J Mar Sci Technol (1998) 3:122-129 Journal of

Marine Science and Technology 9 SNAJ 1998

Original articles

Experimental study on microbubble ejection method for frictional drag reduction

HIROHARU KATO, KENTO MIURA, HAJIME YAMAGUCHI, and MASARU MIYANAGA

Department of Environmental and Ocean Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

Abstract: The formation of air bubbles ejected through a single hole in a flat plate was observed in uniform flow of 2- 10m/s. It was confirmed that the size of the air bubbles was governed by main flow velocity and air flow rate. According to previous experiments, the size of the bubbles is an important factor in frictional drag reduction by microbubble ejection. Usually bubbles larger than a certain diameter (for example 1 mm) have no effect on frictional drag reduction. Three dif- ferent methods were proposed and tested to generate smaller bubbles. Among them, a 2D convex (half body of an NACA 64-021 section) with ejection holes at the top was the best and most promising. The diameter of the bubbles became about one-third the size of the reference ejection on a flat plate. Moreover, the bubble size did not increase with increasing flow rate. This is a favorable characteristic for practical pur- poses. The skin friction force was measured directly with a miniature floating element transducer, and decreased drasti- cally by microbubble ejection from the top of the 2D convex shape.

Key words: microbubble, frictional drag, drag reduction, ejection method

Introduction

The reduction of skin friction by microbubbles is prom- ising for practical uses such as for a ship's hull, because the reduction rate can reach as high as 80% in the best conditions.

The pioneering work was by McCormick and Bhattacharyya. 1 They found a reduction of drag in an axisymmetric body by covering the surface with hydro- gen bubbles. A group of scientists at Pennsylvania State

Address correspondence to: H. Kato Received for publication on Feb. 2, 1998; accepted on Sept. 29, 1998

University made extensive studies in the 1980s. 2-7 More recently, Kato et al. s,9 and Guin et al. l~ measured the reduction of skin friction directly with a miniature floating element transducer.

Bogdevich et al. 11 showed that the reduction rate of skin friction correlated well with the maximum gas con- centration in the boundary layer. Madavan et al. 3 tried to correlate the volumetric fraction of air Q,/(Qo + Qw) with the reduction rate. They also experimented by changing the pore size of the porous plate through which air was injected. Contrary to their expectations, injection pore size had no major effect on the amount of skin-friction reduction. Guin et al. 1~ found that the near- wall void fraction tended to collapse the drag-reduction data better than the average void fraction.

Another important factor is the size of the bubbles. When microbubble injection is applied to a low-speed ship's hull model, we often observe an increase of drag. In such cases, the diameter of the bubbles is 2-3 ram. Obviously the bubble size is too large compared with the scale of the boundary layer.

Kato et al. 9 examined the effect of bubble size by changing the main flow velocity. The bubble size decreased according to the increase in the main flow velocity, resulting in a larger reduction rate of skin fric- tion. Kato et al. 8 also changed the bubble size by chang- ing the surface tension. Water with 0.1% ethanol, whose surface tension is lower than that of pure water, was more effective, although the difference was not large.

Examining this previous work, the authors recog- nized that it was important to control bubble size, in other words, to generate bubbles smaller than a certain diameter to reduce skin friction. When we apply microbubbles on a relatively slow ship, such as a coaster, we need a device to control the size of the bubbles.

In this paper, we consider the mechanism and physi- cal properties governing the size of bubbles, then pro- pose a few methods to control the size of bubbles. Those

H. Kato et al.: Microbubble ejection method 123

methods were examined experimentally to test whether they were effective for generating smaller bubbles than those ejected through holes on a flat plate.

Experimental apparatus

The experiments were done in a recirculating water tunnel at the University of Tokyo. The tunnel has a rectangular cross section of 120mm x 50mm.

The test body with a convex shape, was secured to the bottom of the test section, as shown in Fig. 1. The out- line of two side windows is shown by a broken line. The test body was the same as in earlier investigations. 8,9 The wall shearing stress was measured by a floating element transducer with an element of 5mm diameter. The capacity was 1 g shear force, corresponding to 500Pa of shear stress. Four transducers were mounted flush with the surface of the test body in the first experiment, with no device for controlling bubble size (Fig. 1). A detailed description of the transducer with a discussion of its accuracy is given by Guin et al. 1~

Air flow rate was measured by a rotameter (Ueshima Brooks, Model 1560, Tokyo, Japan) with an accuracy of 2% error. The air flow rate at the ejection hole in- creased a little because of the difference between the static pressure at the rotameter and that at the ejection point. The correction factor was 1.09-1.11. The velocity in the boundary layer with main flow velocity was mea- sured by a laser doppler velocimeter (Kanomax, Osaka, Japan) with accuracy of 1% error. All the data were installed in transient recorders with a sampling rate of 2 ms. Normally, data of 8 K were taken and processed by a microcomputer.

