Numerical Examples - Interaction Forces
Remery [1] carried out model tests to study the phenomena occurring with a moored ship during the passage of another ship. The tests were performed by varying the size and speed of the passing ships, at a water depth of 1.15 times the draft of the moored vessel and with the ship moored parallel to the passing ship. The experimental results obtained for the forces and moment acting on the moored ship (257 m long) due to the passage of another ship (302 m long) are used for a comparison with the present method. As the details of the ship geometries are unknown, the underwater sectional area distribution has been taken as parabolic (ideal) based on Eq.(2. 13), for the purpose of present study. A mid-ship section area coefficient of 0.99 has been chosen for the estimation of the section area at that section which is needed for use in this equation. As another option, to get the feel of influence of ship's form (real) on the interactive forces and moment, the geometry of a bulk carrier of 175 m long, having the same CB value as the moored ship, has been scaled up to 257m to represent the moored ship and up to 302 m to represent the moving ship.
The experimental results for a lateral separation distance of 30m in a water depth of 1.15 times the moored ship draft are presented in non-dimensional form in Figs.2, 3 & 4. The surge force obtained by the present method, both ideal and real cases, agrees well with the experimental values in all the separation distances. The sway force deviates by about 50% in ideal case when compared to the experimental values, but the trend is fairly good and there is no phase shift. The values improved substantially for the real form case when compared to the values obtained using the idealised form (parabolic sectional area distribution). The sectional area slope, representing the flow velocity around the ship, is higher in the real form case and as the experiments are done for the real ship models these values are more appropriate. Both the present theory and Remery's experiment values for yaw moments have a fairly good trend and agreement.
Fig.2. |
Surge force on moored ship (Lm257m) due to passing ship (LP =302m, η=30m, h/T= 1.15, ST'=2 ST/(Lm+LP), ST=ξ; X, Y and N are non-dimensionalised based on Eqs.2.10 to 2.12) |
Fig.3. |
Sway force on moored ship (Lm=257m) due to passing ship (LP =302m, η=3Om, h/t=1.15) |
Fig.4. |
Yaw moment on moored ship (Lm=257m) due to passing ship (LP=302m, η=30m, h/T=1.15) |
Subsequently, the hydrodynamic interaction effects on a moored container ship due to the passage of a bulk carrier (particulars of both the ships are given in Table 1 below) are studied. The theoretical and experimental values of surge force, sway force and yaw moment acting on the container ship for a water-depth to ship-draft ratio (h/T) of 1.1, separation-distance to ship-length ratio (η/Lmm) of 0.167 and passing ship speed (U) of 4.0 knots are shown in Figs. 5 to 7. Similar representation for η/Lm=0.20 (Figs. 8 to 10), η/Lm=0.265 (Figs.11 to 13) and η/Lm=0.40 (Figs. 14 to 16) are also shown below. The model tests were carried out at scale 1175 in the Towing tank for manoeuvres in shallow water (co-operation Flanders Hydraulics - Ghent University) in Antwerp, Belgium.
Table 1. Particulars of moored and passing ships
|
Moored Ship |
Passing Ship |
Ship Type |
Container Ship |
Bulk Carrier |
Length (m) |
289.804 |
298.828 |
Breadth (m) |
40.252 |
37.969 |
Draft (m) |
13.500 |
13.500 |
CB |
0.5804 |
0.8361 |
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