Irregular Sea Research Articles

Optimal control of nonlinear wave energy point converters

In this paper the optimal control law for a single nonlinear point absorber in irregular sea-states is derived, and proven to be a closed-loop controller with feedback from measured displacement, velocity and acceleration of the floater. However, a non-causal integral control component dependent on future velocities appears in the optimal control law, rendering the optimal control law less useful for real time implementation. To circumvent this problem a causal closed-loop controller with the same feedback information is proposed, based on a slight modification of the optimal control law. The basic idea behind the control strategy is to enforce the stationary velocity response of the absorber into phase with the wave excitation force at any time. The controller is optimal under monochromatic wave excitation. It is demonstrated that the devised causal controller, in plane irregular sea states, absorbs almost the same power as the optimal controller.

Investigation of depth effects on the wave exciting low frequency drift forces by different approximation methods

The paper presents an experimental and numerical investigation on the slowly varying wave exciting drift forces acting on a body of simple geometry subjected to bichromatic waves and long crested irregular seas. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom and it is restrained from moving. Three different water depths representing shallow, intermediate and deep waters are considered.The objective is, firstly, to investigate the relation between the water depth, the incident wavelength and the resulting slowly varying drift force. The other objective is to assess the accuracy of different approximations to the solution of the second order problem. With this aim in mind, the quadratic transfer functions are calculated with a boundary element method using several different levels of approximation for the second order forces, as described in the following sentences. The most complete approximation solves the boundary value problem completely up to the second order. The first-order approximation is similar to the former; however, the second order boundary value problem is simplified by neglecting the free surface forcing. The simpler method is of zeroth-order with respect to the difference frequency and it is commonly known as Newman's approximation. A fourth approximation is evaluated, which combines Newman's approximation with a contribution from the second order incident wave potential.A fifth approximation is applied to the vertical second order forces only and it consists on, first, calculate the steady vertical second order force in monochromatic waves corrected by an additional setdown, and second, apply Newman's approximation together with the corrected second order steady vertical forces. The additional setdown is derived from the second order incident bichromatic wave potential as the difference frequency tends to zero.Second order WAMIT code is used for the frequency domain hydrodynamic calculations. The numerical results are compared with experimental data in bichromatic waves and in irregular waves.This study shows that the contribution from the second order velocity potential must be considered for shallow waters calculations to achieve accurate results. For small difference frequencies, second order scattering potential effects are small; therefore, in this case, a good practical approximation consists on considering the second order potential is contributed by the incident waves only.

Rolling of a transport barge in irregular seas, a comparison of motion analyses and model tests

With sea transport of heavy objects in focus, model tests of a barge in irregular waves have been performed. Securing the transported object to the deck of the barge is of vital importance, and an optimum load level to be used in the structural design is desirable. The aim is to investigate methods for predictions of barge roll motion and related sea fastening forces. Response from linear and non-linear numerical analyses is compared with results of model tests. It is found that the numerical analyses give slightly conservative results, and that the nonlinear time-domain analyses gives only marginally more accurate results than the linear frequency domain method.

Computationally efficient approaches to fatigue analysis of deepwater risers

Riser long-term fatigue performance is an important design consideration. Although extensive application of irregular sea analysis in time domain with the rainflow counting technique for post-processing is regarded as the most accurate of the approaches for fatigue analysis, it does suffer from some limitations, such as the computational effort. For this reason, two computationally efficient approaches are employed to perform the fatigue analysis of a deepwater top-tensioned riser, based on the Longuet-Higgins distribution and time domain scaling respectively. With Longuet-Higgins distribution irregular wave sea states are expanded into their individual wave bins. These regular wave simulations are of short duration and consequently run quickly. Using the time domain scaling technique, the number of irregular wave runs can be performed for a comparatively small number of load cases and hence reduces the calculation time. The results showed a reasonable accuracy and significant efficiency for both approaches, compared with those from the equivalent rainflow analysis. With much less computational effort and disk storage requirement, the approaches outlined in this paper can therefore be used for the fatigue assessment of deepwater risers in industry practice.

