International Research Exchange Meeting of Ship and Ocean Engineering in Osaka
Study on Heel Stabilization for
Cruise Ship by using Active Fin
and Anti-Rolling Tank
Jae-Han Kim and Yonghwan Kim
Department of Naval Architecture and Ocean Engineering,
Seoul National University, Korea
22 December 2012
Wind-Induced Heel of Cruise Ship
Wind-induced heel of cruise ship
•
‒
Large superstructure of cruise ship makes her vulnerable to
lateral wind load.
‒
Wind-induced heel of cruise ship is considered in the seakeeping
Wind
point of view.
‒
Heel stabilization is recommended to improve passenger comfort
and seakeeping performance.
Prediction of heel moment
•
‒
Wind-induced heel moment to the ship is computed numerically.
‒
Wind speed profile: DNV Recommended Practice C205 (October
Wind-induced heel of cruise ship
2010)
‒
Calculation of heel moment (Fujiwara & Ueno, 2006)
‒
Heel moment coefficient from wind tunnel experiment in
Fincantieri (Serra, 2002)
Stabilization of heel effect
•
‒
Actuator: Stabilizing fin, anti-rolling tank (U-tube tank)
‒
Linear optimal control algorithm: LQG
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Computational Program
WISH-CRUISE
•
‒
Computational methods of heel moment and motion stabilization integrate to the program WISH-CRUISE.
‒
WISH-CRUISE is extension based on WISH (computer program for nonlinear wave induced load and ship motion) which
is developed in Seoul National University.
‒
Assessment of seakeeping performance of cruise ship in time domain can be carried out by using the program WISHCRUISE.
WISH-CRUISE
Motion control
Wind-induced
heel moment
Comfort analysis
WISH
(Ship motion analysis
in time domain)
Added resistance
International Research Exchange Meeting of Ship and Ocean Engineering in Osaka
Computation
result
Seakeeping analysis
3
Prediction of Wind-Induced Heel
I.
Model cruise ship
II. Wind speed profile model
III. Computation of heel moment
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Model Cruise Ship
Similar cruise ships to model cruise ship
•
‒
It seems to be sister ships
Caribbean Princess, computational model cruise ship,
experimental model cruise ship
‒
Model Cruise Ship
Caribbean Princess
Length (LBP)
242 m
242 m
Breadth
36 m
36 m
Depth
8.3 m
8.4 m
Displacement
51,000 ton
52,000 ton
Caribbean Princess (Fincantieri, 2004)
Specification and shape of superstructure are necessary to
obtain the heel moment accurately.
→ Superstructure of Caribbean Princess is considered in the
Model cruise ship of Fujiwara & Ueno (2006)
present study.
Test model No. 1852 (1/125, Fincantieri)
Solution panels of model cruise ship
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Parameters for Computation of Wind Load
Coordinate system for numerical computation
•
‒
Apparent wind velocity is computed from vector summation of
true wind velocity and forward speed of ship.
Definition of parameters
•
‒
Parameters for wind load computation are obtained from
specifications of the superstructure of Caribbean Princess.
Coordinate system
Definition of parameters for calculation
Length overall, LOA
275.7 m
Breadth, B
36.0 m
Frontal projected area, AF
1738.3 m2
Lateral projected area, AL
9093.0 m2
Height of top of superstructure, HBR
46.2 m
Height from calm water surface to center of
lateral projected area C, HC
17.3 m
Mean height of the ship (equal to AL/LOA),
HL
33.0 m
air density (kg/m3), ρA
1.2754 kg/m3
International Research Exchange Meeting of Ship and Ocean Engineering in Osaka
Lateral view of model cruise ship
Frontal view of model cruise ship
6
Wind Speed Profile
z
Wind speed profile for heel moment
•
U(z)
‒
Logarithmic wind speed profile model
‒
DNV (2010), “Wind loads”, Recommended Practice C205, Section 5
‒
The 10 minutes mean wind speed at 10m height above the still water
U(H)
level is to be used as a wind parameter U(H).
H = 10m

