|
5.4 Dynamic passage of long bank
In order to compare the different models in a real bank passage some additional simulations were made for the tanker by use of a track-keeping algorithm. A vertical type bank was used and a speed of six knots was ordered. Fig.24 and Fig.25 show the required rudder angle for keeping the ship on a track parallel to the bank at different lateral distances. The first diagram represents a water depth of 1.2 times the ship draught and the latter 1.1 times the ship draught.
Fig.24 Required rudder angle for h/T=1.2
Fig.25 Required rudder angle for h/T=1.1
For the 20% bottom clearance, Mod 2 requires a significantly higher rudder angle than Mod 3 . The reason for this is that the high suction force that Mod 2 provides at this depth leads to a large drift angle, which in turn due to the induced turning moment leads to the large rudder angle. As for the 10% bottom clearance, the suction force has been changed to a repulsion force, which leads to a drift angle with bow towards the bank. This, in turn, leads to a turning moment, which is in opposite direction to the direct bank induced turning moment.
The major part of the suction force for the 20% bottom clearance is related to the propeller load. This effect may, in the present model, be somewhat overestimated. In order to avoid problems with unreasonable effects, especially at zero speed (where CT is not defined), an empirical limit of CT =3.0 has been used. Further studies in this area have been started. The Ch'ng model (Mod 3 in Fig.25) provides extremely high rudder angles for the 10% bottom clearance; in fact it is not possible to maintain the track in none of the five lateral distances tested.
6. CONCLUSION
Based on recent and previous experiments, a comprehensive mathematical model for predicting the stationary sway force and the yaw moment due to bank effects has been developed.
Compared with the SSPA's old model, the new model includes more influencing variables. It can handle vertical, sloping and flooded banks, or any combination of them. The new model is in general more accurate and robust, especially the model for vertical and sloping banks. It is able to predict both suction and repulsion forces. Compared with the available experiments, however, the models for flooded banks and propeller effect are less satisfactory and call for further improvement.
When comparing SSPA model with the experiments by Ch'ng [9] and Vantorre [6] it is found that in general SSPA model (and experiments) compares well with their results. An exception may be that the tests carried out by Ch'ng provided very high turning moments in very shallow waters. This is also illustrated by the very high-required rudder angles when using the Ch'ng model in the simulation study.
REFERENCES
[1] D.-Q. Li & M. Leer-Andersen, "Literature survey on the research for bank effects", SSPA Report No. 8088-2, 1998.
[2] I.W. Dand, "On ship-bank interaction", Trans RINA, Vol.124, 1981.
[3] N.H. Norrbin, "Theory and Observations on the Use of a Mathematical Model for Ship Manoeuvring in Deep and Confined Waters", Proc.8th Symposium on Naval Hydrodynamics, Pasadena, Ca., 1970.
[4] N.H. Norrbin, "Bank effects on a ship moving through a short dredged channel", The 10th Symposium on Naval Hydrodynamics, 1974.
[5] N.H. Norrbin, "Bank effects and optimal section shape for ship canals", 26th PIANC Int'l Navigation Conference, Brussels, Section 1, 1985.
[6] M. Vantorre, "Experimental study of bank effects on full form ship models". Mini symposium on ship manoeuvrability, Fukuoka, Japan, pp.85-102, 1995.
[7] M.R. Renilson & A. Munro, "The effect of shape and angle on bank interaction". The Naval Architecture, March, 1989.
[8] M.R. Renilson & P.W. Ch'ng, "Effect of bank slope and water depth on the forces on a ship in restricted water". MARSIM & ICSM9O, Japan, 1990.
[9] P.W. Ch'ng, L.J. Doctors & M.R. Renilson, "A method of calculating the ship-bank interaction forces and moments in restricted water". Int'l Shipbuilding Progress, Vol.40, No.421, 1993.
[10] D.-Q. Li, "Experiments on bank effects", SSPA Report No.20000028-1, SSPA Sweden AB, 2000.
