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Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-016

... 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**of...
Abstract

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 of excess is predicted via the separability assumption. Further statistical information is generated implementing the mixture technique. Results are presented for the case study of two-degrees-of-freedom system. 1. INTRODUCTION The Morison-type fluid force is known to have a non-Gaussian probability distribution with thick tails (high kurtosis). If the equations of motion were quasi-static, the high kurtosis of the exciting force would pass unabated into the response. When the dynamics is taken into account, it is found that the motion becomes more Gaussian. This is beneficial in terms of the reliability analysis of offshore platform structures. For example, in the present study, where a range of dynamic responses were analysed, from the very resonant to the nearly quasi-static case, the response coefficient of excess (defined as kurtosis-3 always remained between 0.0 and 2.5 whereas the quasi-static response would have a coefficient of excess in the range 2.48 to 4.96. An exact method does exist for analysing the kurtosis, but it is too cumbersome to be undertaken routinely. In previous work a simplification of this task was proposed, and its performance was assessed. The previous study was valid for a 1 degree of freedom (1 DOF) system. Here, the method is extended to more than one DOF structures. Section 2 recalls the earlier 1 DOF relations and develops the new theory providing the formulation of the general N degrees of freedom problem. The predicted quantity is the 4th order statistical moment of the platform displacement; other response statistics such as level exceedance probabilities, distributions of maxima (envelope statistics) can be estimated subsequently, leading to probabilistic fatigue life evaluations.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-006

... linear diffraction theory. Theoretical calculations were made using experimentally determined mono- and bi-frequency domain wave drift damping

**coefficients**for the prediction of off-diagonal quadratic frequency response functions. Preliminary results indicate that predictions based on monochromatic wave...
Abstract

ABSTRACT The results of experimental measurements of the slowly varying surge motion of a soft moored rectangular barge in the bi-frequency domain are compared to numerical predictions based on a Volterra model and linear diffraction theory. Theoretical calculations were made using experimentally determined mono- and bi-frequency domain wave drift damping coefficients for the prediction of off-diagonal quadratic frequency response functions. Preliminary results indicate that predictions based on monochromatic wave drift damping underestimated experimental results, while those employing bi-chromatic wave drift damping provided better agreement. INTRODUCTION The response of large moored vessels and floating offshore structures to irregular seas is dominated by large amplitude, low frequency quadratic nonlinear motions. As the use of such soft mooring systems for deep water drilling, production and storage facilities is rapidly increasing, the development of more accurate numerical prediction tools, of which experimental verification is an integral part, becomes ever important. Dalzell (1976) conducted the first model tests to determine the quadratic frequency response function (OFRF) for added wave resistance in random seas. In addition, Dalzell developed a cross-bi-spectral method to estimate the OFRF for low frequency, second-order added resistance (drift force). OFRF I for added resistance was theoretically analyzed by Dalzell and Kim (1976) and applied to the prediction of surge drift motion of a moored ship in random head seas by Kim and Breslin (1976). Pinkster (1980) measured and calculated the OFRF for the drift force of vessels in head seas using Dalzell's method. Slow drift motion of a moored vessel in random waves has usually been predicted in the time domain by solving an, equation of motion using drift force and damping coefficients: estimated from theoretical or experimental studies using monochromatic waves. For instance, one such extensive theoretical and experimental time: domain investigation was conducted by Wichers (1987).