Scour below submarine pipelines under irregular wave attack

Submarine pipelines are widely used coastal structures, and scour around them can influence their stability. In this study, scour around rigid submarine pipelines under normal-incidence irregular wave attack on horizontal and (1/10) sloping beaches is studied. This paper presents experimental results concerning scour under irregular wave attack. Multiple regression analysis is used to develop models to predict the scour depth under pipelines under the influence of irregular wave attack. The representative wave parameters that characterize the irregular sea state that causes the same scour depth as regular wave attack were determined.

Optimal Active Control and Optimization of a Wave Energy Converter

This paper investigates optimal active control schemes applied to a point absorber wave energy converter within a receding horizon fashion. A variational formulation of the power maximization problem is adapted to solve the optimal control problem. The optimal control method is shown to be of a bang-bang type for a power takeoff mechanism that incorporates both linear dampers and active control elements. We also consider a direct transcription of the optimal control problem as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard NLP solver. Since the system model is bilinear and the cost function is not convex quadratic, the resulting optimization problem is not a quadratic program. Results will be compared with an optimal command latching method to demonstrate the improvement in absorbed power. All time domain simulations are generated under irregular sea conditions.

Inversion of sound speed profile in three-dimensional shallow water based on transmission time

Horizontal deflection often occurs when a ray propagates in shallow water with an irregular sea bottom, which makes it difficult to determine eigen-ray trajectory and transmission time. A new method for seeking eigen-ray in three dimensions was proposed and sound speed profile (SSP) was inverted in three-dimensional shallow water using the fastest eigen-ray transmission times to form the cost function. In order to satisfy long-time monitoring of SSP, a kind of sonobuoy was developed with the function of DGPS, short wave radio controlling and dada transmission and experiment was implemented in the South China Sea. It is indicated that the sonobuoy has high reliability and stability in rough sea condition. The precision of SSP inversion can be enhanced dramatically by considering horizontal deflections of eigen-ray. In addition, the influence of small mismatch of seabed depth on precision of inversion can be neglected.

The influence of forward speed on ship motions in abnormal waves: Experimental measurements and numerical predictions

Ship encounters with abnormal waves are increasingly well documented and it is therefore important to be able to model such encounters in order to assess the risks involved and whether there is a requirement for more stringent design rules.This paper presents the results of an experimental investigation into the influence of abnormal waves on a vessel travelling with forward speed in irregular seas. The vessel studied in this case is a naval frigate travelling at a range of speeds. To put the motions measured in abnormal waves into context comparisons are made to those in random seas with a variety of significant wave heights, both non-severe and severe. A further objective is to compare experimental measurements with motion predictions from both a two-dimensional linear strip theory and a three-dimensional partly nonlinear seakeeping model.Results demonstrate that abnormal waves may not necessarily be the worst conditions that a ship can encounter. However, accelerations derived from the rigid body motions appear to be in excess of rules values. This has implications for design due to the unexpected nature of abnormal wave occurrence and the consequent likelihood of encountering such a wave at a higher speed (hence in a more severe operating condition) than a random sea of an equivalent height.The three-dimensional partly nonlinear model demonstrates improved agreement with experimental measurements of rigid body motions, compared to the two-dimensional strip theory. It is therefore considered to have greater potential as a design tool for abnormal wave encounters. Further validation with a wide range of sea states and vessel types is required.

