Drift Loads Research Articles

A Wave Drift Force Model for Semi-Submersible Types of Floating Wind Turbines in Large Waves and Current

The correct prediction of slowly varying wave drift loads is important for the mooring analysis of floating wind turbines (FWTs). However, present design analysis tools fail to correctly predict these loads in conditions with current and moderate and large waves. This paper presents a semi-empirical method to correct zero-current potential-flow quadratic transfer functions (QTFs) of horizontal wave drift loads in conditions with current and moderate and large waves. The method is applicable to column-stabilized types of substructures or semi-submersibles. In the first step, the potential-flow QTF is corrected for potential-flow wave–current effects by applying a heuristic method. Second, the generalized Exwave formula corrects for viscous drift effects. Viscous drift effects become important for moderate and large waves. Conditions with current in the same direction as the waves increase the viscous drift contribution further. The method is validated by comparing QTF predictions with empirical QTFs identified from model test data for the INO Windmoor semi. While potential-flow QTFs agree well with the empirical data for small seastates without current, they underestimate the wave drift loads for moderate and large seastates. Conditions with current increase the underestimation. The semi-empirical correction method significantly improves predictions.

A Deep-Penetrating Geochemical Prospecting Experiment of Mahuagou Gold Deposit in the Core of the Huangling Anticline, Western Hubei, China

The Mahuagou gold deposit is among the most important gold deposits in the core of the Huangling Anticline. However, the geochemical exploration on the surface of the mining area presents challenges due to the thin overburden. This paper focuses on the overburden soil of the Fengxiangshugou (FXS)-Mahuanggou (MHG) section as the research object. It utilizes chemical form analysis of gold, soil halogen survey, and heat-released mercury survey to determine the key deep-penetrating geochemical methods for the mining area. The results indicated that Si and Al components of samples exhibit minimal variation, suggesting that drift loads did not influence the overburden soil. Based on the systematic clustering, As, Sb, Mo, Bi, W, and Hg emerge as ore-body or ore-belt front elements of hydrothermal gold deposits. In the study area, the predominant chemical form of gold in soil is the strong organic bond. Compared to the total amount, strong organic bound gold and heat-released mercury show higher anomaly contrasts, making them crucial indicators of faults, intrusions, and hidden ore bodies. Consequently, chemical form analysis of gold and heat-released mercury surveys can enhance the anomaly contrast, proving beneficial for geochemical prospecting for weak anomalies in this area.

Dynamic analysis of the subsea production system with lazy-wave risers attached to FPSO.

The lazy-wave riser is an input and output riser for a flexible development system, which is widely used in all the riser and pipeline systems. Because of the influence of various factors, its configuration description, control and motion which have a strong nonlinear character are complex during the running process of the lazy-wave riser. Reference to the specific structure and environmental parameters of a certain lazy-wave risers system with a 300 thousand tons FPSO, with the basis of the specific process of the flexible riser system at work, the lazy-wave risers were discretized into lumped mass models, combined with AQWA, the simplified dynamic model of the whole system at the depth of 2100m has been established by the large hydrodynamic analysis software OrcaFlex. The dynamic response characteristics of the lazy-wave risers have been given by using time domain coupling method. With and without the consideration of the 2nd wave drift load in the simulation process, the effects of the 2nd wave drift load on the results are obtained. The simulation results reveal the difficulty of simulation convergence caused by a large number of risers and flexible components. The 2nd order wave drift loads have a significant effect on the riser system, resulting in the increasement of the effective tension at each end of each riser. To counteract the magnitude of the FPSO response caused by such loads, the number of mooring lines needed to be increased or combined with dynamic positioning techniques to optimize the design.

