Wave-induced Motion Research Articles

Analysis of wave-induced vertical ship responses by Hilbert-Huang transform method

Time series of wave-induced ship responses are analysed by the Hilbert-Huang Transform (HHT) method. The results of the analysis of numerically simulated motions and loads on a chemical tanker in head waves are compared with the analysis of experimental data from laboratory model tests. The Empirical Mode Decomposition, which is a first part of HHT method is applied to the sea surface elevations of two sea states (high and low seas) and the wave-induced vertical motions and bending moments and the results are discussed. It is found that the decomposition of the experimental data into intrinsic components compares well with the decomposition of the numerically simulated ones for both high and low seas. The first two or three intrinsic mode functions carry the major part of the energy of both experimental and numerical simulated data. The time-frequency distribution of energy, called Hilbert spectrum, is calculated by the second part of HHT method. The Hilbert spectrum of the sea surface elevation is compared with Hilbert spectrum of wave-induced ship motions and moments in an attempt to study the time-frequency characteristics of ship response. The results of the present work provide confidence in the usage of numerical simulation data for the decomposition into intrinsic components of ship responses, avoiding the need for experimental data from laboratory model tests.

Motion Analysis of A Wind-Wave Energy TLP Platform Considering Second-order Wave Forces

Offshore wind energy has become a major energy source, and various studies are underway to increase the economic feasibility of floating offshore wind turbines (FOWT). In this study, the characteristics of wave-induced motion of a combined wind-wave energy platform were analyzed to reduce the variability of energy extraction. A user subroutine was developed, and numerical analysis was performed in connection with the ANSYS-AQWA hydrodynamic program in the time domain. A platform combining the TLP-type FOWT and the Wavestar-type wave energy converter (WEC) was proposed. Each motion response of the platform on the second-order wave load, the effect of WEC attachment and Power take-off (PTO) force were analyzed. The mooring line tension according to the installation location was also analyzed. The vertical motion of a single FOWT was increased approximately three times due to the second-order sum-frequency wave load. The PTO force of the WEC played as a vertical motion damper for the combined platform. The tension of the mooring lines in front of the incident wave direction was dominantly affected by the pitch of the platform, and the mooring lines located at the side of the platform were mainly affected by the heave of the platform.

Comparative study on response of jacket platforms under regular waves using Airy’s and Stokes’ fifth-order wave theories

Despite the random nature of ocean waves, to provide engineering solutions, regular wave theories are commonly used to estimate wave forces from the Morison equation in offshore structural analysis. These wave theories can be defined by three basic parameters, namely water depth, wave height and wave period. The applicability of a particular wave theory to a given set of wave characteristics and water depth is governed chiefly by the ratios of water depth and wave height to the wavelength. Airy’s linear wave theory, on account of its simplicity, is a popular choice, especially for preliminary calculations and for providing insight into the basic characteristics of wave-induced water motion. It is, however, applicable to small wave heights and in many conditions the linear theory is incapable of providing a satisfactory assessment of the water particle kinematics. A nonlinear theory is then required, and Stokes’ fifth order wave theory, based on the expansion of the wave solution in series form, provides a more accurate representation of the free-surface and is generally used for high waves in deep water. In this paper, a comparative study is conducted between the wave forces obtained from Morison equation utilising Airy’s wave theory and Stokes’ fifth order wave theory, acting at different levels of a jacket platform. Two sets of water depth, wave height and wave period are selected so that they satisfy the region of applicability of Airy’s wave theory and Stokes’ fifth order wave theory respectively. Two example four-legged jacket platforms are considered. It is found that for design purposes, in most cases the wave forces and structural responses from Airy’s wave theory are more conservative as compared to those from Stokes’ fifth order wave theory, though the converse is obtained in case of deep water conditions near the seabed. Overall, in deep water, high wave conditions, apart from Stokes’ fifth order wave theory, Airy’s wave theory may be used for preliminary estimations of wave forces and deck displacements, but in shallow water conditions, Stokes’ fifth order wave theory is entirely invalid.

