Hydrodynamic Load Models Research Articles

Optimal experimental design for identification of hydrodynamic loading models

Abstract Hydrodynamic model-scale experiments are an intrinsic part of the design of marine structures, as they enable validating and calibrating the involved hydrodynamic numerical models. Such seakeeping experiments are generally conducted using a simple spring-based mooring system, with fixed properties throughout the tests. In the context of cyber-physical testing, the marine structure is kept in position in the laboratory by a virtual mooring system, the properties of which can be adjusted on the fly. This paper provides an algorithmic approach for maximizing the information gain from the test by optimizing the mooring stifness and damping parameters that define the experiment. The method is verified with synthetic data generated for the INO Windmoor 12MW floater, and is shown to be robust to noise and unmodeled effects.

Applying Bayesian optimization to predict parameters in a time-domain model for cross-flow vortex-induced vibrations

As the demand for harvesting offshore energy increases worldwide, the need for slender structures, such as marine risers and power cables, will increase. The dominating loads for deep water applications will primarily be caused by current-structure interactions, where vortex-induced vibrations (VIV) are known to be a challenging response type to handle correctly during design. Semi-empirical time-domain models are promising for VIV prediction, but uncertainties related to simplifications in the hydrodynamic load model and empirical parameters lead to over-conservative designs, where the parameters are estimated from model tests within a relatively low Reynolds number range. The aim of this paper is to present an efficient tool to estimate empirical hydrodynamic parameters directly from test data. To illustrate the method, the hydrodynamic parameters were estimated from pure cross-flow VIV model tests in a steady current with Reynolds numbers in the range of 40,000-120,000. The parameters were updated sequentially by using a Bayesian optimization framework, with the aim of minimizing an objective function that incorporates the response errors between time-domain VIV simulations and model test data. It is shown that three empirical parameters can be obtained simultaneously, resulting in small response errors but the optimal parameters were overly sensitive to variations in the flow velocity. The optimal parameters were used to reconstruct the drag amplification related to cross-flow VIV and in forced motion simulations to illustrate how the parameters in the load model would map into the traditional formulation in terms of the added mass and excitation coefficient.

Comparison of laboratory wave generation techniques on response of a large monopile in irregular sea

As the offshore wind industry moves toward larger monopile turbines, model testing and validation of hydrodynamic load models become more important for new designs of turbines. Wave generation is an important aspect of hydrodynamic model testing. When generating irregular waves with a piston-type wavemaker, first order wavemaker theory is commonly used. This leads to generating spurious free waves in the tank. Using second order wavemaker theory reduces the generation of these spurious waves. In this study, the two wave generation techniques have been used in the measurement of the dynamic responses of a monopile with (full-scale) natural period of 5 sec. The effect of superharmonic spurious waves on the response statistics was minor. A marginal improvement in experimental repeatability of the second mode response in large wave events was observed by using second order wavemaker theory.

Study of dynamic debris impact load on flexible debris-resisting barriers and the dynamic pressure coefficient

The use of steel flexible barriers to mitigate landslide risk on natural hillsides is becoming common in the past decade in Hong Kong. The current design approach for this kind of barrier structure involves the adoption of the hydrodynamic load model to predict dynamic impact forces, followed by non-linear structural analyses of flexible barriers using numerical programs based on the pseudo-static force method. From local design guidelines, the dynamic pressure coefficient, a critical input parameter in the hydrodynamic load model, is taken as 2.0. This empirically considers the effect of impacts from boulders up to 2.0 m in diameter. With a view to rationalising the design approach, a series of physical impact tests and numerical analyses was conducted to investigate the dynamic debris impact on flexible barriers and the resulting barrier response. The physical impact tests involved up to 9 m3 of debris resisted by a 1.5 m high steel ring-net barrier. The tests were conducted in the 28 m long large-scale flume facility at the Kadoorie Centre in Hong Kong. Numerical modelling using computer programs LS-DYNA and NIDA-MNN was conducted to analyse the dynamic response of flexible barriers with different structural forms. The study aims to evaluate the dynamic pressure coefficient and to verify the current design approach based on the suggested dynamic pressure coefficient from this study. Results indicate that a dynamic pressure coefficient of 1.0 is, in general, appropriate for design purposes if the debris comprises primarily water and fine-grained particles.

