Nomenclature
x,	coordinate along the length of the airfoil;	t,	time of vibration;
±yt,	thickness coordinates above and below the line extending along the length of the airfoil;	p1,	horizontal coordinate of the front end on the vibrating part;
h,	maximum thickness of the airfoil;	p2,	horizontal coordinate of the back end on the vibrating part;
c,	chord of the airfoil;	CL,	airfoil lift coefficient;
yv,	vertical position coordinate of the vibrating part;	CD,	airfoil drag coefficient;
A,	amplitude of vibration;	f,	frequency of vibration.

1 Introduction

Flow control techniques can improve the aerodynamic performance of airfoils effectively, and improve the economic impact of both civil and military aircraft by enhancing load capability and lowering fuel cost. Several flow control techniques ^[1-3] have been studied by academic and industry groups. For example, blowing or suction was found to be effective in increasing lift and decreasing drag of airfoils ^[4], and the effects of suction and blowing were varying ^[5]. Suction was more effective at the leading edge of airfoils while blowing was more effective at downstream locations. The plasma actuator has proved to be effective in controlling flow separation and increasing the lift-to-drag ratio when placed at the leading edge ^[6-9], although it needs an extra device and notable energy to produce plasma. The zero-net-mass-flux jet method has been studied numerically and experimentally ^[10-13]. It was found that specific jet positions and frequencies can delay flow separation in the boundary layer and significantly increase the lift-to-drag ratio ^[14].

The flow control technique proposed in this paper is supported by numerous research. Several experiments by Seifert et al. showed that periodic oscillatory blowing applied at the leading edge on the upper surface of the airfoil could delay separation ^[15-16]. The effects of leading-edge oscillating-flap excitation on an airfoil with various oscillating modes were also investigated by Hsiao et al. ^[17]. Their results showed that the flow over the airfoil could be strongly influenced by excitation. The influence was positive, and the oscillating modes of flap motion strongly influenced the aerodynamic performance. The above mentioned studies all used only experimental methods and focused on rigid flap oscillation out of the upper surface, which made significant demands on the structure. In this study, we attempt to use film to keep the oscillation just on the surface of the airfoil, considering that the low-speed aircraft has light weight and flexible skin like the film on the surface.

Sinha ^[18] developed a capacitive actuated active flexible wall transducer to produce oscillating force for flow control. The optimum frequencies for control were higher compared with oscillatory blowing or oscillating microflaps. The need for transducers and control systems to produce high-frequency oscillation has made this method complex, and the device is heavy. Thus, a simple film vibrating device with the low frequency is used in this study.

Recently, Kang et al. ^[19-20] conducted a numerical study on the aerodynamic performance around a locally flexible airfoil. Their results showed that self-excited vibration of the flexible part enhanced the lift of the airfoil due to the formation of coherent vortices. Our work focuses on active local vibration, including numerical analyses of the influence of different parameters such as the airfoil angle of attack, the oscillation frequency, the width, and the location. Experiments were also carried out to demonstrate the improvement in the aerodynamic performance by local vibration on the airfoil.

The aforementioned studies indicate that the vibration frequency is the most important parameter of local vibration, because the fluid and vibration of a flexible structure are coupled, and the flow over the airfoil can be influenced only when the vibration frequency of the flexible structure matches the frequency of the shear layer vortices or the wake shedding frequency ^[21]. Shear layer vortices and wake shedding vortices have been studied for decades. In 1964, Tani ^[22] found that a bubble was formed by the separation of the laminar boundary layer with subsequent reattachment. Then, a previous study demonstrated that laminar boundary-layer separation on the airfoil surface resulted in periodic vortex shedding and subsequent pairing downstream ^[23]. Recently, Yarusevych et al. ^[24] performed a series of studies on this subject. Their study focused on the development of coherent structures in the separated shear layer and wake of an airfoil, and found that the dominant frequency of roll-up vortices was different from the wake vortex shedding frequency. In particular, they discussed the Strouhal number of the dominant frequency of the separated shear layer disturbances and the wake vortex shedding frequency ^[25-26]. Therefore, by learning from previous works, the separation point and dominant frequencies of the flow are studied in this work, which provides the basic results for the analysis of airfoil with vibration.

