IDENTIFICATION, CLASSIFICATION AND
HERARCHIZATION OF PARAMETERS INFLUENCING
INTERACTION FORCES BETWEEN QUAY AN
BERTHING VESSEL
Abramowicz-Gerigk T.
Gdynia Maritime University, Al. Zjednoczenia 3, 81-345 Gdynia, Poland
Abstract: The paper presents parameters influencing the interaction forces induced by a self-berthing ship between the ship side and the quay. The classification and hierarchization of the parameters has been done according to the accuracy of the model experiments program arrangements and the formulation of mathematical model of the interaction forces.
1. Introduction
The main data sources for the prediction of hydrodynamic forces for mathematical models of ship motions are model experiments and computational fluid dynamics (CFD) methods. The CFD methods have been already tested for berthing assisted by tugboats, for example (Chen et al, 2000), but the influence of propellers and thrusters is still unsolved. The study of self-berthing requires the recognition of interaction forces due to working propellers, rudders and thrusters. Therefore the program of self–berthing experiments has been developed for twin-propeller, twin-rudder, self-propelled car-passenger ferry model equipped with a bow thruster. The presented preliminary classification and hierarchization of the influencing parameters will help to decide which parameters are the most important in the modeling of the interaction forces.
2. Mathematical model of twin-propeller twin-rudder ship
The change in heel, draft and trim during self-berthing can be assumed negligible therefore the three dimensions of freedom mathematical model has been chosen to describe ship manoeuvring motions. The mathematical model of propeller twin-rudder ship recently proposed by (Lee & Fujino, 2003) is based on modular type MMG mathematical model originally developed for single-propeller single-rudder ship. Figure 1
shows the coordinate system for manoeuvring motions. The derivatives of hydrodynamic forces and yaw moment of the hull were developed for open water conditions.
Fig.1. Coordinate system
Surge, sway and yaw motions are described as follows.
sin
)
F
F
)(
t
1
(
)
T
T
)(
t
1
(
)
U
(
X
r
X
vr
)
Y
X
(
v
X
v
X
u
X
)
r
x
vr
u
(
m
) S ( N ) P ( N R ) S ( ) P ( R 2 rr v vr 4 vvvv 2 vv u 2 G
(1)
cos
)
F
F
)(
a
1
(
r
Y
vr
Y
r
v
Y
v
Y
r
)
u
X
v
Y
(
v
Y
r
Y
v
Y
)
r
x
ur
v
(
m
) S ( N ) P ( N H 3 rrr 2 vrr 2 vvr 3 vvv u 2 r v r v 2 G
(2) sin ) F F ( 2 b ) t 1 ( cos ) F F )( x a x ( ) T T ( 2 b ) t 1 ( r N vr N r v N v N r N v N r N v N ) ur v ( mx r I ) S ( N ) P ( N R ) S ( N ) P ( N H H R ) S ( ) P ( 3 rrr 2 vrr 2 vvr 3 vvv r v r v G zz (3) where:S and P - subscripts for starboard and portside, Y0 x y G0 U QUAY d 0 X0
b - distance between twin propellers or between twin rudders, aH - rudder-hull interaction lateral force ratio,
AR - rudder area,
FN - rudder normal force,
Izz - yaw moment of inertia,
t - thrust deduction factor,
tR - rudder resistance reduction factor,
T - propeller thrust, U - ship speed
u, v, r - surge, sway, yaw velocities,
X, Y, N - hydrodynamic surge, sway forces and hydrodynamic yaw moment, Xu, v,r, Yv,r, Nv,r - derivatives of hydrodynamic forces and yaw moment of the hull,
xG - coordinate of the centre of gravity (from midship, positive forward),
xH - coordinate of the center of the lateral force induced on hull by the rudder–hull
interaction,
xP - coordinate of the propeller position,
xR - coordinate of the rudder position,
- rudder angle
The extra yaw moment due to the lateral distance between twin-propellers and the lateral distance between twin-rudders is considered. The model proposed by (Lee & Fujino, 2003) contains the unique parameters for twin-propeller twin-rudder ship which are the specific inflow velocity in y-direction at port and starboard propeller and effective propeller wakes for both propellers. The flow straightening factor used to calculate the effective rudder angle is also used differently in case of left and right turn for both rudders. The effects of propeller loads and effect of manoeuvring motion are contained in the expression of wake fraction at propeller position.
