Heave Period Research Articles

Numerical investigation on vortex-induced vibration of catenary riser conveying fluid under top-end heave excitation

ABSTRACT Due to the catenary shape of steel catenary risers (SCR), the heave motion of the floating platform can generate an equivalent oscillatory flow field and excite the vortex-induced vibration (VIV) of SCR. Internal flow conveyed by SCR further complicates the VIV response. A semi-empirical model is improved to simulate the VIV of SCR with internal flow under top-end heave excitation. VIV characteristics such as displacement temporal–spatial distribution and amplitude spectra spatial distribution are analysed and the fatigue damage is calculated. The effects of heave period, heave amplitude, internal flow volumetric flow rate and internal flow density on VIV of SCR are discussed. The heave excitation with short period or large amplitude tends to excite high-order-mode response and enlarge the fatigue damage. The VIV response becomes less regular and the fatigue damage is reduced when the internal flow volumetric flow rate or density increases.

Experimental Investigation on the Motion Characteristics of Air-Floating Tripod Bucket Foundation during Free Floating

In recent years, multi-bucket foundations have been studied and gradually adopted in engineering practices as a novel foundation for offshore wind turbines within a range of water depth of 30 to 50 m. This study investigated the motion characteristics of air-floating tripod bucket foundation (AFTBF) through a series of experiments during free air-floating. The experimental results show that the surge force appears to be the most important factor influencing pitch moment and motion, whether it is a change in water depth or a draft for AFTBF. The maximum amplitudes of surge acceleration and pitch angle show a trend of increasing with narrower spacing and decreasing with wider spacing, while the heave acceleration shows an opposite trend. The added mass and damping of heave motion for AFTBF increase with shallower water due to the increasing pressure difference between the inside and bottom of bucket foundation. The shallower the water depth and the larger the draft, the longer the resonance period of heave.

Using Transient Modeling to Define the Effects of Heave on Wellsite Operations

Summary The drilling industry is striving to be more efficient, reducing time, costs, and emissions to provide energy solutions for a more climate-conscious world. Reducing nonproductive time (NPT) and invisible lost time (ILT) by utilizing modeling software to optimize tripping operations is one method to combat this. Additional factors such as sea heave have a significant impact on tripping operations on semisubmersible drilling vessels, which do not show a linear response to increased heave. These vessels have compensation systems, but they are often not in use or not completely accurate. Typical heave experienced in the North Sea is between 0.5 and 3-m amplitude and 10–30-second heave period. In this study, transient modeling software is used to create a digital twin of the wellbore to safely predict the tripping speed and define the effect heave has on the tripping operations, from causing additional swab and surge pressures when in or out of slips to reducing tripping speed and improving efficiency by reducing mud gelling at connections. To further understand the effect heave has on tripping operations, experimental simulations of varying heave magnitude were completed in wellbore sections of 0°, 30°, 60°, and 90° inclination. Model validation was completed before running simulations. The results indicate that in horizontal holes, low heave magnitudes result in no bit or pressure response. The same cannot be said for vertical wells, which show smooth bit movement and pressure response throughout the heave magnitude spectrum. However, in a horizontal hole when the wave height is of a larger magnitude, sufficient to break wellbore friction, bit displacement is observed to display jerky axial stick and slip movement, and resultant increased swab and surge pressures are shown even when accounting for the reduced pressure fluctuations due to string eccentricity in an inclined wellbore. It is proposed that much of the related mechanical and pressure response is due to the properties of the drilling mud, string elasticity, and the forced frequency of the waves on the natural frequency of the drilling rig and drillstring. It is clear from definitive and experimental simulations that extra care must be taken when the heave is significant to maintain wellbore stability and reduce wellbore pressure cycling.

Experimental study on pressure oscillation phenomenon of vertical upward bubble submerged jet under heave conditions

With the vigorous progress of nuclear industry under marine environment, the ocean motion will exacerbate the pressure oscillation phenomenon caused by the change of the steam-liquid interface during the jet, causing great harm and challenges to the security and steady operation of device related to steam submerged jets. Therefore, the effects of heave motion on the steam bubble morphology and pressure oscillation phenomenon of jets with vertically upward low mass fluxes were experimentally investigated. The experimental results show that when the heave motion is upward, the steam bubble will be stretched obviously in the necking and detachment stages; while when the heave motion is downward, the steam bubble will accumulate at the nozzle outlet during the growth initial stage. Compared with the land environment, the heave motion increases the dominant frequency and pressure pulses average amplitude, and the dominant frequency and pressure pulses average amplitude have a positive correlation with the heave amplitude and a negative correlation with the heave period. In addition, there is a positive correlation between the Strouhal number and the heave maximum acceleration amplitude. An experimental correlation is proposed to predict the dominant frequency in heave motion, and the error is basically within ±30%.