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-046

... vertical 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...
Abstract

ABSTRACT As subsea technology has developed, the use of satellite templates from marginal oil and gas fields has become more common. The connecting pipelines are usually buried in trenches in order to reduce the interference with activities such as fishing equipment, anchors, installation of cables and other offshore structures. However, experience shows that the burying itself may cause problems for the pipelines in operation due to high temperature of the transported oil or gas, inducing large axial stresses. These stresses may cause vertical pipe instability 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 between the pipe and the surrounding soil. The analytical models presented in the paper have been applied on the 9" Tommeliten-Edda North pipeline, which recently has experienced buckling type of behaviour. The calculation results show that the pipe should develop vertical buckling, with span lengths of 40–45 m and amplitudes of 4–6 m. It should further be expected buckling deformations to occur at an intermediate distance of 1.9–3.3 km. These analytical results correspond closely to the actual behaviour, which showed that the deformation pattern had a span length at seabed of 30 m and an amplitude of 5 m. INTRODUCTION Compression forces will be induced in pipelines by the restraint of axial extensions caused by temperature increases during oil/gas transportation. These forces may cause vertical buckling of a buried pipeline, Fig. 1. This buckling mode involves an overall column-type response without gross distortion of the pipeline cross-section. Analytical methods for prediction of vertical buckling behaviour, i.e. buckling load, length, amplitude and distance between adjacent but independent pipe deformations, are presented.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-011

... The Umverstty of Texas at Austm Austin, Texas, USA 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...
Abstract

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 that Cd and Cm differ from the values obtained under sinusoidal conditions by more than 30% to 40% in the inertia/drag regime of the Keulegan-Carpenter number. INTRODUCTION It has been known for some time that force coefficients obtained in periodic or sinusoidal oscillatory flow experiments are larger than those measured for cylindrical structures exposed to random wave-induced flows. However, physical understanding and modeling of hydrodynamic forces induced on circular cylinders has been accomplished to a large extent by sinusoidal oscillatory flow studies in the laboratory. These studies, such as Sarpkaya (1976, 1986), Williamson (1985) and Obasaju, et al, (1988), have identified the basic influence of changes in the fluid flow parameters on the hydrodynamic forces induced on the cylinder. Ikeda, et aI, (1988), oscillated cylinders in a tank and showed the strong influence of previously shed vortices on the inline force through measurement of the drag and inertia coefficients for Morison's equation. The present investigation examines the inline and transverse forces exerted on smooth circular cylinders under random oscillatory flow conditions. The forces in random oscillatory flow are directly compared to those induced under sinusoidal oscillatory flow conditions by focusing on experimentally measured force coefficients for the inline and transverse forces. The experiments were conducted in an experimental apparatus capable of generating either sinusoidal or random planar oscillatory flow. This latter study illustrates that, although results from sinusoidal experiments may not be directly applicable to random flow conditions, the fundamental understanding gained in these experiments can lend significant insight into interpretation and modeling of forces induced in random flows.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-052

.... 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 for such...
Abstract

ABSTRACT Results are presented of a comparison between the observed behaviour of two model flexible riser systems subject to environmental loads and simulated floating production system vessel motion, and the behaviour predicted using a flexible riser computer modelling program. 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 for such systems is identified. 1. INTRODUCTION This paper presents the results of a comparison between the observed behaviour of two model-scale flexible riser systems subject to environmental loads and simulated floating production system (FPS) vessel motion, and the behaviour predicted using C\ state-of-the-art flexible riser computer modelling program. The study was instigated by BP as a result of experiences gained on the concept design studies for a floating production, storage and offloading unit for BP's 23/26a North Sea field in 85m water depth. The development plan intended the use of a bow-moored tanker with turret and flexible risers. Originally thought to be an impractical concept for this water depth at the 20 year return storm condition, through extensive use of a computer modelling program for flexible risers and refinement of flexible riser design the concept was deemed feasible. Further work of an investigative nature, out with the main project, was thus undertaken. The primary objective of the work was to examine in detail the accuracy and modeling capabilities of the program. A secondary objective was to compare the behaviour of the two different riser systems under identical imposed loadings. Lightweight pipes were specifically chosen for the study since they were representative of elastomeric flexible pipe constructions and because they would ensure large deflections under hydrodynamic loading.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-017

... water particle 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...
Abstract

