719

2010,22(5):719 -724 DOI: 10.1016/S1001-6058(09)60108-6

EXPERIMENTAL INVESTIGATION ON THE DRAG REDUCTION CHARACTERISTICS OF TRAVELING WAVY WALL AT HIGH REYNOLDS NUMBER IN WIND TUNNEL* YAO Yan Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, China Beijing Electromechanic Engineering Institute, Beijing 100074, China, E-mail: yaoyanyy@163.com LU Chuan-jing Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, China State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200030, China SI Ting Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China ZHU Kun

Beijing Electromechanic Engineering Institute, Beijing 100074, China (Received March 29, 2010, Revised July 10, 2010) Abstract: Drag reduction experiments of the traveling wavy wall at high Reynolds number, ranging from 1.46106 to 5.83106 based on the free-stream velocity and the model length, were conducted. A suit of traveling wavy wall device was developed and its characteristics of drag reduction at high Reynolds number were investigated. The drag forces of the traveling wavy wall with various wave speeds ( ) were measured at different wind speeds (U ) in the FL-8 low-speed wind tunnel and compared with the drag force of the flat plate. The results show that the mean drag force of the traveling wavy wall decreases as the value of increases, at different wind velocities, the values of corresponding to minimal drag force of the traveling wavy wall are different, when the values of are larger than 0.6, the mean drag forces of the traveling wavy wall are smaller than those of the flat plate, and the drag reduction can be up to 60%. The drag reduction effectiveness of traveling wavy wall is thus achieved. Furthermore, as the value of increases, the traveling wavy wall can restrain the separation and improve the quality of flow field.

c/c U

/c U/c U

/c U Key words: flow control, drag reduction, traveling wavy wall, wind tunnel test 1. Introduction

Minimizing the surface friction of aircraft and ships is a long-term goal in engineering design. Generally, the surface friction accounts for as large as 50% of the total resultant drag. For submarines, the ratio can be up to 70%. In recent years, the research of drag reduction becomes more and more attractive.

Conventional methods for the drag reduction make use of the low-resistance streamline shape and

* Biography: YAO Yan (1978-), Female, Ph. D. Candidate, Engineer

decrease surface protruding structures as far as possible. The examples can be taken for the car of the streamline body and the submarine of water droplet shape and so on. However, these methods are all passive and the effect of its drag-reducing has been proved limited. Contrarily, more and more active flow control technologies for drag reduction have been developed, one of which is based on the traveling wavy wall. In this method, a smooth wavy wall undergoes the motion in the form of a streamwise traveling wave and is found to exhibit restraining turbulence intensity and separation as the phase speed of the traveling wave is increased to reach some

720

values comparable to the free stream velocity. It is obvious that the flow structures between a

traveling wavy wall and a traveling flat plate are different. As is well known, the resistance of a flat plate is caused by the boundary layer[1], while the flow over the fixed wavy wall is strongly affected by the normal pressure gradient on the surface and the centrifugal force due to alternating convex and concave curvatures[2]. Furthermore, experiments and direct numerical simulations have been carried out to investigate viscous flow passing a traveling wavy wall[2-15]. Kendall[2] studied experimentally the effects of a traveling wavy wall. And observed a decrease in pressure perturbations compared to flow over a fixed wavy wall. Taneda and Tomonari[3,4] demonstrated experimentally that when the wave phase speed is smaller than the external flow velocity U , the boundary layer separates at the back of the wave crest, but when is larger than U , the boundary layer does not separate. Wu et al.

c

c[6] analyzed Tanedas[3,4]

and Savchenkos[5] experimental results, found that stable vortices can indeed be trapped by traveling flexible wavy wall at each trough of the wave under carefully selected conditions. For the case of two-dimensional flexible wavy wall, and have proven that at a critical wave speed c the flow may become naturally periodic along the x direction. If this periodicity can be achieved by real viscous flow, than the near-wall shear layer must be also periodic, implying a zero total drag. When the wave can be approximated by a sinusoidal wave, the two- dimensional inviscid theory predicted that the critical wave speed is 0.414

[6], which has been exactly confirmed by a later Navier-Stokes computation[7]. Techet[8] used LDV measured the velocity distribution in an area close to traveling wavy wall and found that oscillation can inhibit turbulent.

