2nd International Symposium on Seawater Drag Reduction Busan, Korea, 23-26 MAY 2005

Influence of Local Ultrasonic Forcingon a Turbulent Boundary Layer

Y.S. Park and H.J. Sung (Korea Advanced Institute of Science and Technology, Korea)

ABSTRACT

An experimental study was carried out to investigate the effect of local ultrasonic forcing on a turbulent boundary layer. The ultrasonic forcing system was constructed by adhering six ultrasonic transducers to a flat plate over which water was flowed. In this system, the ultrasonic waves projected into the water by the transducers caused cavitation, giving rise to an enormous number of tiny air-bubbles. Stereoscopic particle image velocimetry (SPIV) was used to probe the flow characteristics. The SPIV results showed that imposition of the ultrasonic forcing caused a substantial increase in the mean wall-normal velocity but a decrease in the mean streamwise velocity. The ultrasonic forcing reduced the skin friction coefficient by up to 60% immediately downstream of the transducers; this effect gradually dissipated with moving downstream. The Reynolds shear stress and the production of turbulent kinetic energy were reduced near the wall. Imposition of the ultrasonic forcing shifted the streamwise vortical structures away from the wall, leading to a reduction in skin friction.

INTRODUCTION

Ships play an important role in worldwide transportation. They are characterized by very large size and slow speed compared with other vehicles. Three key types of drag impeding the movement of ships through water are free-surface wave drag, pressure drag, and skin friction drag. The free-surface wave component is proportional to the square of the ship speed, and hence is very small due to the low speed of ships. The pressure drag is small due to the optimization of body shape of ships. In contrast, the skin frictional drag component accounts for approximately 80% of the total drag, and thus its reduction is very important. Recent advances in the understanding of the coherent structure of wall-bounded turbulent flow have intensified interest in reducing skin friction by controlling the coherent structure. In a turbulent boundary layer, skin friction is

closely associated with the downward sweep motion induced by the streamwise vortices in the vicinity of the wall. Thus, effective control of the streamwise vortices is crucial to reducing the skin friction and consequently the drag. Direct numerical simulations have demonstrated that attenuation of the streamwise vortices by means of active blowing/suction over the entire wall significantly reduces the skin friction. From a practical viewpoint, however, this active control strategy is difficult to implement because it requires a dense population of sensors and actuators on the wall. Many attempts have been made to develop a practical method for reducing wall skin friction. The approaches taken include modification of the wall surface by installing riblets, the use of a compliant wall and local injection of air or water. The last of these approaches deserves more detailed study because it provides an efficient and simple means for locally actuating the wall-bounded flow. Moreover, the strength of the actuation can be controlled with relative ease by changing the injection amplitude. Previous studies have shown that uniform steady blowing through a spanwise slot decreases the wall-region flow velocity and skin friction behind the spanwise slot. These studies showed that the streamwise vortices causing high skin friction are lifted up from the wall by the uniform blowing, leading to a reduction in the wall-region velocity and skin friction. Moreover, it has been shown that imposition of periodic blowing/suction through a spanwise slot leads to the generation of a spanwise vortical structure; this vortical structure creates a reverse flow near the wall and consequently reduces the wall-region streamwise velocity and skin friction. The injection of air microbubbles into a liquid flowing past a wall has proved to be one of the most successful and robust methods for drag reduction. This phenomenon was first described by McCormick & Bhattacharyya (1977), who studied a system in which hydrogen microbubbles were produced by electrolysis. Kato et al. (1999) found that microbubble injection decreased the velocity gradient at the wall and the skin friction. They also observed that the streamwise