Abstract This paper concerns an investigation of the effects of nonlinearity of drag loading on offshore structures excited by 2D wave fields, where the nonlinear term in the Morison equation is replaced by an equivalent cubic expansion. The equivalent cubic expansion coefficients for the equivalent drag model are obtained using the least mean square procedure. Numerical results are given. The displacement response and the stress response processes obtained using the above loading model are compared with simulation results and those obtained from equivalent linearization of the drag term. 1. Introduction The loading imposed on structural members of an offshore structure subjected to wave action represents one of the major steps in design of deepwater bottom-supported structures. The wave loading is normally estimated using the well-known Morison equation for a member with dimensions such that the presence of the member does not significantly disturb the wave field. This paper concerns an investigation of the effects of nonlinearity of drag loading on offshore structures excited by irregular 2D wave fields, where the nonlinear term in the Morison equation is replaced by an equivalent cubic expansion. The structural system is modelled by a linear system with a finite number of degrees of freedom. A system reduction based on an eigenmode expansion is applied, where the frequency response matrix of the system is expressed in two terms, corresponding to the quasi-static contribution and the dynamic contribution, respectively. The first order wave theory is applied to relate the surface elevation with the local kinematics of water particles. The influence of the velocity of the structure is ignored in the drag term. It is assumed that the sea surface can be considered as a realization of a stationary zero-mean Gaussian process, which is also homogeneous in the horizontal space parameters.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-057

... (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 of...
Abstract

ABSTRACT In the design and analysis of multi-leg mooring systems, it is significant, but difficult, to determine the tensions in the mooring legs. The analysis is complicated primarily because of the nonlinear behavior of the cables. The equilibrium equations of the moored body are indeterminate if the number of mooring legs is more than the number of unconstrained degrees of freedom being considered at the moored body. In the presence of spatially variable sub-surface currents, it is generally not appropriate to approximate the cable behavior by catenary equation since the current-induced drag forces are both position- and orientation-dependent. A method based on direct spatial integration will be demonstrated for the nonlinear static analysis of three-dimensional multi-leg mooring system response to steady currents. INTRODUCTION A multi-leg mooring system, which is comprised of cables, anchors and the moored body, provides efficient restrain in all directions to the moored body by transmitting the forces on the cables and moored body to the anchors. Such a system has been employed in a wide variety of applications in the ocean (Nordell and Meggitt, 1981; Knapp, 1987). A few examples of multileg mooring systems include the systems used to restrain tension leg platforms and guyed towers for deepwater oil operations. A state-of-the-art review regarding the behavior of cables as mooring system components, the types and selection of cables, and the various classes of anchors and their applications was presented by Skop (1988). In the design and analysis of multi-leg mooring systems, it is significant, but difficult, to determine the tensions in the mooring legs. The analysis is complicated primarily because of the nonlinear behavior of the cables (Leonard, 1988). Due to this reason, some analyses of multi-leg mooring systems are based on the mathematical programming, i.e. optimization schemes.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-032

...<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...
Abstract

ABSTRACT The high frequency vibration of the tendons of tension leg platforms (TLPs) with slender columns and pontoons is investigated 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 multiples 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 considered: the effect of integrating the kinematics up to the free water surface and the effect of the nonlinear drag term of the Morison equation. 1. INTRODUCTION The tension leg platform is one of the leading concepts for oil production in deep waters. The vertical tethers or tendons 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 frequency 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 component, 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. 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)).

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-012

... 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 the...
Abstract

ABSTRACT An original applied study has been developed, concerning the analysis and the prediction of the hydrodynamic forces Which act upon arbitrarily oscillating bodies in the sea. The Morison formulations have been applied also for the case of constant drag and mass coeffiCIents, when the wake veloc1tles which are produced by the body motions in all the past histories are opportunely corrected; moreover the wake velocities have been here computed also on the basis of the unsteady turbulent theory, which is available from the existing literature. The predicted results have been compared with the experimental ones, coming from a deal of lab pendulum tests. The said tests have been performed both on single and on coupled cylinders, with particular care for the overall configuration cases and possibilities. Starting from the 1st case of square cylinders, the study has been after- wards generalized to the case of circular cylinders, more adequate - in many cases - to represent and to model the spatial and the physical reality. INTRODUCTION The design of the majority of the offshore structures for offshore petroleum drilling and product1on operations requ1res a careful prediction of the hydrodynamic forces Which act on their components. Many of them are, in most cases, members having circular and other cross sections, with their submerged parts frequently close to the free surface of the water. In Chung (1976) as far as the floating structures are concerned constant values of the added masses have been considered, and also zero wave damping values (obtained for an infinite fluid). Among the first Chung (1977) published real comparisons of experimental added masses and wave damping coefficients with theoretical coefficients computed by the Frank's method, showing that agreements are much better for circular cross sections, and better for heaving than for swaying motions.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-018

