) 0.0004 0 -0.0006 -0.0012

Fig. 16 Cross correlation of the downstream

pressure wave on the upper surface, Fig. 17 Maximum values of the space-time

correlations of the pressure fluctuations

IV. Conclusion An experimental study of the static and dynamic pressure distributions over a SC(2)-0714 airfoil in a transonic

wind tunnel is presented. The flow two dimensionality are determined by comparing the steady pressure coefficient of the center chord wise with steady pressure coefficient of z/c=-0.5 and z/c=0.75. The results demonstrate that the flows are essentially two-dimensional flow.

(s)

corr

ela

tion

coe

ffic

ien

t

-0.03 -0.02 -0.01 0 0.01 0.02 0.03-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

R(ref,b,)

R(ref,ref,)

R(ref,a,)

R(ref,c,)

0U/c

(xi-x

ref)/

c

-1.5 -1 -0.5 0 0.5 1-0.2

-0.1

0

0.1

0.2

0.3

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The buffet boundary is given; the onset points are defined as the rms value of unsteady pressure extremely changed at different flow condition. The buffet boundary have little difference between Reynolds number at 3.7×106

and 5.0×106. The spectrogram of unsteady pressure coefficient is obtained at M∞=0.78. The result included spectrogram result at different x/c position under several angles of attack. Results show that reduces frequency increases from 0.44 to 0.63 when the angle of attack increases. The spectrum graph have some low frequency oscillation appears. It may be caused by background turbulence and unsmooth of the model surface.

Lee29, 30 proposed a possible mechanism of self-sustained shock oscillation during transonic buffeting. In order to examine the close loop feedback model, we chose M∞=0.78 α=3.5° condition as an example. The time takes of pressure wave propagated downstream was integrated from mean position of the shock wave to the trailing edge. The cross-correlation coefficients of pressure fluctuations of several Kulite transducers on the upper surface are used to calculate the pressure wave’s propagation upstream within the separation region between the shock wave and the airfoil trailing edge. Buffet frequency is approximately 73Hz by using Lee’s feedback model, which agrees well with the result measured by kulite transducer.

V. Acknowledgment The present work is supported by the Foundation for Fundamental Research of the Northwestern Polytechnical

University (No. JC-201103) and Nation Key Laboratory Research Foundation of China (No.9140C420301110C42). The authors wish to thank Dr. Cui Yongdong from Temasek Laboratories, National University of Singapore, give us great advice for this paper.

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