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A new equation for calculating wave loads on offshore structures

Published online by Cambridge University Press:  26 April 2006

R. C. T. Rainey
R. C. T. Rainey
Affiliation:
WS Atkins Engineering Sciences, Woodcote Grove, Epsom, Surrey KT18 5BW, UK
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Abstract

This paper derives an equation for the potential-flow wave loading on a lattice-type offshore structure moving partially immersed in waves. It is for the limiting case of small lattice-member diameter, and deals entirely in member-centreline fluid properties, so that it can be applied computationally by a simple ‘stick model’ computer program. This field is currently served by a simple two-term semiempirical formula ‘Morison's equation’: the new equation is effectively a replacement for the Morison inertial term, allowing the Morison drag term (or some refinement of it) to describe exclusively the effects of vorticity, which can in principle be calculated to greater accuracy when isolated in this way.

The new equation calculates the potential-flow wave load accurate to second order in wave height, which is a great improvement on ‘Morison's equation’: such results can currently only be sought by very much more complicated and computationally intensive methods, of currently uncertain repeatability. Moreover the third-order error is localized at the free-surface intersection, so the equation remains attractive for fully nonlinear problems involving intermittent immersion of lattice members, which are currently beyond even the most sophisticated of these computationally intensive methods. It is shown that the primary reason for this large contrast in computational efficiency is that the loads are derived from energy considerations rather than direct integration of surface pressures, which requires a lower level of flow detail for a given level of load-calculation accuracy.

These improvements must of course be seen against the current levels of uncertainty over the calculation of vorticity-induced loads, which in many applications completely dwarf inaccuracies in potential-flow load calculation. The conditions are accordingly established under which the improvements are comparable to the total wave load predicted by the Morison drag and inertia terms in combination. They are that the lattice member diameter is greater than its length/10, or the relative fluid motion/5, or the structure's motion radius/20, or the wavelength/30: if any one of these conditions is satisfied, the new equation is worthwhile even when used in combination with simple vorticity-induced load calculations from a Morison drag term.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 204 , July 1989 , pp. 295 - 324
Copyright
© 1989 Cambridge University Press

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References

Angwin, J.: 1986 Results of a joint semisubmersible/submersible wave drift force project. Proc. Intl Symp. on Developments in Deeper Waters, vol. 1, paper 12. London: Royal Institution of Naval Architects.
Batchelor, G. K.: 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Eatock-Taylor, R. & Hung, S. M. 1985 Wave drift enhancement effects in multi-column structures. Appl. Ocean Res. 7, 128–137.Google Scholar
Eatock-Taylor, R. & Jefferys, E. R. 1986 Variability of hydrodynamic load predictions for a tension leg platform. Ocean Engng 13, 449–490.Google Scholar
Havelock, T. H.: 1940 The pressure of water waves upon a fixed obstacle. Proc. R. Soc. Lond. A 175, 409–421.Google Scholar
Isaacson, M. de St. Q. 1979 Nonlinear inertia forces on bodies. J. Waterway Port, Coastal Ocean Div. ASCE 105 (WW3), 213–227.Google Scholar
Isaacson, M. de St. Q. 1982 Nonlinear-wave effects on fixed and floating bodies. J. Fluid Mech. 120, 267–281.Google Scholar
John, F.: 1950 On the motion of floating bodies, II: Simple harmonic motions. Comm. Pure Appl. Maths 3, 45–101.Google Scholar
Korsmeyer, F. T., Lee, C.-H., Newman, J. N. & Sclavounos, P. D. 1988 The analysis of wave effects on tension leg platforms. Proc. OMAE Conf., Houston, paper 88–611. New York: Soc. Naval Arch. & Mar. Eng.
Lamb, H.: 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Lighthill, M. J.: 1960 Note on the swimming of slender fish. J. Fluid Mech. 9, 305–317.Google Scholar
Lighthill, M. J.: 1979 Waves and hydrodynamic loading. Proc. 2nd Intl Conf. on the Behaviour of Offshore Structures, vol. 1, pp. 1–40. Cranfield: BHRA Fluid Engineering.
Lighthill, M. J.: 1986a An Informal Introduction to Theoretical Fluid Mechanics. Clarendon.
Lighthill, M. J.: 1986b Fundamentals concerning wave loading on offshore structures. J. Fluid Mech. 173, 667–681.Google Scholar
Longuet-Higgins, M. S. & Cokelet, E. D. 1976 The deformation of steep surface waves on water, I: A numerical method. Proc. R. Soc. Lond. A 350, 1–26.Google Scholar
MacCamy, R. C. & Fuchs, R. A., 1954 Wave forces on piles: a diffraction theory. Tech. Memo. 69. Washington: US Army Corps of Engineers Beach Erosion Board.
McIver, P.: 1987 Mean drift forces on arrays of bodies due to incident long waves. J. Fluid Mech. 185, 469–482.Google Scholar
Mavrakos, S. A.: 1988 The vertical drift force and pitch moment on axisymmetric bodies in regular waves. Appl. Ocean Res. 10, 207–218.Google Scholar
Milne-Thomson, L. M.: 1968 Theoretical Hydrodynamics, 5th edn. Macmillan.
Miloh, T.: 1984 Hamilton's principle, Lagrange's method and ship motion theory. J. Ship Res. 28, 229–237.Google Scholar
Munk, M. M.: 1936 Aerodynamics of Airships, div. Q. In Aerodynamic Theory vol. vi, (ed. W. F. Durand). Springer.
New, A. L., McIver, P. & Peregrine, D. H., 1985 Computations of overturning waves. J. Fluid Mech. 150, 233–251.Google Scholar
Peregrine, D. H., Cokelet, E. D. & McIver, P., 1980 The fluid mechanisms of waves approaching breaking. Proc. 17th Conf. Coastal Engng, pp. 512–528. ASCE.
Pinkster, J. A.: 1979 Mean and low frequency wave drifting forces on floating structures. Ocea Engng 6, 593–615.Google Scholar
Rainey, R. C. T.: 1984 A New Equation for Calculating Wave Loads on Offshore Structures. Montreal: Transport Canada Library, ref. 83186214 QC 157 R26.
Rainey, R. C. T.: 1986 A new theory and its application for stability criteria covering waveinduced tilt phenomena on semi-submersibles. Proc. Intl Conf. Stationing and Stability of Semisubmersibles, pp. 41–59. London: Graham & Trotman.
Sarpkaya, T. & Isaacson, M. de St. Q. 1981 Mechanics of Wave Forces on Offshore Structures. Van Nostrand Reinhold.
Standing, R. G., Dacunha, N. M. C. & Matten, R. B. 1981 Mean wave drift forces: theory and experiment. Rep. OT-R-8175. London: Department of Energy.
Taylor, G. I.: 1928a The energy of a body moving in an infinite fluid, with an application to airships. Proc. R. Soc. Lond. A 120, 13–21.Google Scholar
Taylor, G. I.: 1928b The forces on a body placed in a curved or converging stream of fluid. Proc. R. Soc. Lond. A 120, 260–283.Google Scholar
Thompson, J. M. T. & Stewart, H. B. 1986 Non Linear Dynamics and Chaos. Wiley.
Vinje, T. & Brevig, P., 1981 Numerical calculations of forces from breaking waves. Proc. Intl Symp. on Hydrodynamics in Ocean Engng, pp. 547–566. Trondheim: Norwegian Hydrodyn. Labs.
Wehausen, J. V. & Laitone, E. V., 1960 Surface Waves. In Handbuch der Physik, vol. 9, pp. 446–778. Springer.
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