International Conference on Ship Drag Reduction SMOOTH-SHIPS, Istanbul, Turkey, 20-21 May 2010 A New Power-saving Device for Air Bubble Generation: Hydrofoil Air Pump for Ship Drag Reduction I. KUMAGAI, N. NAKAMURA, Y. MURAI, Y. TASAKA & Y. TAKEDA Faculty of Engineering, Hokkaido University, Sapporo, Hokkaido, Japan Y. TAKAHASHI R&D Engineering Inc., Setagaya-ku, Tokyo, Japan ABSTRACT: We have invented a new power-saving device for drag reduction of ship with microbubbles which reduces the energy for the bubble injection. The new device, which consists of angled hydrofoils with air introducers, has been installed on a coaster and 10-15% of the net power saving is achieved. This device utilizes a low-pressure region produced above the hydrofoil as the ship moves forward, which drives the atmospheric air into the deep water. Here we present its principal and fundamental processes such as the entrainment of the air into the water based on laboratory experiments on fluid dynamic behavior around a moving cylinder beneath a free surface. 1 INTRODUCTION 1.1 Hydrofoil air pump for ship drug reduction A research area for drag reduction of ship with microbubbles has been active in recent years (Ceccio 2010) because of the energy saving potential and of the environmental safety for the marine pollution. The injection of air microbubbles into a turbulent boundary layer over the ship hull modifies the boundary layer and reduces its skin friction. Although recent applications of drag reduction technology with microbubbles to the ship reduce about 10-15% of the energy regarding the skinfriction in the turbulent boundary layer, the energy necessary for the injection of air bubbles by using conventional bubble generators, which is about 5-10%, is generally ignored. This means the net power saving is only 0-5%. Recently we have invented a new power-saving device which reduces the energy for the bubble injection (Murai & Takahashi 2008). Figure 1 shows the new facility called WAIP (Winged Air Induction Pipe) which has an angled hydrofoil with an air introducer. We have installed WAIPs on a coaster and 10-15% of the net power saving is achieved (Fig. 2, Murai et al. 2010). Figure 1. Side view of WAIP. This device utilizes a low-pressure region produced above the hydrofoil as the ship moves forward, which drives the atmospheric air into the deep water. However fundamental flow physics concerning this facility has not been clarified yet because extremely complicated phenomena, which are the free-surface effect on lift forces of the hydrofoils, the process of air entrainment through the air-water interface, and bubble generation,
should be expected if the free surface comes close to the hydrofoil of the WAIP. respectively. By using Equations 1-4, the total power W can be rewritten as 1 A W = ρb ghαu C α C U 3 0 P D 0 2 B. (5) Figure 2. Shaft power with and without air injection by WAIP (Murai et al. 2010). 1.2 Theory of the Hydrofoil air pump As a first-order approach, if we consider the hydrofoil moving at the velocity U 0 under the water surface, then the total power W necessary for bubble injection at air volume flux Q into the water can be expressed as W = W0 WL + WD. (1) Here W 0 is the power for bubble injection into the water depth of H, that is, W0 = ρ ghq, (2) where ρ is the density of the water. W L is the saved power by negative pressure above the hydrofoil 1 2 WL = CP ρu0 Q (3) 2 and W D is the power concerning drag force by the installed hydrofoil on the ship hull 1 2 WD = CD ρu0 A, (4) 2 where C P, C D, and A are the negative pressure coefficient of the hydrofoil, the corresponding drag coefficient, and the projected area of the hydrofoil, Figure 3. Snapshots for air entrainment and bubble generation by WAIP. The WAIP moves from right to left. Here the air volume flux Q=αBU 0, where α and B are the mean void fraction and the vertical crosssectional area of the microbubble layer over the ship
hull. Hence, the power for bubble injection is saved by installing the hydrofoil facilities when A L CPα > CD CDsinθ C. (6) B H Here L, h b, and θ are chord length of the hydrofoil, thickness of the microbubble layer, and the angle of attack, respectively. Since the power saving by the hydrofoil pump depends on U 0 3 (Eq. 5), this facility has a higher performance for the high speed vessels. We also note that the Equation 5 gives the critical velocity U c for the air injection only by the hydrofoil pump, that is, the velocity when W=0: U c = 2gHα. (7) C α ( L/ h ) C sinθ P b D As an example, if we consider a hydrofoil with the NACA 65-410 (C P =1.50, C D =0.015 at θ=10 ) shape and use H=2~5 m, α=5%, L=50 mm, and h b =20 mm, then U c =5.3~8.5 