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Modification of ship hydrodynamic interaction forces and moment by underwater ship geometry
Ocean Engineering 33 (2006) 1090–1104 www.elsevier.com/locate/oceaneng
Modification of ship hydrodynamic interaction forces and moment by underwater ship geometry K.S. Varyani *, P. Krishnankutty Department of Naval Architecture and Marine Engineering, Universities of Glasgow and Strathclyde, Henri Dyer Building, 100 Montrose St., Glasgow G4 0LZ, Scotland, UK Received 12 January 2005; accepted 17 July 2005 Available online 4 November 2005
Abstract The hydrodynamic interaction forces/moments acting on a moored ship due to the passage of another ship in its proximity is researched by considering the influence of ship form against the idealized approach of the use of parabolic sectional area distribution. Comparisons with experimental results show that the interaction effects are predicted better by inclusion of ship’s form. q 2005 Elsevier Ltd. All rights reserved. Keywords: Hydrodynamic interaction; Moored; Stationary; Passing ship; Ship form.
1. Introduction The hydrodynamic interaction of a ship with other ships or with waterway boundaries affects its course keeping and maneuvering. This can also have an impact on moored ships and coastal structures. The forces and moments are more significant on the moored ship than on the moving ship. As the moving ship is under the control of helm the normal interactive effects can be counteracted. The magnitude of the interaction forces also depends on the speed, size and geometry of the moving vessel, lateral distance between the moving vessel and the stationary one, and the water depth. Hydrodynamic interaction between two ships is typically observed when they pass in confined waters. Besides, the
* Corresponding author. Tel.: C141 548 4465; fax: C141 552 2879. E-mail address: [email protected] (K.S. Varyani).
0029-8018/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2005.07.010
K.S. Varyani, P. Krishnankutty / Ocean Engineering 33 (2006) 1090–1104
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interaction forces are much bigger in confined water compared to deep water. The interaction between ships and waterway boundaries affects the maneuvering and course keeping of the ships, on one hand, and impacts coastal structures or other moored ships, on the other. All this sets particular importance to studying and modeling ship interaction effects, mainly in restricted waterways. Major interaction forces components are surge, sway and yaw. The peak values are important from the design aspect of mooring system. The movement and mooring line loads of the moored ship are dependent on these interaction forces. Even though the sway force is much larger than the surge force, the surge displacement is greater than the sway displacement due to much lower damping in surge motion of the moored vessel. Thus the load on the mooring lines can become exceedingly high due to surge motion. By knowing the movement constraints of the berthed ship, which may be due to the restriction imposed for cargo handling facilities, the speed and separation distance limits of the passing ship can be ascertained. For berthed tankers, the cargo handling manifolds allow a maximum movement of only G3.0 m in surge and 3 m in sway, OCIMF, (1978), and for berthed container ships the movements are more restricted due to the limited reach of the cranes. Yeung (1978) and Yeung and Tan (1980) have shown that the approach stage of the initial transient is most critical for the purpose of navigational safety. This is because the ship is subject to an attraction force towards the moored ship and at the same time is subjected to a ‘bow-in’ turning moment. Thus the passing ship with zero rudder-angle would tend to head into the moored ship. The hydrodynamic forces and moment on a moored ship resulting from the passing of another ship at various separation distances, water depths and passing ship sizes, were estimated by Wang (1975) using slender body theory. The hydrodynamic interaction problem between moored and passing ships was studied by Krishnankutty (1987), Krishnankutty and Varyani (2003) and Varyani et al. (2003), using the slender body theory with singularity distribution technique for the computation of forces in surge and sway modes and yaw moment acting on moored vessel. The analysis was further carried out for the estimation of mooring line forces for the idealized mooring line arrangement, such as head-stern and breast lines, neglecting the spring lines in the configuration considered. A rapid increase of the size of the vessels and their speed has considerably increased the interaction effects while they move in the proximity of other vessels. Experimental studies of Remrey (1974), using tanker models, reveal the effect of the size of the passing vessels and the separation distances on the interaction forces and moments on a moored vessel. The experiments were carried out in shallow water condition with the water depth about 1.15 times the draft of the moored vessel and with the vessels parallel to each other. The vessel was moored by means of a flexible system with linear elasticity. The force in the mooring system was measured by varying its stiffness. An impulse function technique to solve the equations of motion in the time was used rather than the frequency domain approach. In the present paper the hydrodynamic interaction forces/moments acting on a moored ship due to the passing of another ship in its proximity is researched by considering the influence of ship form against idealised approach of the use of parabolic sectional area distribution for a wide range of depth– draft ratios.