Precontrol of short-period motion for a Tension Leg Platform

The Tension Leg Platform (TLP) is a hybrid, compliant platform designed to sustain springing and ringing responses that are correlated to short-period motion. Since the period of short-period motion is within the wave energy concentration region, TLPs may experience sensitive short-period motion, such as resonance and green water, that usually cause serious damage to TLPs. In this study, a precontrol methodology is presented as a solution to prevent TLP-sensitive short-period motion. By applying the precontrol methodology, the parameters of TLP can be predetermined, allowing TLP motion performance to meet the requirements of short-period motion before sensitive motions actually occur. For example, the damping coefficient should be less than 4.3, the tendons’ stiffness should be larger than 0.91 × 108, and the dimensionless draft should be less than 0.665. The development of a precontrol methodology is based on a solid theoretical foundation. First, a series of simple and high-fidelity numerical models are proposed to simulate the natural period of roll, natural period of heave, and green water height. Second, a constraint regime is generated based on the numerical models and the sensitive motion range of short-period motion. The constraint regime is divided into two parts: the control range (corresponding to sensitive short-period motion) and the feasible range (the complementary set of control ranges in the whole parameter constraint domain). Finally, TLP parameters are derived from the calculated feasible range. The precontrol methodology goes beyond the conventional approach of real-time control by changing the control from a remedial action to a preventive action.

Heave Plates with Holes for Floating Offshore Wind Turbines

Abstract The paper presents an innovative solution which is heave plates with holes. The long-known heave plates are designed to damp the heave motion of platforms. They are most often used for Spar platforms. The growing interest in this type of platform as supporting structures for offshore wind turbines makes it necessary to look for new solutions. Based on the available literature and the authors’ own research, it was concluded that the main element responsible for the damping of heave plates is not so much the surface of the plate, but its edge. Therefore, it was decided to investigate the effect of the holes in heave plates on their damping coefficient. Model tests and CFD calculations were performed for three different structures: a smooth cylinder, a cylinder with heave plates with a diameter of 1.4 times the diameter of the cylinder, and a cylinder with the same plate, in which 24 holes were cut (Fig. 1). Free Decay Tests (FDT) were used to determine the damping coefficient and the natural period of heave, and then the values obtained were compared. The full and punched heave-plate designs were also tested with regular waves of different periods to obtain amplitude characteristics. The results obtained are not unequivocal, as a complex motion appears here; however, it is possible to clearly define the area in which the damping of a plate with holes is greater than that of a full plate.

Model tests and numerical simulations on the parametric resonance of the deep draft semi-submersible under regular waves

Parametric resonance of the deep draft semi-submersible (DDS) under regular waves are investigated experimentally and numerically. Special focus is put on the occurrence of parametric resonance under weak or failure mooring condition. Firstly, model tests with and without mooring chains are conducted in wave flume. From results of model without mooring chains, it is observed that parametric resonance occurs when wave period is about the natural period of heave and half of the natural period of pitch or roll. The steady amplitude of parametric resonance is larger under higher wave. In heading waves, parametric resonance occurs in roll direction, while parametric resonance occurs in both roll and pitch direction for beam wave. For the model with 12 mooring chains, parametric resonance does not occur under strong mooring restriction. Whereas for the model with four mooring chains representing a failure mooring condition, parametric resonance occurs in pitch direction. Then, numerical simulations under cases same as experiments are conducted using a potential-theory based weakly nonlinear model. Parametric resonance is successfully reproduced numerically. Furthermore, through comparison with experiments, it is found that the numerical model accurately predicts steady amplitudes and occurring wave periods of parametric resonance except for cases with four mooring chains.

