Slender Offshore Structures Research Articles

Resonant Motions of Dynamic Offshore Structures in Large Waves

In marine engineering, the dynamics of fixed offshore structures (for oil and gas production or for wind turbines) are normally found by modelling of the motion by a classical mass-spring damped system. On slender offshore structures, the loading due to waves is normally calculated by applying a force which consists of two parts: a linear “inertia/mass force” and a non-linear “drag force” that is proportional to the square of the velocity of the particles in the wave, multiplied by the direction of the wave particle motion. This is the so-called Morison load model. The loading function can be expanded in a Fourier series, and the drag force contribution exhibits higher order harmonic loading terms, potentially in resonance with the natural frequencies of the system. Currents are implemented as constant velocity terms in the loading function. The paper highlights the motion of structures due to non-linear resonant motion in an offshore environment with high wave intensity. It is shown that “burst”/“ringing” type motions could be triggered by the drag force during resonance situations.

Experimental Investigation of Vortex-Induced Vibrations on Yawed and Inclined Flexible Cylinders

Abstract An experimental setup was built to investigate the vortex-induced vibration (VIV) phenomenon on yawed and inclined flexible cylinders, in which five yaw angles θ = 0 deg, 10 deg, 20 deg, 30 deg, and 45 deg and five azimuth angles β = 0 deg, 45 deg, 90 deg, 135 deg, and 180 deg were combined. The experiments were carried out in a towing tank facility at Reynolds numbers from 1800 to 18,000, comprising vibrations up to the eighth natural mode. Time histories of displacements were recorded using a submerged optical system that tracks 17 reflective targets. A modal decomposition scheme based on Galerkin’s method was applied, aiming multimodal behavior investigations. Such an approach allowed the analysis of the modal amplitude throughout time, revealing interesting results for such a class of VIV tests. The flexible cylinder total response is generally a combination of two or more modes. Only for azimuths 0 deg, 90 deg, and 180 deg, a unimodal response was observed for the two first lock-in regimes. The frequency response showed that when the response was multimodal, non-dominant modes can follow the vibration frequency of the dominant one. Assuming a priori the independence principle (IP) valid to define the reduced velocities (Vr), it was observed that the resonance region was restricted to 3 ≤ Vr ≤ ~8 for the tested cases, indicating that the IP can be at least partially applied for flexible structures. As the literature scarcely explores the simultaneous yawed and inclined configurations, the present work may contribute to further code validation and improvements regarding the design of slender offshore structures.

Recursive thoughts on the simulation of the flexible multibody dynamics of slender offshore structures

In this work, the floating frame of reference formulation is used to create a flexible multibody model of slender offshore structures such as pipelines and risers. It is shown that due to the chain-like topology of the considered structures, the equation of motion can be expressed in terms of absolute interface coordinates. In the presented form, kinematic constraint equations are satisfied explicitly and the Lagrange multipliers are eliminated from the equations. Hence, the structures can be conveniently coupled to finite element or multibody models of for example seabed and vessel. The chain-like topology enables the efficient use of recursive solution procedures for both transient dynamic analysis and equilibrium analysis. For this, the transfer matrix method is used. In order to improve the convergence of the equilibrium analysis, the analytical solution of an ideal catenary is used as an initial configuration, reducing the number of required iterations.

Prototype Reynolds Number Vortex-Induced Vibration Tests on a Full-Scale Rigid Riser

Slender offshore structures in deep water subjected to currents may experience vortex-induced vibrations (VIV), which can cause significant fatigue damage. Extensive experimental researches have been conducted to study the VIV in the past several decades. However, most of the experimental works have small-scale models and relatively low Reynolds number (Re)—“subcritical” or even lower Reynolds number regime. There is a lack of full understanding of the VIV in prototype Re flow regime. Applying the results with low Re to a full-scale riser with prototype Re might have uncertainties due to the scaling effects. In addition, the surface roughness of the riser is also an important parameter, especially in critical Re regime, which is the case for prototype risers. In the present study, two full-scale rigid riser models with different surface roughness ratios were tested in the towing tank of MARINTEK in 2014. Stationary tests, pure crossflow (CF) free oscillation tests, and forced/controlled motion tests were carried out. Several conclusions could be made: The drag coefficient is dependent on the Re number and surface roughness ratio. At critical and supercritical flow regimes, the displacement amplitude ratio is less sensitive to Re than that at lower Re. The displacement amplitude ratio in subcritical flow regime is significantly larger than that in critical and supercritical flow regimes. Two excitation regions for the ‘smooth riser’ and one excitation region for the “rough riser” are identified.