During the experiment, photographs were taken from both the top and the side simultaneously to observe bubble formation. The size of the bubbles was measured using a film motion analyzer (magnification xl0). The accuracy was +0.05 mm. When a bubble was not spherical, the two major axes were measured and averaged as r = ~a-b.

' J 175 175

FLOW ~ 100 [Z~ a22~ Position of Air Hole

I #l #2 #3 #4

Shearing Stress Pick-Ups '?0-' ?d' ?0-' ?O' Outline of Window

Fig. 1. Details of test section

Unit mm

Bubble formation from a single hole

Bubble formation from a single hole on a flat plate under uniform main water flow was observed to exam- ine the fundamental mechanism. Experimental condi- tions were changed widely as follows resulting in 75 cases in total.

- - Diameter of hole (D): - - Main flow velocity (U): - - Air flow rate (Q):

0.5, 1.0, and 1.5 mm 2, 4, 6, 8, and 10m/s 20, 50, 100, 150, and

230 ml/min

The air hole was drilled 22mm upstream from the center of the test body, as shown in Fig. 1. Velocity distributions of the boundary layer at the air hole were measured by a laser doppler velocimeter. Figure 2 shows a semilog plot of the velocity profile on the ejec- tion hole, showing a turbulent flow even at 2 m/s.

Figure 3 shows successive pictures taken by a high- speed video recorder. Framing rates were 1200, 1800, and 3600f/s, at 2, 4, and 6m/s, respectively. In all three cases, the air column stretched downstream, formed nodes, and finally broke into air bubbles.

At the lower main flow velocity of 2 m/s, the surface of the air column was smooth. Conversely, at the higher velocity of 6 m/s, the surface became turbulent, and the pitch of the node was shorter than that at the lower velocity.

1.2

1.0

u/U

0.8

0.6

2m/s [] 4m/s /X 6m/s

i

0.4 I

0.1 1 10

log Z (mm)

Fig. 2. Velocity distribution of the boundary layer on the ejection hole

124 H. Kato et al.: Microbubble ejection method

Fig. 3. Formation of air bubbles. (a) U = 2m/s, framing rate 1200f/s; (b) U = 4m/s, framing rate 1800f/s; (c) U = 6m/s, framing rate 3600 f/s

One might conceive that this mechanism is a self- exciting phenomenon such as instability on the interface of two fluids, or vapor column instability as proposed by Zuber et al. 12 The results of analyses, however, show that none of these are the governing mechanism of bubble formation.

Meng and Uhlman 13 proposed an empirical formula for the bubble size:

1

-~ = 2.4 ~- (1)

where d is the diameter of the bubble, D is the diameter of the ejection hole, Q is the air flow rate, and U is the main flow velocity. Equation 1 agrees very well with the present experiment, regardless of the size of the air ejection hole (Fig. 4).

The velocity inside the air column should be governed by the main flow (water) velocity, not by the air ejection velocity, because of the large difference in air and water momentums. Therefore, the effective size (diameter) of the air column is proportional to X/Q/U. We can ob- serve those phenomena by a careful observation of the photographs in Fig. 3. The diameter of the air column increased considerably when it flowed downstream at the low main flow velocity of 2 m/s (see Fig. 3a), whereas

the diameter did not increase at the high flow velocity of 6 m/s (see Fig. 3c). Moreover, a large-scale disturbance which governs the size of the air bubbles should be proportional to the diameter of the air column. This mechanism is similar to a Karman vortex street, but the wavelength of the disturbance is shorter than that of a Karman vortex street, because the air column is flexible and is moved transversely by the disturbance.

Examining the experimental results, it can be con- cluded that high water velocity and/or high disturbance are essential to generate smaller air bubbles.

