Abstract

A novel numerical approach, leveraging the 3D time domain Rankine panel method, has been introduced to simulate ship motions while accounting for the effects of ship wave. This method treats ship wave as steady flow, enabling a more accurate representation of physical phenomena. The underlying numerical formulation used to solve the ship wave potential is comprehensively derived, establishing the unsteady disturbance potential's boundary value problem and incorporating the effects of steady motion. Wave forces and motion responses of various ship forms were computed and compared with experimental data and results from other numerical techniques. The findings reveal that calculations based on uniform stream exhibit significantly larger errors than those considering double body flow or ship wave. For the Wigley I and S175 models, the discrepancies between double body flow and ship wave predictions are relatively minor, with ship wave calculations demonstrating slightly higher accuracy. In contrast, for the intricate KRISO Container Ship (KCS) model, where ship wave is more pronounced, the error margin for ship wave calculations relative to experimental results remains within 21.9%, while errors for double body flow calculations can reach up to 50.2%. This highlights the superior accuracy of ship wave-based calculations for the KCS model. Overall, the proposed method effectively captures the influence of steady flow and demonstrates significant advantages in computing pronounced ship wave generated during realistic ship motion.

References

1.
Islam
,
H.
, and
Soares
,
C. G.
,
2022
, “
Head Wave Simulation of a KRISO Container Ship Model Using OpenFOAM for the Assessment of Sea Margin
,”
ASME J. Offshore Mech. Arct. Eng.
,
144
(
3
), p.
031902
.
2.
Terziev
,
M.
,
Tezdogan
,
T.
, and
Incecik
,
A.
,
2021
, “
Modelling the Hydrodynamic Effect of Abrupt Water Depth Changes on a Ship Travelling in Restricted Waters Using CFD
,”
Ships Offshore Struct.
,
16
(
10
), pp.
1087
1103
.
3.
Wang
,
X.
,
Liu
,
L.
,
Zhang
,
Z.
, and
Feng
,
D.
,
2020
, “
Numerical Study of the Stern Flap Effect on Catamaran’ Seakeeping Characteristic in Regular Head Waves
,”
Ocean Eng.
,
206
, p.
107172
.
4.
Kudupudi
,
R. B.
,
Pal
,
S. K.
, and
Datta
,
R.
,
2019
, “
A Three-Step Hybrid Method to Study the Influence of Green Water Impact on a Large Containership in Time Domain
,”
ASME J. Offshore Mech. Arct. Eng.
,
141
(
5
), p.
051804
.
5.
Froude
,
W.
,
1861
, “
On the Rolling of Ships
,”
Trans. Inst. Nav. Archit.
,
3
, pp.
7
62
.
6.
Krylov
,
A.
,
1896
, “
A New Theory of the Pitching Motions of a Ship on Waves and the Stresses Produced by This Motion
,”
Trans. Inst. Nav. Archit.
,
37
, pp.
326
368
.
7.
Haskind
,
M. D.
,
1946
, “
The Oscillation of a Ship in Still Water
,”
Izv. Akad. Nauk SSSR Otd. Tekh. Nauk
,
1
, pp.
23
34
.
8.
St Dinis
,
M.
, and
Pierson
,
W. J.
, Jr.
,
1953
, “
On the Motions of Ships in Confused Seas
,”
Univ Bronx School of Engineering and Science
,
New York
.
9.
Korvin-Kroukovsky
,
B.
,
1955
, “
Investigation of Ship Motions in Regular Waves
,”
Trans. SNAME
,
63
(
7
), pp.
386
435
.
10.
Ogilvie
,
T. F.
, and
Tuck
,
E. O.
,
1969
, “A Rational Strip Theory of Ship Motions: Part I,” University of Michigan, https://hdl.handle.net/2027.42/91655
11.
Salvesen
,
N.
,
Tuck
,
E. O.
, and
Faltinsen
,
O.
,
1970
, “
Ship Motions and Sea Loads
,”
Trans. SNAME
,
78
, pp.
250
287
.
12.
Chapman
,
R.
,
1975
, “
Numerical Solution for Hydrodynamic Forces on a Surface-Piercing Plate Oscillating in Yaw and Sway
,”
Proceedings of 1st International Conference on Numerical Ship Hydrodynamics
,
Gaithersburg, MD
,
Oct. 20–22
, pp.
333
350
.
13.