Comparison of full-scale measurements and seakeeping calculations for two research vessels in the Adriatic Sea

The paper describes two experimental campaigns of seakeeping measurements for two research vessels in the Adriatic Sea and comparison of the experimental results with the seakeeping calculations. The waves and vessel motions are simultaneously measured at seas. Sea surface elevation of wind waves is measured using a wave buoy, freely floating near the vessel. Measurements of vessel motions are performed using motion sensors mounted on the bridge deck. Measurements are performed for different heading angles between the prevailing wave direction and the vessel. Time signals of the measured waves and resulting heave and pitch motions are treated statistically and subjected to spectral analysis. Wave-induced vessel responses are also calculated by the spectral analysis, employing the 3D panel method for transfer functions. Measured wave spectra are approximated by the standard JONSWAP spectra for that purpose. Statistical properties of the measured and calculated wave-induced motions are then compared. The results of the seakeeping calculations are in fair agreement with the measurements, except for mean zero-crossing period of the responses in following seas, where considerable discrepancies are found.

Significant enhancements of the mesospheric Na layer bottom below 75 km observed by a full-diurnal-cycle lidar at Beijing (40.41° N, 116.01° E), China

Abstract. Based on the full-diurnal-cycle sodium (Na) lidar observations at Beijing (40.41∘ N, 116.01∘ E), we report pronounced downward extensions of the Na layer bottomside to below 75 km near mid-December 2014. Considerable Na atoms were observed even as low as ∼ 72 km, where Na atoms are short-lived. More interestingly, an unprecedented Na density of ∼ 2500 atoms cm−3 around 75 km was observed on 17 December 2014. Such high Na atoms concentration was 2 orders of magnitude larger than that normally observed at the similar altitude region. The variations of Na density on the layer bottom were found to be accompanied by warming temperature anomalies and considerable perturbations of minor chemical species (H, O, O3) in the upper mesosphere. Different from the previous reported metal layer bottom enhancements mainly contributed by photolysis after sunrise, these observational results suggest more critical contributions were made by the Na neutral chemical reactions to the Na layer bottom extensions reported here. The time–longitudinal variations of background atmospheric parameters in the upper mesosphere and stratosphere from global satellite observations and ERA reanalysis data indicated that the anomalous structures observed near the lidar site in mid-December 2014 were associated with planetary wave (PW) activities. The anomalies of temperature and O3 perturbation showed opposite phase in the altitude range of 70–75 and 35–45 km. This implied that the vertical coupling between the mesosphere and stratosphere, possibly driven by the interactions of PW activities with background atmosphere and modulation of gravity wave (GW) filtering by stratospheric wind, contributed to the perturbations of background atmosphere. Furthermore, the bottom enhancement on 17 December 2014 was also accompanied by clear wavy signatures in the main layer. The strong downwelling regions are likely due to the superposition of tide and GW, suggesting the wave-induced adiabatic vertical motion of the air parcel contributed greatly to the formation of the much stronger Na layer bottom enhancement on 17 December 2014. These results provide a clear observational evidence for the Na layer bottom response to the planetary-scale atmospheric perturbations in addition to tide and GW through affecting the chemical balance. The results of this paper also have implications for the response of the metal layer to vertical coupling between the lower atmosphere and the mesosphere.

The transitional states of a floating wind turbine during high levels of surge

With the deployment of floating offshore wind turbines, the effect of their wind- and wave-induced platform motion on the turbine’s performance and life is of concern and requires low-order models to develop appropriate control strategies. This work focusses on platform surge as one of the main additional degrees of freedom. The aerodynamic behaviour during the rotor’s transition into propeller state is explored by assessing the spanwise and rotor-integrated aerodynamic forces on the rotor of the NREL 5 MW turbine through a 3D URANS CFD simulation. The CFD findings are compared with a modified actuator disk (AD) theory and 2D Blade-Element Momentum (BEM) approach. In addition to propeller state, where both rotor torque and thrust are negative, two other states were observed with opposite signs of torque and thrust: a braking state, with negative torque but positive thrust, and the second a quasi-windmill state with thrust negative yet torque positive. The results demonstrate that BEM coupled with AD can reliably predict the transitions to these states during such high levels of platform surge and give hints to how the underpinning force balances are affected by temporal perturbations.