Recently, numerical simulations have been performed for turbulent flows near the traveling wavy wall. The results obtained by Shen et al.[9], Lu and Yin[10], Wu et al.[11] and Dong and Lu[12] not only confirmed previous experimental measurements, but also add a detailed instantaneous physical picture including the discovery of velocity bursts originating in the separated region, a detailed analysis of the turbulent kinetic energy budget, and instantaneous vortex structures. Yang and Wu[13] extended previous two-dimensional analytical theory of the inviscid periodic separated flow over an infinitely long traveling wavy wall to axisymmetric flow.

There are drag reduction methods similar to the traveling wavy wall. Cai et al.[16] analyzed the mechanism of drag reducing effect by coupling flexible tubes with turbulent flow based on experimental examination. Zou et al.[17] investigated the cross flow around wavy cylinders at a subcritical

Reynolds number by using the large eddy simulation. It must be pointed out that most of previous

experiments were conducted at low Reynolds number. In the present work, we perform experimental investigation of the traveling wavy wall at high Reynolds number, which ranges from 1.46106 to 5.83106 based on the free-stream velocity U and the experimental model length . The drag forces of the traveling wavy wall, flat plate and fixed wavy wall are also measured in the wind tunnel. The article is organized as follows. In Section 2 the experimental method is described. The experimental device to generating traveling wavy wall with high phase speed is developed and is placed in the wind tunnel to measure the drag force. In Section 3 the experimental results and related discussions are presented. Finally the main conclusions are drawn in Section 4.

L

2. Experimental apparatus and method

The motion equation of the traveling wavy wall is described in the following

(2= siny a x ct ) (1)

where , a and stand respectively for the amplitude, wavelength and phase speed of the traveling wavy wall,

c

x , for the displacement in the horizontal and vertical directions, and for the time. In previous experiments

yt

[3], the phase speed was limited to very low values because of their low mechanical responsive time. Thus up till now, the cases of higher values of the phase speed have been investigated only in the numerical way[9]. In this work, a new method based on the high-frequency gas cylinders is brought out to generate a traveling wave with higher phase speed.

The pole of the gas cylinder is moving with a reciprocating motion, described approximately by

= sin( + )y A ft (2) where A is the reciprocating movement distance of the pole, f the frequency and the phase of the gas cylinder. In this way, if a number of gas cylinders with the same frequency are placed equidistantly and two neighboring ones have an equal phase difference

, the vertices of the poles will move along an approximate sine curve. Note that the shape of this curve is mainly determined by the frequency and the responsive time of the gas cylinders.

Following this consideration, we developed an experimental device as shown in Fig.1, consisting of a

721

flexible plate, seven knightheads, seven air cylinders, seven electromagnetic valves, a control circuit, some fixed supports and a number of windpipes. The seven air cylinders (ISO standard, with compressed air as working medium) with were placed in the fixed support at the same interval . A flexible plate with width of 300 mm was connected to the poles of seven air cylinders by seven metal knightheads. Seven electromagnetic valves controlled by a control circuit system were fixed on the support and connected one by one with the gas cylinders by a number of windpipes. When the gas cylinder was working, air was compressed into one gate and extruded from the other gate of the gas cylinder. Either in or out was decided by the signals of the electromagnetic valve. When the valve was opened, the pole was moving upwards, while when the valve was closed, the pole was moving downwards. The control circuit system could set the frequencies and switches of seven electromagnetic valves. The phase difference of two neighboring gas cylinder was settled to be , and then the flexible plate was moving approximately in the form of Eq.(1). Note that the forehead and the tail of the flexible plate were located in the center line of the whole wave, the forehead is fixed on the support while the tail is free.