Vertical plane response of a ship on irregular seas

This work presents the study of the sea response on the vertical plane for a 40-m length overall coastal patrol vessel (CPV-40) of Colombia’s National Navy. The condition studied is at full load and at patrol and maximum speeds. First, we analyzed the response for regular waves with incidence angles of 90º, 120º, 150º, and 180º, obtaining the response for heave and pitch motions through the SCORES program that uses the method called “girdle theory”. From the response, it was verifiedthat the amplitudeof the response is proportional to the amplitudeof the incident wave. Thereafter, the calculation of the vertical acceleration was made for four ship positions: bow, stern, cabin, and bridge, with the greatest vertical accelerations on the bow. Finally,the study was conducted for irregular sea considering as measuring parameters the vertical acceleration on the bridge and the pitching angle for the patrol operation, from the NATO document, compliance was verified of the study parameters at RMS level. It was found that for this condition the vessel complies and, hence, the personnel will not be affected in the performance of their functions.

Corrigendum to 3D acoustic modelling and waveform inversion in the Laplace domain for an irregular sea floor using the Gaussian quadrature integration method [Journal of Applied Geophysics] 87 (2012) 107–117

Corrigendum to 3D acoustic modelling and waveform inversion in the Laplace domain for an irregular sea floor using the Gaussian quadrature integration method [Journal of Applied Geophysics] 87 (2012) 107–117

Experimental validation of non-linear deterministic prediction schemes for long-crested waves

This paper describes the experimental validation of non-linear deterministic prediction tools for unidirectional seas, based on the use of two different non-linear wave models: (i) a so called “second order model enhanced”, which is analytic, and (ii) the numerical HOS wave model, which is run at order 3 in our simulations. Both prediction models use time traces of the surface elevation measured at one or several wave probes as an initial condition. Two effective data assimilation processes are used to optimize the model-reconstructed probes measurements, and thus ensure proper initial conditions for the forecast. The validation of our prediction tools on model-generated wave data has been reported in the previous paper (Blondel et al., 2010). Accurate predictions were reported compared to linear predictions. In the present study, the predictions are compared to different sets of laboratory measurements collected in a towing tank. The good agreement between the model-predicted surface elevations and the related experimental measurements indicates that our models can predict irregular long-crested seas more accurately than basic linear approaches with computational costs compatible with the short-term constraint.

Quasi-chaotic behaviors of narrow-band response of a non-deterministic resonant system: application to analysis of ship motion in irregular seas

This paper describes similarities between the narrow-band response of a resonant system excited by random inputs and low-dimensional chaos, with particular emphasis on the geometric characteristics of trajectories reconstructed in m-dimensional phase space from measured scalar time series data with a time-delay coordinate system. In this study, the time series data of ship roll angle in irregular waves were analyzed as an example of the narrow-band response of a resonant system. These time series data were measured by one of the authors in Tokyo Bay. The similarities between the narrow-band response of a resonant system excited by random inputs and low-dimensional chaos are verified by numerical simulation data.

3D acoustic modelling and waveform inversion in the Laplace domain for an irregular sea floor using the Gaussian quadrature integration method

Abstract This paper explores the concept of 3D acoustic modelling and inversion in the Laplace domain. We used the Gaussian quadrature integration method to assemble the element mass matrix of a coarse regular rectangular element containing both water and subsurface parts, approximating the properties of these two parts without refining the element into smaller components. The purpose of this investigation was to model an irregular sea floor using 3D Laplace-domain modelling and inversion without increasing the computational cost incurred when using a small grid interval to precisely delineate the sea floor. The algorithm was verified by comparing the analytical solution to the modelled wavefield obtained using the conventional Laplace-domain modelling method and the modelled wavefield obtained using the Gaussian quadrature integration in a two-layer model (with 50-m, 100-m, and 200-m grid spacing and 5, 10, 20, and 40 Gaussian quadrature integration points) where an oblique water–subsurface interface is given. The results show that, under certain conditions, the Gaussian quadrature integration method can generate relatively accurate and consistent wavefields compared to the conventional modelling method. Moreover, we performed 3D Laplace-domain inversion with this Gaussian quadrature modelling technique to obtain synthetic data with a flat and irregular interface using a 100-m and 200-m grid. The results obtained under the conditions herein show that 3D Laplace-domain waveform inversion with Gaussian quadrature integration can generate a more accurate and cost-efficient velocity model compared to that obtained using conventional Laplace-domain waveform inversion.

