Second-Order Difference-Frequency Loads on FPSOs by Full QTF and Relevant Approximations

Volume 1: Offshore Technology ◽

10.1115/omae2020-18132 ◽

2020 ◽

Author(s):

Espen Engebretsen ◽

Zhiyuan Pan ◽

Nuno Fonseca

Keyword(s):

Near Field ◽

Time Domain Analysis ◽

Second Order ◽

Difference Frequency ◽

Irregular Waves ◽

Mooring Line ◽

Diffraction Radiation ◽

Surface Integral ◽

Order Difference ◽

Order Diffraction

Abstract This paper investigates three different approximations of the full Quadratic Transfer Function (QTF) for calculating horizontal plane second-order difference-frequency loads on FPSOs, namely Newman’s approximation, full QTF without free surface integral and the white-noise approximation. Second-order excitation loads obtained from approximated QTFs are compared in frequency-domain with those obtained by the full QTFs computed from second-order diffraction/radiation analysis in WADAM. The comparison is performed for a new-build FPSO in a range of water depths and environmental combinations. The full QTFs from second-order diffraction/radiation analysis are further compared to empirical QTFs as identified from cross bi-spectral analysis of model test results in irregular waves. A mesh convergence study is presented for calculating full QTFs by the near-field approach in a second-order diffraction/radiation analysis. The importance of including viscous damping in heave, roll and pitch is illustrated for the mean wave-drift force in surge and sway. FPSO motions and mooring line tensions from fully-coupled time-domain analysis in OrcaFlex is compared when using approximated QTFs and full QTFs from second-order diffraction/radiation analysis.

Download Full-text

The complete second-order diffraction solution for an axisymmetric body Part 2. Bichromatic incident waves and body motions

Journal of Fluid Mechanics ◽

10.1017/s0022112090001690 ◽

1990 ◽

Vol 211 ◽

pp. 557-593 ◽

Cited By ~ 75

Author(s):

Moo-Hyun Kim ◽

Dick K. P. Yue

Keyword(s):

Transfer Functions ◽

Integral Equation Method ◽

Axisymmetric Body ◽

Second Order ◽

Difference Frequency ◽

Irregular Waves ◽

Total Load ◽

Frequency Wave ◽

Order Diffraction ◽

Incident Waves

In Part 1 (Kim & Yue 1989), we considered the second-order diffraction of a plane monochromatic incident wave by an axisymmetric body. A ring-source integral equation method in conjunction with a novel analytic free-surface integration in the entire local-wave-free domain was developed. To generalize the second-order theory to irregular waves, say described by a continuous spectrum, we consider in this paper the general second-order wave–body interactions in the presence of bichromatic incident waves and the resulting sum- and difference-frequency problems. For completeness, we also include the radiation problem and second-order motions of freely floating or elastically moored bodies. As in Part 1, the second-order sum- and difference-frequency potentials are obtained explicitly, revealing a number of interesting local behaviours of the second-order pressure. For illustration, the quadratic transfer functions (QTF's) for the sum- and difference-frequency wave excitation and body response obtained from the present complete theory are compared to those of existing approximation methods for a number of simple geometries. It is found that contributions from the second-order potentials, typically neglected, can dominate the total load in many cases.

Download Full-text

A Numerical Simulation of Non-Linear Air-Gap for Deepwater Semi-Submersible Platform

10.1115/omae2021-62553 ◽

2021 ◽

Author(s):

Zhuang Kang ◽

Yansong Zhang ◽

Haibo Sui ◽

Rui Chang

Keyword(s):

Air Gap ◽

Second Order ◽

Difference Frequency ◽

Hydrodynamic Performance ◽

Wave Loads ◽

Order Difference ◽

Motion Response ◽

Nonlinear Motion ◽

Non Linear ◽

Simulation Results

Abstract Air gap is pivotal to the hydrodynamic performance for the semi-submersible platform as a key characteristic for the strength assessment and safety evaluation. Considering the metocean conditions of the Norse Sea, the hydrodynamic performance of a semi-submersible platform has been analyzed. Based on the three-dimensional potential flow theory, and combined with the full QTF matrix and the second-order difference frequency loads, the nonlinear motion characteristics and the prediction for air gap have been simulated. The wave frequency motion response, the second-order nonlinear air gap response and nonlinear motion response of the platform have been analyzed. By comparing the simulation results, the air gap response of the platform considering the nonlinear motion is more intense than the results simulated by the first-order motion without considering the second-order difference frequency loads. Under the heavy metocean conditions, for the heave and pitch motion of the platform, the non-linear simulation values for some air gap points and areas are negative which means the wave slam has been occurred, but the calculation results of linear motion response indicate that the air gap above has not appeared the wave slamming areas. The simulation results present that the influence of the second-order wave loads is a critical part in the air gap prediction for the semi-submersible platform.