= 100 mmA= 300 mml

/ 2

Fig.1 The device for generating traveling wavy wall

The experiment was conducted in the FL-8

low-speed wind tunnel, which is a single flat circular wind tunnel with the maximum speed up to 72 m/s and the average turbulence degree 0.1745%. The size of the test section is 3.5 m2.5 m5.5 m. The experimental device was supported by an 8BM03-01 semi-mode balance in the test section (see Fig.1). Although the balance was designed to measure six components of the load, the drag force in the horizontal direction was especially concerned in order to obtain the drag of the traveling wavy wall.

In the experiment, how to measure the drag of the flexible plate separately is a difficult problem. In order to prevent the influence of the resistance of the device, the device was vertically placed on the balance, and a set of oriented equipment consisting of boards and organic glasses was fixed in the wind tunnel as

shown in Fig.2. The front of the oriented equipment was designed to be triangle shape, the upper surface of which was plane with the same height as the forehead of the flexible plate. Note that the oriented equipment surrounding the experimental device was not linked with it but has a little spacing. Then the measured force in the streamwise direction is mainly the drag force of the flexible plate. Fig.2 The photo of experimental models in the wind tunnel

The experimental data were collected by a VXI data acquisition system. Collecting a data point cost 0.02 s. Then in each case we spent more than 6 s to collect 300 data points for analysis. Fig.3 Configuration of experimental models 3. Results and discussions

In the experiment, the drag force of the traveling wavy wall as well as the flat plate and the fixed wavy walls (i.e., ) under five oscillation frequencies were measured. Figure 3 show the shape of the two fixed model, Flat plate model is flat, that is, the height of the air cylinders are its 1/2 of its maximum stroke, the same level as the fixed support. Fixed wavy wall model takes on the fixed wavy shape, similar to sinusoidal wave. The first air cylinder is at the highest point of its stroke.

= 0c

3.1 Drag force of the flat plate and fixed wavy wall To identify flow is turbulent or laminar flow, the

key parameter is the Reynolds number. The critical

722

Reynolds number of the flat-plate boundary layer is generally believed to be in the range of 3105 - 3106, when , the laminar boundary layer theory of plate can be used. And if , in general, the theory of turbulent boundary layer must be used. But when , this is not the case. In the present work, we used to discriminate flow is the laminar or turbulent flow. The Reynolds number based on the free-stream velocity and the length of the experimental model is

53 10Re < 63 10Re >

53 10 3 10Re 66= 1.6 10Re

U6 6= 1.46 10 - 5.83 10Re .

In the case of steady turbulent flow with uniform free-stream velocity U for a flat plate with the length and the width , its total frictional drag coefficient is

L b[1]:

( )1/50.074=ft

L

CRe

, =LULRe (3)

The relationship between the total frictional force

ftF and uniform flow speed U can be expressed as

( )1/52 91= = 0.0372ft ftF U LbC b U L 4 (4)

Figure 4 shows the drag forces for of flat plate and fixed wavy wall at different free-stream speeds. From the figure, it can be seen that with the increase of the free-stream speed, the drag force increases by the square of the speed. Fig.4 Drag forces for flat plate and fixed wavy wall versus the

free-stream speed

The drag force for the flat plate is significantly smaller than that for the fixed wavy wall. The fixed wavy wall not only bears the frictional resistance, but also endures the pressure drag, and behind of the crest of fixed wavy wall there is apparent flow separation. Meanwhile, the experimental data for drag force of flat plate are in good agreement with the theoretical values from turbulent boundary.

3.2 Drag force of the traveling wavy wall at different wave velocities The ratio of the traveling wave speed, , to the

free-stream speed, U , , is an important parameter, and different values of correspond to the different characteristics of the flow field. In unsteady flow, the Strouhal number , is generally introduced to describe the feature of the unsteady flow field. For the two-dimensional traveling wavy wall problem, the Strouhal number is characterized by the length of the wavelength

c/c U

/c U

St

:

= =f cStU U

(5)

which implies the Strouhal number determines the character of the flow field.