Physical model studies and system identification of hydrodynamics around a vertical square-section cylinder in irregular sea waves

In the present study, the results obtained from a series of experiments conducted in a wave flume were investigated to assess the hydrodynamic characteristics and pressure distribution around a vertical square-section cylinder in irregular waves. Experimental measurements were taken at moderately high Reynolds numbers and low Keulegan-Carpenter numbers with the cylinder at different rotation angles. The ARMAX (Auto Regressive Moving Average with exogenous input) parametric model was proposed as a numerical approach to model the variation of the hydrodynamic pressure on the cylinder over time based on the concept of system identification. The validation results demonstrated that the ARMAX model was able to simulate the signals of the wave pressure on the front side of the cylinder but failed for most of the points located after the separation points. The results obtained using the principal component approach and the concept of subspace angle implied that the efficiency of the proposed model depended on the onset of nonlinear behavior in the measured data. It was due to the non-linearity induced by the flow patterns after the separation points.

3-D seakeeping analysis with water on deck and slamming. Part 2: Experiments and physical investigation

A synergic 3-D experimental and numerical investigation is conducted for wave–ship interactions involving the water-on-deck and slamming phenomena. The adopted solver has been developed in Greco and Lugni (in press) and combines (A) a weakly nonlinear external solution for the wave–vessel interactions with (B) a 2-D in-deck shallow-water approximation, which describes water shipping events, and (C) a local analytical analysis of the bottom-slamming phenomenon. This solver can handle regular and irregular sea states and vessels at rest or with limited speed. The experiments examine a patrol ship at rest or with forward speed that is free to oscillate in heave and pitch in regular and irregular waves. In this study, the head-sea regular-wave conditions are examined in terms of (1) response amplitude operators (RAOs) and relative motions, (2) occurrence, features and loads of water-on-deck, bottom-slamming and flare-slamming events and (3) added resistance in waves. A systematic and comprehensive analysis of the phenomena is made available in terms of the Froude number, incoming wavelength-to-ship length ratio and wave steepness for the examined ship geometry. The main parameters that affect the global and local quantities are identified and possible danger in terms of water-on-deck severity and structural consequences are determined. Different slamming behaviors were identified, depending on the spatial location of the impact on the vessel: single-peak, church-roof and double-peak behaviors. A bottom-slamming criterion, using the Ochi's (1964) velocity condition and the Greco and Lugni's (2012) pressure condition, is assessed. A statistical analysis of more than 100 events is needed for the bottom-slamming pressure peaks. The numerical solver is promising. The major discrepancies with the experiments are discussed, and the importance of viscous hull damping and flare impact for the most violent conditions is emphasized. Inclusion of these effects improved the numerical solution.

A Barotropic Model of the Red Sea Circulation

A linear depth-averaged numerical model of the horizontal barotropic circulation of the Red Sea is developed. The flow considered is incompressible, quasi-steady and free from vertical buoyancy currents and horizontal density currents. The model predicts general water circulation as affected by friction stresses at the irregular Red Sea bottom and coastal features, variable Coriolis force, vertical, and lateral turbulent friction, and seasonal non-uniformity of wind stress at the sea surface. The implicit finite-difference solution of the boundary value problem is verified with previous solutions for a rectangular constant-depth sea and for an elliptical lake with uniformly-sloping bottom topography. The model output is shown as plots of seasonally-averaged mass-transport vectors and circulation streamlines in the Red Sea basin.