Hydroelastic interactions between waves and an array of submersible flexible fish cages

In this study, a semi-analytical solution is developed to investigate the wave interference and corresponding dynamic responses of an array of submersible flexible fish cages. The net chamber is modelled as a perforated cylindrical shell, and the penetration flow through the cage interface is described by a porous medium model. Based on the potential flow theory, the solution to this physical problem is expanded as a series of eigenfunctions in the local coordinate system of each cage, and the scattered wave potentials generated by all cages are superimposed wherein Graf's addition theorem is employed for the coordinate transformation. The mean wave drift effect is also explored, which is a nonlinear phenomenon derivable from the first-order solution. The results indicate that the interference of waves is determined by wavenumbers, cage spacings or net porosities, and significant wave responses are manifested near the top part of the cage. Additionally, the first-order wave force vanishes at a ratio of cage diameter to wavelength = 0.59, and, along the direction of wave incidence, the rear cages experience opposite mean wave drift loads relative to those on the front cages. These studies provide benchmark results for understanding the hydroelastic characteristics of multi-cage systems.

Comparative Study on Predicting Ship Maneuvering in Waves Using a Quasi-Steady Method and a Time Domain Approach

_ Numerical prediction of ship maneuvering in waves was considered in this article. The wave drift loads, computed using the potential flow theory, were added into the mathematical modeling group (MMG) equations to account for the effect of waves on the ship maneuvering. Two numerical methods were tested for dealing with the coupled maneuvering-seakeeping problem, namely a time domain approach and a quasi-steady method. For the former approach, a time domain seakeeping computation was conducted that parallels to the maneuvering simulation. For the later one, it is assumed that at each time of the maneuvering process, the wave-ship interaction is in a time harmonic status and, therefore, the wave drift loads could be evaluated using a frequency domain computation. Turning maneuvers of the S-175 container ship in regular waves were numerically tested. The results of the quasi-steady method and the time domain approach show good agreements, which proved the validity of the quasi-steady assumption. The wave drift loads during the turning process were also presented, demonstrating the significant effect of the added resistance on the maneuvering prediction, in contrast to the less remarkable effects of the lateral wave drift force and the wave drift yaw moment. Introduction Ship maneuverability is typically predicted under calm water condition. This provides valuable information at the ship design stage. However, an actual seagoing ship usually maneuvers in waves. To reliably assess a ship’s navigation safety and total performance in a seaway, it is deemed important to understand the maneuvering behavior of a ship in waves. Indeed, ship maneuverability in waves has been increasingly investigated in recent years. Although the physical experiment is still regarded as the most reliable way to investigate ship maneuverability in waves, there are more and more studies providing practical mathematical models of ship maneuvering prediction. Generally, a mathematical model that is suitable for investigating the maneuvering of a ship in waves has to encapsulate the traditional theories of calm water maneuvering and forward-speed seakeeping.

A numerical approach for hydrodynamic performance evaluation of multi-degree-of-freedom floating oscillating water column (OWC) devices

A numerical approach has been developed in this study for hydrodynamic analysis of complex-shaped oscillating water column (OWC) converters. Physically, in the circumstance when the device is free to move or moored in waves, the airflow movement inside the chamber is coupled tightly with the changing of the internal fluid surface and the hydrodynamic response of the device. By taking these coupling effects into account, appropriate boundary integral equations are formulated with supplemental theoretical relations. The boundary value problem is then solved using a higher-order boundary element method (HOBEM). After obtaining the wave force and dynamic air force, the coupled motions and hydrodynamic efficiency are evaluated by integration. In particular, unlike conventional methods limited to fixed OWCs, the proposed method is proved applicable to those floating with coupled rigid-body motions. An optimal turbine parameter is hence mathematically derived to maximise the wave power absorption. Besides the linear quantities, nonlinear wave drift loads are evaluated via a newly derived formulation that accounts for the far-field contribution and the oscillating air pressure over the internal fluid surface. Based on the above methodology and the resulting tool, numerical studies are carried out for three cylindrical OWC scenarios that are floating in waves, attached by a reflector and connected to a submerged caisson, respectively. Different modes of body motion and typical free-surface oscillation modes in the chamber are analysed and discussed. It is found that, for an OWC with an attached arc-shaped reflector or connected to a submerged caisson, its wave power absorption can be characterised by a series of apparent peaks which are associated with the resonant internal fluid and in close proximity to the resonance frequencies of body motions involving surge, heave or pitch. Numerical results also indicate the benefits of floating OWCs from the coupled rigid-body motion modes and OWC’s resonance, expanding the frequency range of efficient conversion and improving the device’s adaptability to variable oceanic environments.

