First in case of Fig. 10 indicating the deep water, slight difference is noted, but relatively good agreement is seen. However in case of H/d = 1.5 where the water depth is relatively shallow, the tendency is quite different from the one in case of the deep water. Especially in case that S < 3.0, disagreement is noted. That is to say, it is almost impossible to align the lateral force by means of exclusively the lateral moving distance.

　

 As a method to express the transitional lateral force quantitatively, modeling of the transitional lateral force coefficient is attempted by introducing the concept of "circulation" as a variable closely related with the magnitude and development of the vortex surrounding the hull. From the fact that the velocity of the separated vortex is in proportion to the lateral moving velocity Uo of the hull, a circulation shown below is hereby considered by substituting as a the lateral moving velocity for the velocity of the separated vortex and by substituting the distance from the hull surface to the vortex for the lateral moving distance of the hull¹¹⁾.

　

Γ = ∫uds ∝∫U²0dt　(3)

　

 The transitional lateral force coefficient obtained by taking the equation shown above is shown in Fig. 12 and 13. They comply with the lateral coefficient in case that H/d is 7.0 and 1.5, respectively. Comparing the above figures with Fig. 10 and 11 obtained taking up the lateral moving distance, it is known that it is possible to use circulation in case of both the deep water and the shallow water. However in case of the shallow water (Fig. 13), the one exclusively with NDA 0.5 becomes smaller than the other ones in the vicinity of Γ≒0.5. By using the circulation obtained by multiplying the lateral moving velocity of the hull with its moving distance, it is considered that modeling of the lateral force coefficient ranging from a resting state to uniform movement has become possible. Investigation for modeling to describe the transitional lateral force coefficient of real ship except Wigley is required using an idea of the circulation in future.

　

　

　

 By applying the 3-dimensional CFD method to the Wigley hull, unsteady hydrodynamic force has been obtained. A summary of the results obtained in this study is as follows:

　

　

　

　

　

 These results in the research are useful information for safe ship operation, and are applicable to ship-handling simulators, structure strengthening of berths, design of fenders, rational assessment of required horse power of tugboats, etc.

　

[1] Lee, Y. S., Sadakane, H. and Toda, Y "Hydrodynamic Forces Acting on a Ship Hull Under Lateral Low Speed Motion II ", Journal of the Japan Institute of Navigation, No. 102, pp. 87-95, 2000.

[2] Sadakane, H. "A Study on Lateral Drag Coefficient for Ship Moving Laterally from Rest", Journal of the Japan Institute of Navigation, No. 95, pp. 193-200, 1996.

[3] Chen, M. and Chen, H. C. "Numerical Simulation of Transitional Flows Induced by a Berthing Ship", International Journal of Offshore and Polar Engineering, ISOPE, Vol. 7, N0.4, pp. 277-284, 1996.

[4] Toda, Y., Lee, Y.S . and Sadakane, H. "Hydrodynamic Forces Acting on a Ship Hull Under Lateral Low Speed Motion III : Basic Consideration Using 3-D CFD Technique", Journal of the Japan Institute of Navigation, No, 106, pp. 87-95, 2002 .

[5] Toda, Y., Lee, Y. H. and Sadakane, H. "Numerical Investigations of Hydrodynamic Forces Acting on a Ship Hull under Lateral Low Speed Motion", Journal of the kansai society of naval architects, No. 238, pp. 77-83, 2002.

[6] Takakura, Y., Ogiwara, S. and Isiguro, T. "Turbulence Models for Transonic Viscos Flow", AIAA paper, 89-1952 CP, 1989.

[7] Watanabe, O., Ming, Z. and Miyata, H. "Numerical Simulation of a Viscous Flow with Free-Surface Wave about a Ship by a Finite-Volume Method", Journal of The Society of Naval Architects of Japan, No. 171,pp.27-39, 1992.

[8] Patel, V.C, Chen, H.C. and Ju, S. "Ship Stern and Wake Flows : Solutions of the Fully-Elliptic Reynolds-Averaged Navier-Stokes Equations and Comparisons with Experiments", Journal of Computational Physics, Vol. 88, N0.2, pp. 305-336, 1990.

[9] Tahara,VY. "Computation of Viscous Flow around Series 60 Model and Comparison with Experiments", Journal of The Kansai Society of Naval Architects, N0.220, pp. 29-47, 1993.

[10] Chen, H.C. and Korpus, R. "A Multi-block Finite-Analytic Reynolds-Averaged Navier-Stokes Method for 3D Incompressible Flows", Individual Papers in Fluid Engineering, edited b F. M. White, ASME FED-Vol. 150, ASME Fluids Engineering Conference, pp. 113-121, 1993.

[11] Lee, Y.VS. "A Study on the Maneuvering Hydrodynamic Forces for Berthing Using CFD Technique", Ph. D. Thesis, Dept. Maritime Science, Kobe University of Mercantile Marine, 2003 .

Yun-Sok LEE

　

Yasuyuki TODA

Hiroyuki SADAKANE