1
z 
 ln 
U  z   U  H  1 
H
 ka
κ: surface friction coefficient

ka = 0.4: von Karman’s constant
z: altitude
z = z0
z=0
ka2
 H
 ln 
 z0 
Definition of wind speed profile model
2
Wind speed profile
50
open sea with waves
coastal areas with onshore wind
45
z0: terrain roughness parameter
40
The height of model
cruise ship is over 40m,
therefore, difference
should be considered.
‒
Terrain roughness parameter z0
‒
DNV RP C205, Table 2.1: to consider difference between open sea
and coastal area
Altitude (m)
35
30
25
20
15
10
‒
Constant terrain roughness parameter
z0 = 0.0001 (for open sea)
z0 = 0.001 (for coastal areas with onshore wind)
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0
0
2
4
6
8
Wind speed (m/s)
10
12
14
Computed wind speed profile at U(H) = 10 m/s
7
Heel Moment
Prediction of heel moment
•
‒
50
Fujiwara, T. and Ueno, M. (2006), Cruising performance of a large
40
Regression analysis of wind-tunnel experimental results has been
carried out.
‒
Altitude (m)
passenger ship in heavy sea, Proceedings of 16th ISOPE, USA
‒
Beaufort No.5 (10 m/s)
Beaufort No.8 (20 m/s)
Beaufort No.11 (30 m/s)
30
20
Estimated formulation of heel moment by wind load
10
K A  CH   C AK  A  q A AL H L
0
0
10
20
30
40
Wind speed (m/s)
where
pressure in the actual sea wind condition
 1
1
q A   AU 2  kq 
2
 H L
 2 cos    

HL

 A 2 
U T dz A   1  kq   A U T2
 2
2


  1
1
 AU 2  kq 
H
2
  L

HL


HL 
1
 
A 2 
U T dz A   1  kq    AU T2  
2


2
HL 



International Research Exchange Meeting of Ship and Ocean Engineering in Osaka
Computed wind profile for prediction of heel
moment (open sea)
3E+08
2.5E+08
Heel moment (Nm)
C H  
heel effect coefficient
From experimental result
From estimated formula
C AK  A  heel moment coefficient

heel angle
A
apparent (relative) wind direction
AL
lateral projected area
Calculation of pressure
component by wind load
HL
mean height of the ship
kq
empirical parameter
x
2E+08
x x x
x
Beaufort No.5 (10 m/s)
Beaufort No.8 (20 m/s)
Beaufort No.11 (30 m/s)
x x x x x x
x
1.5E+08
x
1E+08
5E+07
0x
0
x
x
x
x
x
30
60
90
120
Relative wind direction, A (deg)
150
x
180
Heel moment by wind direction
8
Coefficients for Heel Prediction: CH, CAK
Heel effect coefficient: CH
•
‒
Serra, A. (2002), Experimental wind tunnel tests on large
passenger ships, Report of CETENA Research Plan 2002
‒
Heel moment variation by heel angle
‒
Wind tunnel experiment using modern cruise ship model by
14
Test Model No. 1852
Test Model No. 2036
Fincantieri: Model No. 1852 (Caribbean Princess)
 deg 
0    20  deg 
for  20    0
for
M Y (Nm)
0.00738  1.0
C H    
0.00757  1.0
12
8
Heel moment coefficient: CAK
6
-30
‒
Heel moment variation by apparent wind direction
‒
Heel moment coefficient


H 
C AY   0.0737  C 


 LOA 

C AK  A   

C AY  0.500

-20
-10
0
10
20
30
Heel angle (deg)
Heel moment by heel angle
(experiment, 1/125)
1.4
0.821




lift+drag
1.2
for
HC
 0.097
LOA
H
for C  0.097
LOA
C AY
C CF
C YLI
1
Coeff.
•
10
0.8
drag
0.6
0.4
lift
0.2
C AY  A   CCF  CYLI , lateral wind force coefficient
H C : height from waterline to center of lateral projected area  m 
International Research Exchange Meeting of Ship and Ocean Engineering in Osaka
0
0
30
60
90
A
120
150
180
Lateral wind force coefficient, CAY
9
Analysis of Heel Stabilization
I.
Stabilization using stabilizing fin
II. Stabilization using U-tube tank
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Controller Design: Stabilizing Fin
Controller design of stabilizing fin
•
‒
State-space equation is derived from equation of roll motion to
apply the linear optimal control algorithm LQR (linear quadratic
regulator)
‒
Equation of roll motion
( I 44  I a ,44 )  b44  c44  M Ext  M Fin
Directions of lift force and drag force
‒
Effective angle of attack (lift force)
• Stabilizing moment is calculated from lift and
drag forces and applied into motion simulation
instantaneously.
• Hydrodynamic effects of lifting surface such as
stall and free surface effect are also considered.
 z  lY  l X  vw 
   