Hydrodynamic analysis of resonant waves within the gap between a vessel and a vertical quay wall

Concerning the side-by-side offloading operations at gravity-based terminals, the wave interaction with a vessel alongside a long vertical wall in both normal and oblique seas was investigated. The imaging principle was applied to convert the original to an equivalent wave-diffraction problem by two symmetrical vessels in open seas exposed to bi-directional incident waves. The boundary integral equation method, in conjunction with a higher-order boundary element method (HOBEM), was used to solve the equivalent problem. Besides the linear free-surface elevation and wave loads, the second-order mean wave drift loads on the vessel was calculated based on either the direct pressure integration or using a semi-cylindrical control surface. Moreover, the solution was also developed for the oblique wave interaction with a two-dimensional barge-wall system using the eigenfunction expansion matching method. Systemic numerical studies were then conducted for the cases of a rectangular barge and a Wigley hull in close proximity to a long wall, respectively. Under oblique incidence, both the odd and even modes of fluid motion within the gap can be induced. In the case of a rectangular barge, the linear wave force can be obviously amplified at the location of the (1, 0) resonant mode, while the linear wave moment at the (2, 0) mode. In addition, the negative mean force along the transverse direction, which tends to push the barge away from the wall, can be apparently enhanced at both the odd and even resonant modes. Besides, in oblique seas, the (1, 0) resonant mode can give rise to the significant amplification of the positive mean yaw moment around the centre of the cross-sectional area of the barge, which tends to pull the stern of the barge (that faces incident waves) closer to the wall, while pushing the bow away from the wall. Such amplification gets less noticeable for higher modes. Numerical results also indicate that the hull geometry imposes a significant impact on the resonant waves in the gap. In the case of a Wigley hull, the amplification of the free-surface response is much less apparent when compared with a rectangular barge.

Numerical Study of Wave Drift Load and Turning Characteristics of KVLCC2 Ship in Regular Waves Based on TEBEM

Maritime traffic has increased considerably in recent years, making energy efficiency and navigation safety of ships more crucial than ever. Hence, a two-time scale model based on the Taylor expansion boundary element method (TEBEM) is proposed to predict ship turning trajectories in regular waves. The maneuvering motion is calculated using a three degrees of freedom MMG model that considers the wave drift loads. TEBEM overcomes the shortcomings of the constant panel method in solving tangential induced velocity at a non-smooth boundary and that of the high-order boundary element method in dealing with a high-order derivative of the velocity potential at the corner. This significantly improves the calculation accuracy of the induced velocity and high-order derivative of velocity potential. Firstly, based on the TEBEM, the surge and sway wave drift forces and yaw moment of the KVLCC2 model with drift angle under full wave headings are calculated and compared with computational fluid dynamics results, using which the calculation accuracy of TEBEM is verified. Subsequently, the two-time scale model is used to calculate the turning trajectories of the KVLCC2 model in regular waves with different wave headings, wave frequencies, and wave steepness. The numerical results show that the drift angle has a certain effect on the wave drift loads of the ship, and the proposed model can effectively predict the ship’s turning motion in regular waves.