Experimental study on the effect of second order wavemaker theory on the response of a flexible large diameter monopile in irregular sea

Motivated by the need for larger offshore wind turbines, large diameter monopile foundations are being developed. To ensure safe design, there is a need for model testing and validation of hydrodynamic load models. Scaled model tests with a piston-type wavemaker commonly apply first order wavemaker theory for irregular waves. This approach results in the generation of second (and higher) order spurious (also known as parasitic) free waves in the tank. In this study, the effect of superharmonic spurious waves on the response of a monopile with eigenfrequency close to three times the wave peak frequency is examined experimentally. The bending moment response statistics are not found to be significantly affected by the wavemaker correction. Different wave breaking patterns are observed for individual events, but our results do not indicate any clear relation between breaking waves and the wave generation technique.

Experimental and numerical study of dynamic soil debris impact load on reinforced concrete debris-resisting barriers

In Hong Kong, design practice adopts the hydrodynamic load model to estimate the dynamic soil debris impact load on reinforced concrete debris-resisting barriers. A dynamic coefficient of 2.5 is empirically adopted, which takes into account the effect of the impact of boulders up to 0.5 m in diameter. With a view to rationalising the design of reinforced concrete debris-resisting barriers, the Geotechnical Engineering Office (GEO), in collaboration with the Hong Kong University of Science and Technology (HKUST), initiated a study to investigate the dynamic impact of soil debris. In particular, a series of large-scale impact tests using 4 m3 realistic debris mix and a 1.8-m-high reinforced concrete model barrier were conducted in the flume facility in the Kadoorie Centre in Hong Kong. The tests were well controlled, and the flow kinematics, including flow depth and flow speed, and the time history of the impact load at the wall stem subject to the debris impact were measured, which provided critical test data on assessment of the hydrodynamic load of soil debris hitting reinforced concrete structures. The scale of these physical impact tests under such a controlled environment was unique as compared with other studies in the literature. To further examine the dynamic impact force, a calibrated numerical model using a three-dimensional finite-element computer package, namely LS-DYNA, was adopted to simulate the impact scenario for a real-scale debris flow event of 400 m3, where an arbitrary Lagrangian-Eulerian technique was adopted to simulate debris materials. Based on both the experiments and numerical analyses, debris run-up along the wall stem was observed when the debris hit the model barriers. Under the experimental setting, the hydrodynamic soil debris pressure coefficients were consistently found close to unity, which are generally in line with that used in overseas technical guidelines or design practice. This study enhances fundamental understanding of the soil debris impact mechanism on reinforced concrete barriers and provides scientific evidence to rationalise the design guidelines used in Hong Kong.

Comparison of Nonlinear Wave-Loading Models on Rigid Cylinders in Regular Waves

Monopiles able to support very large offshore wind turbines are slender structures susceptible to nonlinear resonant phenomena. With the aim to better understand and model the wave-loading on these structures in very steep waves where ringing occurs and the numerical wave-loading models tend to lose validity, this study investigates the distinct influences of nonlinearities in the wave kinematics and in the hydrodynamic loading models. Six wave kinematics from linear to fully nonlinear are modelled in combination with four hydrodynamic loading models from three theories, assessing the effects of both types of nonlinearities and the wave conditions where each type has stronger influence. The main findings include that the nonlinearities in the wave kinematics have stronger influence in the intermediate water depth, while the choice of the hydrodynamic loading model has larger influence in deep water. Moreover, finite-depth FNV theory captures the loading in the widest range of wave and cylinder conditions. The areas of worst prediction by the numerical models were found to be the largest steepness and wave numbers for second harmonic, as well as the vicinity of the wave-breaking limit, especially for the third harmonic. The main cause is the non-monotonic growth of the experimental loading with increasing steepness due to flow separation, which leads to increasing numerical overpredictions since the numerical wave-loading models increase monotonically.