m/s. This simple estimation means that not only high-speed marine vehicles but also moderate-speed marine vehicles can save the net power necessary for air bubble injection by installing the hydrofoil air pump WAIP. Since C P >> C D for hydrofoils, the drag force term in Eq. (7) is negligible. That means the U c should correspond to a threshold of air entrainment by the hydrofoil. Figure 3 shows an experimental result on the effect of towing velocity on air entrainment by the WAIP beneath the water surface. Although the critical velocity U c of the WAIP estimated from the Equation 7 is ~0.49 m/sec (NACA 65 3-618, θ=12 ), no air entrainment was observed in our tank experiment even if the towed velocity was greater than the estimated value (Fig. 3a, 0.68 m/sec). The onset of the air entrainment and bubble formation was ~0.77 m/sec (Fig. 3b) and the volume of the air bubbles increased with the towed velocity (Fig. 3c). The reason of the discrepancy between our theory and experiments is that the parameters (C P and C D ) used in our simple estimation are the values for steady condition in infinite fluid. Since the introduction of the free surface influences on the flow behavior around the hydrofoil, the values of C P and C D should change from the infinite case (Hough & Moran 1969; Faltinsen & Semenov 2008). Furthermore non linear free-surface effects on the flow such as breaking wave (Duncan 1981) and air entrainment through the air-water interface are expected in our hydrofoil facility. Hence we have reached the point where we should do experiments to investigate the fundamental flow behavior of the 2-D body moving beneath the free surface in order to optimize the hydrofoil air pump. The main objective of the present work is to understand the effect of the free surface on the flow behavior, threshold of air entrainment, and bubble generation process by a submerged two-dimensional (2-D) body (circular and elliptic cylinders) moving at a constant velocity. The knowledge about the fundamental flow behavior would help us to optimize the hydrofoil air pump for ship drug reduction. 2 EXPERIMENTAL METHOD 2.1 Experimental equipments Figure 4 shows a sketch of our experimental setups. The experimental tank (500 x 500 x 5000 mm) was filled with a tap water. A circular cylinder (diameter d=20 mm, span-wise length L=350 mm) Figure 4. Experimental equipment (a) side view (b) front view.
or an elliptic cylinder (horizontal axis l=50 mm, vertical axis d=10 mm, span-wise length L=400 mm) was submerged in the water at a depth of h and towed by the linear servo actuator (N15SS, IAI) at a constant velocity (U 0 ). In order to observe the fluid motion around the 2-D cylinder, we added tracer particles (DIAION, Mitsubishi Chemical, specific gravity = 1.01, mean diameter φ~90 μm) in the water. We also seeded lighter tracer particles (Flo- Beads, Sumitomo Seika, specific gravity = 0.919, mean diameter φ~180μm) to visualize the air-water interface. The tank was illuminated by a 2-D light sheet (Metal halide lamp and cylindrical lens) at the middle of the tank and the deformation of the airwater interface was monitored by a high speed video camera (Photron FASTCAM-MAX. 250~1000 fps). We also measured the deformation of the air-water interface from above by using a commercial digital camera (CASIO, EX-F1) which moved together with the cylinder. The tracers on the water surface were illuminated by a metal halide lamp whose light intensity was weak enough not to disturb the images of high speed camera. 2.2 Experimental parameters Although our knowledge is extensive on the flow past a cylinder in infinite fluid (Williamson 1996), our understanding of the flow behavior around a cylindrical body close to a free surface is relatively poor while this flow situation is common in practical applications such as marine constructions and hydrofoil vessels. Figure 5. Sketch of the flow around a 2-D cylinder moving beneath a free surface. Figure 5 shows the flow configuration for our problem. For the description of the flow dynamics of a cylinder moving at a constant speed U 0 in an infinite fluid, Reynolds number should be addressed: - Reynolds number, Ud 0 Re D = (8) ν where d and ν are the characteristic length scale (e.g. diameter of the cylinder) and kinematic viscosity of the fluid (water), respectively. We varied the values from 1900 to 19300 for circular cylinders and 900 to 14500 for elliptic cylinders. Since our cylinder moves beneath the water surface, the flow behavior should also be influenced by the following non dimensional parameters. - Froude number, U0 Frh = (9) gh Figure 6. Snapshots of circular cylinders (d=20 mm) at different condition.