Experimental and numerically obtained low-frequency radiation characteristics of the OC5-DeepCwind semisubmersible

Added mass and damping play a significant role in accurate prediction of floating wind turbine (FWT) motions, especially near the resonance frequencies. This paper investigates the still-water hydrodynamic characteristics of a semi-submersible FWT around the natural periods of surge, heave and pitch motion. A higher-fidelity tool (Computational Fluid Dynamics, CFD) based on OpenFOAM is employed in the numerical computations. The tool is validated against experimental measurements (decay tests and forced surge motions) and then applied to investigate the hydrodynamic characteristics of the whole floater and each column at different amplitudes of forced motions. The heave and pitch decay match well with the experimental measurements, whereas the CFD simulations underestimate the damping in the surge decay. However, better agreement is obtained between measured and numerically estimated surge force in the forced oscillations in surge. Furthermore, the added mass derived from the CFD simulation is around 12% larger than that estimated by the potential flow theory, except the estimated heave added mass under the largest heave motion (up to 35% larger). This additional added mass in the CFD simulations is due to the viscous effects. The damping shows a small dependence on the oscillation period and a larger dependence on the oscillation amplitude within the tested period range. At these frequencies, radiation damping is completely negligible compared to the viscous damping due to vortex shedding, and the accuracy of Morison's drag forces in capturing the viscous damping is sensitive to the drag coefficient.

Research on Frost Heave of High Speed Railway in Seasonal Frozen Region Based on Track Geometry Measurements

The frost heave and thawing settlement in the seasonal frozen areas can cause the track geometry change, even seriously affect the driving safety. Taking the HSR-A railway as the research object, this paper divides the change process of track surface during the period of frost heave and thawing settlement into four stages, and equates the four stages into a trapezoidal change process. Then the characteristics of these stages are summarized. Finally, based on the track geometry measurements (TGM), two different linear functions are used to represent the track surface changes before and after frost heave start respectively, and this essay proposes the start time estimations model(STEM) to estimate the start time of frost heave. STEM is applied to 10 typical frost heave positions in the HSR-A. The results show: the estimated effect is good.

Parametric optimization of FPSO hull dimensions for Brazil field using sophisticated stability and hydrodynamic calculations

In this study, hull dimensions of an FPSO were optimized to maximize its operability at Brazil field. In contrast with the previous works which have used simplified models to evaluate some indicators related to stability and hydrodynamic performances of FPSOs for its own optimal design, we developed a generic hull and compartment modeler and sophisticated stability and hydrodynamic calculation modules. With the aid of the developed tools, the hull optimization was performed with initial dimensions of an FPSO originally designed for west Africa field. The optimization results indicated the relative importance of hydrodynamic performances compared with stability performances for the FPSO hull dimensioning by showing that there were 3 active constraints related to them, which were the natural periods of heave and roll and the maximum pitch angle under 1-year return period waves at full load condition. To the author's knowledge, this study is the first attempt to combine altogether the hull and compartment modeling and full set of stability and hydrodynamic calculations precisely to optimize an FPSO's hull dimensions within 30 min. Also, it is worthwhile to mention that the developed methods are generic enough to be applied to all types of ship-shaped offshore platforms.

A physical model approach to nonlinear vertical accelerations and mooring loads of an offshore aquaculture cage induced by wave-structure interactions

A grand aim of aquaculturists is to investigate the interactions between the oceanic environment and aquaculture structures, in order to make the structures more durable to loads caused by waves and current. To that end, we investigate the effects of extreme wave conditions by leveraging a physical model approach. We assume that the floating collar of the cage moves with the wave in heave, leading to extreme conditions. Thus, the wavelength is much larger than the size of the floating collar model and the wave frequency is much lower than the natural period of heave. For the floating collar model without netting, under wave-only conditions, the first- and second-harmonic components of the vertical acceleration are proportional to the wave amplitude ζa, and square of the wave amplitude ζa2, respectively. The third- and fourth-harmonic components exhibit oscillations at non-dimensional wave number νa≈0.055 due to the change of free surface. For the floating cage model under combined waves and current conditions, the first-harmonic component is more likely proportional to ζa, while the second-harmonic component shows erratic behavior. The effects of mooring loads in front and aft mooring lines are also assessed.

An optimization framework of a parametric Octabuoy semi-submersible design

An optimization framework using genetic algorithms has been developed towards an automated parametric optimization of the Octabuoy semi-submersible design. Compared with deep draft production units, the design of the shallow draught Octabuoy semi-submersible provides a floating system with improved motion characteristics, being less susceptible to vortex induced motions in loop currents. The relatively large water plane area results in a decreased natural heave period, which locates the floater in the wave period range with more wave energy. Considering this, the hull design of Octabuoy semi-submersible has been optimized to improve the floater’s motion performance. The optimization has been conducted with optimized parameters of the pontoon’s rectangular cross section area, the cone shaped section’s height and diameter. Through numerical evaluations of both the 1st-order and 2nd-order hydrodynamics, the optimization through genetic algorithms has been proven to provide improved hydrodynamic performance, in terms of heave and pitch motions. This work presents a meaningful framework as a reference in the process of floating system’s design.