On-Bottom Stability of Umbilicals and Power Cables for Offshore Wind Applications

With the increase in offshore wind farms, the demands for umbilicals and power cables have increased. The on-bottom stability of umbilicals and power cables under the combined wave and current loading is the most challenging design issue, due to their light weight and the complex fluid–cable–soil interaction. In the present study, the methodology for dynamic lateral stability analysis is first discussed; and the reliable hydrodynamic load model and cable–soil interaction model based on large experimental test data are described in detail. The requirement of the submerged weight of a cable w s to obtain on-bottom stability is investigated for three types of soil (clay, sand and rock), using the finite element program PONDUS, and the results are w s , r o c k > w s , c l a y > w s , s a n d under the same load conditions. Several different aspects related to optimization design of the on-bottom stability are explored and addressed. There is a significant benefit for the on-bottom stability analysis to consider the reduction factors, due to penetration for clay and sand soil. The on-bottom stability is very sensitive to the relative initial embedment z 0 / D for clay and sand soil, due to the small diameter of the cables, and therefore, reliable prediction of initial embedment is required. In the energy-based cable–soil interaction model, the friction coefficient μ and the development of penetration affect each other and the total effect of friction force F f and passive resistance F r is complicated. The effect of the friction coefficient μ on the on-bottom stability is different from engineering judgement based on the Coulomb friction model. The undrained shear strength of clay is an important parameter for the on-bottom stability of umbilicals and cables. The higher the undrained shear strength of the clay, the larger the lateral displacement. Meanwhile, the submerged weight of sand has a minor effect on the lateral displacement of cables. The method used in the present study significantly improves the reliability of the on-bottom stability analysis of umbilicals and power cables for offshore wind application.

Critical assessment of non-linear hydrodynamic load models for a fully flexible monopile offshore wind turbine

This paper presents a comparison between experimental data of a model-scale 4 MW monopile offshore wind turbine subjected to extreme irregular sea states in finite water and the numerical models suggested in offshore wind energy standards to assess ULS conditions. The model is fully flexible with its 1st and 2nd eigenfrequencies and 1st mode shape tuned to fit those of the full-scale turbine. The measured and simulated bending moments at the sea bottom are decomposed around the eigenfrequencies of the structure, and the Morison equation with stream function wave kinematics is found to trigger transient 1st mode response (so-called ringing response). The amplitude of the simulated 1st mode response is proportional to the incoming wave steepness; such a relationship is not observed experimentally. Similarly, 2nd mode response is triggered by Wienke's slamming model, but generally does not match the experimental data. Although the numerical models from the design standards (Morison's equation with stream function kinematics, plus a slamming model) can give conservative estimates of the extreme responses, the models miss the balance between 1st and 2nd mode responses. The simplification of the physics in the numerical models can thus lead to inaccuracies in response prediction, such as the stress distribution along the monopile.

Semi-active control of monopile offshore wind turbines under multi-hazards

Abstract The present paper studies the control of monopile offshore wind turbines subjected to multi-hazards consisting of wind, wave and earthquake. A Semi-active tuned mass damper (STMD) with tunable natural frequency and damping ratio is introduced to control the dynamic response. A new fully coupled analytical model of the monopile offshore wind turbine with an STMD is established. The aerodynamic, hydrodynamic and seismic loading models are derived. Soil effects and damage are considered. The National Renewable Energy Lab monopile 5 MW baseline wind turbine model is employed to examine the performance of the STMD. A passive tuned mass damper (TMD) is utilized for comparison. Through numerical simulation, it is found that before damage occurs, the wind and wave induced response is more dominant than the earthquake induced response. With damage presence in the tower and the foundation, the nacelle and the tower response is increased dramatically and the natural frequency is decreased considerably. As a result, the passive TMD with fixed parameters becomes off-tuned and loses its effectiveness. In comparison, the STMD retuned in real-time demonstrates consistent effectiveness in controlling the dynamic response of the monopile offshore wind turbines under multi-hazards and damage with a smaller stroke.

Comparison of hydrodynamic loading models for vertical cylinders in nonlinear waves

This paper introduces a comparison study between various hydrodynamic loading models in highly nonlinear waves and discusses its first phase - comparing Morison equation and Rainey corrections on a fixed cylinder in regular steep waves. In this study both of these two models showed similar results when compared against experimental data. Morison equation is found to capture the amplitude of the loading sufficiently well. However, neither model was able to capture higher-order loading components which are apparent in very steep waves and are associated with ringing. The main conclusion of this work is the identification of the need of a more appropriate loading model.