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2. Theoretical formulation The study is concentrated on the estimation and analysis of the surge and sway forces and yaw moment induced on a rigidly moored (stationary) ship by a passing ship. Different cases that are dealt with here are: – Both ships are identical, with a parabolic sectional area distribution along its length assumed. The hydrodynamic effects in deep and shallow waters are estimated. – These estimations are carried out for real ship forms, where the actual underwater geometry of the ships is considered. We consider one ship is stationary and another ship is passing by. The hydrodynamic interaction problem between a moored ship and the passing ship are formulated using a slender body theory with the following assumptions. – The transverse dimensions of the ships (beam and draft) are quite small compared to its length, but can be of different forms – The passing ship moves at a constant speed and is parallel to the moored ship – The fluid is inviscid and incompressible, the flow is irrotational – The disturbances at the free surface are neglected (treated as a rigid boundary) The co-ordinate (xm, ym, zm) is fixed in the moored ship and (xp, yp, zp) is fixed in the passing ship as in Fig. 1. Parameters with suffices m and p, respectively, refer to those related to the moored and passing ships. In addition to the governing (Laplace) equation applied to the fluid domain, the following boundary conditions are in order vf Z 0 on moored ship vnm
(1)
vxp vf ZU vnp vnp
(2)
on passing ship
N U=0
X Y ξ
Lm
η
U>0
Lp Fig. 1. Co-ordinate system in moored-passing ship.
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The velocity potential function of the flow field is estimated using the singularity distribution technique and subsequently the flow velocity components along the moored ship induced by the passing ship are determined. The interaction potential in the unsteady Bernoulli equation gives the pressure distribution and integration of this pressure over the surface gives the net forces on the moored ship. ð ð S 0 p ðxp Þðxp Kxm C xÞ rU 2 Xðx; hÞ Z S 0 m ðxm Þ dxp dxm (3) 2p fðxp Kxm C xÞ2 C h2 g1:5 Lm
Yðx; hÞ Z
rU 2 h p
ð
Lp
S 0 m ðxm Þ
Lm
ð Lp
S 0 p ðxp Þ fðxp Kxm C xÞ2 C h2 g1:5
dxp dxm
The yaw moment obtained from the slender body theory, Wang, is ð ð S 0 p ðxp Þ rU 2 h Nðx; hÞ Z fxm S 0 m ðxm Þ C S 0 m ðxm Þg dxp dxm p fðxp Kxm C xÞ2 C h2 g1:5 Lm
(4)
(5)
Lp
The above equations are for the deepwater case. When the water depth becomes less than twice the draft of the ship, the shallow water effect has to be considered. The bottom condition for an assumed constant water depth of Kh is represented by vf vz Z 0 : By method of image the interaction forces and moment can be written as ð N ð Sp0 ðxp Þðxp Kxm C xÞ rU 2 X Xðx; h; zÞ Z S 0 m ðxm Þ dxp dxm (6) 2p nZKN fðxp Kxm C xÞ2 C h2 C 4n2 h2 g1:5 Lm
Yðx; h; zÞ Z
Lp
ð N ð S 0 p ðxp Þ rU 2 h X S 0 m ðxm Þ dxp dxm p nZKN fðxp Kxm C xÞ2 C h2 C 4n2 h2 g1:5 Lm
(7)
Lp
N ð rU 2 h X Nðx; h; zÞ Z fxm S 0 m ðxm Þ C Sm ðxm Þg p nZKN Lm
ð ! Lp
S 0 p ðxp Þ fðxp Kxm C xÞ2 C h2 C 4n2 h2 g1:5
dxp dxm
(8)
where Sm is the mid-ship section area of the moored ship, S 0 m and S 0 pare the sectional area slopes of the moored and passing ships, n is the number of images. 2.1. Non-dimensional factors The forces and moments are non-dimensionalised as follows X0 Z
X rðUSm =Lm Þ2
(9)
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Table 1 Prototype particulars of the ship models used by Remrey (1974) Particulars
Moored ship
Passing ship
Length between perpendiculars (m) Breadth (m) Draft (m) Displaced volume (1000 m3) Centre of gravity before mid-ship (m) Block coefficient Length–breadth ratio Breadth–draft ratio Longitudinal Gy-radius in air (m) Roll period in water (s)
257.00 36.80 15.70 118.80 6.30 0.80 7.00 2.34 64.30 14.00
250.00 40.40 15.10 129.60 7.00 0.85 6.20 2.67 – –
Y0 Z N0 Z
Y
(10)
rðUSm =Lm Þ2 N rLm ðUSm =Lm Þ2
(11)
Parabolic sectional area distribution Sectional area and its slope for both the ships are given by the formula Si ðxi Þ Z Si f1Kð2xi =Li Þ2 g for i Z m; p
(12)
S 0 i ðxi Þ ZK8Si xi =L2i for i Z m; p
(13)
3. Numerical examples Model tests to study the phenomena occurring with a moored ship during the passage of another ship were carried out by Remery (1974). 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 values of forces and moment acting on a moored tanker (LmZ257.0 m) while another tanker (LmZ250.0 m) passes adjacent to it are compared with the present theoretical results. The ships’ particulars of the models used by Remery are as in Table 1. The results obtained using the present method are further validated with Table 2 Main particulars of the bulk carriers Length between perpendiculars (m) Breadth (m) Depth (m) Draft (m)
175.00 31.10 16.00 12.00
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18.0 Theory (Parabolic) Expt (Remery 1974)
12.0
X'
6.0
–3.0
–2.0
–1.0
0.0 0.0
1.0
2.0
3.0
–6.0
–12.0
–18.0 ST' Fig. 2. Surge force on the moored ship due to passage of ship (SpZ60 m, h/TZ1.15 ).
those presented by Wang (1975) for a range of parametric variations, where the ships were assumed to follow a parabolic sectional area distribution along its length (Eq. (12)). Subsequent to this the interaction effects of two identical bulk carriers were studied, primarily to identify the influence of the underwater form of the ships on the forces and moment. The prototype particulars of the ship are in Tables 1 and 2.
