7. WAVE AND CURRENT INDUCED LOADS
7.6 Steady current loads
7.6.1.1 A steady current gives rise to a steady force in the hor-
izontal plane and a yaw moment. The moment about a horizon- tal axis may also be of importance. Empirical formulae are most often used to calculate current forces and moments on offshore structures. The forces and moments are normally a function of the current velocity squared given in the general form
where C is an empirical current coefficient, and Uc is the cur-
rent velocity. The current coefficients can be established by model tests, either in wind tunnel or water basin/towing tank. If the current forces are important, it is recommended to per- form model tests.
The current loads increase in shallow water. Proximity effects should be accounted for.
The current coefficients in surge and sway can be used to include damping on the hull by using the relative velocity between water and structure to calculate the forces.
The influence of current on the mean wave drift force is dealt with in 7.4.5.
The current may induce vortex induced motions (VIM) of a floater. VIM is dealt with in Ch.9.
The viscous current loads are similar to the viscous wind loads. A discussion on current loads on offshore structures is given in Faltinsen (1990).
7.6.2 Column based structures
7.6.2.1 Viscous current forces on offshore structures that con-
sist of relatively slender large volume structural parts can be calculated using the strip-theory approximation. Although these structures are classified as large-volume structures rela- tive to the incoming waves, they may be treated as slender structures for prediction of pure current loads. This applies for instance to columns and pontoons of semi-submersibles and of TLPs.
7.6.2.2 The current velocity is decomposed into one compo-
nent UcN in the cross flow direction of the slender structural
part and one component in the longitudinal direction. The lat- ter component causes only shear forces and is usually neglected. The cross flow velocity component causes high Reynolds number separation and gives rise to an inline drag force
where Cdis the sectional drag coefficient and D is the diame-
ter.
7.6.2.3 There may be hydrodynamic interaction between
structural parts. If a structural part is placed in the wake behind another part, it will experience a smaller drag coefficient if the free stream is used to normalize the drag coefficient. Such cur- rent blockage effects should be considered when calculating the steady current forces. More details can be found in Ch.6 on Wave and current forces on slender structures.
t i j i j N j i i WA j i e H a a t q (2 ) ( ) , ) 2 ( ) , ( Re ) (
2 c U C F 2 2 1 cN d N c C DU F
7.6.3 Ships and FPSOs
7.6.3.1 For moored ship-shaped structures, it is common to
represent current forces in surge, sway and yaw by empirical global current coefficients, given as a function of the current heading
The coefficients Ci can be estimated based on acknowledged
published or in-house data for similar ships scaling to the size of the current ship. This will normally give sufficiently accu- rate forces. For instance, for Very Large Crude Carriers (VLCCs), a well established set of coefficients are published by OCIMF (1994). However, these coefficients should be used with care for other structures.
The horizontal current forces can also be estimated as described below.
7.6.3.2 The drag force on an FPSO in the longitudinal direction
is mainly due to skin friction forces and it can be expressed as
where S is the wetted surface. The drag coefficient is a function
of the Reynolds number Re and the angle between the current
and the longitudinal axis of the ship, see Hughes (1954).
7.6.3.3 The transverse current force and current yaw moment
on an FPSO can be calculated using the cross flow principle. The assumption is that the flow separates due to cross flow past the ship, that the longitudinal current components do not influ- ence the transverse forces on the cross-section, and that the transverse force on a cross-section is mainly due to separated flow effects. The transverse current force on the ship then can be written as
where the integration is over the length of the ship. CD(x)
above is the drag coefficient for flow past an infinitely long cylinder with the cross-sectional area of the ship at position x. D(x) is the sectional draught.
7.6.3.4 The viscous yaw moment due to current flow is simply
obtained by integrating the moments due to sectional drag forces along the ship. It is important to note that the yaw moment has an additional inviscid part, called the Munk moment,
where Uc is the current velocity in a direction with the x-axis
and A11 and A22 are the added mass coefficients in the x- and y-directions. For a ship with transom stern A22 in the formula
above shall be substituted by
where xstern is the position of stern and
is the 2D added mass of the stern section. x is measured from
the position of the moment point.
References
1) Aranha, J. A. P. (1994): “A formula for wave damping in the drift of floating bodies”. J. Fluid Mech., Vol. 275, pp. 147-55. 2) Chakrabarti, S.K. (1987): “Hydrodynamics of Offshore
Structures”. Springer Verlag.