where g and h are gravity acceleration and water depth, respectively (circular cylinders: 0.1 < Fr h < 7.75; elliptic cylinders: 0.1 < Fr h < 7.5). - Water depth ratio, h a =. (10) d We changed the value from 0.1 to 7.75 for circular cylinders and from 0.1 to 7.5 for elliptic cylinders. - Viscosity ratio, ν air γ = (11) ν where ν air is kinematic viscosity of the air, is about 17 in our experiments. - Weber number, 2 ρu0 s We = (12) σ where ρ, s and σ are water density, characteristic length scale (e.g. air bubble size), and interfacial tension between air and water, respectively. The Weber number is about 14 for the bubble with the diameter of 1 mm. Figure 8. Water surface depression w by a moving cylinder as a function of U 0 at different water depth h. Open and closed symbols denote non-existence and existence of breaking wave with bubble generation, respectively. The broken line represents a theoretical curve according to the Equation 13, where the gravity acceleration g=9.8 m/sec 2. 3 RESULTS AND DISCUSSION 3.1 Circular cylinders Figure 6 shows snapshots of circular cylinders at different conditions. As the towing velocity U 0 increases (Re d increases), the magnitude of the water-surface depression w behind the moving cylinder increases. The waveform behind the cylinder becomes unstable and breaking wave occurs on the forward face of the wave (Fig. 7). Once the breaking wave occurs, the atmospheric air is entrained and small bubbles are created. Figure 7. Breaking wave with bubble formation. (a) top view: the broken line indicates the front line of bubble generation, (b) side view: an x-z image converted from a spatio-temporal slice of the high-speed video images. Figure 9. Regime diagram for bubble generation by a circular cylinder moving at a constant velocity beneath an air-water interface.
Figure 10. Snapshots of elliptic cylinders (d=10 mm) at different condition. Oblique view from below. Figure 8 shows the depression w, which was measured from the image data of water surface profile, as a function of U 0 at different depth h. For small disturbance of the air-water interface, at first order, the depression w could be described by Bernoulli s equation, that is Figure 9 shows a regime diagram for breaking wave with bubble generation by the moving cylinder beneath the water surface. The threshold of bubble formation by breaking wave depends on Re d, Fr h, and normalized depth of the cylinder (a=h/d). 2 U0 w =. (13) 2g As shown in Figure 8, the experimental results have a good agreement with the Equation 13 for small w (w < ~10 mm, U 0 < ~400 mm/sec). However the discrepancy between the measured data and the Equation 13 is apparent when the breaking wave with bubble generation occurs. With the increase of the U 0, the depression w approaches a constant value which seems to depend on h. Figure 12. Effect of angle of attack θ on bubble generation. (h=5 mm, U 0 =580 mm/sec) Figure 11. Regime diagram for bubble generation by an elliptic cylinder moving beneath an air-water interface. 3.2 Elliptic cylinders Figure 10 shows snapshots of elliptic cylinders at different conditions. Although the free surface
depression w increases with the U 0 as in the case of the circular cylinder, the breaking wave with bubble generation was observed only in the case of moderate Re d (Fig. 10d-f) in our parameter range. By comparing with the images of circular cylinders, the bubble generation rate by the elliptic cylinder seems to be smaller than that by the circular cylinder. The regime diagram of the bubble generation for the elliptic cylinders is shown in Figure 11. The bubble generation by the breaking wave occurs in the range of ~4000 < Re d < ~6000. condition (Fig. 12b). For θ = +10 (Fig. 12a), the depression w becomes large because the flow over the hydrofoil tends to attach to the wall of the hydrofoil. As a result, vigorous bubble generation occurs by breaking wave. On the other hand, no bubble generation occurs when θ = -10 (Fig. 12c). Figure 14. Ratio of the wave height η to the wave length λ. Open and closed symbols denote non-existence and existence of bubble formation, respectively. Figure 13. Surface profile for (a) circular cylinders (b) elliptic cylinders at different Re d. The profiles with solid symbols denote that wave breaking with bubble generation was observed in the experiments. The elliptic circular in this figure shows the position of circular cylinder and elliptic cylinder. 3.3 Effect of angle of attack The surface profile of the air-water interface behind the moving 2-D body is strongly influenced by the angle of attack θ. In Figure 12, all the experimental conditions are the same (U 0 =580 mm/sec, h=5 mm) except for the angle of attack θ. For θ = 0, bubble creation by breaking wave is modest in this 3.4 Threshold of breaking wave Figure 13 shows a typical result of surface profiles for circular and elliptic cylinders. In case the wave breaking occurs (Re d =10000, 12000, 14000, 16000 for the circular cylinder and Re d =5000, 5400 for the elliptic cylinder shown in Fig. 13), the slope of the forward wave becomes steep. Figure 14 shows the wave steepness (the ratio of the wave height to the wave length) as a function of Re d. This result shows that breaking wave with the bubble entrainment occurs when the ratio is greater than ~0.1. This value is similar to the wave steepness of the ocean wave breaking (Toffoli et al. 2010).