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turbulence intensity in the buffer layer decreases with increasing microbubble density. Kodama et al. (2000) showed that the reduction in skin friction increased with increasing air injection rate and that the degree of skin friction reduction is influenced by the local void ratio close to the wall. Recently, Xu et al. (2002) and Ferrante & Elghobashi (2004) investigated the effect of microbubbles on a turbulent boundary layer by DNS. On the basis of their simulation results, they presented the following picture of the behavior of these systems: the injected microbubbles create a positive mean velocity normal to the wall which reduces the mean streamwise velocity and displaces the streamwise vortical structures away from the wall, leading to reductions in the Reynolds shear stress and the production rate of turbulent kinetic energy in the wall region. Although the microbubble-based methods described above effectively reduce the skin friction, they are difficult to implement in real applications. These methods require installation of a forcing system that injects microbubbles through a slot or a porous medium on the surface; however, such surface deformations compromise the wall strength and hence are unsuitable for high hydrostatic pressure environments. In the present work we propose a different approach to microbubble production, namely ultrasonic forcing, which does not require direct deformation of the surface. In this method, the ultrasonic forcing is applied simply by attaching ultrasonic transducers to the surface. This approach exploits the well-known cavitation phenomenon whereby ultrasonic waves generate an enormous number of air bubbles in a liquid flow field. When an ultrasonic transducer is driven by a high frequency electrical signal, it expands and contracts rapidly at a rate proportional to the frequency of the applied signal, causing the pressure of the liquid in contact with the transducer to change from negative to positive with respect to atmospheric pressure. When the pressure exceeds the surface tension of the cavities in the liquid, the cavities implode causing the generation of an enormous number of microbubbles. Although ultrasonic forcing is widely used in many industrial fields, the present study represents the first attempt to use it for drag reduction.

EXPERIMENT APPARTUS AND PROCEDURE

Measurements were performed in a recirculating open water channel driven by a centrifugal pump. A settling chamber, a honeycomb, and a contraction were placed in sequence to ensure flow homogeneity. Figure 1 shows a schematic diagram of the test section, ultrasonic forcing system, and PIV experimental setup.

The dimensions of the test section were 250 mm (width) x 250 mm (depth) x 1200 mm (length). The ultrasonic forcing system was installed 200 mm above the bottom wall of the test section. The dimensions of the ultrasonic forcing system were 150 mm (width) x 1000 mm (length). A leading-edge plate (angle:10o,length: 310 mm) was attached to the forcing system to prevent flow separation (see Fig. 1). The boundary layer was tripped at the leading edge of the flat plate using a combination of a trip wire of diameter 2 mm and a roughness strip of length 200 mm. The roughness strip was installed to reduce the two-dimensionality of the wake behind the trip wire. This combination ensured a self-preserving turbulent boundary layer upstream of the local ultrasonic forcing. As shown in Fig. 1, the ultrasonic forcing unit was installed in the middle of the ultrasonic forcing system, which was located 460 mm downstream of the leading edge. The ultrasonic forcing unit consisted of three components: an ultrasonic generator, an ultrasonic transducer, and a vibration plate. The dimensions of the vibration plate were 90 mm (width) x 200 mm (length). The origin of the measurement coordinate axes was taken as the end of the forcing system. The ultrasonic generator converts electrical energy into a high frequency signal, which is then applied to ultrasonic transducers. Six ultrasonic transducers were attached to the vibration plate. By imposing high frequency forcing, these transducers expand and contract rapidly at a rate proportional to the frequency of the applied voltage. These contractions and expansions cause the pressure of the liquid in contact with the vibration plate to change from positive to negative and from negative to positive, respectively with respect to atmospheric pressure. During the contractions, the pressure in the liquid becomes negative, allowing cavities inside the liquid to grow in size. At the next expansion the pressure in the liquid becomes positive, compressing the cavities. When the positive pressure exceeds the

