added resistance , unsteady wave field and my...
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Shigeru NAITO
E. Professor of Osaka University
For Retirement seminar of Professor Papanikolaou in September-30 , 2016
Added Resistance , Unsteady Wave Field and My Memories
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Contents • Part 1 (20min.)
Today’s main talk
Today’s main talk
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Unsteady wave field consists of two wave systems One is k2 wave system, the other is k1 wave system.
1: k2 wave system Ring wave : Waves generated by oscillation of ships without forward velocity This system is the deformed Ring wave by forward velocity of ships.
2: k1 wave system Kelvin wave : Waves generated by forward velocity of ships without oscillation. This system is the deformed Kelvin wave by oscillation of ships.
Today, consider only added resistance due to k2(θ) wave system (3)
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Unsteady wave field
k2 wave system k1 wave system
Deformed Kelvin wave
Deformed Ring wave
Hanaoka Parameter
(Index of Unsteadiness)
Wave number
・
Conservation of wave number
Based on those knowledge of unsteady wave field, let discuss on the Maruo’s formula
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Maruo’s Formula
This formula has two equations. k2 wave term and k1 wave term Each equation is divided into three parts (1) Integral range (2)Kochin function (3) Weighting function
In the weighting function, the effect of the oblique waves appear only in the term of the black arrows.
Coordinate system
k2 wave
k1 wave
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Three Three parts parts of the of the formula formula
(1) Integral range (1) Integral range
•• Existing region of Existing region of an elementary wave an elementary wave
(2) (2) Kochin function (Amplitude functionKochin function (Amplitude function) H() H(ΘΘ))
•• Amplitude and period Amplitude and period of of an elementary wave which propagate a certain an elementary wave which propagate a certain
direction direction ΘΘ from ships to a far field . from ships to a far field . Presenting Presenting ship ship form and form and ship motions.ship motions.
•• Various calculation methods exist. Various calculation methods exist.
(3)(3) Weighting functionWeighting function
•• Mutual relation between Mutual relation between the propagating the propagating direction of direction of elementary waves elementary waves and and the the
effect of the directioneffect of the direction onon ΔΔRR
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Symmetric with respect to Y-axis
B-Wave
A-Wave
Y
X
Red line : k2: B-wave Blue line : k2: A-wave Green line : k1 wave
K1,2 -Wave pattern Generated by a point periodical singularity
Those figures was calculated by Prof Iwasita (Hiroshima Univ.) (7)
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・
K2(θ) Wave number
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Index0
2
Wt ( )
d
0
Wt ( )
d
Notice Weighting function has Strong Directional Characteristics Propagating waves angle 3π/2~(3π/2+θ0) and
(θ0~π/2), namely B-Wave : Most effective on ΔR
Weighting Function
Condition L=4m, Fn=0.2, λ/L=0.5 Ω=1.212, θ0=78.09deg=1.363rad
1.363
Wt1(θ)
θ0
θ
=0.772
Weighting Function (Head wave)
One index
0 0.785 1.571 2.356 3.142
50
5
Wt ( )
Wt1 ( )
Wt2 ( )
0
0
Wt2(θ)
Sharp monotone decreasing function
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Ω=0.274 Ω=0.48
Pay attention to Vertical axes value
Reforming bow form based on this fact, we could have one way to deduce ΔR
0 1.571 3.1420
10
20
30
Wt θ( )
θ
0 1.571 3.1420
2
4
6
8
10
k2 θ( )
θ
0 1.571 3.1420
10
20
30
40
50
Wt θ( )
θ
0 1.571 3.1420
1
2
3
k2 θ( )
θ
0 1.571 3.1420
0.5
1
1.5
k2 θ( )
θ
0 1.571 3.1420
1
2
3
4
5
Wt θ( )
θ
0 1.571 3.1420
0.01
0.02
0.03
0.04
k2 θ( )
θ
0 1.571 3.1420
0.0025
0.005
Wt θ( )
θ
k2 (θ)
Weighting Function and Ω
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振幅関数(Kochin function) Ohkusu,Kobayashi (1984: First Marine Dynamics Symposium)
Complicated behavior of elementary waves in the direction to θ0~π/2 is worthy of note. (11)
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FP
LLWL LWL
Restrained condition: This bow’s ΔR is smaller than it of conventional ships. When λ/L <0.8, ΔR is small. Motion free condition This bow’s ΔR is larger than it of conventional ships, because the whale bow scoop up wave. When λ/L >0.9, ΔR become large. This bow also had some problems on a regulation.
Before Osaka university’s experiments :
However, those results gave us many hints on bow design in waves.
The bow form below the load water line is same. Only that above the load water line can be reformed .
Performance in the still water does not change.