Fig. 3. Sway force on the moored ship due to passage of ship (SpZ60 m, h/TZ1.15).
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18.0 Theory (Parabolic)
12.0
Expt (Remery 1974)
N'
6.0
0.0 –2.5
–2.0
–1.5
–1.0
–0.5
0.0
0.5
1.0
1.5
2.0
2.5
–6.0
–12.0
–18.0 ST' Fig. 4. Yaw moment on the moored ship due to passage of ship (SpZ60 m, h/TZ1.15).
4. Parametric variation As explained in Section 3, the hydrodynamic interaction effects on a moored ship due to the passage of another ship have been studied, validated with experimental and theoretical results and then applied to real ship case. The experimental results published by Remery (1974) are used here for comparing with the present theoretical values. The results are obtained for the same ships used by Remery,
8 6 4 2 X'
0 –2 –4
Real Form Parabolic Sec. Area
–6 –8 –400
–200
0
200
Stagger Distance (m) Fig. 5. Surge force on the moored bulk carrier induced by a passing identical ship (h/TZ1.2).
400
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8 6 4 2 X'
0 –2 –4
Real Form Parabolic Sec. Area
–6 –8 –400
–200
0
200
400
Stagger Distance (m) Fig. 6. Surge force on the moored bulk carrier induced by a passing identical ship (h/TZ1.4).
the particulars are given in Table 1. But as the details of the ship geometries are not known, for the purpose of present research, the underwater sectional area distribution has been taken as parabolic based on Eq. (12). 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 the above equation. Ship with length 257.0 m has been considered moored while ship with length 250.0 m is passing adjacent to it at lateral separation distance of 60 m with speeds of 4.0, 5.5 and 7.0 knots in a water depth of 1.15 times the moored ship draft. The experimental results are presented in non-dimensional form and after averaging them for the three speeds. 8 6 4 2 X'
0 –2 –4
Real Form Parabolic Sec. Area
–6 –8 –400
–200
0
200
Stagger Distance (m) Fig. 7. Surge force on the moored bulk carrier induced by a passing identical ship (h/TZ1.6).
400
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8 6 4 2 X'
0 –2 –4
Real Form Parabolic Sec. Area
–6 –8 –400
–200
0
200
400
Stagger Distance (m) Fig. 8. Surge force on the moored bulk carrier induced by a passing identical ship (h/TZ1.8).
Wang (1975) carried out hydrodynamic interaction studies on a moored ship due to the passage of a ship using slender body theory with the use of singularity distribution technique. The same method has been used in the present study and the results obtained using the present developed software is compared with those presented by Wang. Figs. 2–4 give the non-dimensional forces and moment acting on the moored ship. The surge force obtained by the present method agrees well with the experimental value. The sway force in different cases has been found to deviate by about 50%, but the trend is good and there is no phase shift. The predicted sway force may get enhanced by the ship form effect, which is not contained here. Both the present theory and Remery’s experiment 8 6 4 2 X'
0 –2 –4
Real Form Parabolic Sec. Area
–6 –8 –400
–200
0
200
Stagger Distance (m) Fig. 9. Surge force on the moored bulk carrier induced by a passing identical ship (deep water).
400
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25 Real Form Parabolic Sec. Area
20 15
Y'
10 5 0 –5 –10 –400
–200
0
200
400
Stagger Distance (m) Fig. 10. Sway force on the moored bulk carrier induced by a passing identical ship (h/TZ1.2).
values for yaw moments have fairly good trend and agreement. But here also it may be noted that the form of the vessel can push up these values. 4.1. Ship form effects In the study carried out here for the estimation of forces and moment, initially the assumption of a parabolic sectional area distribution along the ship length for both moored and passing ships is used, where an approximate value for the mid-ship section area need to be input. For the study of the effect of actual form of the ships in the forces and moment, 25 Real Form Parabolic Sec. Area
20 15
Y'
10 5 0 –5 –10 –400
–200
0
200
Stagger Distance (m) Fig. 11. Sway force on the moored bulk carrier induced by a passing identical ship (h/TZ1.4).
400
1100
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25 Real Form Parabolic Sec. Area
20 15
Y'
10 5 0 –5 –10 –400
–200
0
200
400
Stagger Distance (m) Fig. 12. Sway force on the moored bulk carrier induced by a passing identical ship (h/TZ1.6).
both moored and passing ships taken here are identical bulk carriers with the particulars given in Tables 1. The forces and moment are estimated using the offset table defining the vessel geometry. The values of surge and sway forces and yaw moment (non-dimensionalised using Eqs. (9)–(11) used) are calculated for the bulk carriers using the offsets and also using the parabolic variation (Eqs.(12,13)). The surge forces are compared in Figs. 5–8 for shallow waters (h/TZ1.2, 1.4, 1.6 & 1.8) and in Fig. 9 for deepwater condition. These figures show that the form does not have any significant influence on the peak values of the force, but effects are felt in the first and last quarters of the overlap 25 Real Form Parabolic Sec. Area
20 15
Y'
10 5 0 –5 –10 –400
–200
0
200
Stagger Distance (m) Fig. 13. Sway force on the moored bulk carrier induced by a passing identical ship (h/TZ1.8).