In the present work, the amplitude of the traveling wave is constant. By adjusting the oscillation frequency of air cylinder to change the phase speed of the traveling wavy wall. Under different oscillation frequencies =f 2 Hz, 3 Hz, 4 Hz, 5 Hz, 6 Hz, the corresponding phase speeds are = =c f 2.4 m/s, 3.6 m/s, 4.8 m/s, 6 m/s, 7.2 m/s. Table 1 gaves a list of

corresponding to different frequencies and free-stream velocities.

/c U

Table 1 forer different frequencies and free-stream

velocities /c U

/c U 10

U (m/s)12 15

= 2 Hzf 0.24 0.20 0.16 = 3 Hzf 0.36 0.30 0.24 = 4 Hzf 0.48 0.40 0.32 = 5 Hzf 0.60 0.50 0.40 = 6 Hzf 0.72 0.60 0.48

Figure 5 plotted the curve of the drag force for

traveling wavy wall versus oscillation frequency. At the same frequency, the drag force increases with the increase of free-stream velocity; and at the same free-stream velocities, with the increase of oscillation frequency, the drag force reduces; at different free-stream velocities, when traveling wavy wall reach the minimum of drag force, the corresponding values of are slightly different. So is a key parameter for this problem.

/c U /c U

Shen L et al.[9] applied Direct Numerical Simulation (DNS) to study the three-dimensional turbulent boundary layer flow over a traveling wavy wall, and found that the drag force decreases monotonically as increases. Lu/c U [10] simulated the infinite two-dimensional traveling wavy wall using laminar flow model, and proved that the overall

723

flow pattern and dynamics depend strongly on the phase speed c . as increases, the friction force increases, the pressure force decreases monotonically, and the total drag force decreases. The present measurement results are in good agreement with their computational conclusion.

c

Fig.5 The curve of drag force of traveling wavy wall versus frequency

3.3 Comparison of flat plate of drag force for fixed

wavy wall and traveling-wavy wall Figure 5 shows that the drag force of traveling

wavy wall reaches its minimum, at the free stream velocity and the oscillation frequency

. Table 2 gives the comparison of drag forces for the flat plate, the fixed and traveling wavy plate. It can be seen that traveling wave indeed plays a crucial role in reducing the drag force. For the ratio

, ( ), the drag force reduction is about 60%.

= 10 m / sU

6 s

= 6 Hzf

U / 0.c U = 10 m /U Table 2 Drag forces for flat plate,fixedand traveling wavy

walls (Unit: N) = 10 m /sU = 12 m /sU

Flat plate 0.247 0.402 Fixed wavy wall

1.387 1.914

Traveling wavy wall

( ) = 5 Hzf0. 0985 1.123

Traveling Wavy wall ( ) = 6 Hzf

0.0844 0.9744

Compared with the fixed wavy wall, as c/U

increases, the drag force reduces significantly, which can be seen from Figs.4 and 5. The results prove that the flow separation after the wave crest is gradually weakened, as the phase speed increase.

The mechanism of drag reduction of traveling wavy wall has been investigated. Shen et al.s[9] numerical results show that as increases from zero, the separation bubble moves further upstream

and away from the wall, decrerasing in strength. Above a threshold value of , the separation is eliminated. Triantafyllou et al.s

/c U

/c U 1[14] numerical

calculation and experimental studies showed that the traveling wavy wall has the mechanisms of separation elimination, turbulence reduction. However, the Reynolds numbers were relatively low in the previous experiments because of the unattainably high frequency. 4. Conclusions

A suit of smooth flexible traveling wavy wall devices have been designed and experimentally examined for turbulent flows over the wall undergoing streamwise traveling-wave and transverse motions. The Reynolds number based on the free-stream velocity and the experimental length L is

, and the traveling wave amplitude is given by

U6(10 )O a

2 / = 0.26a . By changing the ratio of the traveling wave phase

speed to the free-stream velocity U , it is found that the wall oscillations can be optimized to achieve separation suppression and turbulence reduction, and to reduce drag force.

c

At the same free-stream velocity with incresing oscillation frequency, the wavy wall drag force decreases. That is to say, as increases, the drag force for traveling wavy wall is generally reduced. At different free-stream velocity, when the traveling wavy wall gives minimal drag force, the corresponding values of are also different. Compared with the flat plate, experimental results show that the traveling wavy wall indeed plays the role of drag reduction, as . And the drag reduction is about 60 %. With ingrom zero, experimental studies show that the traveling wavy wall has the mechanisms of separation elimination and turbulence reduction.

