An investigation into the hydrodynamic analysis of vessels with a zero or forward speed

Abstract

The occurrence of irregular frequencies is known to affect the prediction of hydrodynamic coefficients, whether a rigid body or hydroelasticity analysis is used. For conventional ship-like structures, these irregular frequencies lie outside the range of practical interest for rigid body motions. On the other hand, for a large ship-like offshore structure, such as a Floating Production, Storage and Offloading unit (FPSO), the irregular frequencies are in the range of practical interest. Furthermore, they can create difficulties for the analysis of vessels treated as flexible bodies and of multi-hulled vessels. In these cases, distinguishing between genuine physical effects (e.g. wave interaction between hulls) and that of irregular frequencies is important.

The aim of this paper is twofold: first, elimination of irregular frequencies for the zero-forward-speed case and, second, improvement in predictions for the forward-speed case through a more accurate evaluation of the waterline integral term. Although the investigations are illustrated for rigid hulls, namely a rectangular box and a Series 60 hull, the methodology and its effects are equally valid for flexible hulls. For the zero-forward-speed case an extended boundary integral method (the lid method) is used, with the imaginary interior free surface placed approximately 0.1% below the mean free surface. It is confirmed that the lid boundary approach is an efficient and robust method for treating irregular frequencies for stationary rigid floating bodies experiencing low-frequency oscillations. For the forward-speed case a treatment of waterline integral terms is introduced, with reference to sources lying on the free surface. The applications highlight the importance of waterline integral terms which are shown to introduce oscillatory behaviour in the predicted hydrodynamic data. It is also shown that, for the forward-speed case, irregular frequencies do not occur; however, as the forward speed tends to smaller values, the hydrodynamic data exhibit oscillations which depend on the treatment of the waterline integral terms and the use of the direct potential or source distribution method. These methods are also suitable for hydroelasticity analysis with a forward speed.

Keywords

Seakeeping irregular frequency Series 60 hull form Green’s function waterline integral lid method

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References

Inglis

Price

. Irregular frequencies in three dimensional source distribution techniques. Int Shipbldg Prog 1981; 28: 57–62.

Price

. A multiple Green’s function expression for the hydrodynamic analysis of multi-hull structures. Appl Ocean Res 1986; 9(2): 58–66.

Hudson

Price

Temarel

. The occurrence of irregular frequencies in forward speed ship seakeeping numerical calculations. Ocean Engng 2011; 32: 235–247.

Bishop

RED

Price

. A general linear hydroelasticity theory of floating bodies in a seaway. Phil Trans R Soc A 1986; 316: 375–426.

Lee

Sclavounos

. Removing the irregular frequencies from integral equations in wave-body interactions. J Fluid Mech 1989; 207: 393–418.

Ogilvie

Shin

. Integral equation solutions for time dependent free surface problems. J Soc Nav Archit Japan 1978; 143: 43–53.

Ursell

. Irregular frequencies and the motion of floating bodies. J Fluid Mech 1981; 105: 143–156.

Ahmed

Hudson

Price

. Elimination of irregular frequencies in three-dimensional seakeeping predictions. In: International conference on ship and shipping research, Palermo, Italy, 24–27 June 2003, vol. II, pp. 7.1.1–7.1.11. Genoa: Associazone Italiana di Tecnica Navale.

Burton

Miller

. The application of integral equation methods to the numerical solution of some exterior boundary-value problems. Proc R Soc Lond A 1971; 323: 201–220.

10.

Lee

Newman

Zhu

. An extended boundary integral equation method for the removal of irregular frequency effects. Int J Numer Meth Fluids 1996; 23: 637–660.

11.

Yang

. On the singularities of Green’s formula and its normal derivatives, with an application to surface-wave-body interaction problems. Int J Numer Meth Engng 2000; 47: 1841–1864.

12.

Ohmatsu

. On the irregular frequencies in the theory of oscillating bodies. Papers Ship Res Inst, Tokyo, Japan 1975; 48: 1–13.

13.

Xia

Thiagarajan

Haritos

. Some discussion on evaluation of springing loads on tension leg platforms. In: Ocean engineering symposium, 19th international conference on offshore mechanics and Arctic engineering, New Orleans, Louisiana, USA, 2000, pp. 45–54. New York: ASME.

14.