... offshore structure beam sea mooring system calculation frequency structural analysis response analysis storage barge

**coefficient**hydrodynamic analysis upstream oil & gas regular wave artificial intelligence rubber fender equation motion analysis morison equation PIOLeedmgs of the...
Abstract

ABSTRACT This paper presents an outline of a comprehensive program system developed by the authors, which includes many functions for response analysis of a wide variety of offshore structures. Typical calculated results by this system are also presented being compared with field measurements and model test data as well as calculations by the other analysis programs. Through the comparative calculations the validity and flexible applicability of the system have been confirmed and the results presented here may be valuable and useful for the designers and researchers of offshore structures. 1 INTRODUCTION Various analysis program packages for offshore structures have been developed by many companies and organizations in the world so far. Most of the existing program packages for floating offshore structures are composed of motion and structural analysis programs based on Hooft's method [Hooft, 1971]. In these conventIOnal program packages hydrodynamic analysis is based on the Morison equation and/or two-dimensional potential flow theory, and global structural analysis IS executed by using spatial framework model, e.g., see [Akita et al, 1978). Recent remarkable progress of electronic computers, however, has enabled three-dimensional diffraction/radiation analysis to be in practical use and to be incorporated into a conventional analysis program package. This extends the applicability of analysis program and it may become possible to take into account three-dimensional effect of hydrodynamic loading, e.g., on massive structures such as floating artificial islands and floating crane semisubmersibles, on jackups under floating conditions, and on huge-scale barges with large breadth and shallow draft or m shallow waters. We recently completed a comprehensive computer program system in order to respond to diverse analytical problems of a wide variety of offshore structures. This new system, the integrated program system for offshore structures, is abbreviated to IPOS in this paper.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-008

... calculate the

**coefficient**matrices H and A in eqs. (16) and (17) and solve for velocity potential ~ from eq. (15), where (a~/an)k represents the normal vel oci ty components of body motion. NOTES ON CORNERS OR EDGES OF BODY SURFACE The CPM using i nd i rect or direct boundary integral equation formul at i...
Abstract

ABSTRACT This paper presents the description of a higherorder boundary element method (HOBEM) for calculating linear hydrodynamic loadings on large floating bodies and comparison with constant panel methods and HOB EMs that are employed in conjunction with the hybrid boundary integral equation procedure, for a variety of structural configurations. It was concluded from the study that HOB EM has several important features: it uses many fewer boundary elements and much less computer time, with higher accuracy than conventional methods. In addition to these, the computer code for hydrodynamic loadings can easily be used for finite element structural analysis. INTRODUCTION Reliable estimates of the hydrodynamic loadings on large offshore structures are critical in the assessment of structural response, stability and fatigue life. The constant panel method (CPM) introduced by Hess-Smith (1964) has been widely used for calculating hydrodynamic loadings, for example by Faltinsen-Michel sen (1974); Garrison (1979); InglisPrice (1980); Ostergaard-Schell in (1987); and Korsmeyer et al. (1988). In the constant panel approach, the surface of a three-dimensional body is replaced by quadrilateral or triangular facets. Each facet (or panel) represents a source distribution of constant strength with satisfaction of a Newmann boundary condition required at the center (control point) of each panel. Consequently, the constant panel approach has several limitations: the source distribution is discontinuous, i.e., the source strength is constant over each panel and jumps stepwise at the boundary of neighboring panels; for curved body surfaces, the quadrilaterally faceted surface becomes discontinuous as all the four corner points generally do not coincide with those of the neighboring panels. Thus, the faceted surface introduces so-called "leaks". To overcome the foregoing limitations, Webster (1975) proposed the use of triangular panels with linear source distributions located just beneath the actual body surface.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-013