For bollard-pull test the aH coefficient is zero for all rudder angles because no flow is
created around the ship hull. The blockage of the flow has an important influence on the propeller thrust and torque coefficients therefore the distance to the quay, rudder angle and water depth have the influence on propeller characteristics. The derivatives of hydrodynamic forces and yaw moment of the hull will also change according to decrease of water depth to draft ratio however the change due to very low speed should be small. To determine ship manoeuvring motion during self-berthing the additional interaction force and moment due to the berth proximity should be introduced. The force and the moment are dependent on the distance to the quay, water depth, propellers thrusts, rudder angle and bow thruster operation. The proper mathematical model of the interaction forces can be developed on the basis of model experiments. The analysis of the influencing parameters will help to obtain better accuracy of the model tests and will be the basis for the development of a hydrodynamic model.
3. Parameters influencing the interaction forces
The set of parameters influencing the interaction forces consists of ship and environment characteristics. The parameters usually used in modeling of the hydrodynamic forces are the main ship dimensions, and main dimensions ratios, block coefficients, propeller thrust, propeller loading coefficient, Froude number (length and depth Froude numbers), non-dimensional depth and non-non-dimensional distance to the quay. For the stopped vessel in bollard pull condition the reference velocity is used.
The average sinkage of the ship due to squat effects could be considered in the net under keel clearance. The parameters usually used in formulas of regression coefficients are the block coefficient and breadth to length, breadth to draft and draft to length ratios. The parameters can be classified as ship and environment parameters. The ship parameters are presented in Table 1 and the ship-environment and environment parameters are presented in Table 2.
Table 1. Main ship parameters
Class I
ship constant parameters ship operational parametersClass II
main dimensions length on waterline
breadth to draft ratio corresponding draft and trim
length to breadth ratio coordinates of centre of gravity
block coefficient port and starboard rudder angle
aft hull form factor ship velocity
wetted surface area Froude number
displacement port and starboard propeller revolution
port and starboard rudder surface area port and starboard propeller thrust port and starboard rudder height thrust deduction factors
port and starboard rudder aspect ratio effective wake coefficient of propellers coordinates of rudders location effective wake coefficient of rudders open water rudder characteristics propeller loading coefficient
propellers diameters effective rudder inflow speed
coordinates of propellers location bow thruster thrust direction of propellers revolution drift angle
open water propellers characteristics bow thruster diameter
coordinates of bow thruster location open water bow thruster characteristics
4. Hierarchization of the parameters influencing the interaction forces
The model experiments involving force measurements for different combinations of propellers working in push-pull mode, rudder angles and bow thruster operation will be used for determining of the influence of different parameters on the interaction forces which should be implemented in the general hydrodynamic hull force model. The objective of the presented analysis is the classification and preliminary hierarchization of the parameters. However there is no available data regarding the self-berthing tests the general remarks regarding the influence of the main parameters determining ship-bank interaction forces follows from the published results of crabbing, ship-bank and ship-ship interactions investigations (Abramowicz-Gerigk, 2005; Chen & Huang, 2000; Chen & Hwang, 2002; Miao et al, 2003; Qadvlieg & Toxopueus, 1998; Vantorre et al, 2001; Vantorre et al, 2003).
Table 2. Ship-environment parameters
Class III
ship-environment parameters
Class IV environment parameters
depth to draft ratio water density
non dimensional ship-berth distance water depth
approach angle to the berth distance to the berth
ship squat type of berth
reference velocity
In the class I the main characteristics used in empirical expressions of interaction forces are ship length and draft. In regression formulas of coefficients - block coefficient, breadth to length, breadth to draft and draft to length ratios are mainly used. In Class II the most important parameters are propeller thrust, and propeller loading, port and starboard rudder angle and bow thruster thrust, in Class III all parameters should be considered and in Class IV type of the berth.
One of the main parameters from class III is depth to draft ratio. For the depth to draft ratio h/T less than 3 the sway force and yaw moment increase sharply with decrease of h/T. This trend is confirmed by several experimental results cited in (Miao et al, 2003). For h/T less than 3 even a small change in water depth cause a significant change in the hydrodynamic forces.
d 2
B
y (4) where B is the ship beam and d is the distance from the berth to the ship’s centre line. It is clearly shown in Fig. 2 that for h/T =1.5 the lateral force is not as much dependent on ship-berth distance as for lower water depths. There is a strong increase of interaction force with decrease of ship-berth distance for h/t=0.7 and for h/t=1.1 when y is less than 0.45.
Fig. 2. Lateral interaction force to propeller thrust ratio as a function of non-dimensional ship-berth distance for different depth to draft ratios (Abramowicz-Gerigk T, 2005)
Recently published results of crabbing test for a 3 m ferry model, scale 1:70 ( Shin & Lee, 2004) show differences of the measured forces with the data previously published in 1998 by MARIN. The difference has been assumed due to the different rotating conditions of the propellers.