[11] D.-Q. Li, M. Leer-Andersen, P. Ottosson, & P. Trägårdh, "Experimental Investigation of Bank Effects under Extreme Conditions", PRADS' 2001, Shanghai, China, 2001.
SYMBOLS
Fig. 26 Bank variable definition
| Symbol |
Explanation |
Dim. |
| CB |
Block coefficient of ship |
- |
| CY |
=Y/(0.5pU2LT),
sway force coefficient |
- |
| CN |
=N/(0.5pU2LBT),
yaw moment coeffi. |
- |
| CT |
=Tp/(0.5p(U(1-WF)D)2),
Propeller loading coefficient, |
- |
| D |
Propeller diameter |
m |
| Fn |
=U/ (gL), Length Froude Number |
- |
| Fnh |
=U/(gh), Depth Froude Number |
- |
| g |
Gravity constant = 9.81 |
m/s2 |
| L |
Length of ship |
m |
| B |
Ship beam |
m |
| T |
Ship draught |
m |
| h |
Water depth |
m |
| hl |
Water depth over the flooded bank |
m |
| Tp |
Propeller thrust |
N |
| U |
Ship speed |
m/s |
| WF |
Wake factor |
- |
| y |
Lateral distance ship CL to the conjunction of
bank wall and bottom (positive on the starboard side). |
m |
| yl |
width of flooded bank, always positive |
m |
| y' |
Lateral distance from the ship keel to the sloping
bank wall, see Fig.26. |
m |
| α |
Bank slope angle (90° for a vertica bank, positive
on the starboard side) |
deg |
| ζ |
ζ= T/(h-7), water depth parameter. 0<ζ<∞.
The larger the ζ, the shallower the water; ζ = 0 is the case in infinite deep
water whereas ζ=∞ is the case of zero bottom clearance (h=T), which is hardly
possible in reality. |
- |
| ηl |
=0.5B/yl, width parameter
of a flooded bank, 0<ηl<∞ |
- |
| η |
=0.5B/y, distance parameter for vertical banks |
- |
| η' |
=0.5B/y', the generalised ship-bank distance
parameter for both vertical and sloping banks. The larger the η', the closer to
the bank. η' lies in a rang [0, 1]. If the lateral distance y and the bank slope
angle α are known, the parameter η' can be obtained by:
 |
- |
| σ1 |
=hl/h, flooded bank's
depth parameter, 0<σ1< 1. |
- |
|
AUTHOR'S BIOGRAPHY
Da-Qing Li, B.Sc. (1986) from Huazhong University of Science & Technology, China; Lic. (1993) and Ph.D. (1994) from the Chalmers University of Technology, Sweden. Employed at SSPA Research since 1998, his experience covers hydrodynamics in general, Panel/RANSE methods, and grid generation: specialised in propeller/waterjet propulsion, propeller cavitation and erosion, shallow water effects.
Email address: da-qing.li@sspa.se
Peter Ottosson graduated as Master of Science in Naval Architecture from the Chalmers University of Technology in Goteborg in 1976. He has been at SSPA since then, working with research as well as commercial projects within most aspects of ship hydrodynamics but with special attention to ship manoeuvring and seakeeping including model testing as well as simulation work. He has been responsible for development of several time domain simulation programs such as PORTSIM and SEAMAN.
Email address: peter.ottosson@sspa.se
Peter Trägårdh graduated as Master of Science in Naval Architecture from the Royal Institute of Technology in Stockholm in 1971. He has been at SSPA since then, working with research as well as commercial projects within most aspects of ship hydrodynamics but with special attention to ship manoeuvring including model testing as well as simulation work. For some time he gained some practical full-scale experience working with some Swedish shipyards (1979-1985). Member of the 23rd and 24th ITTC Manoeuvring Committees (1999-).
Email address: peter.tragardh@sspa.se
APPENDIX A
Predicted turning circle of the Ropax
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