Methods of generating small air bubbles

In the present study, three different methods were pro- posed and tested to generate smaller air bubbles effec- tively. These were:

1. a 2D convex shape with an ejection hole of 1 mm diameter at the top (in the present study, a half body of an NACA 64-021 section was adopted (Fig. 5));

2. a 2D convergent-divergent nozzle with an ejection hole of 1 mm diameter at the throat (Fig. 6);

3. a transverse wire, with a diameter of 200gm, a little upstream of an ejection hole of 1 mm diameter (Fig. 7).

H. Kato et al.: Microbubble ejection method 125

7 [ @ D=0 5mm 6 I- 9 D=10mm / V'

~. 9 D=l.Smm * /~ d/D 5 [ _ Eq(1) ~ l . / "

4 9

2 9 9

1

0 0 0.5 1.0 1.5 2.0 2.5

;~ Ul) 2

Fig. 4. Diameter of air bubbles ejected on a flat plate

3.0

Air Hole lmm ~ ~j 50 -~l ~-

FLOW I ~

FLOW i~ 30

\ Air Hole lmm ~

Throat Width 1 ~ 5mm (variable)

Fig. 6. 2D convergent~livergent nozzle

Wi re 200 lz m /

Fig. 7. Transverse wire

Fig. 5. 2D convex section with air hole

All three configurations were placed on the test body shown in Fig. 1, keeping the hole position unchanged. The 2D convex shape (hereafter abbreviated as "2D convex") and the 2D convergent-divergent nozzle (hereafter abbreviated as "2D nozzle") are to increase the local flow velocity at the ejection point. Conversely, the transverse wire (hereafter abbreviated as "wire") is to increase the turbulence of flow at the ejection point.

The photographs in Fig, 8 clearly show the effects of the three methods. At 2 m/s, the size of the air bubbles is a few millimeters on a fiat plate with no device, as seen in the top photograph. The bubbles are leaving from the surface because of the large buoyancy force. The bubble size is much smaller at 2D convex and 2D nozzle, as seen in the second and third photographs. The effect of the wire is not obvious, as seen in the bottom photograph.

At 6 m/s, the bubble size becomes much smaller even on the flat plate with no device. Bubbles flow along the surface, which is favorable for drag reduction. The three devices are effective in making the bubbles smaller. However, the bubbles downstream of the 2D nozzle diffuse rather rapidly. This is because the flow separates at the divergent part of the nozzle, and that is not desir- able as a device for drag reduction. Among the three methods, the 2D convex seems the best for drag reduc- tion by microbubbles, because the bubbles become smaller and do not diffuse outside of the boundary layer.

The distribution of bubble size was measured for each case by using a film analyzer to confirm the above conclusions. Figures 9-11 are mean diameters d mea- sured downstream of the 2D convex, the 2D nozzle, and the wire, respectively. The diameter of bubbles on a fiat plate with no device is also shown for comparison.

As seen in Fig. 9, the effect of the 2D convex is greater than expected. Firstly, the bubble size decreased much more than the effect of an increment in the uni- form flow predicted by Eq. 1. The flow velocity at the top of the 2D convex increased about 20%. Therefore the decrease in bubble size should be about 10% according to Eq. 1. However, the bubble size became much less, as seen in Fig. 9. Secondly, the bubble size does not increase even if the air flow rate increases from 50ml/min to 230ml/min. Although the reasons are not clear, these results are favorable for a practical purpose. One possible explanation is the increase in turbulence at the aft part of the 2D convex.

The characteristics of the 2D nozzle are similar to those of the 2D convex when the nozzle throat width was changed from 5 mm to 1 mm. When the throat width was narrower, the bubble size decreased to some extent (Fig. 10).

The drag of the 2D nozzle was estimated by measur- ing the main flow velocity distribution upstream as well as downstream of the nozzle. The drag coefficient was CD -- 0.081 + 0.02 without air ejection. It is much larger than that of the 2D convex (CD = 0.027 + 0.02). It is a drawback to the 2D nozzle.

E ..... E

II

II

h ~

(-~ (,,q

II

E (-q

II

. ,- .