400
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1101
25 Real Form Parabolic Sec. Area
20 15
Y'
10 5 0 –5 –10 –400
–200
0
200
400
Stagger Distance (m) Fig. 14. Sway force on the moored bulk carrier induced by a passing identical ship (deep water).
between the ships. These deviations are only marginal and the effects on the moored ship are not significant. The sway force comparisons are given in Figs. 10–13 for a water depth of 1.2, 1.4, 1.6 & 1.8 times the moored ship draft and in Fig. 14 for deepwater conditions. The repulsion peaks show that the sway mode interaction effect starts earlier and is more significant in the actual case. The sway attraction peak follow the same trend in both forms, but the actual form gives a value about 15% higher than the parabolic form. The change is more or less the same in all water depth cases.
6 4
Y'
2 0 –2 Real Form Parabolic Sec. Area
–4 –6 –400
–200
0
200
400
Stagger Distance (m) Fig. 15. Yaw moment on the moored bulk carrier induced by a passing identical ship (h/TZ1.2).
1102
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6 4
Y'
2 0 –2 Real Form Parabolic Sec. Area
–4 –6 –400
–200
0
200
400
Stagger Distance (m) Fig. 16. Yaw moment on the moored bulk carrier induced by a passing identical ship (h/TZ1.4).
Figs. 15–18 give the non-dimensional yaw moment acting on the moored bulk carrier induced by the passing identical one in shallow waters of depths 1.2, 1.4, 1.6 and 1.8 times the ship draft. Similar graphs for the deepwater condition are given in Fig. 19. All these figures show that the interaction effect in yaw mode commences earlier in the approach phase and ends later in the departing phase. The variation in the hull form is much stronger at the aft and fore ends of the bulk carrier compared to the parabolic variation. These variations have more influence on the yaw moment, and is evident from the graphs. The figures show that the actual form ship gives an increase of more than 30%, compared to the parabolic form, in the yaw moment, which is quite significant. 6 4
Y'
2 0 –2 Real Form Parabolic Sec. Area
–4 –6 –400
–200
0
200
400
Stagger Distance (m) Fig. 17. Yaw moment on the moored bulk carrier induced by a passing identical ship (h/TZ1.6).
K.S. Varyani, P. Krishnankutty / Ocean Engineering 33 (2006) 1090–1104
1103
6 4
Y'
2 0 –2 Real Form Parabolic Sec. Area
–4 –6 –400
–200
0
200
400
Stagger Distance (m) Fig. 18. Yaw moment on the moored bulk carrier induced by a passing identical ship (h/TZ1.8).
5. Summary and conclusion The numerical approach adopted here used slender body assumptions in conjunction with singularity distribution technique. The results are validated with the experimental values of Remery (1974) and the theoretical values presented by Wang (1975). The validated software was extended for further parametric studies of the interaction problem. The main conclusions are: † The character of the forces and the moment, plotted against the relative longitudinal position, was more or less the same for the variations in speeds, passing distances, water depths and sizes of the passing ships. 6 4
Y'
2 0 –2 Real Form Parabolic Sec. Area
–4 –6 –400
–200
0
200
400
Stagger Distance (m) Fig. 19. Yaw moment on the moored bulk carrier induced by a passing identical ship (deep water).
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† The forces and the yaw moment on the moored ship are directly proportional to the size and square of the speed of the passing ship, and inversely proportional to the water depth and the lateral separation distance. † The form of the ships has more influence on the yaw moment (O30% for the bulk carriers studied here when compared with the idealised parabolic form), where as the increase in sway force is about 15% and the effect on surge force is negligible.
Acknowledgements This work forms a part of the TOHPIC project funded by the European Commission (Contract No.G3RD-CT-2000-00491) and the authors wish to record their gratitude to the Commission in extending financial support for carrying out the above work.
References OCIMF, 1978. Guidelines and Recommendations for the Safe Mooring of Large Ships at Piers and Sea Islands. Oil Companies International Marine Forum, London. Krishnankutty, P., 1987. Computer simulation of hydrodynamic interaction and mooring rig force analysis, Master’s Thesis, Stevens Institute of Technology, New Jersey, USA. Krishnankutty, P., Varyani, K.S., 2003. Ship form effects on the forces and moment on a stationary ship induced by a Passing Ship, MCMC, Girona. Remery, G.F.M., 1974. Mooring forces induced by passing ships, offshore technology conference, Houston, Paper 2066, p. 351. Varyani, K.S., Krishnankutty, P., Vantorre, M., 2003. Prediction of Load on mooring ropes of a container ship due to the forces induced by a passing bulk carrier, MARSIM, Kanazawa, Japan. Wang, S., 1975. Dynamic effects of ships passage on moored vessels. Journal of the Waterways, Harbours and Coastal Engineering Division, ASCE 101. Yeung, R.W., 1978. On the interaction of slender ships in shallow water. Journal of Fluid Mechanics 85, 143–159. Yeung, R.W., Tan, W.T., 1980. Hydrodynamic interaction of ships with fixed obstacles. Journal of Ship Research 24, 50–59.