Vortex-induced vibrations of a vertical riser with time-varying tension

Numerical simulations of a vertical tensioned riser in a sheared flow are performed, where the riser top end oscillates sinusoidally in the vertical direction. The oscillating top-end motion causes tension variations and changes in the natural frequencies of the riser. The flow around the structure causes vortex shedding, oscillating lift forces and vortex-induced vibrations (VIV). It is well-known that the vortex shedding is affected by structure motion, and may lock on to the riser’s natural frequencies. However, the vortex shedding frequency must remain close to the Strouhal frequency, and may therefore excite different modes of vibration as the riser tension changes. With this in mind, the overall aim of this paper is to investigate how tension variations affect the VIV response. The riser dynamics are simulated in time domain using a non-linear finite element structural model combined with an empirical hydrodynamic load model. The latter includes a synchronization model which simulates how the vortex shedding reacts to the structure motion to obtain lock-in. Simulations are run using different amplitudes and frequencies for the top-end motion, and the resulting cross-flow displacements and bending strains are studied. The results show that, when the riser top-end oscillates, the VIV response contains several modes, and the dominating mode may vary with time. The number of active modes are found to be strongly dependent on the period of the riser tension.

Non-linear time domain analysis of cross-flow vortex-induced vibrations

A previously proposed hydrodynamic load model for time domain simulation of cross-flow vortex-induced vibrations (VIV) is modified and combined with Morison's equation. The resulting model includes added mass, drag and a cross-flow vortex shedding force which is able to synchronize with the cylinder motion within a specified range of non-dimensional frequencies. It is demonstrated that the hydrodynamic load model provides a realistic representation of the cross-flow energy transfer and added mass for different values of the non-dimensional frequency and amplitude. Furthermore, it gives a reasonable approximation of the experimentally observed drag amplification. The load model is combined with a non-linear finite element model to predict the cross-flow VIV of a steel catenary riser in two different conditions: VIV due to a stationary uniform flow and VIV caused by periodic oscillation of the riser top end. In the latter case, the prescribed motion leads to an oscillating relative flow around the riser, causing an irregular response. The simulation results are compared to experimental measurements, and it is found that the model provides highly realistic results in terms of r.m.s. values of strains and frequency content, although some discrepancies are seen.

DeRisk — Accurate Prediction of ULS Wave Loads. Outlook and First Results

Loads from extreme waves can be dimensioning for the substructures of offshore wind turbines. The DeRisk project (2015-2019) aims at an improved load evaluation procedure for extreme waves through application of advanced wave models, laboratory tests of load effects, development of hydrodynamic load models, aero-elastic response calculations and statistical analysis. This first paper from the project outlines the content and philosophy behind DeRisk. Next, the first results from laboratory tests with irregular waves are presented, including results for 2D and 3D focused wave groups. The results of focused wave group tests and a 6-hour (full scale duration) test are reproduced numerically by re-application of the wave paddle signal in a fully nonlinear potential flow wave model. A good match for the free surface elevation and associated exceedance probability curve is obtained. Finally, the utilization of DeRisk's results in practical design is discussed.

Experimental and numerical study of an aquaculture net cage with floater in waves and current

The mooring loads on an aquaculture net cage in current and waves are investigated by dedicated model tests and numerical simulations. The main purpose is to investigate which physical effects are dominant for mooring loads, and in this respect, to investigate the validity of different rational hydrodynamic load models. Also structural and numerical aspects are investigated. The model tests are performed to provide benchmark data, while the numerical model is used to study the effect and sensitivity of different load models and parameters.Compared to a realistic aquaculture plant, the total system is simplified to reduce the complexity. The system does, however, include all the four main components of an aquaculture plant: net cage, floater, sinker weights and moorings. The net cage is bottomless, flexible and circular. It is attached to a circular, elastic floater at the top and has 16 sinker weights at the bottom. The system is nearly linearly moored with four crow feet mooring lines.The loads are measured in the four mooring lines. A systematic variation of current only, wave only as well as combined current and wave conditions is carried out. The numerical simulation results are first benchmarked towards the experimental data. The mean loads in general dominate over the dynamic part of the loads in combined current and waves, and they significantly increase in long and steep waves, relative to current only. Next, a sensitivity study is carried out. A rigid floater significantly alters the loads in the mooring lines compared to a realistic, elastic floater. The theoretical model for the wave matters. The mooring loads are rather insensitive to a majority of the parameters and models, in particular: frequency dependent added mass of the floater and nonlinear restoring loads. It seems not to be necessary to represent the net cage with a very fine numerical mesh.