Comparative investigation: Closed versus semi-closed vertical cylinder-shaped fish cage in waves

A comparative analysis between a closed cage (CC) and a semi-closed/open-bottom cage (OC) in regular, white-noise and irregular waves is presented. Both cages consist of a vertical circular free surface-piercing cylinder with an external toroidal floater. A main target is to examine experimentally and theoretically the similarities and differences of the hydrodynamic behavior between the two cages. Transfer functions obtained from regular and white-noise waves test show that the two cages have similar performance in surge motion, ovalizing deformations, interior wave elevation and mean drift loads in shorter waves (wavelength to cage diameter ratio λ/D<1). This is not the case for heave, with OC experiencing much larger heave. A clear sinkage (minus average heave) is also observed for OC, which is almost proportional to the square of the incident wave amplitude. The linear potential flow solver WAMIT can provide a reasonable prediction of surge and pitch motions, and mean drift loads for OC in shorter waves (λ/D<1.5), but is unsatisfactory in longer waves and, in general, for heave motion.From the analysis of irregular wave tests, there is a small difference in the standard deviations of the surge motion (wave-frequency component) and interior waves for the semi-closed and closed cages. The slow-drift component is dominant in surge for both cages, with OC having a smaller value due to larger viscous damping associated with flow separation at the bottom. Theoretical evaluations of standard deviations based on transfer functions from a white-noise test and from WAMIT are performed, assuming that the linear superposition principle applies. Reasonable agreement against results from experiments in irregular waves is achieved except for response variables with strong nonlinear effects.Survival conditions for both cages are determined through systematic evaluations. The platform freeboard is identified as the most critical parameter. The minimum freeboard for the closed and semi-closed cage should be at least 1.05 and 1.3 m, respectively, to operate at moderate exposure sea states. The standard deviation of vertical acceleration due to rigid body motions and interior waves could reach 0.72 m/s2 for both cages at high exposure sea states, which might be of concern for fish inside.

Experimental study on a breaking-enforcing floating breakwater

Floating breakwaters are moored structures that attenuate wave energy through a combination of reflection and dissipation. Studies into floating breakwaters have been generally restricted to optimising the attenuation performance. This study presents a novel floating breakwater type that was developed to have good attenuation performance while keeping wave drift loads as small as possible. The floating breakwater was designed as a submerged parabolic beach that enforces wave energy dissipation through breaking. The design was tested in a 3D shallow-water wave basin in captive and moored setups for regular and irregular wave conditions. Results are presented in terms of attenuation performance, motions, and (mooring) loads. The results show that the breaking of waves improves the attenuation performance of the floater in captive setup. However, in moored setup, the attenuation performance was dominated by diffraction and radiation of the wave field, with breaking being of secondary importance. This shows that breaking-enforcing floating breakwaters have potential, but require a high vertical hydrostatic and/or mooring stiffness in order to enforce intense breaking. Mean wave drift loads on the object showed significant difference between breaking and non-breaking waves in both setups, with breaking waves leading to lower normalized loads. This is attributed to breaking-induced set-up and set-down of the water level. As a result, the new breakwater design has a more favourable balance between wave attenuation and drift loads than common (i.e., box-, pontoon-, or mat-type) floating breakwater designs. Tests with varying surface roughness showed that floating breakwaters may benefit from dual-use functions that naturally increase the roughness (e.g., shellfish, vegetation), which have a marginal effect on the attenuation performance, but increase the added mass and hydrodynamic damping and as such, reduce mooring line loads.

A rational model for maneuvering in irregular waves with the effect of waves on the propeller and rudder inflow taken into account

A modular model for maneuvering in regular and irregular waves is presented. A new model is presented for the y-component of the rudder inflow. Moreover, an efficient time-domain method for estimation of slowly varying drift loads in irregular waves is presented. Simulations of turning circles in irregular waves with the time-domain method, are compared to simulations where the difference-frequency loads, with the Newman approximation, is used to estimate the slowly varying drift loads. These two methods show similar accuracy, but the time-domain method is significantly faster. The numerical simulations are compared with new free running experiments of the Duisburg Test Case (DTC). Based on extensive wave documentation in the Ocean basin at SINTEF Ocean, the uncertainty in maneuvering experiments, due to variation of wave height throughout the basin, is investigated. The uncertainty is not insignificant, but it is less than expected. The sensitivity to number of realizations in the same irregular wave spectrum is investigated, both experimental and numerical. For some responses, up to 20 repetitions are needed before the width of the 95% confidence intervals approach convergence.