Wavelet network meta-models for the analysis of slender offshore structures

Mooring lines and risers are crucial components of offshore oil and gas production platforms. The usual design practice requires the use of complex Finite-Element (FE) time-domain simulation tools, to represent their severe nonlinear dynamic behavior. However, such tools may require excessively high computational times; this fact motivates the study of expeditious methods – the so-called surrogate models or meta-models. In this context, this work presents an approach based on Wavelet Networks (WN) – a combination of the feed-forward neural network architecture with the wavelet transform. The goal is to obtain dramatic reductions in processing time, while providing results nearly as good as those from nonlinear dynamic FE methods.Case studies are presented to evaluate the performance of the model, in terms of accuracy and computational time. Extensive parametric studies are performed to fine-tune the model (in terms of several parameters such as type of wavelet function; number of nodes in the hidden layer; size of the training/validation sets), to find the configuration most suited for the problem at hand. It is shown that the WN-based models proposed in this work are more efficient than ANN models; also, the fine-tuned configuration performs substantially better than the standard configuration with typical values for the parameters.

Two-degree-of-freedom VIV of circular cylinder with variable natural frequency ratio: Experimental and numerical investigations

Slender offshore structures possess multiple natural frequencies in different directions which can lead to different resonance conditions when undergoing vortex-induced vibration (VIV). This paper presents an experimental and numerical investigation of a two-degree-of-freedom VIV of a flexibly mounted circular cylinder with variable in-line-to-cross-flow natural frequency ratio. A mechanical spring-cylinder system, achieving a low equivalent mass ratio in both in-line and cross-flow directions, is tested in a water towing tank and subject to a uniform steady flow in a sub-critical Reynolds number range of about 2×103–5×104. A generalized numerical prediction model is based on the calibrated Duffing-van der Pol (structure-wake) oscillators which can capture the structural geometrical coupling and fluid-structure interaction effects through system cubic and quadratic nonlinearities. Experimental results for six measurement datasets are compared with numerical results in terms of response amplitudes, lock-in ranges, oscillation frequencies, time-varying trajectories and phase differences of cross-flow/in-line motions. Some good qualitative agreements are found which encourage the use of the implemented numerical model subject to calibration and the sensitivity analysis of empirical coefficients. Moreover, comparisons of the newly-obtained and published experimental results are carried out and discussed, highlighting a good correspondence in both amplitude and frequency responses. Various patterns of figure-of-eight orbital motions associated with dual two-to-one resonances are observed experimentally as well as numerically: the forms of trajectories are noticed to depend on the system mass ratio, damping ratio, reduced velocity parameter and natural frequency ratio of the two-dimensional oscillating cylinder.

Numerical prediction of the modal response of flexible cylinders in cross-flow with a current dependent form of damping

A quadratic eigenvalue problem (QEP) was posed in order to study the dynamics of flexible cylinders in cross-flow, simulating slender offshore structures such as risers, catenaries or tendons. The Euler–Bernoulli equation was used to model the structure assuming a fluid loading model, and yielding a quadratic eigenvalue problem that included a form of damping dependent not only on the structural damping itself, but also on the free stream velocity and the fluid force coefficients. We solved the QEP using the finite element method. We also derived a simplified analytical solution in this work for comparison with the QEP, however this solution does not consider changes in tension along the length of the cylinder as the QEP does. In our study, the QEP solutions were first validated against the simplified analytical solution, and also against a well-known experimental dataset obtained in 2003, in which a flexible circular cylinder model was used to model the dynamics of a riser undergoing multi-mode vortex-induced vibrations.