In this paper, an alternative flow control technique is proposed that uses a simple local vibrating device to increase lift and reduce drag. An NACA 0012 airfoil is used to study the effect of local vibration on the shedding of shear layer vortices through numerical and experimental methods.

2 Numerical methods

The NACA 0012 is a symmetrical airfoil that is widely used in the aircraft. The thickness of the NACA 0012 airfoil can be calculated from the following equation ^[27]:

(1)

where c=1.

As shown in Fig. 1, a flexible part is placed on the upper surface near the leading edge. The position coordinate of the flexible part during vibration can be defined by the following equation:

(2)

A large eddy simulation (LES) in FLUENT was applied in the numerical simulation with the Reynolds number of 750 000 based on the chord length. A conventional C-type grid layout with 249 336 cells was applied with high resolution around the airfoil with y⁺ < 1, where y⁺ is the wall coordinate. The independence of the results from mesh quality was checked. The SIMPLE algorithm was selected for the velocity-pressure correction and iterative solution of the discretized equations. The spatial derivatives of the pressure equations and momentum equations were computed by a second-order scheme and second-order central difference scheme, respectively. The second-order implicit scheme was chosen as the transient formulation. The dynamic mesh was used to treat the deformation of the vibrating part. The time step was set as 4× 10^-6 s.

It should be noted that the LES was chosen for the analysis in this study by considering the effects of local vibration on the vortex. Reynolds-averaged models can describe the mean flow and effects of turbulence on mean flow properties, without the details of turbulent flows ^[28] affected by local vibration. A direct numerical simulation computes the mean flow and all turbulent velocity fluctuations, but has high computational cost. The LES describes the larger eddies by time-dependent flow equations, and smaller eddies are described by a compact model, which is now acceptable for computation.

2.1 Flow behavior over the static NACA 0012 airfoil

The original NACA 0012 airfoil was simulated under several angles of attack to verify the method used in this study, and to determine the separation point and dominant frequencies of the flow, which will provide the basic results for the analysis of vibrating airfoil. The lift and drag coefficients agreed with the results of Huang et al. ^[5] and Wong and Kontis ^[29], as shown in Fig. 2.

To investigate the separation point, we take the case with 8° angle of attack as an example. Fifty equidistant points near the upper surface and in the wake of the airfoil were monitored. The streamlines at t=10.0 s are shown in Fig. 3. The flow patterns of separation, transition, and reattachment can be observed in Fig. 3, as stated in previous studies ^{[24, 30-31]}, and the separation point is approximately x/c=0.05-0.06. It was also found that large-scale shear layer vortices were shedding after a short separation-bubble ^[32]. In addition, a fast Fourier transform (FFT) analysis was conducted for data on the monitoring points in the boundary layer and wake region. We found that near the leading edge, the frequencies are all below 1 Hz, which indicates that the fluid is stable, and fluctuation is negligible. With the generation of vortices, the dominant frequencies are approximately from 11.0 Hz to 13.6 Hz in the separation area, and nearly 17.1 Hz in the wake flow owing to the shedding vortices.

2.2 Local vibration on the airfoil

Following the analysis of the static NACA 0012 airfoil, we applied local vibration to the airfoil to determine the impacts of various angles of attack, frequencies, widths, and positions on the aerodynamic performance.

2.2.1 Frequency

The frequency is an essential parameter and should be discussed in detail. According to the separation location shown in the static airfoil, the flexible part is placed at x/c=0-0.1 at the leading edge with the width 10% of chord length. The vibration amplitude was set as 0.003 of the chord length, the same as that in the previous work ^[33].