Modification of ship hydrodynamic interaction forces and moment by underwater ship geometry K.S. Varyani *, P. Krishnankutty Department of Naval Architecture and Marine Engineering, Universities of Glasgow and Strathclyde, Henri Dyer Building, 100 Montrose St., Glasgow G4 0LZ, Scotland, UK Received 12 January 2005; accepted 17 July 2005 Available online 4 November 2005
Abstract The hydrodynamic interaction forces/moments acting on a moored ship due to the passage of another ship in its proximity is researched by considering the influence of ship form against the idealized approach of the use of parabolic sectional area distribution. Comparisons with experimental results show that the interaction effects are predicted better by inclusion of ship’s form. q 2005 Elsevier Ltd. All rights reserved. Keywords: Hydrodynamic interaction; Moored; Stationary; Passing ship; Ship form.
1. Introduction The hydrodynamic interaction of a ship with other ships or with waterway boundaries affects its course keeping and maneuvering. This can also have an impact on moored ships and coastal structures. The forces and moments are more significant on the moored ship than on the moving ship. As the moving ship is under the control of helm the normal interactive effects can be counteracted. The magnitude of the interaction forces also depends on the speed, size and geometry of the moving vessel, lateral distance between the moving vessel and the stationary one, and the water depth. Hydrodynamic interaction between two ships is typically observed when they pass in confined waters. Besides, the
* Corresponding author. Tel.: C141 548 4465; fax: C141 552 2879. E-mail address: [email protected] (K.S. Varyani).
0029-8018/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2005.07.010
K.S. Varyani, P. Krishnankutty / Ocean Engineering 33 (2006) 1090–1104
1091
interaction forces are much bigger in confined water compared to deep water. The interaction between ships and waterway boundaries affects the maneuvering and course keeping of the ships, on one hand, and impacts coastal structures or other moored ships, on the other. All this sets particular importance to studying and modeling ship interaction effects, mainly in restricted waterways. Major interaction forces components are surge, sway and yaw. The peak values are important from the design aspect of mooring system. The movement and mooring line loads of the moored ship are dependent on these interaction forces. Even though the sway force is much larger than the surge force, the surge displacement is greater than the sway displacement due to much lower damping in surge motion of the moored vessel. Thus the load on the mooring lines can become exceedingly high due to surge motion. By knowing the movement constraints of the berthed ship, which may be due to the restriction imposed for cargo handling facilities, the speed and separation distance limits of the passing ship can be ascertained. For berthed tankers, the cargo handling manifolds allow a maximum movement of only G3.0 m in surge and 3 m in sway, OCIMF, (1978), and for berthed container ships the movements are more restricted due to the limited reach of the cranes. Yeung (1978) and Yeung and Tan (1980) have shown that the approach stage of the initial transient is most critical for the purpose of navigational safety. This is because the ship is subject to an attraction force towards the moored ship and at the same time is subjected to a ‘bow-in’ turning moment. Thus the passing ship with zero rudder-angle would tend to head into the moored ship. The hydrodynamic forces and moment on a moored ship resulting from the passing of another ship at various separation distances, water depths and passing ship sizes, were estimated by Wang (1975) using slender body theory. The hydrodynamic interaction problem between moored and passing ships was studied by Krishnankutty (1987), Krishnankutty and Varyani (2003) and Varyani et al. (2003), using the slender body theory with singularity distribution technique for the computation of forces in surge and sway modes and yaw moment acting on moored vessel. The analysis was further carried out for the estimation of mooring line forces for the idealized mooring line arrangement, such as head-stern and breast lines, neglecting the spring lines in the configuration considered. A rapid increase of the size of the vessels and their speed has considerably increased the interaction effects while they move in the proximity of other vessels. Experimental studies of Remrey (1974), using tanker models, reveal the effect of the size of the passing vessels and the separation distances on the interaction forces and moments on a moored vessel. The experiments were carried out in shallow water condition with the water depth about 1.15 times the draft of the moored vessel and with the vessels parallel to each other. The vessel was moored by means of a flexible system with linear elasticity. The force in the mooring system was measured by varying its stiffness. An impulse function technique to solve the equations of motion in the time was used rather than the frequency domain approach. In the present paper the hydrodynamic interaction forces/moments acting on a moored ship due to the passing of another ship in its proximity is researched by considering the influence of ship form against idealised approach of the use of parabolic sectional area distribution for a wide range of depth– draft ratios.
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2. Theoretical formulation The study is concentrated on the estimation and analysis of the surge and sway forces and yaw moment induced on a rigidly moored (stationary) ship by a passing ship. Different cases that are dealt with here are: – Both ships are identical, with a parabolic sectional area distribution along its length assumed. The hydrodynamic effects in deep and shallow waters are estimated. – These estimations are carried out for real ship forms, where the actual underwater geometry of the ships is considered. We consider one ship is stationary and another ship is passing by. The hydrodynamic interaction problem between a moored ship and the passing ship are formulated using a slender body theory with the following assumptions. – The transverse dimensions of the ships (beam and draft) are quite small compared to its length, but can be of different forms – The passing ship moves at a constant speed and is parallel to the moored ship – The fluid is inviscid and incompressible, the flow is irrotational – The disturbances at the free surface are neglected (treated as a rigid boundary) The co-ordinate (xm, ym, zm) is fixed in the moored ship and (xp, yp, zp) is fixed in the passing ship as in Fig. 1. Parameters with suffices m and p, respectively, refer to those related to the moored and passing ships. In addition to the governing (Laplace) equation applied to the fluid domain, the following boundary conditions are in order vf Z 0 on moored ship vnm
(1)
vxp vf ZU vnp vnp
(2)
on passing ship
N U=0
X Y ξ
Lm
η
U>0
Lp Fig. 1. Co-ordinate system in moored-passing ship.