... artificial intelligence

**coefficient**value thruster**coefficient**tunnel bluff body solidity joodel electrical industrial apparatus reynolds number hull vehicle towirg tank sensitivity flume wind tunnel upstream oil & gas fran resistance tank rov variation vorticity...
Abstract

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 measured at the same Reynolds number in different facilities result from differences in the level of free stream turbulence in each. This appears to influence flow separation from the corner radii of the hulls, am hence the vortex shedding, with resultant variations in resistance am transverse forces, since ROVs will generally operate in high levels of freestream turbulence, it is argued that similar conditions should be created, and carefully controlled, in subsequent experimental programmes. In addition to corner radius effects, the influence of hull solidity factor am the effects of blockage to the inflow am outflow of thrusters were also investigated. A faired, enclosed hull form, developed in the light of the experimental findings, was tested in a wind tunnel, am the results are discussed. INTRODUCTION ROVs have been in regular use now for over two decades and yet, while considerable advances have been made in the capability of the equipment fitted am their telemetry, control am diagnostic systems, the actual vehicles themselves have developed very little. The hydrodynamics of these bluff hulls remains poorly quantified with the result that they are often underpowered, especially in the transverse plane, and rely on control techniques rather than good design for dynamic stability. A number of ROVs that are regularly deployed are incapable of operating in even a moderate crosscurrent. Even their static stability is limited; they are frequently deployed with floats tied on to the structure to counter the mass of sane extra piece of equipment that has been bolted on.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-039

... numerical values for these parameters has been carried out 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...
Abstract

ABSTRACT Environmental and structural data from a monitoring system installed on a steel jacket platform in the Sicily channel has been examined for reliability. Significant data has been chosen to assess the design assumptions for the dynamic behaviour of the platform such as added mass, marine growth and axial pile group stiffness. A parametric structural dynamic identification is achieved by the modal parameter technique, comparing the theoretical and experimental response of the platform. I. INTRODUCTION This paper is concerned with a dynamic study of the Vega steel jacket platform. The significant uncertainties connected with mathematical modelling and their influence on the predicted structural response are investigated. Recently the comparison between the design hypotheses and the structural response of offshore structures has been performed using the information collected by monitoring existing platforms. This study is carried out using experimental data recorded from a steel jacket platform in the Mediterranean to obtain the dynamic identification of the platform using a simplified numerical model of the structure. Experimental results have always made a significant contribution to the development of structural analysis and design, and form the most effective method of research in the study of complex physical phenomena and in the formulation of suitable empirical laws to model them. But in the last few years a substantial change has occurred which results from the introduction of new and very effective techniques to analyse the structures, increasing the types of structures which can be handled directly by numerical methods. However such methods can not replace the role of experimental analysis, which is fundamental to the knowledge of structural behaviour. In structural analysis there are two basic approaches. The first is called "direct", where stresses and strains in a structure are determined on the basis of definition of external loads.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-014

... 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...
Abstract

ABSTRACT Sample calculations illustrate uncertainties in predicting second-order wave forces and low-frequency motions of a large moored structure. The results, for a "deep-draught floater" in regular and irregular waves, demonstrate sensitivity 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 numbers. The introduction of a current substantially increased the damping, but had generally a simplifying influence. The calculations also illustrate different ways of estimating the extreme second-order response, and combining this with the first-order response. 1. INTRODUCTION In 1989 BMT took part in a comparative evaluation of computer programs, organised by the Royal Norwegian Council for Scientific and Industrial Research (NTNF). The results of this investigation were discussed at a Workshop in Bergen, and will no doubt be published in due course. The project highlighted several sources of uncertainty in predicting low-frequency responses of floating and moored structures in waves, in particular those of estimating the damping and extreme responses. The present paper describes results from a follow-up study at BMT, which demonstrated how recent research data may be used in calculations of this type, and how changes in the assumptions and procedures affect the results. The problem posed by NTNF was to calculate wave forces on, and motions of, two vessels in regular and irregular waves; to estimate maximum responses in a storm of six hours duration for first and second-order motions separately, and then for the combined process. The two vessels were a turret-moored production ship of 230m length, and a four-column deep-draught floater (DDF), the latter being a very large semi-submersible type structure.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-010