Dynamic manoeuvres of KCS with CFD free-running computation and system-based modelling

Future state projection is an important prerequisite for the maritime autonomous surface ships (MASS) to initiate a collision-avoidance manoeuvre. Forecasts of MASS′ trajectories and motions are fundamentally based on the vessel's mathematical manoeuvring model, which is also referred to as the hydrodynamic digital twin nowadays. Using the benchmark container ship KCS as an object of study, this paper adopts a 3-DOF modular-type manoeuvring (MMG) model to predict the vessel trajectories in calm water and under the presence of steady current and regular waves. The current effects are treated as additional ship over water speed, while the wave effects are considered by superimposing the mean second-order wave drift loads to the calm water hull hydrodynamics. Concurrently, selected manoeuvring cases including turning circle and zig-zag are solved using the unsteady Reynolds-averaged Navier-Stokes (uRANS) equations based CFD method, where a hierarchy of overset grids is utilised to allow self-propulsion and active rudder steering. The computed vessel trajectories and velocities are compared with that predicted by the MMG model and show reasonable agreement. The wave loads experienced by the vessel when turning in waves are also analysed and discussed.

Identification of wave drift force QTFs for the INO WINDMOOR floating wind turbine based on model test data and comparison with potential flow predictions

The paper presents a comparison between empirical and numerical quadratic transfer functions (QTFs) of the horizontal wave drift loads on the INO WINDMOOR floating wind turbine. The empirical QTFs are determined from cross bi-spectral analysis of model test data obtained in an ocean basin. Validation of the identified QTF is provided by comparing low frequency motions reconstructed from the empirical QTF with measurements. The numerical QTFs are calculated by a panel code that solves the wave-structure potential flow problem up to the second order. Systematic comparisons between numerical and empirical QTFs allows identification of tendencies of empirical QTFs and limitations of the second order potential flow predictions. The study is limited to hydrodynamic loads from waves only, i.e. without current. For small seastates, the results indicate that the second order potential flow predictions of the surge QTFs agree quite well with the wave drift coefficients identified empirically from the model test data. For moderate and high seastates, second order predictions underestimate the surge wave drift coefficients for all compared diagonals of the QTFs. The discrepancies between predictions and empirical coefficients are not small, especially at the lower frequency range (below around 0.10 Hz) where the potential flow wave drift forces tend to zero.

Experimental investigation of a closed vertical cylinder-shaped fish cage in waves

Wave-induced response of a closed floating fish cage consisting of a vertical circular cylinder with an external toroidal floater is studied theoretically and experimentally. A main purpose was to investigate how the internal sloshing would influence the global response of the cage, the interior wave elevation and also the mean drift loads. An ocean basin laboratory was used in order to minimize tank wall effects. An optical system involving eight markers was used to obtain experimental values for radial elastic deformations of the cylindrical part. The closer a coupled natural period between body motions and sloshing is to a corresponding natural sloshing period, the more nonlinear sloshing can be. In the examined case, the highest coupled natural period between surge, pitch and sloshing is 0.8 times the highest natural sloshing period. Linear potential flow theory can, in general, explain experimental transfer functions of rigid-body motions and sloshing due to rigid-body motions obtained by both regular wave and truncated white noise tests. Theoretical second order mean wave drift forces based on a rigid body and potential flow agree also well with experimental results. Resonant 3D sloshing was excited due to ovalizing hydroelastic structural modes in both regular waves and white-noise tests. The closeness between the corresponding structural and sloshing frequencies caused large response. A linear hydroelastic analysis based on WAMIT and LS-DYNA could partly explain the response. Parametric resonant pitch response occurred experimentally at large wave periods partially due to in and out of water motion of portions of the floater and was explained by treating the pitch as uncoupled motion modeled by the Mathieu equation. The pitch motion predicted by linear potential flow theory was, in general, unsatisfactory when the floater was partly out of the water occasionally.