Faltinsen
,
O.
, and
Zhao
,
R.
,
1991
, “
Numerical Predictions of Ship Motions at High Forward Speed
,”
Philos. Trans. R. Soc. Lond. Ser. A
,
334
(
1634
), pp.
241
252
.
14.
Ma
,
S.
,
2005
, “
2.5D Computational Method for Ship Motion and Wave Loads of High Speed Ships
,”
Ph.D. thesis
,
Harbin Engineering University
,
Harbin
.
15.
Wicaksono
,
A.
, and
Kashiwagi
,
M.
,
2018
, “
Wave-Induced Steady Forces and Yaw Moment of a Ship Advancing in Oblique Waves
,”
J. Mar. Sci. Technol.
,
23
(
4
), pp.
767
781
.
16.
Newman
,
J. N.
,
1985
, “
Algorithms for the Free-Surface Green Function
,”
J. Eng. Math.
,
19
(
1
), pp.
57
67
.
17.
Wu
,
H.
,
Zhang
,
C.
,
Zhu
,
Y.
,
Li
,
W.
,
Wan
,
D.
, and
Noblesse
,
F.
,
2017
, “
A Global Approximation to the Green Function for Diffraction Radiation of Water Waves
,”
Eur. J. Mech. B/Fluids
,
65
, pp.
54
64
.
18.
Duan
,
W. Y.
,
Yu
,
D. H.
, and
Shen
,
Y.
,
2016
, “
Algorithm for Infinite Depth Water Wave Green Function and Its High Order Derivatives
,”
J. Ship Mech.
,
20
(
1/2
), pp.
10
22
.
19.
Bingham
,
H. B.
,
2016
, “
A Note on the Relative Efficiency of Methods for Computing the Transient Free-Surface Green Function
,”
Ocean Eng.
,
120
, pp.
15
20
.
20.
LI
,
Z.-F.
,
Ren
,
H. L.
,
Shi
,
Y. Y.
, and
Li
,
H.
,
2018
, “
Computation of Time Domain Free Surface Green Function Based on the Improved Precise Integration Method
,”
J. Ship Mech.
,
22
(
7
), pp.
818
826
.
21.
Zhang
,
T.
,
2019
, “
Research on Time Domain Numerical Modeling and Simulation Ship Motions in Waves
,”
Ph.D. thesis
,
Dalian Maritime University
,
Dalian
.
22.
Sengupta
,
D.
,
Datta
,
R.
, and
Sen
,
D.
,
2016
, “
A Simplified Approach for Computation of Nonlinear Ship Loads and Motions Using a 3D Time-Domain Panel Method
,”
Ocean Eng.
,
117
, pp.
99
113
.
23.
Yeung
,
R. W. C.
,
1973
, “A Singularity-Distribution Method for Free-Surface Flow Problems With an Oscillating Body,” University of California, Berkeley, CA.
24.
Nakos
,
D. E.
,
1990
, “
Ship Wave Patterns and Motions by a Three Dimensional Rankine Panel Method
,” Ph.D. thesis,
Massachusetts Institute of Technology
,
Cambridge, MA
.
25.
Kring
,
D. C.
,
1994
, “
Time Domain Ship Motions by a Three-Dimensional Rankine Panel Method
,” Ph.D. thesis,
Massachusetts Institute of Technology
,
Cambridge, MA
.
26.
Duan
,
W.
,
Chen
,
J.
, and
Zhao
,
B.
,
2015
, “
Second-Order Taylor Expansion Boundary Element Method for the Second-Order Wave Diffraction Problem
,”
Eng. Anal. Boundary Elem.
,
58
, pp.
140
150
.
27.
Tang
,
K.
,
Zhen
,
Q. Z.
,
Hong
,
L.
,
Jiang
,
D. P.
,
Chen
,
X.
, and
Li
,
Y. L.
,
2021
, “
Time-Domain Analysis of Side-by-Side Floating Bodies by the Three-Dimensional Hybrid Green Function Method
,”
Ships Offshore Struct.
,
16
(
5
), pp.
516
528
.
28.
Yang
,
Y. T.
,
Zhu
,
R. C.
, and
Gao
,
H.
,
2022
, “
Study on Higher-Order Rankine Source Method for Hydrodynamic and Motion Responses of Vessels Sailing in Waves
,”
Shipbuild. China
,
63
(
1
), p.
