... NON·GAUSSIAN RANDOM LOADING P Koliopulos and E Yallmer Department of CIvil and MUnicipal Engmeermg University College London London, UK ABSTRACT Dynamical response analysis of tubular offshore platform structures to wave forces is considered. The non-Gaussianity of the response in terms of its coefficient...

... bi-frequency domain sum frequency frequency monochromatic wave mooring system equation upstream oil & gas surge response experiment dual wave subsea system coefficient drift force drift motion wave drift amplitude surge drift motion prediction excitation slow drift motion...

... pipe instabillty or buckling. This paper presents analytical methods for prediction of buckling potential, i.e. buckling load, length and amplitudes. The predicted behaviour will be presented as a function of geotechnical properties such as breakout resistance and an equivalent coefficient of friction...

... Abstract It has been recognized for some time that sinusoidal oscillatory flow experiments generate hydrodynamic force coefficients larger than those measured in a random sea environment. The present study investigates forces induced on cylinders by random oscillatory flows. The results show...

.... Significant results are the validation of the modelling program over a range of environmental conditions and the establishment of representative drag coefficients for sections of riser with distributed bluff-faced buoyancy modules. The need for an improved understanding of the drag characteristics...

... acceleration vector perpen- dicular to the cylinder at position r at the time t. Drag coefficient. Coefficient of inertia. Mass density of water. The normal vectors Un and Un can be ·expressed in terms of a unit vector with directional cosines s = (SI' 82, S3) along the cylinder axis as follows 135 [ ] Un(r, t...

... (leonard, 1979; Chiou, 1989). The advantage of using this method for solving a two-point boundary- value problem rather than a finite difference method is that large sets of matrix coefficients need not be generated, stored in the computer memory, and solved simultaneously. Only a small number...

...<eedmgs of the Fllst (1990) European OffshO/e Me(ham(s SymposIUm TlOndhelm, NO/way, 20-22 August 1990 CopYllght © 1990 by The IntelnatlOnal Souety ofOffshOle and Polar EngmeelS ISBN 0-9626104-4-5 NUMERICAL PREDICTION OF HIGHER ORDER WAVE INDUCED LOADS ON TETHERED PLATFORMS o G Nwogu and M Biram Hydraulics Laboratory, National Research CouncIl Ottawa, Canada ABSTRACT The high frequency vibration of the tendons of tension leg plat- forms (TLPs) with slender columns and pontoons is investi- gated in this paper. The equations for the two-dimensional rigid body motion of a TLP in heave, surge and pitch are solved in the time domain using a Runge-Kutta time-stepping procedure. The wave loads are computed using the relative velocity formulation of the Morison equation. High frequency tendon loading occurs at wave periods that are integer multi- ples of the platform heave and pitch periods. This is a result of different types of nonlinearities in the fluid loading. Here specifically, the contribution of two nonlinear effects are con- sidered: the effect of integrating the kinematics up to the free water surface and the effect of the nonlinear drag term of the Morison equation. The numerical results confirm the occur- rence of higher harmonic pitch motions predominantly due to free surface effects. 1. INTRODUCTION The tension leg platform is one of the leading concepts for oil production in deep waters. The vertical tethers or ten- dons which connect the platform to the seabed are kept in tension by the excess buoyancy of the platform. The large axial stiffness of the tendons results in natural frequencies for the heave, pitch, and roll motions well above the exciting wave frequencies. However, recent studies have shown that the high frequency modes of motion can be excited, leading to high fre- quency vibrations of the tendons or tendon ringing. While the variance of the high frequency component of the tendon force is often much smaller than that of the wave frequency compo- nent, a proper understanding of this phenomenon is required for an accurate estimation of the probability distribution of the extreme tendon tensions, and tendon fatigue life predictions. 265 Most previous investigations of tendon ringing phenomenon have assumed it to be due to second order wave loading effects (e.g. De Boom et al. (1984), and Petrauskas (1987 This clearly explains the occurrence of tendon vibrations caused by waves with periods twice the natural heave and pitch periods. However, high frequency tendon loads were observed in model tests of a TLP in irregular waves with peak periods up to five times the platform natural periods. This must be due to effects higher than second order. In the present paper, attention is focussed on platforms with column and pontoon diameters less than one-fifth of the short- est wavelength. The wave loads on the platform can thus be computed using the relative velocity formulation of the Mori- son equation. The nonlinear equations of motion are solved in the time domain. The contributions of two different nonlinear effects to the high frequency tendon force are investigated: 1. effect of integration of wave kinematics up to the free surface instead of the still water level; 2. effect of retaining the nonlinear drag damping term of the Morison equation. The platform motions and tether forces are initially computed for regular waves with the kinematics obtained using the Fourier approximation of Reinecker and Fenton (1981). An efficient time domain procedure is then used to compute the motions and forces in irregular waves. 2. EQUATIONS OF MOTION Consider the surge, heave, and pitch motions of a tethered platform due to long-crested waves propagating along the pos- itive x direction (see Figure 1). The equations of motion for Incident Waves - HEAVE SURGE x Figure 1. Definition sketch for platform motions. the platform can be written as MX+BX+KX=F(t) (1) where X = (XI,X2,X3 ) is the displacement vector with the subscripts 1, 2, 3 denoting surge, heave and pitch respectively, B is the structural and wave radiation damping matrix, K is the stiffness matrix due to hydrostatic and tendon restoring forces, and F is the exciting force vector. 2.1 Hydrodynamic Force Vector The wave loads on slender members of a structure can be com- puted using the relative velocity formulation of the Morison equation. The x and z components of the normal force acting on a segment of an arbitrarily inclined cylinder (see Figure 2) can be expressed as (2) where CM and CD are the inertia and drag coefficients respec- tively, Dc and Ac are the projected width and cross-sectional area of the cylinder, p is the density of water, and (u~x,u~z) and (unx , unz ) are the x and z components of the relative veloc- ity, u', and acceleration respectively, normal to the cylinder. If the cylinder is located between coordinates (Xt,Y1,Zl) and (X2' Y2, Z2) relative to the principal platform axes, then direc- tion cosines can be defined as follows: X2 - Xl Y2 - Y1 cos a = cosf3 = L L Z2 - zl cos, = --L- (3) 266 z y x Figure 2. Sketch of wave loading on an inclined cylinder. where (4) The components of the normal velocity and acceleration vec- tors are given by u = (u - ~1 - Z~3) si~22a - (w - ~2 + X~3)COS(HOS, I Unz = (w-X2 +xX3 )sm u-X1 -ZX3 )cosacos, Unx U sin2 a - to cos a cos, unz to sin2 , - U cos a cos, (5) where u, w and U, to are the horizontal and vertical water par- ticle velocities and accelerations respectively. The total hydrodynamic force on the platform is composed of a Morison type force on the cylindrical members and a force due to the hydrodynamic pressure acting on the corner mem- bers which connect the columns to the pontoons. In order to compute the forces (or moment), the cylindrical members of the TLP are first divided into N. segments. The kmematics are evaluated at the centroids of the segments, and then used to calculate the segment forces llFx and llFz . The forces due to the hydrodynamic pressure, p" acting on Ncm corner mem- bers are also evaluated. The total exciting force vector is thus given by N& Ncm L: llFx + L: p.An", 1=1 1=1 N& Ncm L: llF .. + L: p,Az .=1 ,=1 N, L:[IlFx.z. - llFZlx,j+ .=1 Nem Cp L: p,(Ax,z,n", - A .. x,) .=1 (6) where (XI> z.) are the coordinates of the centroid of the ith segment, A Az are the projected areas of the corner members in the X and Z directions, and n", = { +1 -1 members faC'ing -x direction members facing +x direction (7) and C" is an empirical pressure coefficient. The above compu- tation of the wave...