Nine different frequencies from 0 Hz to 40 Hz were applied in the numerical simulations with the angle of attack of 8°, and the results are shown in Fig. 4. The effect of frequency is remarkable when it is close to the dominant fluctuation frequency, which has also been pointed out by the previous researchers ^[21]. The benefit to the lift coefficient is negligible. However, the vibration can decrease the drag coefficient by over 10% under 15 Hz-20 Hz, which corresponds to the experimental results of Munday and Jacob ^[33], who revealed that a camber oscillating within a particular frequency band would delay separation over an airfoil.

To analyze the drag reduction mechanism, the flow patterns of vibrating and static airfoils were compared. In Fig. 5, the vorticity contours of the static airfoil are shown in four stages. In Fig. 5(a), at , four large-scale vortices appear on the upper surface behind the separation bubble. Vortex 1 with the large rolling velocity catches up with Vortex 2 at the moment , as shown in Fig. 5(b). Then, Vortices 1 and 2 merge into a larger vortex as shown in Figs. 5(c) and 5(d). When local vibration of 15 Hz is given, the resonance effect causes the vortices on the upper surface to be more regular in moving and shedding, which can be seen in Fig. 6. Three large vortices are rolling separately without merging, which will reduce the drag significantly.

With the increase in the vibration frequency, the interaction between the shedding vortex and vibration vortex leads to complex phenomena. The flow pattern at 40 Hz in Fig. 7 shows that eight smaller vortices are formed on the upper surface. However, the difference in rolling speeds causes the merging behavior, which introduces extra drag. It can be concluded that periodic travelling vortices can be found at specific frequencies and can decrease the drag significantly.

2.2.2 Width

The film widths 0.1, 0.05, 0.025, and 0.012 5 of the chord length were studied with the angle of attack of 8°, while the location was set at x/c=0.05 near the separation point, the vibration frequency was set to 15 Hz, and the amplitude was set to 0.003c. The results show that the lift coefficient barely changes with the change in the width, while the drag coefficient deceases notably with narrowing of the film. The drag coefficient decreases by over 15% at the optimum width, which is shown in Fig. 8.

Altering the vibration width changes the excitation intensity to the flow on the upper surface of the airfoil. The flow patterns with different widths under the typical time in one period are depicted in Fig. 9. It is found that more shear vortices are produced, and drag further decreases at narrower widths than wider ones. However, a film that is too narrow makes structural design difficult. Considering the balance between the vibration effect and the structure, 0.025c was chosen as the optimum vibration width.

2.2.3 Position

Four positions, i.e., x/c=0.015-0.040, x/c=0.040-0.065, x/c=0.065-0.090, and x/c=0.090-0.115, were studied at the angle of attack of 8°, the vibration width of 0.025c, the frequency of 15 Hz, and the amplitude of 0.003c. The effect on drag reduction is shown in Fig. 10. There exists a specific position x/c=0.065-0.090, which can reduce the drag by over 23%. We observe that this position is just close to the separation point of the static airfoil at the angle of attack of 8°. The flow patterns depicted in Fig. 11 show that local vibration just around the separation point is the most efficient mode since the vibration can effectively excite the shear layer vortices just behind the short separation-bubble to introduce more and smaller vortices forming on the shear layer.

2.2.4 Angle of attack

Cases with several angles of attack were studied with vibration positions x/c=0.065-0.090, the width of 0.025c, the frequency of 15 Hz, and the amplitude of 0.003c. The simulation results are shown in Fig. 12. We find that the vibration scheme introduces extra drag in small angles of attack since the separation effect is negligible. However, with the increase in the angle of attack, the vibration scheme can reduce the drag significantly by delaying separation and smoothing the shear vortex rolling. Also, it is found that local vibration is effective for the medium angles of attack and ineffective for too high angles.