Capability of a potential-flow solver to analyze articulated multibody offshore modules

Within the EU-funded Space@Sea project, a standardized floating solution for offshore space was developed, and modularity was one of the key elements. Computational tools used to design and analyze such modules must be validated. The objective here was to critically examine the capability of a potential-flow solver to predict wave-induced motions and loads on offshore systems consisting of such articulated modules, as this kind of solver is often used to assess the safety and effectiveness of articulated multibody offshore structures. A frequency-domain analysis considered only the hydrodynamic interactions between two floating modules, by locking the motions of interacting structures. A time-domain analysis treated also the mechanical coupling effects between the two articulated floating modules. Comparative computations from a RANS-based solver and experimental model measurements were available to validate the results. Although the agreement was reasonable between numerical predictions and experimental measurements for the floating modules in wave frequencies far away from their natural frequencies, deviations were observed in waves at frequencies in the neighborhood of the module’s natural frequencies. Generally, the agreement between numerically predicted and experimentally measured hinge forces was favorable. The effects of incident wave angles on hinge forces revealed that numerically predicted hinge forces at all incident wave heading angles compared favorably to measurements. An accurate evaluation of wave-induced motions and loads on articulated floating structures was possible only by accounting also for nonlinearities associated with the connecting joints.

On compensation for wave-induced roll in dynamic positioning control

Dynamic positioning (DP) for station-keeping control keeps the position and heading of the vessel constant regardless of environmental disturbances from wind, waves and currents. If the point of interest on the vessel has a significant vertical offset, it will be influenced also by the roll, pitch and heave motions. Although such motions are usually neglected in DP control, there is an opportunity to also influence these since thrusters will not only influence the horizontal plane motion of a vessel, but also generate roll and pitch moments. In this paper, we formulate the problem of DP control when explicitly considering the first-order wave-induced roll motion and thruster roll moment. It is shown that the control performance can be significantly improved when the DP system’s point of interest, and the location of the thrusters, have a significant vertical offset compared to the vertical position of the center of rotation. The proposed control algorithm is demonstrated in a realistic simulation of a relatively small ship during launch-and-recovery of a remotely operated vehicle (ROV) where the DP’s point of interest is at the lower end of the launch-and-recovery-system (LARS) that extends below the keel of the ship. It is shown that the positioning performance can be improved with 20–45% reduced error, depending on the sea state.

Extension of a coupled mooring–viscous flow solver to account for mooring–joint–multibody interaction in waves

To account for nonlinear wave–structure interaction, mooring dynamics and the associated viscous flow effects, a coupled mooring–viscous flow solver was formerly developed and validated (Jiang et al. in Mar Struct 72:783, 2020a, Validation of a dynamic mooring model coupled with a RANS solver). This paper presents an extension of the coupled mooring–viscous flow solver to solve mooring dynamics interacting with an articulated multibody offshore system. The presently extended solver is verified by comparing the predicted motions of and loads on a moored floating box to those obtained from the formerly validated solver, which was aimed for solving mooring dynamics interacting with a single floating body. The almost identical results obtained from both solvers verify the presently developed multi-module coupling technique for solving the mooring dynamics and articulated multibody dynamics in a coupled manner. Apart from the code comparison and verification, the numerical predictions are also validated against experimental tank measurements both for a single body and an articulated multibody. The good agreements between the numerical predictions and the experimental measurements validate the presently extended solver, where wave-induced body motions together with loads acting on mooring lines and joint connections were examined. Developed as an open-source tool, the extended solver shows a potential of the coupled methodology for analyzing an articulated multibody offshore system, moored with various mooring configurations in extreme sea states, which goes beyond the state of the art.