Guilbaud

Boin

. Linearised free surface flow calculations by a panel method using the diffraction-radiation with forward speed Green function. In: 3rd international conference on computational fluid dynamics technology in ship hydrodynamics, London, UK, 6–7 February 2003, pp. 101–115. London: RINA.

15.

Cheetham

May

. Hydrodynamic analysis of ships side by side. In: 1st international aerospace CFD conference, Paris, France, 18–19 June 2007, 8pp.

16.

Hudson

Price

. Comparison of numerical evaluation techniques for the hydrodynamic analysis of a ship travelling in waves. Trans RINA 1999; 141: 236–258.

17.

Hudson

Price

. A validation study on mathematical models of speed and frequency dependence in seakeeping. Proc IMechE Part C: J Mechanical Engineering Science 2000; 214(1): 181–202.

18.

Bailey

Hudson

Price

. Comparisons between theory and experiment in a seakeeping validation study. Trans RINA 2001; 143: 45–78.

19.

Bruzzone

Gualeni

Sebastiani

. Applications of Green’s function methods to the seakeeping computations for high speed vehicles. In: 13th international conference on ships and shipping research, Venice, Italy, 19–22 September 2000, pp. 9.1.1–9.1.11. Comitato Organizzatore NAV2000.

20.

Hong

Lee

. Solution of the radiation problem by the B-spline higher order Kelvin panel method for an oscillating cylinder advancing in the free surface. J Ship Ocean Technol 2002; 6(1): 34–53.

21.

Maury

Delhommeau

. Comparison between numerical computations and experiments for seakeeping on ship models with forward speed. J Ship Res 2003; 47: 347–364.

22.

Wehausen

Laitone

. Surface waves. In: Flügge

(ed) Handbuch der Physik, vol. 9, part 3. Berlin: Springer, 1960, pp. 446–778.

23.

. Hydroelasticity of floating bodies. PhD Thesis, Brunel University, Uxbridge, Middlesex, UK, 1984.

24.

Iwashita

Okhusu

. The Green function method for ship motions. Ship Technol Res 1992; 39: 3–21.

25.

Bessho

. On the fundamental singularity in the theory of ship motions in a seaway. Mem Defence Acad Japan 1977; 17(3): 95–105.

26.

Chen

. Highly oscillatory properties of unsteady ship waves. Proc IMechE Part C: J Mechanical Engineering Science 2000; 214(6): 813–823.

27.

Noblesse

Yang

. Practical free-surface Green functions for wave diffraction-radiation with forward speed. In: 8th international conference on numerical ship hydrodynamics, Busan, Republic of Korea, 22–25 September 2003, pp. 46–58. Washington, DC: National Academies Press.

28.

Todd

. Some further experiments on single-screw merchant ship forms – Series 60. Trans SNAME 1953; 61: 516–589.

29.

Hudson

Price

Temarel

. Methods to reduce the effects of irregular frequencies in hydrodynamic analysis of vessels with forward speed. In: 8th international symposium on practical design of ships and other floating structures, Shanghai, People’s Republic of China, 16–21 September 2001, pp. 847–855. Amsterdam: Elsevier.

30.

Chen

Noblesse

. Super Green function. In: 22nd symposium on naval hydrodynamics, Washington, DC, USA, 9–14 August 1998, pp. 860–874. Washington, DC: National Academies Press.

31.

Gerritsma

Beukelman

. The distribution of the hydrodynamic forces on a heaving and pitching ship model in still water. In: 5th symposium on naval hydrodynamics, Bergen, Norway, 10–12 September 1964, pp. 219–257. Washington, DC: Office of Naval Research.

32.

van Leeuwen

. The lateral damping and added mass of an oscillating ship model. Report 23, Shipbuilding Laboratory, Delft University of Technology, Delft, The Netherlands, 1964.

33.

Iwashita

. Numerical seakeeping calculations based on the 3-D Green’s function method. Ship Technol Res 1997; 44(3): 111–132.

34.

Gerritsma

. Ship motions in longitudinal waves. Int Shipbldg Prog 1960; 7: 42–95.

35.

Gerritsma

Beukelman

. Comparison of calculated and measured heaving and pitching motions of a Series 60, C_b = 0.7 ship model in regular longitudinal waves. In: 11th international towing tank conference, Tokyo, Japan, 10–20 October 1966, pp. 436–445. Tokyo: Society of Naval Architects of Japan.