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Fig.9. 
Sway-force and yaw-moment comparison between double-body solution, free-surface solution, and experimental results. Head-on ship motions. Relative Froude number: 0.67. Ship separation: Yo/Bo=1.6.
 
Fig.10: 
Sway-force and yaw-moment comparison between present solution with and without trim and sinkage, and experimental results. Head-on ship motions. Relative Froudenumber: 0.67. Ship separation: Yo/Bo=1.6.
 
Fig.11: 
Sway-force and yaw-moment comparison between present solution with no-penetration and zero gradient boundary conditions on the channel walls, and experimental results. Head-on ship motions. Relative Froude number: 0.67. Ship separation: Yo/Bo=1.6.
 
5.CONCLUDING REMARKS
 In this paper, the unsteady chimera RANS method has been validated against some available experimental measurements and employed to study the ship-ship interaction problems. In the study, the time-domain sway-force and yaw-moment results track the experimental measurements very well, even though there are minor differences in the settings of the numerical study and the original experiments. It is also shown that the effect of the sinkage and trim of the own ship do not significantly change the interaction force and moment. Other interesting findings include the importance of the presence of the free surface and the influence of the wall boundary condition on the results.
 
 For safe operation of a ship while operating in the proximity of other ships and near obstacles, accurate interaction forces and moments acting on the ships are required. At the current time, this vital information is typically obtained from extrapolation of model-test data and from operator's experiences over the years. Very few systematic and reliable data exist at the full scale. Advanced physics-based computational methods make possible to modelactual viscous-flow phenomena at a level not previously possible. The current computation method offers the ability of modeling complex ship geometry, multiple ships operating in the proximity of each other, and near obstacles. In addition, computations can be done at full-scale Reynolds number where the viscous effects on the ships are Although a great deal of improvenments and further studies are still required, the results presented in this paper clearly demonstrate the potential of using the chimera RANS method for ship-ship interaction and navigation channel-design related problems
 
REFERENCES
[1]H.C. Chen. and V.C. Patel, "Near-Wall Turbulence Models for Complex Flows Including Separation," AIAA Journal, Vol. 26, No 6, pp. 641-648,1988.
[2]H.C. Chen. and V.C. Patel, and S. Ju,, "Solutions of Reynolds-Averaged Navier-Stokes Equations for Three-Dimensional Incompressible Flows," Journal of Computational Physics, Vol. 88, No. 2, pp. 305-336,1990.
[3]H.C. Chen, and R. Korpus, "A Multi-block Finite-Analytic Reynolds-Averaged Navier-Stokes Method for 3D Incompressible Flows," ASME FED-Vol. 150, pp. 113-121, Proceedings of the ASME Fluids Engineering Conference, Washington, D.C., June 20-24,1993.
[4]H.C. Chen, and M. Chen, "Chimera RANS Simulation of a Berthing DDG-51 Ship in Translational and Rotational Motions," International Journal of Offshore and Polar Engineering, Vol. 8, No.3,pp. 182-191,1998.
[5]H.C. Chen, T. Liu, E.T. Huang, and D.A. Davis, "Chimera RANS Simulation of Ship and Fender Coupling for Berthing Operations," International Journal of Offshore and Polar Engineering, Vol. 10, No. 2, pp.112-122,2000.
[6]H.C. Chen, T. Liu, and E.T. Huang, "Time-Domain Simulation of Large Amplitude Ship Roll Motions by a Chimera RANS Method," International Journal of Offshore and Polar Engineering, Vol. 12, No. 3, pp. 206-212,2002.
[7]H.C. Chen, T. Liu, K.A. Chang, and E.T. Huang, "Time-Domain Simulation of Barge Capsizing by a Chimera Domain Decomposition Approach," Proceedings of the 12th International Offshore and Polar Engineering Conference, KitaKyushu, Japan, May 26-31,2002.
[8]H.C. Chen, W.M. Lin, W.Y. Hwang, "Validation and Application of Chimera RANS Methods for Ship-Ship Interactions in Shallow Water and Restricted Waterway," in Proceedings of 24th Symposium on Naval Hydrodynamics, Fukuoka, Japan, 8-3 July 2002.
[9]I.W. Dand, 1981, "Some Measurements of Interaction Between Ship Models Passing on Parallel Courses," National Maritime Institute, R108,1981.
[10]N.E. Suhs, and R.W. Tramel, "PEGSUS 4.0 Users Manual," Report AEDC-TR-91-8, Arnold Engineering Development Center, Arnold Air Force Station, TN, 1991.
 
AUTHOR'S BIOGRAPHY
 Dr. Hamn-Ching Chen is a Professor of Civil and Ocean Engineering at Texas A&M University. He received his B.S. (1976) and M.S. (1978) degrees in Power Mechanical Engineering from National Tsing Hua University, Taiwan, and his Ph.D. degree in Mechanical Engineering from The University of Iowa. Before joining Texas A&M, he was a Research Scientist at Iowa Institute of Hydraulic Research from 1982 to 1988, and a Senior Research Scientist at the Marine Hydrodynamics Division of Science Applications International Corporation from 1988 to 1990. He served as the Chair of ASCE Turbulence Committee and Associate Editor of Journal of Engineering Mechanics from 2000 to 2002, and is currently an Associate Editor of ASCE Journal of Waterway, Port, Coastal and Ocean Engineering. His research interests are in the development of numerical methods and turbulence models for applications involving submarines, ship berthing operations, ship-ship interactions, bridge pier scour, channel migration, body-wave-current interactions around coastal and offshore structures, and internal and film cooling of turbine blades.
 
 Dr. Woei-Min Lin is the Manager of SAIC's Ship Technology Division. He holds a B.S. Degree in Naval Architecture and Marine Engineering (1977) from the National Cheng-Kung University, Taiwan; M.S. (1982) and Ph.D. (1985) in Ocean Engineering from the Massachusetts Institute of Technology; and an M.S. in Electrical Engineering (1990) and an M.S. in Technical Management (1990) from the Johns Hopkins University. Dr. Lin has 25 years of experience in theoretical and computational fluid dynamics related to marine vehicles. Dr. Lin is a member of SNAME and ASNE.
 
 Dr. Daniel Liut is a Senior Engineer at Science Applications International Corporation Ship-Design division. He graduated from the Argentine Naval Academy in 1984. In 1989, he obtained a B.S. degree in Aerospace Engineering at Universidad del Aire, Córdoba, Argentina. After retiring from the Navy (1995), Dr. Liut worked in different projects for ship design and control at Virginia Polytechnic Institute & State University (USA), leading to a M.S. (1994) and Ph.D. (1999) degrees. At SAIC, Dr. Liut has worked in different assignments, such as slamming-effect studies, finite-volume developments for green-water-on-deck prediction, and finite-analytical Navier-Stokes research for different projects, such as sailing-boat design for the One World team for the America's Cup.
 
 Dr. Wei-Yuan Hwang is the Applied Research Program Manager at the Department of Information Technology, USMMA. His work includes the development, execution and coordination of research projects, applications of computer simulation, and math modeling. He also assists in promoting and supporting teaching and learning through enabling technologies. He received Ph.D. (1980) in Ocean Engineering from Massachusetts Institute of Technology, B.S. (1972) in Mechanical Engineering from National Taiwan University, and a Technology Management Certificate (1985) from Polytechnic Institute of New York. He is a member of SNAME and serves on H-10 Ship Controllability Panel.







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