Nonlinear coupling and instability of heave, roll and pitch motions of semi-submersibles with bracings

Nonlinear coupling is an important safety consideration for offshore floating structures. Traditional mathematical models like linear motion equations are inadequate for predicting the nonlinear resonance of semi-submersible platforms with bracings. In this study, we proposed a mathematical model that considers the nonlinear effects of heave motion on pitch restoring coefficient, pitch motion on buoyancy, and bracings on buoyancy. Regular wave tests and numerical simulations were performed to investigate the characteristics of coupled motions and to validate the proposed mathematical model. Under head, quartering and beam sea conditions, motion instability of the semi-submersible platform occurred when the incident wave period approached the natural period of heave. In addition, a double-period phenomenon and unique pitch-motion profile were observed. Good agreements between experimental and nonlinear numerical results validated the ability of the proposed mathematical model to accurately simulate nonlinear effects and predict motion instability. Using the validated model, factors affecting the motion instability were analysed and measures to minimize instability were recommended.

1MW OTEC 구조물의 운동 응답에 대한 수치 및 모형시험 연구

The 1MW OTEC (Ocean Thermal Energy Conversion) platform was designed for application in equatorial seas. In this study, the OTEC platform was investigated using numerical and experimental methods. An octagon-shaped OTEC platform was investigated using the Ocean Engineering Basin of KRISO. These experiments included various tests of regular waves, irregular waves and irregular waves with current (wave+current). The responses of the platform in regular waves showed good agreement between the numerical and experimental results, including the motion RAO, wave run up, and mean drift force. The peak period of heave and pitch motions were observed around 0.5 rad/s, and the effect of the total reflection was found under short wave conditions. The standard deviation (STD) of the platform motion was checked in irregular waves of equatorial and Hawaiian seas. The STD of the pitch was less than <TEX>$4^{\circ}$</TEX> different from the operability requirement under equatorial conditions and the surge STD of the wave frequency showed good agreement between the numerical and experimental results. The STD values of the surge and pitch were increased 66.6% and 92.8% by the current effects in irregular waves, but the pitch STD was less than <TEX>$4^{\circ}$</TEX> under equatorial conditions. This study showed that the STD of the surge was affected by spring effects. Thus, the watch circle of the platform and tension of the mooring lines must be evaluated for a specific design in the future.

The nonlinear finite element modeling and performance analysis of the passive heave compensation system for the deep-sea tethered ROVs

To improve the safety of the launch and recovery of the deep-sea remotely operated vehicle (ROV) under harsh sea states, the passive heave compensator is usually equipped. Through dynamic modeling and performance analysis of the compensation system, it can provide theoretical reference for the design and operation of the system. Firstly, the geometrically exact beam element was used to obtain the two-dimensional nonlinear finite element model of umbilical cable, and the continuous dynamics model of the compensator was built and discretized to one finite element, and then inserted as the first element of the whole model. The Newmark method was used to solve the total finite element model numerically. Finally, the performance of the passive heave compensation system under different effects such as the ship heave period, the stroke of the compensator, the working depth of ROV and the sea current speed were analyzed. The results show that the condition of smaller ship heave period, the longer stroke of heave compensator, under the critical depth and the less sea current speed will produce the better performance of passive heave compensation, and the performance for cable tension is better than that for cage heave motion.

Experimental Study on the Suppression of a Vertical Circular Cylinder with a Heave Plate

Studies of floating structures are becoming increasingly important due to their increased application. The hydrodynamic motion response of floating structures must be controlled within a certain range, especially in the resonance region. In this study, a scale model of a circular cylinder having a height of 300 mm, outer diameter 60 mm, natural heave period 0.78 s and a natural pitch period 1.12 s, was designed and analyzed for hydrodynamic load. We compared this model with other models of cylinders with various heave plates systems. In order to find the size effect of the heave plate, two heave plates of 60 and 80 mm in diameter with a thickness of 5 mm. At first, a free decay experiment was carried out to examine the damped heave and pitch period, as well as the hydrodynamic coefficients in the resonance frequency. The motion response was also analyzed to obtain the heave and pitch motion response in a series of regular waves having periods between 0.51 s and 1.24 s. It was observed that the heave plate significantly enhanced the damped heave period, whereas it had a negligible effect on the damped pitch period. Moreover, the peak of heave Response Amplitude Operator (RAO) was observed to be reduced for the heave plate in the resonance region and the peak of heave RAO was shifted to a long period. Furthermore, a comparatively small peak heave RAO was observed in the experiments. It was indicated that pitch motion has an effect on heave motion in the pitch resonance frequency.