... bodies in the sea. The design of the majority of the offshore The Mor1son formulations have been applied structures for offshore petroleum drilling also for the case of constant drag and mass and product1on operations requ1res a careful coeffiCIents, when the wake veloc1tles which prediction...

... of floating structures. This time- domain motion analysis includes two types of motion equations for random waves; the equation to use constant hydrodynamic coefficients at a representative wave frequency and the equation to use convolu- tion integrals expressed with memory effect functions or retardation...

... (IS) as: 1 NOD a~I NOD Hii= - [ ! Aik -! Hik ~Ik+ I] i=I,2, .. NOD ~Ii k=I an k k=I k;i (20) which contains no singularity. Thus, this procedure also makes it possible to avoid the direct calculation of Ci in equation (16). We may now calculate the coefficient matrices H and A in eqs. (16) and (17) and solve...

... ABSTRACT Series of experiments was conducted variously in a towing tank, a flume am a wind tunnel to obtain steady flow coefficients for bluff-bodied workboat ROVs. The attributes of these different test facilities are contrasted, and it is suggested that variations in the coefficient values...

... by the dynamIC identification procedure. The following parameters were studied: i) Topside masses, ii) mass of the drilling rig, iii) added mass coefficient for the jacket, iv) added mass coefficient for the risers, v) thickness of marine growth, vi) enclosed water in the jacket legs, vii) stiffness matrix...

... to numerical modelling procedures and to assumptions made about the damping. When there was no current, the damping was affected by first-order velocities, and the damping coefficient by boundary layer forces and by the partial development of flow separation and vortex shedding at low Keulegan-Carpenter...

...-Carpenter numbers. Both reg- ular and random wave environments were simulated in the laboratory. The total wave forces on the cylinder were mea- sured using a sophisticated experimental arrangement. The hydrodynamic coefficients were computed using least-square- fit technique. The drag coefficients...

... Kaasen MARINTEK A/S Pel S TeIgen STATOIL, R&D Trondhelm, Norway Abstract Basically, two different methods exist for motion prediction of floating bodies, model tests and numerical simulations. Com- bining the two methods; using model test results to determine hydrodynanuc coefficients and to calibrate...

... with the bearing element submerged in artificial seawater, and the conduit cradle was painted with the glass flake epoxy system planned to be used inside ·the tether conduits. 247 Fig. 6: Photograph of the radial bearing test rig. Slip Test The purpose of this test was to establish the coefficient of friction...

... though some strong artificial damping had been introduced. The set-down in regular waves was reasonably well predicted by considering the submerged volume of the test cylinder. The results were analyzed by a force model of a Morison type, but with a simple buoyancy term added. The force coefficients were...

... of the time derivative skewness and kurtOSIs of the response respectively. ' A limit state IS defmed from the statistical moments of the response In order to model how these moments change With real- Izations of the basic variables, as e.g. significant wave height H. ' drag and mertla coeffiCients, structural...