3-D seakeeping analysis with water on deck and slamming. Part 1: Numerical solver

A three-dimensional seakeeping numerical solver is developed to handle occurrence and effects of water-on-deck and bottom slamming. It couples (A) the rigid-ship motions with (B) the water flowing along the deck and (C) bottom slamming events. Problem A is studied with a 3-D weakly nonlinear potential flow solver based on the weak-scatterer hypothesis. Problem B, and so local and global induced green-water loads, are investigated by assuming shallow-water conditions onto the deck. Problem C is examined through a Wagner-type wedge-impact analysis. Within the coupling between A and B: the external seakeeping problem furnishes the initial and boundary conditions to the in-deck solver in terms of water level and velocity along the deck profile; in return the shallow-water problem makes available to the seakeeping solver the green-water loads to be introduced as additional loads into the rigid-motion equations. Within the coupling between A and C: the instantaneous ship configuration and its kinematic and dynamic conditions with respect to the incident waves will fix the parameters for the local impact problem; in return the slamming and water-entry pressures are integrated in the vessel region of interest and introduced as additional loads into the rigid-motion equations. The resulting numerical solver can study efficiently the ship interaction with regular and irregular sea states and the forward motion with limited speed of the vessel. This is crucial to perform reliable and feasible statistical investigations of vessel behavior. Main elements of the solver are described and validated against reference numerical solutions and model tests.

Heave Compensator를 고려한 파랑 중 해상 크레인 설치작업 수치해석

In this study, a numerical analysis of offshore installation using a floating crane with heave compensator is carried out in time domain. The motion analysis of crane vessels is based on floating body dynamics using convolution integral and the crane wire is treated as simple spring. The lifted structure is assumed as a rigid body with 3 degree-of-freedom translational motion. The heave compensator is numerically modelled by the generalized spring-damper system. Firstly, forced motion simulations of crane wire system are carried out to figure out the basic principle of heave compensator. The transfer function of crane wire system is obtained and effective wave period of heave compensator are found. Then, coupled analysis of crane vessel, crane wire, and lifted structure are performed in regular and irregular sea conditions. Two different crane vessels and two lifted structures (suction pile and manifold) are considered in this study. Through a series of numerical calculations, the effective zone of heave compensator is investigated with respect to wave period and crane wire length.

Estimation of ship speed loss and associated CO2 emissions in a seaway

A reliable prediction of attainable ship speed at actual seas is essential from economical and environmental aspects. A methodology for estimating the attainable speed in moderate and severe sea is proposed. The irregular sea is handled as a series of regular waves with different amplitudes and frequencies. The added resistance in regular waves is obtained by either a direct pressure integration method or an asymptotic small wavelength formula. The in-and-out-of-water-effect and ventilation of a propeller in severe seas is accounted for by a quasi-steady averaging of experimental data for different propeller submergences. The propulsion results for regular waves are used in simulating results in irregular waves. It is shown that for higher sea states this effect has much more influence on the speed loss than the added resistance in waves. The speed loss is calculated by taking into account the engine and propeller performance in actual seas as well as the mass inertia of the ship. The attainable ship speed is obtained as time series. Correlation of speed loss with sea states allows predictions of propulsive performance in actual seas. The expected CO2 emission for a containership is estimated for the Northern route of North Atlantic.

Discrete control of resonant wave energy devices

Aiming at amplifying the energy productive motion of wave energy converters (WECs) in response to irregular sea waves, the strategies of discrete control presented here feature some major advantages over continuous control, which is known to require, for optimal operation, a bidirectional power take-off able to re-inject energy into the WEC system during parts of the oscillation cycles. Three different discrete control strategies are described: latching control, declutching control and the combination of both, which we term latched-operating-declutched control. It is shown that any of these methods can be applied with great benefit, not only to mono-resonant WEC oscillators, but also to bi-resonant and multi-resonant systems. For some of these applications, it is shown how these three discrete control strategies can be optimally defined, either by analytical solution for regular waves, or numerically, by applying the optimal command theory in irregular waves. Applied to a model of a seven degree-of-freedom system (the SEAREV WEC) to estimate its annual production on several production sites, the most efficient of these discrete control strategies was shown to double the energy production, regardless of the resource level of the site, which may be considered as a real breakthrough, rather than a marginal improvement.