Stabilization control of 3-DOF parallel vessel-borne platform with dynamic uncertainties and unknown disturbances

The wave-induced vessel motions inevitably affect and even menace the operation of onboard equipment, such as excavators, cranes and drilling configurations. Vessel-borne stabilization platforms as a vessel motion compensation device can provide a good solution scheme for the safe offshore operation in tough environmental conditions. To compensate the wave-induced vessel motions in roll, pitch and heave degrees of freedom, this paper proposes a novel stabilization control scheme for a three degrees of freedom parallel vessel-borne platform with dynamic uncertainties and unknown time-varying disturbances. Here the conventional super-twisting algorithm is innovatively modified to mitigate its inherent chattering whereby a new adaptive super-twisting extended state observer (STESO) is constructed to realize the finite-time estimates of the total disturbances lumped by dynamic uncertainties and unknown time-varying disturbances of the vessel-borne platform without relying on any prior knowledge of its upper bounds. Further, a novel adaptive super-twisting sliding mode (STSM) control law with the adaptive STESO is designed to stabilize vessel-borne platforms at a desired position and orientation in the inertial space. The simulation results on a benchmark platform indicate that the wave-induced vessel motions can be compensated by the platform for more than 98% in both 0.5m and 2.5m significant wave heights, such that the workability and safety during offshore activities in tough environmental conditions is increased.

Comparative Study on Added Resistance and Seakeeping Performance of X-Bow and Wave-Piercing Monohull in Regular Head Waves

Bow shape has been recognized as an important factor influencing the seakeeping performance and added resistance of ships. This paper presents a numerical comparative study on added resistance and seakeeping of model ships with ‘X-bow’ and a wave-piercing monohull in regular head waves using a computational fluid dynamics (CFD) software. Different wave heights, wavelengths and forward speeds are considered in the systematic investigation in order to characterize the added resistance and wave-induced motions, and to explore the local wave patterns. The results show a considerably different hydrodynamic characteristic by different bow shapes.

An experimental assessment of the effect of current on wave buoy measurements

Wave measurement buoys provide characterisation of wave climates that forms the basis for the design of offshore systems. These buoys are commonly subjected to currents which affect the resulting wave measurements, and if not accounted for will result in errors in the estimated sea state parameters. The present work provides results and observations from experiments aimed at assessing the impact that currents have on wave buoy measurements, thereby informing processing techniques to more accurately include this effect. Through scaled testing (circa 1:15) in a combined wave–current test tank, buoy motions (diameter, D = 0.24 m) are recorded in current only, waves only, and combined wave–current including oblique conditions. From these, the wave-induced motions are extracted and compared against three prediction methods based on established transfer function approaches as well as a frequency-domain hydrodynamic coefficient (HC) model based on potential flow. The scaled buoy was observed to have large, complex, irregular oscillatory vortex-induced motions (VIM) exceeding the buoy diameter. Both the magnitude and frequency of these oscillations was found to be significantly altered by the mooring stiffness and configuration whilst the addition of collinear waves was found not to affect the magnitude of VIM. Furthermore, due to the lack of VIM heave response and a large difference between the frequencies of the vortex-induced and wave induced horizontal motions, it was found that the VIM did not significantly alter the interpretation of the wave climate for the tested conditions. The HC model was found to accurately capture the observed modified hydrodynamics for opposing wave–current conditions, where larger horizontal motions than (typically) predicted are observed for all frequencies. This behaviour is concluded to result from increased excitation forces owing to the higher wavenumbers. The experiments highlight the potential effects of VIM on wave measurement performance of wave buoys, along with the complex and mooring-dependent nature of the response. Altered dynamics in the presence of currents are described which must be accounted for to avoid errors and the presented prediction methods provide a mechanism to account for these effects in wave processing methodologies which can subsequently reduce uncertainty in our understanding of the offshore environment.