Analytical method for loads determination on floating solar farms in three typical environments

Floating solar energy is an industry with great potential. Farms can be installed on lakes, reservoirs or offshore. Numerous projects are under study or have been realised. This study presents three reference cases for floating solar farms, with adapted environmental data: a small lake (2.5 MWp – Mega Watt Peak - island), a large lake (7.5 MWp island) and offshore (2.5 MWp island). Mooring is one of the biggest challenges of floating solar photovoltaics (PV), compared to ground-mounted solar PV. To date, most mooring designs of industrial projects have been performed by computing environmental loads using an analytical analysis. This study aims to present one of the methodologies currently used in industry to perform a mooring design and to highlight the areas where further research is necessary before continuing developing industrial projects. Wind and current loads are computed with drag forces, considering drag coefficients from norms, wind tunnel tests, computational fluid dynamics modelling and the literature. Waves drift loads are computed with the Maruo formula. Results show that wind loads dominate for all cases, except for the offshore conditions, where waves have a significant contribution to the total load (around 50%). Even though the large lake island is 3 times larger than the offshore island, the total load applied on the offshore island is higher. The main challenges in the mooring design for each case are also underlined.

Numerical simulations of a ship obliquely advancing in calm water and in regular waves

Numerical simulations of the S-175 containership obliquely advancing at constant forward speed in calm water and in regular waves were conducted using a potential flow method. A double-body potential and trailing vortex sheets, which modeled the flow field around the ship obliquely advancing in calm water, yielded transverse forces and yaw moment due to the lift effect. Perturbation potentials describing the free surface flow yielded first-order wave-induced motions and second-order wave loads. Evaluating and then averaging the associated second-order wave loads obtained the steady wave drift forces and moments. Generally, numerical predictions compared favorably to experimental measurements. A systematic analysis demonstrated that, in short beam waves, the transverse wave drift force attained considerable amplitudes, and these amplitudes increased rapidly at larger drift angles. The transverse force due to wave drift effects in beam waves and due to the lift effects in calm water were nearly of equal magnitude. Therefore, when predicting wave drift loads acting on a maneuvering ship, the effect of drift angle should be accounted for.

The Effect of Mooring Line Parameters in Inducing Parametric Resonance on the Spar-Buoy Oscillating Water Column Wave Energy Converter

Although it is widely accepted that accurate modeling of wave energy converters is essential for effective and reliable design, it is often challenging to define an accurate model which is also fast enough to investigate the design space or to perform extensive sensitivity analysis. In fact, the required accuracy is usually brought by the inclusion of nonlinearities, which are often time-consuming to compute. This paper provides a computationally efficient meshless nonlinear Froude–Krylov model, including nonlinear kinematics and an integral formulation of drag forces in six degrees of freedom, which computes almost in real-time. Moreover, a mooring system model with three lines is included, with each line comprising of an anchor, a jumper, and a clump weight. The mathematical model is used to investigate the highly-nonlinear phenomenon of parametric resonance, which has particularly detrimental effects on the energy conversion performance of the spar-buoy oscillating water column (OWC) device. Furthermore, the sensitivity on changes to jumper and clump-weight masses are discussed. It is found that mean drift and peak loads increase with decreasing line pre-tension, eventually leading to a reduction of the operational region. On the other hand, the line pre-tension does not affect power production efficiency, nor is it able to avoid or significantly limit the severity of parametric instability.