Strong transient effects of the flow around a harmonically plunging NACA0012 airfoil at low Reynolds numbers

The flow pattern around a NACA0012 airfoil undergoing harmonic plunging motion corresponding to the deflected wake phenomenon reported by Jones and Platzer (Exp Fluids 46:799–810, 2009) is investigated in detail using direct numerical simulations. An arbitrary Lagrangian–Eulerian formulation based on an unstructured side-centered finite volume method is utilized in order to solve the incompressible unsteady Navier–Stokes equations. The Reynolds number is chosen to be 252, and the reduced frequency of plunging motion (k = 2π fc/U ∞) and the plunge amplitude non-dimensionalized with respect to chord are set to be 12.3 and 0.12, respectively, as in the experimental study of Jones and Platzer (2009). The present numerical simulations reveal a highly persistent transient effect, and it takes two orders of magnitude larger duration than the heave period to reach the time-periodic state. In addition, the three-dimensional simulation reveals that the flow field is three-dimensional for the parameters used herein. The calculation reproduces the deflected wake and shows a good agreement with the experimental wake pattern. The instantaneous vorticity contours, finite-time Lyapunov exponent fields and particle traces are presented along with the aerodynamic parameters including the lift and thrust coefficients.

Study on a Mechanical Semi-Active Heave Compensation System of Drill String for Use on Floating Drilling Platform.

There are some disadvantages for existing heave compensation systems of drill string used for the Floating Drilling Platform (FDP), including high energy consumption, large and complex structure, and expensive manufacturing and maintenance costs. In view of the above, we present a streamlined mechanical semi-active heave compensation system (MSAHC) in this study. This system consists of active compensation part with the pinion and rack and passive compensation part. In order to evaluate system performance of the MSAHC, we establish its simulation model with AMEsim software. In the process of simulation, displacement of rotary hook and energy consumption is regarded as performance parameters of the system. And the change rule of two performance parameters are analyzed by changing these design parameters including gear radius of the pinion and rack, scale coefficient of PID, rotary hook load, heave height and heave period of the FDP, and accumulator volume. Then, based on the simulation results of the MSAHC system performance, we have selected out a best set of design parameters from them. Moreover, the feasibility of the design scheme of the MSAHC is effectively verified by comparison with the existing three heave compensation system. The result shows that the energy consumption of the MSAHC is lower than the active heave compensation system (AHC) and the semi-active heave compensation system (SAHC) when achieving a same compensation effect as well as the accumulator volume of MSAHC is half of the passive heave compensation system (PHC). Therefore, the new designed MSAHC not only ensure compensation effect but also lower energy consumption, and its structure is simplified by adopting the simple mechanical structure to decrease manufacturing cost, maintenance cost and floor space.

Study on Nonlinear Motion Behavior of Coupled Heave-Pitch for the Classic Spar Platform Based on AQWA

This paper used AQWA software to research the nonlinear motion characteristic of heave-pitch coupling of classical Spar platform in regular waves. With classic Spar platform as an example, the wave amplitude and periodic changes’ effect to the nonlinear motion behavior of coupled heave-pitch is researched. After calculation, the critical periods corresponding to the different incident wave amplitude are obtained, based which, gets the instability parameter domain of coupling resonance of platform in the wave period-amplitude plane. The results in this paper show that the heave-pitch coupled resonance of platform depends on the wave amplitude and the ratio of the natural period of heave and pitch, and the incident wave period.

Navigation Condition Effect on Ship Motion in some Sea State

According to analyzing the identity of ocean wave, theory of wave energy spectrum was applied to compute the curve of wave elevation vs. time in some sea state. Based on ship motion equations, ship motion was acquired by the simulation software of the of ship strip theory in some situation. How different navigation conditions effect on ship motion is researched in some sea state. The results show the change of degree of abaft the beam badly influenced the amplitude and periods of pitch, it also influenced periods of heave and amplitude of roll. The change of ship speed influenced the amplitude and periods of pitch, it also influenced periods of heave and roll.