Figure 1 : Schematic diagram of experiment

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surface tension of the cavities, the cavities implode and an enormous number of microbubbles of air are generated. This phenomenon is known as cavitation. The bubble size is on the order of several micrometers and the velocity of the bubbles is very fast normal to the vibration plate. The ultrasonic forcing frequency was fixed at 27.5 kHz, which was found to generate the greatest number of microbubbles. For the SPIV measurements, an angular displacement method was employed. However, aberrations due to variations in the refractive index and particle image distortion may generate nonuniformities in the magnification. These image distortions and optical aberrations were compensated for by employing the calibration procedure developed by Soloff et al. (1997). Two CCD cameras (Kodak ES-1.0, 1024 x 1024 pixel CCD array size) coupled to a PC running image acquisition software were used to acquire images. Each camera was fitted with an 85 mm lens (PC Micro Nikkon) to minimize the image distortion. The flow plane of interest was illuminated with a two head Nd:YAG laser (Big Sky Laser, Ultra). Each laser was capable of producing 8-ns, 30-mJ pulses at a repetition frequency of 15 Hz. The pulses for the laser and the CCD cameras were generated and delayed using a pulse delay generator (Berkeley Nucleonics, BNC-555). The laser beam was carried by an optical arm and an appropriate combination of cylindrical lenses was employed to produce a collimated light sheet on the center of the slot (z=0). Measurements were taken at multiple x-y planes by traversing the light sheet and camera across the desired regions. To investigate forcing effects over a wide region, velocity measurements were performed over the range -80 mm<x<240 mm. The field of view of each camera was 90 x 90 mm; hence the whole velocity measurement field was divided into 4 regions. At each measurement region, 3717 velocity fields were acquired. The iterative multigrid image processing method (Scarano & Riethmuller 1999) was used to increase the spatial resolution and CBC (Correlation based Correction, Hart 1999) was used to improve the signal-to-noise ratio. The final interrogation window size was 16 x 16 pixels with a 50% overlap. This gave a spatial resolution of 0.71 mm between measurement points. For vector post-processing, the local median filter criterion (Westerweel 1994) was used.

RESULT AND DESCUSSTION

The free-stream velocity was set to U =0.15 m/s and the momentum thickness ( ) at the end of the ultrasonic forcing unit (x=0) was =3.633 mm. The Reynolds number based on was Re =545. To see the influence of the present ultrasonic forcing, we

evaluated the behavior of the skin friction coefficient

fC , defined as

2)(2UuC f . (3)

where u is the friction velocity, which is calculated

under the assumption of a viscous sublayer, i.e.,

yU . The nearest measuring position from the

wall was y=0.78 mm, which corresponds to about

y =6.3 in wall units. When the present friction

velocity was compared with the friction velocity obtained by CPM (Computational Preston Method, Nitsche et al. 1983), the difference was found to be less

than 3%. The response of fof CC / to the present

ultrasonic forcing is shown in Fig. 2. The streamwise evolution is normalized by the momentum thickness

( o ) at the end of the ultrasonic forcing (x=0). The

subscript ‘o’ indicates the case without ultrasonic

forcing; thus foC and o represent the skin friction

coefficient and the momentum thickness in the absence

of forcing. As can be seen in Fig. 2, fC is

significantly reduced by the forcing and the local forcing effect is gradually attenuated on moving downstream. As the flow moves downstream, there is a

slight overshoot beginning at about region ox / =50

to infinity. The maximum reduction of skin friction is

about 60% in the initial region ox / <5. The data in

Fig. 2 clearly show that the ultrasonic forcing effectively reduces the skin friction. To investigate the effect of forcing on the mean streamwise velocity, contour plots of the mean streamwise velocity were examined (Fig. 3). Hereafter, the streamwise direction is normalized by the

momentum thickness without forcing ( o ), the wall-

x/ o

Cf/C

fo

0 20 40 600

0.2

0.4

0.6

0.8

1

1.2

no forcingforcing

Figure 2 : Distribution of skin friction.

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Figure 3: Contours of mean streamwise velocity field.

x/ o

y+

0 5 10 15 200

100

200

300a) no forcing

x/ o

0 5 10 15 20

0.10

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.00

v/Ub) forcing

Figure 4: Contours of mean wall-normal velocity field.normal direction is normalized by the friction velocity

without forcing ( u ), and the velocity components

(mean velocity, turbulence intensity, and Reynolds shear stress) are normalized by the free-stream velocity