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The velocity potential function of the flow field is estimated using the singularity distribution technique and subsequently the flow velocity components along the moored ship induced by the passing ship are determined. The interaction potential in the unsteady Bernoulli equation gives the pressure distribution and integration of this pressure over the surface gives the net forces on the moored ship. ð ð S 0 p ðxp Þðxp Kxm C xÞ rU 2 Xðx; hÞ Z S 0 m ðxm Þ dxp dxm (3) 2p fðxp Kxm C xÞ2 C h2 g1:5 Lm
Yðx; hÞ Z
rU 2 h p
ð
Lp
S 0 m ðxm Þ
Lm
ð Lp
S 0 p ðxp Þ fðxp Kxm C xÞ2 C h2 g1:5
dxp dxm
The yaw moment obtained from the slender body theory, Wang, is ð ð S 0 p ðxp Þ rU 2 h Nðx; hÞ Z fxm S 0 m ðxm Þ C S 0 m ðxm Þg dxp dxm p fðxp Kxm C xÞ2 C h2 g1:5 Lm
(4)
(5)
Lp
The above equations are for the deepwater case. When the water depth becomes less than twice the draft of the ship, the shallow water effect has to be considered. The bottom condition for an assumed constant water depth of Kh is represented by vf vz Z 0 : By method of image the interaction forces and moment can be written as ð N ð Sp0 ðxp Þðxp Kxm C xÞ rU 2 X Xðx; h; zÞ Z S 0 m ðxm Þ dxp dxm (6) 2p nZKN fðxp Kxm C xÞ2 C h2 C 4n2 h2 g1:5 Lm
Yðx; h; zÞ Z
Lp
ð N ð S 0 p ðxp Þ rU 2 h X S 0 m ðxm Þ dxp dxm p nZKN fðxp Kxm C xÞ2 C h2 C 4n2 h2 g1:5 Lm
(7)
Lp
N ð rU 2 h X Nðx; h; zÞ Z fxm S 0 m ðxm Þ C Sm ðxm Þg p nZKN Lm
ð ! Lp
S 0 p ðxp Þ fðxp Kxm C xÞ2 C h2 C 4n2 h2 g1:5
dxp dxm
(8)
where Sm is the mid-ship section area of the moored ship, S 0 m and S 0 pare the sectional area slopes of the moored and passing ships, n is the number of images. 2.1. Non-dimensional factors The forces and moments are non-dimensionalised as follows X0 Z
X rðUSm =Lm Þ2
(9)
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Table 1 Prototype particulars of the ship models used by Remrey (1974) Particulars
Moored ship
Passing ship
Length between perpendiculars (m) Breadth (m) Draft (m) Displaced volume (1000 m3) Centre of gravity before mid-ship (m) Block coefficient Length–breadth ratio Breadth–draft ratio Longitudinal Gy-radius in air (m) Roll period in water (s)
257.00 36.80 15.70 118.80 6.30 0.80 7.00 2.34 64.30 14.00
250.00 40.40 15.10 129.60 7.00 0.85 6.20 2.67 – –
Y0 Z N0 Z
Y
(10)
rðUSm =Lm Þ2 N rLm ðUSm =Lm Þ2
(11)
Parabolic sectional area distribution Sectional area and its slope for both the ships are given by the formula Si ðxi Þ Z Si f1Kð2xi =Li Þ2 g for i Z m; p
(12)
S 0 i ðxi Þ ZK8Si xi =L2i for i Z m; p
(13)
3. Numerical examples Model tests to study the phenomena occurring with a moored ship during the passage of another ship were carried out by Remery (1974). 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 values of forces and moment acting on a moored tanker (LmZ257.0 m) while another tanker (LmZ250.0 m) passes adjacent to it are compared with the present theoretical results. The ships’ particulars of the models used by Remery are as in Table 1. The results obtained using the present method are further validated with Table 2 Main particulars of the bulk carriers Length between perpendiculars (m) Breadth (m) Depth (m) Draft (m)
175.00 31.10 16.00 12.00
K.S. Varyani, P. Krishnankutty / Ocean Engineering 33 (2006) 1090–1104
1095
18.0 Theory (Parabolic) Expt (Remery 1974)
12.0
X'
6.0
–3.0
–2.0
–1.0
0.0 0.0
1.0
2.0
3.0
–6.0
–12.0
–18.0 ST' Fig. 2. Surge force on the moored ship due to passage of ship (SpZ60 m, h/TZ1.15 ).
those presented by Wang (1975) for a range of parametric variations, where the ships were assumed to follow a parabolic sectional area distribution along its length (Eq. (12)). Subsequent to this the interaction effects of two identical bulk carriers were studied, primarily to identify the influence of the underwater form of the ships on the forces and moment. The prototype particulars of the ship are in Tables 1 and 2.
Fig. 3. Sway force on the moored ship due to passage of ship (SpZ60 m, h/TZ1.15).
