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 510%, 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 = ρ B ⎢ gH αU 0 − ⎜ CPα − CD ⎟ U 03 ⎥ . (5)
2⎝
B
⎠ ⎦
⎣
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 U0 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 W0 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. WL is the saved
power by negative pressure above the hydrofoil
WL = CP
1
ρU 0 2Q
2
(3)
and WD is the power concerning drag force by the
installed hydrofoil on the ship hull
1
2
WD = CD ρU 0 A ,
2
(4)
where CP, CD, 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=αBU0, 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
CPα >
A
L
CD CD sin θ C.
B
H
(6)
Here L, hb, 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 U03 (Eq. 5), this facility
has a higher performance for the high speed vessels.
We also note that the Equation 5 gives the critical
velocity Uc for the air injection only by the hydrofoil
pump, that is, the velocity when W=0:
Uc =
2 gH α
.
CPα − ( L / hb )CD sin θ
(7)
As an example, if we consider a hydrofoil with the
NACA 65-410 (CP=1.50, CD=0.015 at θ=10°) shape
and use H=2~5 m, α=5%, L=50 mm, and hb=20 mm,
then Uc=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 CP >> CD for hydrofoils, the drag force
term in Eq. (7) is negligible. That means the Uc
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 Uc of the WAIP
estimated from the Equation 7 is ~0.49 m/sec
(NACA 653-618, 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 (CP and CD) 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 CP and CD 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 (U0). 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 (FloBeads, 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 U0 in an
infinite fluid, Reynolds number should be addressed:
- Reynolds number,
U d
Re D = 0
ν
(8)
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,
U
Frh = 0
gh
Figure 6. Snapshots of circular cylinders (d=20 mm) at different condition.
(9)
where g and h are gravity acceleration and water
depth, respectively (circular cylinders: 0.1 < Frh <
7.75; elliptic cylinders: 0.1 < Frh < 7.5).
- Water depth ratio,
h
a= .
d
(10)
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,
γ=
ν air
ν
(11)
where νair is kinematic viscosity of the air, is about
17 in our experiments.
Figure 8. Water surface depression w by a moving cylinder as a
function of U0 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/sec2.
- Weber number,
ρU 02 s
We =
3 RESULTS AND DISCUSSION
σ
(12)
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 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.
3.1 Circular cylinders
Figure 6 shows snapshots of circular cylinders at
different conditions. As the towing velocity U0
increases (Red 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 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 U0 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
w=
U 02
.
2g
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 Red, Frh,
and normalized depth of the cylinder (a=h/d).
(13)
As shown in Figure 8, the experimental results have
a good agreement with the Equation 13 for small w
(w < ~10 mm, U0 < ~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 U0, 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, U0=580 mm/sec)
3.2 Elliptic cylinders
Figure 11. Regime diagram for bubble generation by an elliptic
cylinder moving beneath an air-water interface.
Figure 10 shows snapshots of elliptic cylinders at
different conditions. Although the free surface
depression w increases with the U0 as in the case of
the circular cylinder, the breaking wave with bubble
generation was observed only in the case of
moderate Red (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 < Red < ~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.
3.4 Threshold of breaking wave
Figure 13. Surface profile for (a) circular cylinders (b) elliptic
cylinders at different Red. 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 (U0=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
Figure 13 shows a typical result of surface profiles
for circular and elliptic cylinders. In case the wave
breaking occurs (Red=10000, 12000, 14000, 16000
for the circular cylinder and Red=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 Red. 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
REFERENCES
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on the hydrofoil air pump “WAIP”. Measurements
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ACKNOWLEDGEMENTS
This work is supported by New Energy and
Industrial Technology Development Organization
(NEDO) of Japan (grant no. 08 B 36002).