Remodeling the bow into sharp (12)
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Measurement set up: Diffraction force acting on Bow
Wire
Bow part Load Cell
Ship motions:Restrained Similar to Air force measurement system
(1983 Osaka University)
Three bow forms were tested
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1988(KSAJ) . 1990(Eng. Science, F. Dynamics)
Wave ray tracing (Calculation)
Blunt Bow
Sharp Bow
Extensive difference
Measurement of diffraction force acting on bow part
Wave breaking point
By making only the form of bow above the load water line sharp, we can changed the propagating direction of reflected and radiated waves.
The wave ray from this area can not propagate to the far field
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Ordinary Bow Beak-Bow
Ship motion : Free
Osaka university JMU
Ordinary Bow
Ordinary Bow
Ordinary Bow
Ordinary Bow
Ordinary Bow
Beak-Bow and Ax-Bow :
The bow shape above the load waterline :
Sharp
The hull form below the load waterline :
Same as the hull of ordinary ship
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Measurement of Speed Loss in Actual Seas (JMU)
Comparison between Ax-Bow and Ordinary Bow
H>4m
In high wave sea, the speed loss of Ax-Bow Ship is small.
Wave height(m)
Ordinary Bow
Speed drop
Ordinary Bow
Ordinary Bow
Already a lot of this ship have been built.
Probable Density Function of Speed
On board data
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The bulbous bow affects wave making resistance characteristics.
Slow speed ship → wave making resistance is small. The ballast condition
sea surface → below the load waterline → sharpened bow part below the load
waterline. → reduce the added resistance not only in full load condition but also in ballast condition
Upright stem line Leadge Bow
Ax-Bow
Ordinary Bow
In old time, a ship with similar bow shape existed.
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Company name has changed as follows. NKK+HZ→Universal Ship Building+IHI → Japan Marine United(JMU)
Mt.Fuji
Sea trial of Ax-Bow ship in Suruga bay
My home town
Recently, the stem line of bow is standing upright have been developed by some corporations. OSB (Onomiti CO.) SEAWORTHY (Tuneisi CO., Hiroshima Univ.) Seaworthy Bow (Ooshima CO.)
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COVE Bow Form : Developed by NMI group
center line
upper deck
COVE
original shape
static swell up
static swell up+1.5mstill water
These concept on improvement bow form 1. Change the propagate direction of elementary waves generated by forward ships in waves. 2. Consider the static swell up
center line
upper deck
COVE
original shape
static swell up
static swell up+1.5mstill water
waterline at design draught
water line at 1.5mabove the static swell up line
about S.S.9
Water line at design draught
Water line at 1.5m above the static swell up line
COVE : Concave Shape Optimized in Waves
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Appendage STEP : NMI
Osaka Prefecture Univ.(Ikeda) : By putting on the bow front above the load water line a small appendage, they could reduce ΔR.
SK-BOW: Knuckled- shape Bow
(Shin-kurushima CO., Hiroshima Univ.)
Other examples
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Moderate seas Heavy seas
Safety Propulsive performance Concern Racing, Deck wetness Capsizing
Power, Fuel oil consumption Speed loss
Sea condition
Recently ship length becomes longer and her Fn number lower, then
relatively wave length becomes short, weather becomes moderate.
Then the study of the bow form in small λ/L has to be continued.
For each ship type there will be an optimum bow form.
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Trivial comments 1. I talked on mutual relation between the bow form and the added resistance in short head waves. 2. It is important for bow form development to focus on the propagating direction of elementary waves generated by ships in waves. Attention to the weighting function Wt(θ) 3. Even a small change of the propagating direction, it’s effect on ΔR can not ignore, and in some cases it exhibit a large effect. It would also need to be considered the following problems. ・In quartering waves including rudder-ship interaction, steady turning Mt., ・Viscosity, ・Utilization of a bow fin with housing device etc.
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Part2 Our Memories
Murooji in Nara prefecture Beginning April in 2008 : Papa stayed several weeks in Osaka.
1985? In front of the building of NAOE, Osaka Univ. (23)
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Himeji Castle with students and department staff 2002
New year’s greetings at the home of the late E. Prof.Nakamura (1993/12~1994/2)
1991 4th IMDC Kobe At one session Papa was the chairman and I co-chairman. Together E. Prof. Takarada
Papa with his wife and daughter in 1994
at Temple of Poseidon, Sounion, Athens
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Kyoto Arashiyama with Profs. Francescutto and Vassalos( 1996)
The lakeside Syojiko at the foot of Mt. Fuji (201?)
2008 My retirement party at Osaka
Trio of Borsalino in Osaka With E. Professor Y.Himeno 2013/2/4
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Although the old noble horse live
a quiet life in a barn,
his soul is in the wider world.
Although the noble person becomes
old, his vigorous spirit
continues to have
high- ambitions,
and
will fly freely into the sky! Near the Ness lake : Scotland(2004)
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Your new voyage to future has just started.
Thank you very much for your kind attention.
Good Voyage !
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