Computations of Nonlinear Surge Motions of Tension Leg Platforms
Authors: Salvesen Nils , von Kerczek Christian H. , Vue Dick K. , Stern Frederick 
Published: October 2008

ABSTRACT
A new computational method for predicting the surge motions of tension legplatforms (TLP?s) due to wind, current and wave excitation is presented. Thesecond-order wave-drift forces as well as the linear hydrodynamic coefficientsand the wave-induced exciting forces are computed by a three-dimensional hybridfinite-element method. A new formula for predicting the viscous drag forces ispresented. Both the new and the conventional Morison drag formulas are used ina time-domain computation procedure to predict the nonlinear surge motions fora given TLP configuration. The surge displacement components are presented fora maximum design-wave condition and for the maximum wave-drift condition. It isshown that the new drag formula predicts smaller values of steady surgedisplacements and larger values of slowly-varying amplitudes than Morison'sdrag formula. This difference indicates that the Morison drag formula probablyover predicts the additional viscous forces due to interactions betweencurrent, wave-frequency motions and slowly-varying motions. The results showthat the maximum values of surge displacement are larger at the maximumwave-drift condition than at the maximum design-wave condition.

INTRODUCTION
The pretension vertical mooring system used for the TLP practically eliminatesthe heave motions. The surge motions, on the other hand, may be fairly large. Also, the additional tensions in the tendons that are due to the effects ofwind, current and wave excitation are important considerations in the design ofTLP?s. In order to reduce the surge motions and the additional tension in thetendons, TLP?s are designed in a manner that their natural periods of surge andheave are considerably outside the range of the period where the wave energy isa maximum. Typically, the surge natural period of the TLP is about 100 seconds, and the heave natural period is about three seconds. However, since the waveradiation damping is nearly zero at these periods, large surge motions andlarge additional tendon tension may arise even with fairly small amplitudeexcitations if the periods of these excitations are close to the naturalperiods of the TLP. Both second-order wave-drift and unsteady wind forces cancause surge excitations at periods close to 100 seconds. Second-order (doublefrequency) wave springing excitation will introduce vertical excitations atperiods close to three seconds. Unfortunately, very little is known about themagnitude of the wave-springing forces. In this paper attention is focused onthe prediction of the maximum surge displacement due to wind, current and waveexcitations.
A new computational method is presented here for predicting the nonlinear surgemotions for TLP?s. The computations consist of three main parts:potential-flow computations;viscous-force predictions; andnonlinear time-domain surge computations.
The potential-flow calculations are performed first by a three-dimensionalhybrid-finite-element method. The added mass, the wave-damping coefficients, the linear wave-exciting forces and the second-order wave drift forces arecomputed by the finite-element method. These quantities are then used as inputfor the nonlinear time-domain surge-motion computations.