Figure 3 presents the lateral forces on the hull induced by the propellers working in push-pull mode for different rudder angles of the rudder behind the balancing propeller. The forces have been measured for the model placed parallel to the quay at the distance of half breadth from the model center line. Lateral Force 1 has been measured (for outward turning propellers) at University of Ulsan (UOU) in Korea, Lateral Force 2 at MARIN in Wageningen, Netherlands. The dependence on rudder angle behind the balancing propeller is stronger for Lateral Force 1 (MARIN). The character of the dependence on is almost linear, what means that the measurements done for rudder angle 0o and the
2 8 1 D T V P T 2
8
7
.
0
D
T
c
H
D
u
Pbalancing UR R P R
The force on the rudder behind the baking propeller is assumed negligible because of very small inflow velocity. The velocity of induced flow uR for the rudder behind the balancing
propeller is calculated according to Inoue. The reference velocity VT for bollard pull
condition dependent on propeller’s thrust TP has been proposed by (Vantorre et al, 2003)
and used in the formula for the interaction force between ship side and berth for ship in bollard-pull condition:
Fig. 3. Lateral forces measured during crabbing tests for vessels with different rotating conditions: Lateral Force 1 (MARIN), Lateral force 2 (UOU)
(5) Non-dimensional under keel clearance hT can be defined using the effective draft heff:
(6) where zm is an average sinkage of the ship due to squat effect (Vantorre et al, 2003).
5. Conclusions
To recognise the influence of the distance to the berth and water depth to draft ratio on the performance of propellers working in push-pull mode with different rudder angles and the
T h T h eff T heff hzm
bow thruster the set of model tests has been proposed. The execution of a systematic experimental program is very time consuming due to the big number of parameters influencing the interaction forces. The relationship between the parameters and their influence on the interaction forces has been investigated with the aim of development of a semi–empirical model of the interaction forces.
The simulated interactions still need further adjustments, done by experts, to account for interactions (Chen & Hwang, 2002, Vantorre et al, 2001). Therefore the model tests of different kinds of interactions are necessary for practical applications in mathematical models of ship manoeuvring simulators as well as for the validation of CFD methods. The usual tests done in towing tanks are carried out for small models (model scale 1:70 1:75, 1:85), what needs to consider big scale effects and less accuracy of measurements of very small forces. The model tests arranged for 1:24 scale model will give much better accuracy. The research regarding the interaction forces between the self-berthing vessel and the quay is conducted at Gdynia Maritime University according to the research project No. 4T12C01029 sponsored by Polish Ministry of Education and Science.
References
1. Abramowicz-Gerigk T.(2005): Modeling of Ship-Berth Interaction Forces for a Self-Berthing Vessel. 2nd International Congress of Seas and Oceans,
Szczecin-Świnoujście, 20-24 September 2005.
2. Chen H., Huang E. (2000): Validation of a Chimera RANS Method for Transient Flows Induced by a Full–Scale Berthing Ship. Twenty Second Symposium on Naval Hydrodynamics, The National Academy of Sciences 2000, http://www. nap.edu/ openbook/ 0309065372/html.
3. Chen H, Lin W., Hwang H.(2002): Validation and Application of Chimera RANS Method for Ship-Ship Interactions in Shallow Water and Restricted Waterway. 24th Symposium of Naval Hydrodynamics, Fukoku, Japan, 2002.
4. Lee S., K., Fujino M. (2003): Assessment of a Mathematical Model for the Manoeuvring Motion of a Twin–Propeller Twin-Rudder Ship, Internatio-nal Shipbuilding Progress, Volume 50, No 1&2.
5. Miao Q., Xia J., Chwang A., Duffy J.(2003): Numerical Study of a Ship Travelling in a Channel.The 8th International Conference on Numerical Ship Hydrodynamics,
September 22-25, 2003 Busan, Korea.
6. Qadvlieg F., Toxopeus S.(1998): Prediction of Crabbing in the Early Design Stages. Practical Design of Ships and Mobile Units M.W.C. Oosterveld and S.G. Tan editors, http://www.marin.nl/original/publica- tions / Prads 1998 -Prediction of Crabbing.
7. Shin H., Lee H. (2004): Crabbing Test of 3 m Ferry Model. Journal of Naval Architects of Korea Vol. 41 No1, February 2004.
8. Vantorre M., Delefortrie G., Eloot K., Laforce E. (2003): Experimental Investigations of Ship-Bank Interaction Forces. International Conference MARSIM’2003, Kanazawa.
9. Vantorre M., Laforce E., Verzhbitskaya E. (2001): Model Test Based Formulations of Ship-Ship interaction Forces for Simulation Purposes. IMSF 28th Annual General Meeting, htp://www.imsf.org/gm2001_ program.htm.