3) Chakrabarti, S.K. (1990): “Nonlinear Methods in Offshore Engineering”. Developments in Marine Technology, 5. Elsevier Science Publishers B.V.
4) Dev, A.K. and Pinkster, J.A. (1997) “Viscous Mean and Low Frequency Drift Forces on Semisubmersibles”. Proc. Vol. 2, 8th BOSS Conf., Delft, The Netherlands, pp. 351-365.
5) Faltinsen, O.M. (1990): “Sea Loads on Ships and Offshore Structures”, Cambridge University Press.
6) Faltinsen, O.M., Newman, J.N., Vinje, T., (1995), Nonlin- ear wave loads on a slender vertical cylinder, Journal of Fluid Mechanics, Vol. 289, pp. 179-198.
7) Finne, S., Grue, J. and Nestegård, A. (2000) “Prediction of the complete second order wave drift damping force for offshore structures”. 10th ISOPE Conference. Seattle,
WA, USA.
8) Haslum, H. A. and Faltinsen O. M, “Alternative Shape of Spar Platforms for Use in Hostile Areas”, OTC 1999. 9) Herfjord, K. & Nielsen, F.G., “A comparative study on
computed motion response for floating production plat- forms: Discussion of practical procedures.”, Proc. 6th. International Conf. Behaviour of Offshore Structures (BOSS '92), Vol. 1, London, 1992.
10) Hughes, G. (1954) “Friction and form resistance in turbu- lent flow, and a proposed formulation for use in model and ship correlation”. Transaction of the Institution of Naval Architects, 96.
11) Kim, M-S., Ha, M-K. and Kim, B-W. (2003): “Relative motions between LNG-FPSO and side-by-side positioned LNG carriers in waves”. 13th ISOPE Conference, Honolulu. 12) Kim, S., Sclavounos, P.D. and Nielsen, F.G. (1997) “Slow-drift responses of moored platforms”. 8th Int.
BOSS Conference, Delft.
13) Krokstad, J.R., Stansberg, C.T., Nestegård, A., Marthin- sen, T (1998): “A new nonslender ringing load approach verified against experiments”. Transaction of the ASME, Vol. 120, Feb. 1998
14) Lee, C.-H. and Sclavounos P.D. (1989) “Removing the irregular frequencies from integral equations in wave- body interactions”. Journal of Fluid Mechanics, Vol. 207: pp. 393-418.
15) Lee, C-H., Maniar, H. and Zhu, X. (1997) “Computationas of wave loads using a B-spline panel method”. Proc. of 21st
Symp. on Naval Hydrodynamics. Trondheim, Norway. 16) Molin, B. (1994): “Second-order hydrodynamics applied
to moored structures. A state-of-the-art survey”. Ship Technology Research, Vol. 41, pp. 59-84.
17) Molin, B. (2001) “On the piston and sloshing modes in moonpools”. J. Fluid Mech, Vol.430. pp. 27-50.
18) Newman, J.N. (1974): “Second Order, Slowly Varying Forces in Irregular Waves”. Proc. Int. Symp. Dynamics of Marine Vehicles and Structures in Waves, London. 19) Newman, J.N. (1977) “Marine Hydrodynamics”. MIT Press. 20) Newman, J.N., & Lee, C.-H., “Sensitivity of wave loads to the discretization of bodies.”, Proc. 6th. Conf. on the Behaviour of Offshore Structures (BOSS '92), Vol. 1, London, 1992.
21) Newman, J.N. (1994) “Wave effects on deformable bod- ies,” Applied Ocean Research, 16, 1, pp. 47-59.
2 6 , 2 , 1 6 , 2 , 1 ( ,Uc) C ( )Uc F
)
,
(
2
1
2
d
R
C
SU
F
cx
c d e | sin | sin ) ( ) ( 2 1 2 c L D cy dxC x D x U F
) ( sin cos 11 22 2 A A U Mc c D stern sternA x A22 222, D stern A222,22) NORSOK Standard N-003 (2004) “Action and action effects”. 23) OCIMF (Oil Companies Int. Marine Forum) (1994) “Pre- diction of wind and current loads on VLCCs”. 2nd Edition.
24) Sarpkaya, T. and Isaacson, M. (1981) “Mechanics of Off-
shore Structures”. Van Nostrand Reinhold Company. 25) Stansberg, C.T., Yttervik, R. and Nielsen, F.G. (1998)
“Wave Drift Forces and Responses in Storm Waves”. OMAE’98.