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K.S. Varyani, P. Krishnankutty / Ocean Engineering 33 (2006) 1090–1104
18.0 Theory (Parabolic)
12.0
Expt (Remery 1974)
N'
6.0
0.0 –2.5
–2.0
–1.5
–1.0
–0.5
0.0
0.5
1.0
1.5
2.0
2.5
–6.0
–12.0
–18.0 ST' Fig. 4. Yaw moment on the moored ship due to passage of ship (SpZ60 m, h/TZ1.15).
4. Parametric variation As explained in Section 3, the hydrodynamic interaction effects on a moored ship due to the passage of another ship have been studied, validated with experimental and theoretical results and then applied to real ship case. The experimental results published by Remery (1974) are used here for comparing with the present theoretical values. The results are obtained for the same ships used by Remery,
8 6 4 2 X'
0 –2 –4
Real Form Parabolic Sec. Area
–6 –8 –400
–200
0
200
Stagger Distance (m) Fig. 5. Surge force on the moored bulk carrier induced by a passing identical ship (h/TZ1.2).
400
K.S. Varyani, P. Krishnankutty / Ocean Engineering 33 (2006) 1090–1104
1097
8 6 4 2 X'
0 –2 –4
Real Form Parabolic Sec. Area
–6 –8 –400
–200
0
200
400
Stagger Distance (m) Fig. 6. Surge force on the moored bulk carrier induced by a passing identical ship (h/TZ1.4).
the particulars are given in Table 1. But as the details of the ship geometries are not known, for the purpose of present research, the underwater sectional area distribution has been taken as parabolic based on Eq. (12). 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 the above equation. Ship with length 257.0 m has been considered moored while ship with length 250.0 m is passing adjacent to it at lateral separation distance of 60 m with speeds of 4.0, 5.5 and 7.0 knots in a water depth of 1.15 times the moored ship draft. The experimental results are presented in non-dimensional form and after averaging them for the three speeds. 8 6 4 2 X'
0 –2 –4
Real Form Parabolic Sec. Area
–6 –8 –400
–200
0
200
Stagger Distance (m) Fig. 7. Surge force on the moored bulk carrier induced by a passing identical ship (h/TZ1.6).
400
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8 6 4 2 X'
0 –2 –4
Real Form Parabolic Sec. Area
–6 –8 –400
–200
0
200
400
Stagger Distance (m) Fig. 8. Surge force on the moored bulk carrier induced by a passing identical ship (h/TZ1.8).
Wang (1975) carried out hydrodynamic interaction studies on a moored ship due to the passage of a ship using slender body theory with the use of singularity distribution technique. The same method has been used in the present study and the results obtained using the present developed software is compared with those presented by Wang. Figs. 2–4 give the non-dimensional forces and moment acting on the moored ship. The surge force obtained by the present method agrees well with the experimental value. The sway force in different cases has been found to deviate by about 50%, but the trend is good and there is no phase shift. The predicted sway force may get enhanced by the ship form effect, which is not contained here. Both the present theory and Remery’s experiment 8 6 4 2 X'
0 –2 –4
Real Form Parabolic Sec. Area
–6 –8 –400
–200
0
200
Stagger Distance (m) Fig. 9. Surge force on the moored bulk carrier induced by a passing identical ship (deep water).
400
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1099
25 Real Form Parabolic Sec. Area
20 15
Y'
10 5 0 –5 –10 –400
–200
0
200
400
Stagger Distance (m) Fig. 10. Sway force on the moored bulk carrier induced by a passing identical ship (h/TZ1.2).
values for yaw moments have fairly good trend and agreement. But here also it may be noted that the form of the vessel can push up these values. 4.1. Ship form effects In the study carried out here for the estimation of forces and moment, initially the assumption of a parabolic sectional area distribution along the ship length for both moored and passing ships is used, where an approximate value for the mid-ship section area need to be input. For the study of the effect of actual form of the ships in the forces and moment, 25 Real Form Parabolic Sec. Area
20 15
Y'
10 5 0 –5 –10 –400
–200
0
200
Stagger Distance (m) Fig. 11. Sway force on the moored bulk carrier induced by a passing identical ship (h/TZ1.4).
400
1100
K.S. Varyani, P. Krishnankutty / Ocean Engineering 33 (2006) 1090–1104
25 Real Form Parabolic Sec. Area
20 15
Y'
10 5 0 –5 –10 –400
–200
0
200
400
Stagger Distance (m) Fig. 12. Sway force on the moored bulk carrier induced by a passing identical ship (h/TZ1.6).
both moored and passing ships taken here are identical bulk carriers with the particulars given in Tables 1. The forces and moment are estimated using the offset table defining the vessel geometry. The values of surge and sway forces and yaw moment (non-dimensionalised using Eqs. (9)–(11) used) are calculated for the bulk carriers using the offsets and also using the parabolic variation (Eqs.(12,13)). The surge forces are compared in Figs. 5–8 for shallow waters (h/TZ1.2, 1.4, 1.6 & 1.8) and in Fig. 9 for deepwater condition. These figures show that the form does not have any significant influence on the peak values of the force, but effects are felt in the first and last quarters of the overlap 25 Real Form Parabolic Sec. Area
20 15
Y'
10 5 0 –5 –10 –400
–200
0
200
Stagger Distance (m) Fig. 13. Sway force on the moored bulk carrier induced by a passing identical ship (h/TZ1.8).