Efficient numerical calculation of frequency-domain matching method based on an analytical control surface

The matching method based on an analytical control surface has been developed to predict wave-induced motions and loads of ships with forward speed. Taking advantage of several computational techniques, this study proposes an efficient scheme for the numerical calculation of this novel method. Different from the conventional domain decomposition strategy, the control surface is analytical, and the physical quantities on it are expanded into the Fourier-Laguerre series. Therefore, the integration over the control surface associated with the forward speed Green function is performed analytically, avoiding the convergence problem caused by the singular and oscillatory behaviors of the forward speed Green function. Because the introduction of the analytical control surface may cause large computational burdens, an efficient scheme is developed by combing threaded parallelism, Chebyshev series approximation, and shared B-spline data. The excellent agreement between numerical results and experimental measurements shows that the present numerical method is reliable and practical in several applications. Furthermore, the numerical validation reveals that the present numerical scheme is affordable on the standard computing platform.

Geometrically Reduced Modelling of Pulsatile Flow in Perivascular Networks

Flow of cerebrospinal fluid in perivascular spaces is a key mechanism underlying brain transport and clearance. In this paper, we present a mathematical and numerical formalism for reduced models of pulsatile viscous fluid flow in networks of generalized annular cylinders. We apply this framework to study cerebrospinal fluid flow in perivascular spaces induced by pressure differences, cardiac pulse wave-induced vascular wall motion and vasomotion. The reduced models provide approximations of the cross-section average pressure and cross-section flux, both defined over the topologically one-dimensional centerlines of the network geometry. Comparing the full and reduced model predictions, we find that the reduced models capture pulsatile flow characteristics and provide accurate pressure and flux predictions across the range of idealized and image-based scenarios investigated—at a fraction of the computational cost of the corresponding full models. The framework presented thus provides a robust and effective computational approach for large scale in-silico studies of pulsatile perivascular fluid flow and transport.

On the coupling between surface waves and the motion in a flexible porous surface layer

The coupling between surface waves and the motion in a flexible porous surface layer is investigated theoretically. We apply a Lagrangian formulation for the viscous fluid and the fluid-saturated porous medium. In the floating porous layer, which we assume to be much thinner than the wavelength, we apply a macroscopic version of Darcy’s law. The interface between the porous layer and the underlying fluid is permeable, and the wave-induced vertical motion at the interface leads to wave damping. In addition, the viscous shear stress at the interface also dampens the waves. We here investigate the relative strength of the two mechanisms. Furthermore, we calculate the Lagrangian mean drift in the porous surface layer. The present study may provide a physical model for wave damping in the presence of unconsolidated rubble ice and the slow particle drift in rubble-ice layers.

An experimental investigation on vortex-induced motion (VIM) of a tension leg platform in irregular waves combined with a uniform flow

Vortex-induced motion (VIM) of a tension leg platform (TLP) is critical to avoid structural and fatigue damages to the tendons and risers. Many previous studies have conducted model tests for TLPs in towing tanks. However, the models were usually established using linear springs to replicate the underwater moorings. In this study, a TLP model with full-water-depth tendons and top tension risers (TTRs) was developed. A series of model tests were conducted in a large-scale wave tank at three incidence angles (θ=0°, 22.5°, and 45°) for the reduced velocity ranging from 4 to 11.5 and two extra cases of flow combined with irregular waves. The maximum transverse amplitude of 0.32D was observed at a reduced velocity of 7.0 when θ=0°. On the other hand, the in-line and yaw motion experienced increasing amplitudes with reduced velocities and no lock-in region was identified. The most significant responses of transverse and yaw motion appeared at 0° and 22.5° headings, respectively, while no critical heading was recognized for surge motion. The competing mechanics between VIM and the wave-induced motion were revealed in the cases of combined flows and irregular waves. The tensions in tendons and TTRs that result from VIM were found as significant as those induced by wave loads, which highlights the necessity of considering VIM in the design of TLP. Furthermore, the result showed that the VIM amplitudes were considerably suppressed under the nonlinear stiffness and larger damping provided by the tendons and TTRs.