직교격자를 이용한 단순 세장 구조물의 와유기 진동 해석

For long slender offshore structures, such as cables and pipe lines, their interaction with surrounding fluid flow becomes an important issue for global design of ocean systems. We employ a long circular cylinder as a representative case of slender offshore structure. A flexibly mounted cylinder in cross-flow generates complex vortex shedding and results in oscillation of the structure. In this paper, flow behind a circular cylinder at Re=100 is simulated. The vortex shedding pattern and flow induced motion are examined in the cross flow configuration as well as with various yaw-angled configurations. The "Lock-in" phenomenon is also observed when reduced velocity is approximately 4.0. The MAC Grid system, which is the typical grid system for Cartesian mesh and pressure correction methods, are used for solving the incompressible Navier-Stokes equations. Predictor/Corrector method is applied for obtaining a non-linear response of structure at the flexibly mounted. The existance and motion of the body is represented by the immersed boundary technique.

Prediction of Wave and Current Forces on Slender Structures Using Artificial Neural Networks

Hydrodynamic forces generated from waves and currents on slender cylinders are of great concern for design of offshore structures. Numerous analytical and experimental methods such as Morison equation have been suggested to estimate the wave forces on slender offshore structures. However, such methods have shown some inaccuracies in their estimations. In recent years, artificial neural networks have received a great deal of attention and have been used effectively in many engineering subjects. In this paper, artificial neural networks are used to predict waves and current forces on slender cylinders. The data generated from laboratory experiments is used to train and evaluate the prediction performance of the artificial neural networks applied in the present research. A number of neural networks are designed, trained and evaluated. Results indicate the success of application of neural networks approach which can efficiently predict the waves and current forces on slender cylinders after conducting appropr...

Hydrodynamic coefficients for calculation of hydrodynamic loads on offshore truss structures

Abstract The current American Petroleum Institute's recipe [API RP 2A WSD, Recommended practice for planning, designing and constructing fixed offshore platforms, working stress design. API, USA, 1993.] for calculation of hydrodynamic loads on offshore truss structures is compared with the corresponding North Sea Design Practice, as given by the rules of Det Norske Veritas. Most emphasis is put on the hydrodynamic coefficients and the estimation of design current as these issues are identified to be particularly critical. Use of the updated API (1993) recommendations in which the drag coefficient for roughened cylinders is increased from a minimum of 0·6 (API 1991) to 1·05 (API 1993) and where current is included, could lead to a general increase in the estimated load level on slender offshore structures [Petrauskas, C., Heideman, J.C. & Berek, E.P., Extreme wave force calculation procedure for the 20th edition of API RP 2A. OTC paper 7153, In Proc. OTC 1993, Houston, Texas, 1993, pp. 201–211]. The main emphasis with regard to the impact of the new API recommendations, however, is that a consistent approach is provided to the calculation of 100-yr directional loads. This includes taking into account the effect of marine growth on force coefficients, modifying the wave kinematics for directional spreading, and considering current blockage effects, conductor shielding effects, and joint occurrence of wave height and current (i.e., using the associated current as being representative of the current that would lead to the 100-yr load). It is concluded that a consistent approach, such as that underlying the new API RP 2A (1993) recipe, is preferable to the current North Sea Design Practice [Det Norske Veritas, Environmental conditions and environmental loads. DNV classification notes 30.5, 1001.] in this field, and thus that the North Sea Design Practice should be updated. This relates in particular to selection of hydrodynamic coefficients. Measurement programmes to obtain full scale global force data simultatneously with wave and current data are furthermore recommended.