400
K.S. Varyani, P. Krishnankutty / Ocean Engineering 33 (2006) 1090–1104
1101
25 Real Form Parabolic Sec. Area
20 15
Y'
10 5 0 –5 –10 –400
–200
0
200
400
Stagger Distance (m) Fig. 14. Sway force on the moored bulk carrier induced by a passing identical ship (deep water).
between the ships. These deviations are only marginal and the effects on the moored ship are not significant. The sway force comparisons are given in Figs. 10–13 for a water depth of 1.2, 1.4, 1.6 & 1.8 times the moored ship draft and in Fig. 14 for deepwater conditions. The repulsion peaks show that the sway mode interaction effect starts earlier and is more significant in the actual case. The sway attraction peak follow the same trend in both forms, but the actual form gives a value about 15% higher than the parabolic form. The change is more or less the same in all water depth cases.
6 4
Y'
2 0 –2 Real Form Parabolic Sec. Area
–4 –6 –400
–200
0
200
400
Stagger Distance (m) Fig. 15. Yaw moment on the moored bulk carrier induced by a passing identical ship (h/TZ1.2).
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6 4
Y'
2 0 –2 Real Form Parabolic Sec. Area
–4 –6 –400
–200
0
200
400
Stagger Distance (m) Fig. 16. Yaw moment on the moored bulk carrier induced by a passing identical ship (h/TZ1.4).
Figs. 15–18 give the non-dimensional yaw moment acting on the moored bulk carrier induced by the passing identical one in shallow waters of depths 1.2, 1.4, 1.6 and 1.8 times the ship draft. Similar graphs for the deepwater condition are given in Fig. 19. All these figures show that the interaction effect in yaw mode commences earlier in the approach phase and ends later in the departing phase. The variation in the hull form is much stronger at the aft and fore ends of the bulk carrier compared to the parabolic variation. These variations have more influence on the yaw moment, and is evident from the graphs. The figures show that the actual form ship gives an increase of more than 30%, compared to the parabolic form, in the yaw moment, which is quite significant. 6 4
Y'
2 0 –2 Real Form Parabolic Sec. Area
–4 –6 –400
–200
0
200
400
Stagger Distance (m) Fig. 17. Yaw moment on the moored bulk carrier induced by a passing identical ship (h/TZ1.6).
K.S. Varyani, P. Krishnankutty / Ocean Engineering 33 (2006) 1090–1104
1103
6 4
Y'
2 0 –2 Real Form Parabolic Sec. Area
–4 –6 –400
–200
0
200
400
Stagger Distance (m) Fig. 18. Yaw moment on the moored bulk carrier induced by a passing identical ship (h/TZ1.8).
5. Summary and conclusion The numerical approach adopted here used slender body assumptions in conjunction with singularity distribution technique. The results are validated with the experimental values of Remery (1974) and the theoretical values presented by Wang (1975). The validated software was extended for further parametric studies of the interaction problem. The main conclusions are: † The character of the forces and the moment, plotted against the relative longitudinal position, was more or less the same for the variations in speeds, passing distances, water depths and sizes of the passing ships. 6 4
Y'
2 0 –2 Real Form Parabolic Sec. Area
–4 –6 –400
–200
0
200
400
Stagger Distance (m) Fig. 19. Yaw moment on the moored bulk carrier induced by a passing identical ship (deep water).
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† The forces and the yaw moment on the moored ship are directly proportional to the size and square of the speed of the passing ship, and inversely proportional to the water depth and the lateral separation distance. † The form of the ships has more influence on the yaw moment (O30% for the bulk carriers studied here when compared with the idealised parabolic form), where as the increase in sway force is about 15% and the effect on surge force is negligible.
Acknowledgements This work forms a part of the TOHPIC project funded by the European Commission (Contract No.G3RD-CT-2000-00491) and the authors wish to record their gratitude to the Commission in extending financial support for carrying out the above work.
References OCIMF, 1978. Guidelines and Recommendations for the Safe Mooring of Large Ships at Piers and Sea Islands. Oil Companies International Marine Forum, London. Krishnankutty, P., 1987. Computer simulation of hydrodynamic interaction and mooring rig force analysis, Master’s Thesis, Stevens Institute of Technology, New Jersey, USA. Krishnankutty, P., Varyani, K.S., 2003. Ship form effects on the forces and moment on a stationary ship induced by a Passing Ship, MCMC, Girona. Remery, G.F.M., 1974. Mooring forces induced by passing ships, offshore technology conference, Houston, Paper 2066, p. 351. Varyani, K.S., Krishnankutty, P., Vantorre, M., 2003. Prediction of Load on mooring ropes of a container ship due to the forces induced by a passing bulk carrier, MARSIM, Kanazawa, Japan. Wang, S., 1975. Dynamic effects of ships passage on moored vessels. Journal of the Waterways, Harbours and Coastal Engineering Division, ASCE 101. Yeung, R.W., 1978. On the interaction of slender ships in shallow water. Journal of Fluid Mechanics 85, 143–159. Yeung, R.W., Tan, W.T., 1980. Hydrodynamic interaction of ships with fixed obstacles. Journal of Ship Research 24, 50–59.