Recursive analysis of added mass, damping coefficient, and wave-exciting force using time-series data of two-dimensional floating body’s motion only

To achieve the safe operation and control of a ship and floating structure, a sequential understanding of the wave-induced motions is desirable in actual seas, which vary due to loading and operating conditions. However, it is difficult to measure wave elevation and wave-exciting forces as time history and to evaluate seakeeping directly in the actual seas. We propose estimating the wave-exciting forces and the parameters in the equation of motion simultaneously based on the dual Kalman filter approach. A two-dimensional problem is considered to establish a method under the assumption that the displacements, velocities, and accelerations of a floating body in waves are measurable. The proposed method is verified using the results of numerical and tank tests.

A new method to couple FEM mooring program with CFD to simulate Six-DoF responses of a moored body

The objective of this study is to develop an accurate and efficient coupled program, which incorporates computational fluid dynamics, a six-DoF motion solver, and nonlinear finite-element cable analysis program MOORING3D. The new coupled method aims at studying dynamic responses of moored structures in environments which cannot be modeled by conventional approach. The novelty of the coupled method also lies in that we develop the methodology for an overset grid system of embedding, overlapping, and moving structured grids. Large eddy simulation was used as the turbulence model. The level-set method was applied to capture free surface effects. Two buoys were studied. Wave-induced motions of the first buoy were simulated by both coupled CFD-mooring method and commercial software. The discrepancy was investigated to illustrate advantages of the coupled method in addressing viscous and nonlinear hydrodynamic effects. The wave-current-body interaction of another buoy was simulated with RAOs being compared against experiments and vortex-induced motion being investigated. The conclusions indicated that the coupled CFD-FEM method provides feasible solutions for floating systems exposed to complicated environmental conditions.

Online wave direction and wave number estimation from surface vessel motions using distributed inertial measurement arrays and phase-time-path-differences

A common approach for finding the direction of ocean waves is to use the phase-time-path-differences (PTPDs) between a static array of various types of sensors mounted on either the sea surface or seabed. However, some practical drawbacks of such arrays are that they tend to be expensive, difficult to install, and fixed in location. We show that the PTPD approach can be generalized to a portable shipboard array of spatially distributed sensors rendering it more practical. In this respect, we derive a nonlinear PTPD model for shipboard sensor arrays and prove that the wave direction and wave number can be resolved from a minimum of three noncollinear sensors using observability analysis. Moreover, based on our PTPD model, we propose an unscented Kalman filter algorithm for online estimation of the wave direction and wave number, which offers a convenient framework for adding multiple measurements and incorporating uncertainties. Our experimental results from model basin testing with a model ship equipped with several inertial measurement units (IMUs) confirm that the wave direction and wave number can be estimated from the wave-induced motions of a surface vessel with a minimum of three noncollinear IMUs. In this study, we consider parameter estimation for regular waves and assume a dynamically positioned surface vessel with small roll and pitch angles.

RANS Prediction of Wave-Induced Ship Motions, and Steady Wave Forces and Moments in Regular Waves

The wave-induced motions, and steady wave forces and moments for the oil tanker KVLCC2 in regular head and oblique waves are numerically predicted by using the expanded RANS solver based on OpenFOAM. New modules of wave boundary condition are programed into OpenFOAM for this purpose. In the present consideration, the steady wave forces and moments include not only the contribution of hydrodynamic effects but also the contribution of the inertial effects due to wave-induced ship motions. The computed results show that the contribution of the inertial effects due to heave and pitch in head waves is non-negligible when wave-induced motions are of large amplitude, for example, in long waves. The influence of wave amplitude on added resistance in head waves is also analyzed. The dimensionless added resistance becomes smaller with the increasing wave amplitude, indicating that added resistance is not proportional to the square of wave amplitude. However, wave amplitude seems not to affect the heave and pitch RAOs significantly. The steady wave surge force, sway force and yaw moment for the KVLCC2 with zero speed in oblique waves are computed as well. The present RANS results are compared with available experimental data, and very good agreements are found between them.