9 L~

H. Kato et al.: Microbubble ejection method 127

Table 1. Comparison of the three devices for bubble size reduction

Flat plate 2D 2D Transverse (reference) convex nozzle wire

Bubble size Normal Small Small Small only at high speeds

Near wall Bubble position Near wall at Near wall Spread high speed

Own drag Small Small Large Applicability Yes Yes No

Small No

4.0

3.5

3.0 d (ram)

2.5

2.0

1.5

1.0

0.5

0

O

A []

I

0 2

I~ ,~ Q=50ml/min 0 9 [] Q=100ml/min

9 /k Q=150ml/min

9 0 Q=230ml/min

Open Symbols

Flat Plate

,6 O

[ ]

A

t

I I I

4 6 8 10

U(m/s)

Fig. 9. Air bubble diameters measured downstream of the 2D convex section

d (mm)

o

0

Nozzle Width 9 O 5.0mm

A 3.0ram [] 2.0ram

1.0mm Open Symbols 100ml/min Solid Symbols 230ml/min

o * Flat Plate

o $

0 I I I I I I I I I

0 5 10 U (m/s)

Fig. 10. Air bubble diameters measured downstream of the 2D convergent-divergent nozzle

6

d(mm)

5

2

Q h

ZX ~ 100ml/min 0mm

[] 100ml/min lmm O

A 230ml/min 0mm

O 230ml/min lmm

9 Flat Plate

6 o 6

[] 9 !

[]

? I I I 0 2 4 6 8 10

U (m/s)

Fig. 11. Air bubble diameters measured downstream of the wire 200 I.tm in diameter

Figure 11 shows the mean bubble diameter down- stream of a transverse wire of 200gm diameter. It was expected that disturbance by the wire would cause a reduction in bubble size. However, the wire was effec- tive only at large velocities (more than 6 m/s).

We summarize the results in Table 1. Comparing all items, the 2D convex is the best, as mentioned above.

Direct measurement of wal l shear ing stress downst ream of the 2D convex

As concluded in the previous section, the 2D convex is the most promising device for skin friction reduction by microbubbles. A 2D convex with seven air ejection holes of 1 mm in diameter was tested, and the skin fric- tion was measured downstream. The two photographs in Fig. 12 show the appearance of microbubble ejection

128 H. Kato et al.: Microbubble ejection method

Cf I /Cf i l 9 Cf2/Cf i2 9 Cf3/Cf~3 C f4 /C f ,4

1.2 ~

1.0 Cf/Cfo

0.6 I

0.4 $ 4 5 9 9

0.2 9 9 9 O ~ l ~ 9 ~ A I ~ t

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Nominal Air Flow Rate Q hBU

F ig . 13. Reduction of wall shearing stress by air ejection from the 2D convex section

Fig. 12. Air bubbles generated from the top of the 2D convex section. U = 6 m/s; Q = 7 l/rain

at 6m/s and an air ejection rate of 71/min. The micro- bubbles covered the downstream surface well, although the diffusion was considerable. If we can reduce this diffusion, the effect of microbubbles on skin friction reduction must be greater. This is an important problem for future research.

The reduction of skin friction (wall shearing stress) by microbubbles was measured directly using four minia- ture floating element transducers, whose locations are shown in Fig. 2. The test conditions were:

- - main flow velocity (U): 5, 6, 8, and 10m/s; - - air flow rate (Q): 0, 1, 2, 3, 5, 7, and 101/min.

Figure 13 shows the reduction rate, C/Cso (accuracy +9%), where C~ and CI~ are skin friction coefficients with and without microbubbles, respectively. The num- bers 1-4 indicate the different transducers. The abscissa is the nondimensional nominal air flow rate, Q/(hBU), where h is the height of the 2D convex (5.24mm), B is the width of the test section (50 mm), and U is the main flow velocity.

The data diminish well with the nondimensional air flow rate for each group. The microbubbles are very effective near the air ejection point (see CI1/C~ol ). How- ever, the effect decreased rapidly downstream, as seen from the data for Cj:, C O, and Cr4.

Figure 14 shows a comparison between the 2D con- vex and a flat plate at the same downstream location. The abscissa is nondimensional air flow rate, Q/(6BU), where 3 is the displacement thickness of the boundary layer, B is the section width, and U is the main flow velocity. The effect of the 2D convex is clear in Fig. 14.

Although we can obtain a net reduction of drag by injecting air at the top of the 2D convex, it is difficult to

CffC~

1.2

1.0

0.8

0.6

0.4

0.2

0 0.8 1.0

Q

6 BU

9 2D Convex Flat Plate

\ \

! 1

0.2 0.4 0.6

Air Flow Rate

Fig. 14. Comparison between the 2D convex and the flat plate (transducer No. 1)

know whether we can get a net energy saving when we apply microbubble ejection to the hull surface because we need considerable energy input to eject the microbubbles from the hull surface. According to a recent analysis, TM we can expect a few percent net gain in energy with a car-ferry 187m in length.