3 Experiments 3.1 Experimental setup

The experiments were carried out in a low-turbulence, low-speed wind tunnel. The wind tunnel was 50.58 m×8 m×18 m in the length, width, and height directions, respectively, with the test section of 18 m×4 m×3 m. The maximum velocity was 55 m/s in the test section. The airfoil model NACA 0012 with the chord length c of 0.8 m was made of the acrylic material, as shown in Fig. 13. The vibrating part was made of thin stainless steel strips, and set on the upper surface at x/c=0.012~5-0.052~5; the vibration amplitude of 0.004 m was introduced via an electrical motor. The frequencies can be adjusted by changing the voltage. According to the similarity criterion, the wind tunnel velocity was set to 12.5 m/s, and the Reynolds number was 7.5×10⁵. The force sensors were made by ME-SYSTEM of Germany, with the measurement ranges of 40 N, 260 N, and 520 N in three directions, measurement accuracy of 0.3% full scale, and the sampling frequency of 1 kHz. The pressure sensors were made by SCANIVALVE of the U. S. A., with measurement range of ±10 inch water column, measurement accuracy of ±0.15% F.S., and the sampling frequency of 625 Hz.

3.2 Experimental results

When the vibration frequency of the airfoil is zero, the model can be considered as a static airfoil. Pressure data of the sample points were analyzed through the FFT. The results indicate that the dominant frequency of the flow fluctuation on the upper surface is 19.8 Hz. Figure 14 shows the FFT results of two typical points, Points 1 and 2, as defined in Fig. 1. The flow fluctuation is attributed to the shedding of shear layer vortices.

According to the shear layer vortex shedding frequency and the limitations of the mechanical vibration device, three frequencies (9.2 Hz, 14.5 Hz, and 19.5 Hz) were used to investigate the influence of the local vibration frequency on the lift and drag of the model.

The experimental results reveal that the lift barely changes with the change in the frequency, similar to the results of numerical simulations. But the drag coefficient decreases dramatically at all angles of attack as shown in Fig. 15; especially at 19.5 Hz, the maximum decrease reaches up to 80%. However, the results are slightly different from the numerical simulations in the small angles of attack region. After the careful investigation, the reason for this difference could be the poor flatness and smoothness of the vibrating part of the model due to machining operations and installation, which causes separation of the flow even at small angles of attack, unlike the results of the numerical model.

4 Conclusions

In this paper, an alternative flow control technique by local vibration is proposed to improve the aerodynamic performance of an airfoil. A typical airfoil, NACA 0012, which has been widely studied numerically and experimentally, is introduced to study the effect of local vibration.

The numerical results suggest that local vibration on the upper surface of the airfoil can control the aerodynamic performance; in particular, it can diminish the drag at certain angles of attack. After studying some parameters, it is found that local vibration is effective for medium angles of attack. The vibration induced near the separation point, which can trigger shear layer vortices behind the short separation-bubble and cause additional and smaller vortices to form on the surface, can decrease the drag coefficient by over 23%. When choosing the optimum width of the vibrating part, the tradeoff between drag reduction and structural design should be considered. The frequency is the key parameter in this technique. A significant decrease in the drag coefficient is achieved when the excitation frequencies are near the dominant frequencies of the shear layer vortices and wake vortices. By analyzing the flow pattern of the shear layer, it is shown that vibration near the separation point can inject extra energy into the newborn vortex, changing its rolling and emerging form. Vortices of suitable size and number will reduce the drag of the outer flow by replacing sliding friction with rolling friction in the boundary layer.

The experiments focus on the influence of vibration frequency on the flow control performance of the wing model. The results reveal that the lift coefficient barely changes, similar to the results of numerical simulations. However, the drag coefficient decreases by 80% with vibration at frequencies near the shear layer vortices shedding frequency, which is better than the results of numerical simulations.

The numerical and experimental results show that, by carefully choosing the vibration location, width, frequency, and amplitude, the proposed technique can be applied as an alternative and effective method to control the aerodynamic performance of the commercial aircraft. In particular, the method has the optimum effect in control of vortices and drag reduction at medium angles of attack, and may be used in the takeoff and landing of commercial aircraft, and to stabilize the dynamic stall vortex of a retreating helicopter rotor blade. Further works will be carried out to investigate the dynamic behavior of vortices quantitatively. In addition, experiments with a more precise model will be conducted in the future to obtain more solid results.