,U

/c U

/c U

/ 0.c U 6/c U

References

[1] SCHLICHTING H., GERSTEN K. and KRAUSE E. et al.

Boundary-layer theory[M]. 8th Edition, New York: Springer, 2000.

[2] KENDALL J. M. The turbulent boundary layer over a wall with progressive surface waves[J]. Journal of Fluid Mechanics, 1970, 41: 259-281.

[3] TANEDA S., TOMONARI Y. An experiment on the flow around a waving plate[J]. Journal of the Physical Society of Japan, 1974, 36: 1683-1689.

[4] TANEDA S. Visual study of unsteady separated flows around bodies[J]. Prog. Aerosp. Sci., 1977, 85: 287-348.

[5] SAVCHENKO Y. N. Hydrodynamic effects of a traveling wave[R]. Kyiv, Ukraine: USSR Bionics Trans., JPRS L/ 9420, 1980.

724

[6] WU Jian-ming, WU Chui-jie and WU Jie-zhi et al. Preliminary study of nonlinear flow over traveling wavy wall[C]. International Symposium on Nonsteady Fluid Dynamics. Toronto, Canada, 1990, 359-368.

[7] WU Jie-zhi, WU Jian-ming. Vorticity dynamics on boundaries[J]. Advances in Applied Mechanics, 1996, 32: 119-275.

[8] TECHET A. H. Experimental visualization of the near-boundary hydrodynamics about fish-like swimming motion[D]. Ph. D. Thesis, Cambridge, MA, USA: MIT, 2000.

[9] SHEN Lian, ZHANG Xiang and YUE D. K. P. et al. Turbulent flow over a flexible wall undergoing a streamwise traveling wave motion[J]. Journal of Fluid Mechanics, 2003, 484: 197-221.

[10] LU Xi-yun, YIN Xie-zhen. Propulsive performance of fish-like traveling wavy wall[J]. Acta Mechanica, 2005, 175: 197-215.

[11] WU Chui-jie, XIE Yan-qiong and WU Jie-zhi. Fluid roller bearing effect and flow control[J]. Acta Mechanica, sinica 2003, 19(5): 476-484.

[12] DONG Gen-jin, LU Xi-yun. Numerical analysis on the propulsive performance and vortex shedding of fish-like traveling wavy plate[J]. Int. J. Num. Methods Fluids, 2005, 48(12): 1351-1373.

[13] YANG Zhu, WU Jie-zhi. Drag reduction by axisymmetric traveling wavy wall[J]. Journal of University of Science and Technology of China, 2005, 35(4): 471-479.

[14] TRIANTAFYLLOU M. S., TECHET A. H. et al. Vorticity control in fish-like propulsion and maneuvering[J]. Integr. Comp. Biol., 2002, 42: 1026-1031.

[15] ZHANG Zhi-xin, LUO Zhen-ou. Numerical calculation of three-dimensional boundary layers over moving wavy wall[J]. Journal of Hydrodynamics, Ser. A, 2000, 15(3): 287-292(in Chinese).

[16] CAI Shu-peng, JIN Guo-yu and LI Da-mei et al. Drag reduction effect of coupling flexible tubes with turbulent flow[J]. Journal of Hydrodynamics, 2008, 20(1): 96-100.

[17] ZOU Lin, LIN Yu-feng. Numerical simulation of turbulent flow around wavy cylinders at a subcritical Reynolds number and the investigation on drag reduction[J]. Chinese Journal of Hydrodynamics, 2010, 26(1): 31-36(in Chinese).