Conc lus ions

1. The size of the microbubbles is governed by the main flow velocity and the air ejection flow rate when they are generated from a hole in a flat plate. A very simple formula (Eq. 1) by Meng and Uhlman ~3

H. Kato et al.: Microbubble ejection method 129

was val id, and was reconf i rmed by the present exper iment .

2. The e jec ted air fo rms an air co lumn st retch ing down- st ream. Though it is not yet c lear the large- scale d i s turbance caused by the e jected air co lumn itself can be the main mechan ism generat ing the mic robubb les .

3. Three d i f ferent methods were examined to generate smal ler bubbles : - - a 2D convex shape with an e ject ion ho le at the

top; - - a 2D convergent -d ivergent nozz le wi th an ejec-

t ion ho le at the throat ; - - a t ransverse wire at the e jec t ion hole. Among the three methods , the 2D convex was the most e f fect ive at reduc ing the size of air bubbles .

4. It was also conf i rmed by d i rect measurement of the fr ict ion that the 2D convex shape was the most p rom- ising dev ice to reduce skin fr ict ion.

Acknowledgments. The authors express their acknowl - edgments to Y. Takahash i and Y. Yosh ida, IH I Co., for va luab le discussions. They also thank M. Tsuda for her he lp dur ing the preparat ion of this paper .

References

1. McCormick ME, Bhattacharyya R (1973) Drag reduction of a submersible hull by electrolysis. Nav Eng J 85:11-16

2. Madavan NK, Deutsch S, Merkle CL (1984) Drag reduction of turbulent skin friction by microbubbles. Phys Fluids 27:356-363

3. Madavan NK, Deutsch S, Merkle CL (1985) Measurements of

local skin friction in a microbubble-modified turbulent boundary layer. J Fluid Mech 156:237-256

4. Madavan NK, Deutsch S, Merkle CL (1985) Numerical investiga- tion into the mechanisms of microbubble drag reduction. J Fluid Eng 107:370-377

5. Merkle CL, Deutsch S, Pal Set al (1986) Microbubble drag reduc- tion. Proceedings of the 16th Symposium on Naval Hydro- dynamics, Berkeley, pp 199-215

6. Pal S, Merkle CL, Deutsch S (1988) Bubble characteristics and trajectories in a microbubble boundary layer. Phys Fluids 31:744- 751

7. Pal S, Deutsch S, Merkle CL (1989~kA comparison of shear stress fluctuation statistics between microbubble modified and polymer modified turbulent boundary layers. Phys Fluids A1:1360-- 1362

8. Kato H, Miyanaga M, Haramoto Yet al (1994) Frictional drag reduction by injecting bubbly water into a turbulent boundary layer. Cavitation and gas-liquid flow in fluid machinery and devices. FED vol 190, ASME, pp 185-194

9. Kato H, Miyanaga M, Yamaguchi H et al (1994) Frictional drag reduction by injecting bubbly water into a turbulent boundary layer and the effect of plate orientation. In: Serizawa A, Fukano T, Bataille J (eds) Advances in multiphase flow. Elsevier, Amsterdam, Kyoto, pp 85-96

10. Guin MM, Kato H, Yamaguchi H, et al (1996) Reduction of skin friction by microbubbles and its relation with nearwall bubble concentration in a channel. J Mar Sci Technol 1:241 254

11. Bogdevich VG, Evseev AR, Malyaga AG et al (1977) Gas- saturation effect of near-wall turbulence characteristics. 2nd International Conference on Drag Reduction, Cambridge, UK, BHRA, pp 25-37

12. Zuber N, Tribas M, Westwater JW (1961) International develop- ment heat transfer ASME, p 230

13. Meng JCS, Uhlman JS Jr (1989) Microbubble formulation and splitting in a turbulent boundary layer for Turbulence reduction. Symposium in Honor of Maurice Holton on his 70th Birthday

14. Yoshida Y, Takahashi Y, Kato H et al (1998) Study on the mecha- nism of resistance reduction by means of micro-bubble sheet and on applicability of the method to full-scale ship. 22nd Symposium on Naval Hydrodynamics, Washington