4 CONCLUSIONS We have explored laboratory experiments on freesurface waves generated by two-dimensional bodies (circular and elliptic cylinders) moving at a constant velocity U 0 beneath an air-water interface in order to understand the fundamental fluid dynamic behavior on the hydrofoil air pump WAIP. Measurements of the free surface profile and visualization of the air bubbles yield the threshold and the regime diagrams of the bubble generation, which are described by cross-sectional shape of the cylinders, Reynolds number Re d, Froude number Fr h, and normalized depth of the cylinder a. For circular cylinders, as Re d and Fr h numbers increase, the surface deformation becomes substantial in the downstream of the cylinder and breaking wave with air entrainment occurs. The bubble generation by the breaking wave is also observed in the case of the elliptic cylinder although the condition of the bubble generation in the Re d -Fr h regime diagram is different from that observed in the case of the circular cylinder. In any cases of the cylinders, the ratio of the wave height to the wave length, which should be the physical criterion of the breaking wave, is about 0.1 when the bubble generation occurs. The phase diagrams for bubble generation obtained in this study provide useful information for not only optimization of the hydrofoil facility for the drag reduction of ship but also the design of marine constructions. REFERENCES Ceccio, S.L. 2010. Frictional drag reduction of external flows with bubble and gas injection. Annu. Rev. Fluid Mech. 42: 183-203. Duncan, J.H. 1981. An experimental investigation of breaking waves produced by a towed hydrofoil. Proc. R. Soc. Lond. A 377:331-348. Faltinsen, O.M. and Semenov, Y.A. 2008. The effect of gravity and cavitation on a hydrofoil near the free surface. J. Fluid Mech. 597: 371-394. Hough, G.R. and Moran, J.P. Froude number effects on twodimensional hydrofoils. J. Ship. Res. 13, 1:53-60. Kodama, Y. 2009. Toward practical application of air lubrication to ships for drag reduction. Journal of the Japan Society of Mechanical Engineers, Vol. 112, No.1086: 46-49 (in Japanese). Murai, Y. and Takahashi, Y. 2008. Frictional drag reduction ship. Patent Number: 4070385, Japan. Murai, Y., Kumagai, I., Tasaka, Y., Takeda, Y., and Takahashi, Y. 2010. Hydrofoil type of bubble generator for marine drag reduction. Transactions of the Japan Society of Mechanical Engineers, Series B, vol. 76, 763: 483-485. Reichl, P., Hourigan, K., and Thompson, M.C. 2005. Flow past a cylinder close to a free surface. J. Fluid Mech. 533: 269-296. Sheridan, J., Lin J.-C., and Rockwell, D. 1997. Flow past a cylinder close to a free surface. J. Fluid Mech. 330: 1-30. Toffoli, A., Babanin, A., Onorato, M., and Waseda, T. 2010. Maximum steepness of oceanic waves: Field and laboratory experiments. Geophysical Research Letters 37: L05603, doi:10.1029/2009gl041771. Williamson, C.H.K. 1996. Vortex dynamics in the cylinder wake. Annu. Rev. Fluid. Mech., 28: 477-539. ACKNOWLEDGEMENTS This work is supported by New Energy and Industrial Technology Development Organization (NEDO) of Japan (grant no. 08 B 36002).