14
.
29.
Zhang
,
W.
, and
Zou
,
Z.
,
2015
, “
Time Domain Simulations of Radiation and Diffraction by a Rankine Panel Method
,”
J. Hydrodyn.
,
27
(
5
), pp.
635
646
.
30.
He
,
G. H.
,
Chen
,
L. M.
,
Zhang
,
J. S.
, and
Zhang
,
S. J.
,
2017
, “
Iterative Rankine HOBEM Analysis of Hull-Form Effects in Forward-Speed Diffraction Problem
,”
J. Hydrodyn.
,
29
(
2
), pp.
226
234
.
31.
Mei
,
T.
,
Liu
,
Y.
,
Ruiz
,
M. T.
,
Lataire
,
E.
,
Vantorre
,
M.
,
Chen
,
C.
, and
Zou
,
Z.
,
2021
, “
A Hybrid Method for Predicting Ship Maneuverability in Regular Waves
,”
ASME J. Offshore Mech. Arct. Eng.
,
143
(
2
), p.
021213
.
32.
Yao
,
C. B.
, and
Dong
,
W. C.
,
2014
, “
Evaluation Method for Kelvin Source Green's Function
,”
J. Shanghai Jiaotong Univ.
,
48
(
1
), pp.
98
105
.
33.
Yao
,
C.
, and
Dong
,
W.
,
2015
, “
A Comparison Study on Numerical Methods to Evaluate the Kelvin Source Green's Function
,”
J. Harbin Eng. Univ.
,
36
(
1
), pp.
98
103 and 108
.
34.
Song
,
Y.
,
Zhu
,
R.
,
Hong
,
L.
,
Xi
,
C.
,
Huang
,
Q.
, et al
,
2016
, “
Kelvin Source Green's Function Distributing on Horizontal Line Segments and Applications in Ship Wave Problems
,”
The Second Conference of Global Chinese Scholars on Hydrodynamics
,
Wuxi, China
,
Nov. 11–14
.
35.
Dawson
,
C.
,
1977
, “
A Practical Computer Method for Solving Ship-Wave Problems
,”
Proceedings of 2nd International Conference on Numerical Ship Hydrodynamics
,
Berkeley, CA
,
Sept. 19–21
.
36.
Peng
,
H.
,
Ni
,
S.
, and
Qiu
,
W.
,
2014
, “
Wave Pattern and Resistance Prediction for Ships of Full Form
,”
Ocean Eng.
,
87
, pp.
162
173
.
37.
Chen
,
X.
,
Zhu
,
R.
,
Miao
,
G.
, and
Fan
,
J.
,
2015
, “
Calculation of Ship Sinkage, Trim and Wave Drag Using High-Order Rankine Source Method
,”
Shipbuild. China
,
56
(
3
), pp.
1
12
.
38.
Raven
,
H. C.
,
1996
, “A Solution Method for the Nonlinear Ship Wave Resistance Problem,”
Ph.D. thesis
,
Technische Universiteit Delft
,
Delft
.
39.
Chen
,
X.
,
Zhu
,
R.
,
Ma
,
C.
, and
Fan
,
J.
,
2016
, “
Computations of Linear and Nonlinear Ship Waves by Higher-Order Boundary Element Method
,”
Ocean Eng.
,
114
, pp.
142
153
.
40.
Wang
,
X.
,
Zhu
,
R.
,
Chen
,
X.
, and
Song
,
Y.
,
2018
, “
A Solution of Ship Waves With Nonlinear Free Surface by High Order Panel Method
,”
J. Harbin Eng. Univ.
,
39
(
2
), pp.
229
235
.
41.
Ma
,
C.
,
Zhang
,
C.
,
Chen
,
X.
,
Jiang
,
Y.
, and
Noblesse
,
F.
,
2016
, “
Practical Estimation of Sinkage and Trim for Common Generic Monohull Ships
,”
Ocean Eng.
,
126
, pp.
203
216
.
42.
Wen-Jun
,
Z.
,
2020
, “
Time Domain Nonlinear Hydrodynamic Analysis and Large Amplitude Motion Prediction of Ship Based on Multi-domain Method
,”
Ph.D. thesis
,
Shanghai Jiao Tong University
,
Shanghai
.
43.
Shao
,
Y.