V
u

S
w


 E  tan 1 
Fin inclination by controller
Effects of ship motion and wave
‒
State-space equation
0

  
     c44
   I  I
 44 a ,44
1

  1
dC
b44       S L cos  0

 2
d
I 44  I a ,44   
V  u    z  l  v   l
2
2
S
w
Y
w
Y
I 44  I a ,44
 0 0   P 
 1 1   

 S
Fin angle
Control input
• Two stabilizing fins are controlled simultaneously to reduce heel and roll motion.
• LQR controller is applied to determine the control inputs of two stabilizing fins in real time.
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Motion Stabilization: Control Algorithm
Optimal control algorithm: LQR
•
‒
State observer: Kalman Filter
•
LQR (linear quadratic regulator) control is an

current and past measurement (Kalman, 1960).
optimal control. Optimal control input u should
minimize performance index J.
‒

Augmented state space equation includes the process
and measurement noises.
Control performance is tuned by adjusting the
state and control input weight matrices

State observer based on Kalman filter




J  0 xsT (t )Qxs (t )  u T (t )Ru (t ) dt
xˆ (t )  Axˆ (t )  Bu (t )  L( y (t )  Cxˆ (t ))
Q  state weight matrix
where 
R  control input weight matrix
xˆ (t ) : estimated state

‒
Kalman filter is an optimal state observer based on the

x(t0 )  x0
L : observer gain  Kalman filter gain 
LQR + Kalman filter → LQG (linear quadratic Gaussian)
Control input u is obtained by solving algebraic
Riccati equation.
Disturbance
PA  AT P  PBR 1BT P  Q  0
Control input : u (t )   R 1BT P x(t )
r
Controller
(LQR)
Control input
Plant
(Motion analysis)
y
LQG (linear quadratic Gaussian)
•
‒
Application of LQG controller can make the
robustness of the designed controller better by
Estimated states
State observer
(Kalman Filter)
Measured
output
reducing the noise effect, so that the overall
Noise
performance of the active stabilizing fin improves.
Diagram of designed controller
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Motion Stabilization: Stabilizing Fin
Motion stabilization by using stabilizing fin
‒
Wind + wave → roll + heel
‒
LQG control algorithm (LQR + Kalman filter)
‒
Wind-induced heel and wave-induced roll motion of the ship can be
4
No fins
LQR
3
Roll RMS (deg)
•
stabilized by applying stabilizing fins.
‒
Stabilizing fins are effective when the ship is advancing with enough
2
1
speed.
‒
0
Saturation of control input is observed due to mechanical limitation of
30
60
90
120
150
180
Wind direction (deg)
actuator.
‒
0
Result of heel stabilization by using stabilizing fin
Example of computation: model cruise ship, regular wave, Fn=0.211
wind speed=20m/s, wind direction=90°
12
Angle of fin (port side)
Angle of fin (starboard)
30
10
20
Control input (deg)
Roll (deg)
8
6
4
2
10
0
-10
-20
0
-30
-2
0
100
200
Time (sec)
(a) Roll & heel
300
400
0
100
200
300
400
Time (sec)
(b) Control input (fin angle)
International Research Exchange Meeting of Ship and Ocean Engineering in Osaka
Motion stabilization by fin stabilizer
13
Anti-Rolling & Heeling Tank: U-tube Tank
Heel stabilization by using U-tube tank
•
‒
U-tube tank is usually considered as anti-rolling tank.
‒
U-tube tank can also be actuated as anti-heeling tank.
‒
Internal fluid height in the tank can be controlled by
using hydraulic pump or compressed air.
‒
In the present study, pressure of actuator is considered
w/2
Starboard
w/2
Port
r
τ(t)
Equilibrium level
z
hr
G
wr
y
rd
as a control input.
hd
Dimension of tank
•
‒
‒
Dimension of U-tube tank
In general, volume of internal fluid in the tank is
1025 kg/m3
determined about 1~2% of ship displacement.
Density of fluid in the tank
In the present study, arbitrary dimension of the tank is
Fluid height in the reservoir (hr)
3.0 m
Width of vertical reservoir (wr)
2.0 m
Height of horizontal duct (hd)
1.0 m
Length between two reservoir (w)
30 m
applied to perform the simulation.
Volume of internal fluid
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860 m3
14
Controller Design: Active U-tube Tank
State-space model to design the controller of U-tube tank
•
‒
Controller of U-tube tank is also designed by adopting the LQG algorithm
‒
Equation of motion: roll motion and U-tube tank
I
44
 I a ,44  
x4  b44 x4  c44 x4  a4  c4  FExt
(Roll motion of the ship)
Moment by tank
a  b  c  a 4 
x4  c 4 x4  FT  r
(Height variation of
internal fluid in the tank)
Control input
‒
Derivation of state-space equation to apply the LQR control