Motion predictive control for DPS using predicted drifted ship position based on deep learning and replay buffer

Typically, a Dynamic Positioning System (DPS) uses a PID feed-back system, and it often adopts a wind feed-forward system because of its easier implementation than a feed-forward system based on current or wave. But, because a ship’s drifting motion is caused by wind, current, and wave drift loads, all three environmental loads should be considered. In this study, a motion predictive control for the PID feed-back system of the DPS is proposed, which considers the three environmental loads by utilizing predicted drifted ship positions in the future since it contains information about the three environmental loads from the moment to the future. The prediction accuracy for the future drifted ship position is ensured by adopting deep learning algorithms and a replay buffer. Finally, it is shown that the proposed motion predictive system results in better station-keeping performance than the wind feed-forward system.

Impact of Wind Speed and Direction and Key Meteorological Parameters on Potential Pesticide Drift Mass Loadings from Sequential Aerial Applications.

ABSTRACTPesticide spray drift is potentially a significant source of exposure to off‐target, adjacent aquatic habitats. To estimate the magnitude of pesticide drift from aerial or ground applications, regulatory agencies in North America, Europe, and elsewhere rely on spray drift models to predict spray drift deposition for risk assessments. Refined assessments should ultimately depend on best‐available data for exposure modeling. However, when developing lower tier “screening” assessments designed to indicate whether further refinement is needed, regulators often make conservative assumptions with a resulting increased level of uncertainty in estimating environmental exposure or risk. In the United States, it is generally accepted that, to ensure conservative regulatory assessments, it is reasonable to assume that the wind speed might be 4.47 m/s (10 miles per hour [mph]), the relative humidity and temperature are highly conducive to drift, and the wind is blowing directly toward a receiving water for any given single spray event in a season. However, what is the probability these conditions will all co‐occur for each of 4 sequential spray events spaced a week apart (common practice for insecticides)? The refined approach in the present study investigates this question using hourly meteorological data sets for 5 United States Environmental Protection Agency (USEPA) standard crop scenarios to understand how real‐world data can reduce unnecessary uncertainty for sequential applications. The impact of wind speeds, temperatures, relative humidity, and wind direction at different times of day on annual drift loadings has been examined using a stepwise process for comparison with corresponding regulatory default loading estimates. The impacts on drift estimates were significant; interestingly, the time of day of the applications impacted variability more than did the selected crop scenario. When all these real‐world factors were considered, estimated 30‐y total drift loads ranged from 2% to 5% greater than the default estimate (2 of 30 cases due to high afternoon wind speeds) to 51% to 86% reductions (25 of 30 cases) with an overall average reduction of 63%. Integr Environ Assess Manag 2020;16:197–210. © 2019 The Authors. Integrated Environmental Assessment and Management published by Wiley Periodicals, Inc. on behalf of Society of Environmental Toxicology & Chemistry (SETAC)

Effect of wave spreading including multi-directional wave interaction on the responses of a spar platform

This paper deals with the effect of directionality of waves on the responses of a spar-type floating offshore platform. Here, a spar-type offshore platform restrained by four catenary mooring cables is modelled as per the work done by Chen et al. (Ocean Eng 28:863–887, 2001). The numerical model and numerical simulation have been validated by comparing the results (natural periods, RAOs and statistics of response) available in the literature (Steen et al. in Offshore Technology Conference 2004; Wangz et al. in J Mar Sci Appl 8:168–174, 2010). The multi-directional sea spectrum is represented by the product of a cosine power spreading function and a uni-directional JONSWAP wave spectrum. The Quadratic Transfer Functions have been generated for the calculation of drift loads, taking into account the multi-directional wave interaction. The responses of the platform have been obtained under long-crested (uni-directional) and short-crested (multi-directional) sea states and the results thus obtained are compared. Further, the variations in responses due to change in power of spreading function and total spreading angle are also investigated. It is found that due to the multi-directional wave interaction, the second order drift loads assume higher values in all degrees of freedom. Subsequently, in short-crested seas, the structure exhibits higher responses in all degrees of freedom when multi-directional wave interaction is considered. This highlights the need for incorporation of the multi-directional wave interaction while modelling short-crested seas for a realistic assessment of response behaviour of the system.