,
2010
, “Numerical Potential-Flow Studies on Weakly-Nonlinear Wave-Body Interactions With/Without Small Forward Speeds,”
Ph.D. thesis
,
Norwegian University of Science and Technology
,
Trondheim
.
44.
Mei
,
T. L.
,
Zhang
,
T.
,
Candries
,
M.
,
Lataire
,
E.
, and
Zou
,
Z.-J.
,
2020
, “
Comparative Study on Ship Motions in Waves Based on Two Time Domain Boundary Element Methods
,”
Eng. Anal. Boundary Elem.
,
111
(
Feb.
), pp.
9
21
.
45.
Newman
,
J. N.
,
1979
, “
The Theory of Ship Motions
,”
Adv. Appl. Mech.
,
18
, pp.
221
283
.
46.
Hess
,
J. L.
, and
Smith
,
A. M. O.
,
1964
, “
Calculation of Nonlifting Potential Flow About Arbitrary Three Dimensional Bodies
,”
J. Ship Res.
,
8
(
4
), pp.
22
44
.
47.
Raven
,
H. C.
,
1988
, “
Variations on a Theme by Dawson: Recent Improvements of a Potential Flow Calculation Method for Ships
,”
Proceedings of the 17th Symposium on Naval Hydrodynamics
,
The Hague, The Netherlands
,
Aug. 29–Sept. 2
, pp.
151
172
.
48.
Wu
,
G. X.
,
1991
, “
A Numerical Scheme for Calculating the mj Terms in Wave-Current-Body Interaction Problem
,”
Appl. Ocean Res.
,
13
(
6
), pp.
317
319
.
49.
Chen
,
X. B.
, and
Malenica
,
B.
,
1998
, “
Interaction Effects of Local Steady Flow on Wave Diffraction-Radiation at Low Forward Speed
,”
Int. J. Offshore Polar Eng.
,
8
(
2
), pp.
147
153
.
50.
Xu
,
H.
, and
Yue
,
D.
,
1994
, “
Computations of Fully-Nonlinear Three-Dimensional Water Waves
,”
Proceedings of the Symposium on Naval Hydrodynamics
,
Seoul, South Korea
,
Aug. 23–28
, pp.
177
202
.
51.
Longuet-Higgins
,
M. S.
, and
Cokelet
,
E. D.
,
1976
, “
The Deformation of Steep Surface Waves on Water-I. A Numerical Method of Computation
,”
Proc. R. Soc. A: Math. Phys. Sci.
,
350
(
1660
), pp.
1
26
.
52.
Huang
,
Y.
,
1997
, “Nonlinear Ship Motions by a Rankine Panel Method,”
Ph.D. thesis
,
Massachusetts Institute of Technology
,
Cambridge, MA
.
53.
Kim
,
K. H.
, and
Kim
,
Y.
,
2008
, “
On Technical Issues in the Analysis of Nonlinear Ship Motion and Structural Loads in Waves by a Time-Domain Rankine Panel Method
,”
The 23rd International Workshop on Water Waves and Floating Bodies
,
Jeju, South Korea
,
Apr. 13–16
, pp.
1
4
.
54.
Journée
,
J. M. J.
,
1992
, “Experiments and Calculations on 4 Wigley Hull Forms in Head Waves,” Delft University of Technology Report.
55.
Jiang
,
Z. Y.
,
2008
, “
A Study of 3D Computational Technology for Predicting Linear Ship Motions in Frequency Domain
,”
Ph.D. thesis
,
Dalian University of Technology
,
Dalian
.
56.
ITTC
,
1978
, “
Comparison of Results Obtained With Compute Programs to Predict Ship Motions in Six-Degrees-of-Freedom and Associated Responses
,”
Proceedings of 15th ITTC
,
The Hague, Netherlands
,
September
, pp.
79
90
.
57.
Simonsen
,
C. D.
,
Otzen
,
J. F.
,
Joncquez
,
S.
, and
Stern
,
F.
,
2013
, “
EFD and CFD for KCS Heaving and Pitching in Regular Head Waves
,”
J. Mar. Sci. Technol.
,
18
(
4
), pp.
435
459
.
58.
Martić
,
I.
,
Degiuli
,
N.
,
Farkas
,
A.
, and
Gospić
,
I.
,
2020
, “
Evaluation of the Effect of Container Ship Characteristics on Added Resistance in Waves
,”
J. Mar. Sci. Eng.
,
8
(
9
), p.
696
.
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