b
 44

A
x4  
 
 x  
1
 4
 
a 4b44
   

  
 B  I 44  I a ,44 

0



1  a4 c 4
 c44 

A  a


a4 b
a A
0
0

1  a 4 c44
 c 4 

B   I 44  I a ,44 

0

b
B
1

1


 a4 r 





A
  x4  a A




 x 
0


0




4
 
F

T

 FExt
a 4
     r 
1  a 4 c4



 
 c    
B
I
I





a
44
,44



B
B   I 44  I a ,44 
   




0
 0 


0



1  a4 c
 c4 

A  a

0
System matrix for fluid level in the tank
where A  I 44  I a ,44 
• Stabilizing moment is calculated
from height variation of internal
fluid in the U-tube tank and
applied into motion simulation
instantaneously.
• Dynamics of internal fluid in the
tank should be considered to
obtain the stabilizing moment from
the control input.
Control input
a4 a 4
a 4 a4
, B  a 
a
 I 44  I a,44 
• Designed controller by using state-space equation integrates to the WISH-CRUISE.
• Control input from U-tube tank is applied simultaneously to reduce heel and roll motion.
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Motion Stabilization: Active U-tube Tank
Motion stabilization by using active U-tube tank
4
‒
Wind + wave → roll + heel
‒
LQG control algorithm (LQR + Kalman filter)
‒
Wind-induced heel and wave-induced roll motion of the ship can be
No tank
LQR
3
Roll RMS (deg)
•
stabilized by applying U-tube tank.
‒
Motion stabilization by using tank can be effective regardless of
forward speed of the ship.
‒
1
0
Performance of stabilization is dependent on the dimension of tank
0
30
60
90
120
150
180
Wind direction (deg)
and capacity of actuator.
‒
2
Result of heel motion stabilization by using
U-tube tank (regular waves)
Example of computation: model cruise ship, regular wave, wind
speed=20m/s, wind direction=90°
12
20
10
15
Tank level (deg)
Roll (deg)
8
6
4
2
10
5
0
0
-2
0
100
200
Time (sec)
(a) Roll & heel
300
400
-5
0
100
200
300
400
Time (sec)
(b) Control input (tank fluid height)
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Motion stabilization by active U-tube tank
16
Conclusions
•
Computational methods to predict the wind-induced heel and to stabilize the motion of cruise
ship are developed.
•
Heel moment by wind load is computed using the estimated formulation. In this procedure,
heel effect coefficient is corrected using another wind tunnel experimental result.
•
Motion stabilizations by using stabilizing fin or active U-tube tank are considered based on
linear optimal control algorithm LQG.
•
These computational methods integrate to the time-domain seakeeping analysis program for
cruise ship, called WISH-CRUISE.
•
From result of numerical computations, it is observed that wind-induced heel of cruise ship
can be reduced effectively by applying active fins or active U-tube tank.
•
For more realistic simulation, mechanical limitation of control actuator will be considered
appropriately.
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Thank You
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