Wave load resistance of high strength concrete slender column subjected to eccentric compression

A computer based iterative numerical procedure has been developed to analyse reinforced high strength concrete columns subjected to horizontal wave loads and eccentric vertical load by taking the material, geometrical and wave load non-linearity into account. The behaviour of the column has been assumed, to be represented by Moment-Thrust-Curvature relationship of the column cross-section. The formulated computer program predicts horizontal load versus deflection behaviour of a column up to failure. The developed numerical model has been applied to analyse several column specimens of various slenderness, structural properties and axial load ratios, tested by other researchers. The predicted values are having a better agreement with experimental results. A simplified user friendly hydrodynamic load model has been developed based on Morison equation supplemented with a wave slap term to predict the high frequency non-linear impulsive hydrodynamic loads arising from steep waves, known as ringing loads. A computer program has been formulated based on the model to obtain the wave loads and non-dimensional wave load coefficients for all discretised nodes, along the length of column from instantaneous free water surface to bottom of the column at mud level. The columns of same size and material properties but having different slenderness ratio are analysed by the developed numerical procedure for the simulated wave loads under various vertical thrust. This paper discusses the results obtained in detail and effect of slenderness in resisting wave loads under various vertical thrust.

Influence of wind–waves energy transfer on the impulsive hydrodynamic loads acting on offshore wind turbines

This paper draws some preliminary considerations about the direct wind effects on the kinematics and dynamics of steep extreme waves propagating near offshore wind turbines. Most of the hydrodynamic load models currently employed in designing offshore wind turbines take into account only indirectly the role of the wind. In fact, once the sea severity upon a certain wind speed is established, the sea state is fully determined by means of the significant wave height and the peak spectral period. In contrast, recent experimental results show that the local wind strongly influences the evolution of steep waves. A wind–waves energy transfer model is here implemented in a fully nonlinear potential flow model for wave-propagation. First, the laboratory experimental evidences about the influence of the wind on the propagation of steep waves are confirmed numerically by simulating the 2D propagation of a Gaussian wave packet. Second, real environmental conditions are reproduced in the near field of an offshore wind turbine using linear–nonlinear potential flow models within a novel coupling strategy. Different wind-wave relative speeds are simulated attempting to quantify the influence of the wind on the wave propagation. Although a reliable evaluation of this influence is still an open issue, the importance of some physical parameters, such as the duration of the energy transfer, is highlighted.

Non-Gaussian Model for Ringing Phenomena in Offshore Structures

Significant interest has been shown in identifying the nonlinear mechanisms that induce a ringing type response in offshore structural systems. This high frequency transient type response has been observed in offshore systems, particularly in tension leg platforms (TLPs). Given the implications of this behavior on the fatigue life of TLP tendons, it is essential that ringing be considered in the overall response evaluation. This study presents two non-Gaussian probabilistic models of nonlinear viscous hydrodynamic wave forces that induce ringing. The response of a single-degree-of-freedom system exposed to these non-Gaussian wave force models is then evaluated using analytical and numerical studies based on the Ito⁁ differentiation rule and the Monte Carlo simulation procedure, respectively. The results demonstrate that the proposed models induce ringing type response in a simplified structure. This study provides a probabilistic framework for modeling ringing type phenomenon which will serve as a building block for more refined hydrodynamic load models.

Flexible riser analysis — comparison of results from computer programs

The paper presents results from static and dynamic analyses of standard flexible riser systems performed by 11 different institutions using their in-house computer programs. The study was initiated by the International Ship and Offshore Structures Congress (ISSC) Committee V.7 ‘Slender Marine Structures’, and partly included in the 1991 Congress report presented in Wuxi, China. This study presents only the results from the analyses and does not comment on the programs' efficiency or ability to model the various physical effects. The main conclusions from the study are: - static analysis of flexible risers is today a straightforward task although it does not represent important uncertainties when dealing with simple riser systems. In some cases it is possible that significant discrepancies may be obtained if different modelling of tangential drag forces and riser/seafloor interaction are used. - Results from dynamic analyses show a larger scatter, and a coefficient of variation of 10–15% in dynamic tension must be expected. Hydrodynamic loading and structural damping models are seen to be the main sources for this uncertainty. The paper contains a complete description of the test cases and reports results in such a way that it can provide a ‘benchmark’ test for users and programmers of computer codes for flexible riser analysis.