...-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**...
Abstract

ABSTRACT This paper presents results of a series of experiments conducted on a 0.3m diameter fixed vertical cylinder in a wave tank. The experimental study was aimed to increase the drag forces on the cylinder without increasing the inertial forces by inducing flow-separation around the cylinder. For this purpose an innovative device was designed based on the hydrodynamic flow-behaviour at low Keulegan-Carpenter numbers. Both regular and random wave environments were simulated in the laboratory. The total wave forces on the cylinder were measured using a sophisticated experimental arrangement. The hydrodynamic coefficients were computed using least-squarefit technique. The drag coefficients increased to a maximum of five times due to the attachment of the device. The inertial coefficients are found to be insensitive to the device due to flow transparency. An example study is, also, included to show the usefulness of this increased drag forces in reducing the near resonant responses of a large diameter deep water structure. INTRODUCTION Many offshore platforms proposed for the deep water applications are characterized by large diameter vertical cylinders piercing the free-surface (examples: Tension Leg Platform, Monotower Platform and Tripod Tower Platform). The member diameter for these type of structures is around 15m. For such large members the mechanism of wave loading is mainly from the inertial effect and the drag forces are very small or even negligible in case of moderate sea. This is because of the behavior of the oscillatory flow at low Keulegan-Carpenter (Kc) numbers. For waves of small amplitudes with high frequencies, which generally occur everyday in the North-Sea, the 15m diameter member will have Kc numbers less than or equal to 2. At low Kc numbers there is little time available for the wake to form/develop before the flow-reversal occurs. This physical phenomena had been confirmed by many researchers.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-005

... 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...
Abstract

Abstract Basically, two different methods exist for motion prediction of floating bodies, model tests and numerical simulations. Combining the two methods; using model test results to determine hydrodynamic coefficients and to calibrate numerical models, and performing parameter variations by means of numerical simulations may give the most cost-effective analysis. The ultimate success of this approach depends on the effectiveness of the numerical (mathematical) modeling. Most numerical models predict first-order excitation and response with sufficient accuracy. However, with regard to second-order effect, there are variations both in excitation forces and the damping models. Normally, the second-order (low-frequency) motions are assumed to be uncoupled from the first-order motion this assumption is not generally valid, and that may be the reason why, for supply vessels moored in linear springs, large discrepancies have been observed between model test results and numerical simulations. This paper presents a numerical model where the equations of motion are simulated in the time domain in 6 degrees of freedom. Wave excitation forces and moments are modeled to second order, while the equations of motion are given in their genuine non-linear form. By numerical simulations, it is demonstrated that important contributions to the low-frequency yaw motion for both the supply vessel and a production tanker is the inertia coupling between roll and pitch motions. The instantaneous yawing moment is approximately proportional to the product of roll and pitch velocities. These observations agree well with model test results for a supply vessel, where these coupling effects are included in the measured wave drift moments. To the authors' knowledge, the magnitude of this coupling effect has not been demonstrated before. A consequence of this effect is that in order to reduce the low-frequency yaw motions, it may become necessary to reduce the roll motions.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-030

... conducted 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**...
Abstract