Design Criteria for Offshore Structures Under Combined Wind and Wave Loading

Offshore codes do not give sufficient guidance regarding design criteria for loads resulting from combinations of stochastic environmental processes such as wind and waves. To assist design engineers in defining such criteria, a suite of methods that use environmental data to calculate the probability distributions of load effects resulting from combination of stochastic loads were investigated. An approach has been developed for using the results to calculate structure-specific and generalized load combination criteria. Extensive application of this approach in connection with Environment Canada’s wind and wave data bases for the Canadian East Coast region formed the basis for some interesting conclusions regarding the process of estimating combined extreme loads on offshore structures. It was found that data based on actual measurements of wave height and wind speed are preferable to hindcast data, since the latter have artificially high correlations that lead to overly conservative results. External analyses are most reliable when 20 or more years of data are used with analysis methods based on distribution tails. Reasonably good results can be achieved with 10 yr of data. Methods based on the point-in-time data and using mathematically convenient assumptions regarding distribution types and process characteristics can lead to large errors if the assumptions made are not substantiated by appropriate data. Load combination solutions are highly dependent on the geographic location and data base. Therefore, a separate analysis should be carried out for the structure and location being considered if possible. Wind and wave load combination solutions are sensitive to correlations and assumed distribution types; closed-form solutions for independent and Gaussian correlated processes can lead to significant errors. If site-specific analyses are not practical, companion action factors of 0.65, 0.60, and 0.55 for return periods of 20, 100, and 1000 yr, may be used for wind and wave loading on slender offshore structures in the Canadian East coast region. For wide structures in the same region, the suggested companion factors for the same return periods are 0.75, 0.70, and 0.65.

Fatigue life estimation for dynamically sensitive slender offshore structures exposed to non-Gaussian wave loading: Karunakaran, D.N., Leira, B.J. Spidsoe, N. and Moan, T. Conf. Fatigue and Fracture in Steel and Concrete Structures, ISFF '91, Madras, India, Dec 1991 Vol 2 (Oxford & IBH Publishing Co. Pvt. Ltd, New Delhi, India, 1991) 1245–1260

Fatigue life estimation for dynamically sensitive slender offshore structures exposed to non-Gaussian wave loading: Karunakaran, D.N., Leira, B.J. Spidsoe, N. and Moan, T. Conf. Fatigue and Fracture in Steel and Concrete Structures, ISFF '91, Madras, India, Dec 1991 Vol 2 (Oxford & IBH Publishing Co. Pvt. Ltd, New Delhi, India, 1991) 1245–1260

Environmental Load Effect Analysis of Guyed Towers

A general method for dynamic load effect analysis of slender offshore structures subjected to short crested random waves, current and wind, is given. The structure is represented by a three-dimensional space frame model utilizing dash-pots and linear or nonlinear spring elements to represent guy lines and coupling between structure and foundation. The component mode synthesis formulation is adopted for reduction of the number of degrees of freedom. The hydrodynamic forces are computed by Morison’s equation, accounting for finite wave elevation, directionality, and relative fluid-structure motion. Various kinematic models for the fluid field in the splashing zone are compared. To get a reasonable representation of nonlinearities in the loading and the structural model, a Monte Carlo approach is adopted. Starting with simulated samples of the random fluid field and wind forces, time series of structural responses are found by numerical time integration utilizing the Newmark β-family of time integration operators. Numerical results for a guyed tower at 450-m water depth are presented. The statistical uncertainties associated with the stochastic time domain simulations are discussed. A significant discrepancy is found between linearized frequency domain solutions and the present nonlinear time domain formulation. The importance of an adequate representation of superharmonic responses is particularly discussed. The differences in results due to various solution methods are found to vary significantly with sea-state conditions.

Load spectra for slender offshore structures in waves and currents

AbstractThe influence of currents on the wave induced dynamic response of offshore structures with slender members is assessed by deriving appropriate load spectra. The analysis permits the implications of the modified Morison equation to be examined, and suggests that methods of equivalent linearization commonly employed may yield unconservative results. An alternative formulation is proposed, in which the equations of motion are linear in the structural kinematics but the non‐linear dependence of drag force on fluid particle motions is retained. This leads to a load spectral density matrix expressed as a sum of terms, involving convolutions of the wave kinematics spectra. Results are obtained for a plane frame idealization of an offshore jacket structure. These demonstrate the strong influence of current, and the importance of retaining in the loading terms up to the third power of wave particle velocity.