(U ). Measurements were taken at multiple x-y planes

by traversing the light sheet and camera across the desired regions. Minor discontinuities in the contours

are observed at the boundaries ox / =24 and 48; these

discontinuities are due to the overlap regions of the measurement fields. In the absence of forcing, the boundary layer thickness increases very slowly as the flow goes downstream. The velocity contours are nearly parallel to the wall. The isocontour level of velocity is narrow near the wall but widens on moving

away from the wall such that for y >200, the

isocontours become almost constant. The narrow isocontour level near the wall indicates that the

x/ o30 40 50 60 70

10.90.80.70.60.50.40.30.20.10

U/U

30 40 50 60 70

10.90.80.70.60.50.40.30.20.10

U/U

y+

0 10 200

100

200

300

400b) forcing

y+

0 10 200

100

200

300

400a) no forcing

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Figure 4: Contours of mean wall-normal velocity field.velocity gradient is large. Imposition of the ultrasonic forcing causes a dramatic decrease in the mean streamwise velocity (Fig.3b); in particular the velocity

reduction rate is very large at ox / <24. As the flow

moves downstream, the effect of the ultrasonic forcing weakens and the velocity field gradually converges to that observed in the absence of forcing. The ultrasonic forcing causes the isocontour level to be wider than is observed in the absence of forcing in the region

ox / <24. Thus the forcing decreases the velocity

gradient near the wall, which leads to a reduction in skin friction. Next we inspected the forcing effect on the mean wall-normal velocity. Contour plots of the mean wall-

normal velocity in the region 0< ox / <24 are shown

in Fig. 4. Different contour level ranges are used for the forcing and no-forcing cases because the forcing has a significant effect on the mean wall-normal velocity. The contour spacing for the no-forcing case is 1/20 that for the forcing case. In the absence of the forcing, the mean wall-normal velocity is less than

0.5% of U because the flow is a turbulent boundary

layer. However, the mean wall-normal velocity is dramatically increased by the imposition of ultrasonic forcing. The maximum mean wall-normal velocity is

about 15% of U , that is, the forcing increases the

mean wall-normal velocity by more than 30 times. This significant enhancement can be attributed to the microbubbles generated by the ultrasonic forcing. Ferrante & Elghobashi (2004) showed by DNS that injection of microbubbles into a turbulent boundary layer increased the mean wall-normal velocity up to

6% of U . This suggests that the injection of

microbubbles into the flow by ultrasonic forcing may have a similar effect on the flow field.

The combined effect of the mean velocity gradient and the Reynolds shear stress was inspected by checking the production of turbulent kinetic energy, which is defined as,

Production = .yUuv (5)

Figure 5 shows contour plots of the production of turbulent kinetic energy for the forcing and no-forcing cases. Near the wall, the production is very large due to the high velocity gradient and Reynolds shear stress in this region. Imposition of the ultrasonic forcing causes a reduction in the wall-region mean streamwise velocity, leading to a reduction in yU / (Fig. 3).

The combined effect of this reduction in yU / and

the reduction in uv ( uv is not shown in this paper) is a reduction in the total production of turbulent kinetic energy. A similar reduction in the production of turbulent kinetic energy can be seen in the DNS results of Ferrante & Elghobashi (2004). Away from the wall, however, the production of turbulent kinetic energy is greater for the system subjected to ultrasonic forcing than for the system without forcing. This can be attributed to the fact that the imposition of ultrasonic forcing causes the location of peak Reynolds shear

stress to shift to higher y .

Quadrant analysis of the Reynolds shear stress provides detailed information on the contribution of flow events to the production of turbulent kinetic energy. In this analysis, the Reynolds shear stress is divided into four categories, denoted Q1–Q4, according to the signs of uand v. Q1 (u>0, v>0) contains outward motion of high-speed fluid; Q2 (u<0, v>0) contains outward motion of low-speed fluid; Q3 (u<0, v<0) contains inward motion of low-speed fluid; and Q4 (u>0, v<0) contains an inrush of high-speed fluid referred to as a sweep event.