ABSTRACT The full scale testing of two elastomer components of the Snorre TLP tether system, the radial bearing and the conduit seal, is presented. The tests verify that the design requirements specified to ensure proper functioning during the 30 years service life are met. 1. INTRODUCTION Elastomers play a key role in the design of tether systems for Tension Leg Platforms (TLP's). Figure 1 illustrates the main load bearing components of the tether system for the Snorre TLP, which will be installed in 1992 on the Saga Petroleum a.s operated Snorre Field in the Norwegian sector of the North Sea. The anchor latch and the cross load bearing (CLB) both incorporates a flexjoint which accommodates for angular displacements due to TLP offset. The CLB shown in Figure 2 also incorporates two other elastomer components: the radial bearing which transfers the horizontal component of the tether tension into the TLP hull, and; the conduit seal which allows the tether conduits to be dry during operation. McIntosh and Stevenson (1988) report good in service performance of the similar elastomer components of the Hutton TLP. The only exception has been the conduit tube seal for which a number of in service failures are reported. This problem has recently been solved by installing new conduit seals of a modified design. This paper presents the full scale testing of the Snorre CLB radial bearing and conduit seal. The test programs were designed to provide the necessary data to validate essential functional and strength aspects of the designs. Design data of the two elastomer components are presented in paragraphs below. For descriptions of the Snorre TLP platform and tether system, references are made to Gaul and Pettersen (1989) and Hannus et. al. (1990). Conclusions are presented in section 4.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-050

... 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...
Abstract

ABSTRACT This investigation is concerned with the forces acting on weakly buoyant pipelines under tow. Experiments have been made at a scale of about 1/13 in a wave flume, of a prototype pipeline of diameter D = 0.8 m. Unfortunately the prototype length of the test cylinder was only about 70 m and the model was therefore moving appreciably in waves, even 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 correlated with the KeuleganCarpenter number and gave plausible values, but with a fair amount of variability. The prediction of the force time series and hence of the local forces was reasonable, but the highest local force peak per period was consistently underpredicted, often severely. The relevance of tests on such short cylinders for irregular wave situations is questionable, and little emphasis was therefore put on interpretation of those test results. MOTIVATION FOR THE PRESENT STUDY It may in some cases be advantageous to assemble a marine pipeline in a shipyard or a similar land-based facility and tow it to its destination. The simplest preparation for tow-out would then be to ballast It so that its excess buoyancy under still water conditions is only a few percent of its weight. (According to Karat (1988) typically 3 to 6 %). The present paper considers a pipeline with a diameter of 32" (0813 m) and in a design seastate which have been given by Karal (1988) as follows: Significant wave height 2.5 m and average zero crossing period m the range 5 to 15 s.

Proceedings Papers

Paper presented at the The First ISOPE European Offshore Mechanics Symposium, August 20–22, 1990

Paper Number: ISOPE-E-90-040

... deViation 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**...
Abstract

ABSTRACT A Jack-Up is analyzed at a site with a water depth of 83 musing time domain simulation of irregular seas. The response statistical moments are estimated for a number of case studies, incrementing the basic variables. Based on the statistical information from these analyses a reliability analysis is performed considering the long-term statistics of combined environmental loads. The probability of exceeding levels of the axial force in one leg is studied, Static and dynamic analyses, long term and conditional extreme storm event analyses are performed. INTRODUCTION Jack-Up platforms have become a standard tool for operations m shallow water, generally less than 100m. The last years there has been a growing interest to use jack-up platforms to achieve early production Jack-ups are now also applied for all year operations m hostile environments like the North Sea. The horizontal stiffness of a jack-up platform is typically an order of magnitude less than the stiffness of a corresponding jacket structure. Thus the dynamic effects become significant as the fundamental period of a jack-up may typically be m the range 4–8 seconds where also the wave energy is becoming significant. Due to its flexibility a design of a Jack-up IS a great challenge. The larger flexibility of a jack-up implies Other simplified dynamic analysis may be questioned as the knowledge about damping values are difficult to establish due to the items listed above. See also Refs.[1–5). The purpose of this paper has been to establish the reliability of one jack-up structure at a particular site based on a best possible representation of the physical response behaviour by time domain simulation analyses. A reliability analysis is performed by a transformation of the response results. A description of this method is given in the following. For a description of reliability methods m general see [7,8,23)