x/ o

0 4 8 12 16 20 24

0.001

0.0009

0.0008

0.0007

0.0006

0.0005

0.0004

0.0003

0.0002

0.0001

0

b) forcing production

x/ o

y+

0 4 8 12 16 20 240

100

200

300a) no forcing

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Here, Q1 and Q3 events contribute to the negative Reynolds shear stress (positive production: uv>0) and Q2 and Q4 events contribute to the positive Reynolds shear stress (negative production: uv<0). To see the details of the impact of ultrasonic forcing in the quadrant analysis, the number of quadrant events and the summation of the product (uv) were examined (Table 1). For no-forcing, the numbers of Q2 (ejection) and Q4 (sweep) events are almost twice those of Q1 and Q3 events. The summation of the product of u and v is much larger for Q2 and Q4 than for Q1 and Q3, indicating that the sweep and ejection events dominate (Kim et al. 1987). The event numbers are not much changed by the ultrasonic forcing; however, the summation of the sweep product is decreased by about 30% by imposition of the forcing. The total summation of the product is about 20% lower for the flow subjected to ultrasonic forcing than for the flow without forcing. This suggests that the near-wall streamwise vortical structures are shifted away from the wall by the ultrasonic forcing, causing the interaction of the vortices with the wall to become weaker. As mentioned earlier, the skin friction is closely associated with the sweep motion induced by the streamwise vortices in the vicinity of the wall. Thus the forcing-induced shift of the streamwise vortices away from the wall should lead to a reduction in the skin friction.

CONCLUSIONS

The influence of local ultrasonic forcing on a turbulent boundary layer was studied experimentally, with SPIV being used to probe the flow characteristics. Imposition of the ultrasonic forcing caused the generation in the boundary layer of an enormous number of air microbubbles with fast wall normal velocities. We found that these microbubbles enhanced the positive mean wall-normal velocity in the downstream. In the vicinity of the forcing unit, the mean wall-normal velocity was increased to about 30 times that observed

Table 1: Event number and summation of product of u and v.

in the absence of forcing. This forcing-induced increase in the wall-normal velocity caused a reduction in the near-wall mean streamwise velocity gradient and, as a consequence, the skin friction was reduced. However, the effect of the forcing was found to gradually dissipate as the flow moved downstream, with the skin friction and near-wall velocity recovering to those observed in the absence of forcing at

ox / >40. The maximum reduction in the skin

friction (~60%) was observed in the vicinity of the forcing unit. Imposition of the ultrasonic forcing shifted the streamwise vortices causing high skin friction away from the wall, thereby weakening the interaction of the vortices with the wall. As a consequence, the wall-region velocity and skin friction were reduced. Moreover, the forcing-induced shift of the streamwise vortices away from the wall caused significant reductions near the wall in the Reynolds shear stress, the strength of sweep motion, and the production of turbulent kinetic energy. These phenomena are in good agreement with previous observations of flows injected with microbubbles or subjected to uniform blowing.

REFERENCES

Ferrante A and Elghobashi S., “On the Physical Mechanisms of Drag Reduction in a Spatially Developing Turbulent Boundary Layer Laden with Microbubbles.” J Fluid Mech Vol.503, 2004, pp. 345-355 Kato H, Iwashina T, Miyanaga M and Yamaguchi H., “Effect of Microbubbles on the Structure of Turbulence in a Turbulent Boundary Layer.” J Mar Sci Technol, Vol. 4, 1999, pp. 155-162 Kodama Y, Kakugawa A, Takahashi T and Kawashma H., “Experimental Study on Microbubbles and Their Applicability to Ships for Skin Friction Reduction.“ Int J Heat and Fluid Flow Vol.21, 2000, pp. 582-588 MaCormick M and Bhattacharyya R., “Drag reduction of a Submersible Full by Electrolysis.” Nav Engg J,Vol. 85, 1973, pp.11-16 Soloff SM, Adrian RJ and Liu ZC., “Distortion Compensation for Generalized Stereoscopic Particle Image Velocimetry.” Meas Sci Technol Vol.8, 1997, pp. 1441-1454 Xu J, Maxey MR and Karniadakis G., “Numerical Simulation of Turbulent Drag Reduction Using Micro-Bubbles.” J Fluid Mech Vol. 468, 2002, pp. 271-281

event number summation of uv no-

frocingultrasonic

forcingno-

frocing ultrasonic

forcingQ1 (u>0,

v>0)665 835 0.01088 0.011802

Q2 (u<0, v>0)

1166 1057 0.03212 0.033458

Q3 (u<0, v<0)

733 621 0.010550

0.010066

Q4 (u>0, v<0)

1153 1204 0.03873 0.028520

sumaiton 3717 3717 0.04942 0.040110

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