Download Full-text

Nonlinear Wave Disturbance Around a Vertical Circular Column

21st International Conference on Offshore Mechanics and Arctic Engineering, Volume 1 ◽

10.1115/omae2002-28620 ◽

2002 ◽

Cited By ~ 1

Author(s):

C. T. Stansberg ◽

H. Braaten

Keyword(s):

Linear Prediction ◽

Harmonic Component ◽

Nonlinear Effects ◽

Second Order ◽

Wave Disturbance ◽

Difference Frequency ◽

Irregular Waves ◽

Order Effects ◽

Sum Frequency ◽

Circular Column

The wave disturbance close to vertical columns is analysed. In particular, the deviations from linear predictions are investigated, by experimental as well as by numerical methods. Thus a second-order numerical diffraction model is established by means of a diffraction analysis code (WAMIT) and compared to model tests with a single, fixed column with diameter 16m. Tests in regular, bi-chromatic as well as irregular waves are run. Significant nonlinear effects are observed, especially in steep waves, with the maximum elevation in front of the column increasing from 11.5m in a linear prediction to around 19m, in a 12s regular wave with 22m wave height. The main nonlinear effects in front of the column are identified as second-order sum-frequency and difference-frequency terms, plus a significant nonlinear increase in the first harmonic component. The WAMIT prediction of the second-order effects agrees fairly well with the measurements, although with some overprediction and underprediction, respectively, of the sum-frequency and difference-frequency (LF and mean set-up) terms in the steepest waves. For the underprediction of the first harmonic, however, a theory beyond second order is required.

Download Full-text

Computation of Slowly Varying Second-Order Hydrodynamic Forces on Floating Structures in Irregular Waves

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.3257151 ◽

1989 ◽

Vol 111 (3) ◽

pp. 223-232 ◽

Cited By ~ 2

Author(s):

T. Matsui

Keyword(s):

Velocity Potential ◽

Near Field ◽

Fluid Pressure ◽

Hydrodynamic Forces ◽

Second Order ◽

Irregular Waves ◽

Floating Structures ◽

Slow Drift ◽

Submerged Body ◽

Element Technique

An exact second-order formulation is presented for computing the slowly varying second-order hydrodynamic forces on floating structures in irregular waves. The near-field approach based on direct integration of the fluid pressure on the submerged body surface is employed in conjunction with numerical first-order solutions by means of the hybrid finite element technique. Green’s second identity is exploited to evaluate the second-order forces due to the second-order velocity potential. Numerical results are presented for the slow drift excitation forces on an articulated column and a semi-submersible platform. It is shown that the contribution from the second-order velocity potential is more significant to the roll moment than to the sway and heave forces on the semi-submersible.

Download Full-text

Influence of Second-Order Difference-Frequency Wave Loads on the Floating Wind-Wave Hybrid Platform

Volume 7B: Ocean Engineering ◽

10.1115/omae2017-61273 ◽

2017 ◽

Cited By ~ 1

Author(s):

Hyebin Lee ◽

Yoon Hyeok Bae ◽

Kyong-Hwan Kim ◽

Sewan Park ◽

Keyyong Hong

Keyword(s):

Wind Wave ◽

Computational Effort ◽

Second Order ◽

Difference Frequency ◽

Linear Wave ◽

Wave Loads ◽

Wave Load ◽

Frequency Wave ◽

Order Difference ◽

Hybrid Platform

A wind-wave hybrid power generation system is a floating offshore energy platform which is equipped with a number of wind turbines and wave energy converters (WECs) to harvest energy from various resources. This wind-wave hybrid platform is moored by eight catenary lines to keep its position against wind-wave-current environment. In most cases, the resonant frequency of horizontal motion of moored platform is very low, so a resonance is hardly seen by numerical simulation with linear wave assumptions. However, the incident waves with different frequency components are accompanied by sum and difference frequency loads due to the nonlinearity of the waves. Typically, the magnitude of the second-order wave loads are small and negligible, but once the second-order wave loads excite the platform at its natural frequency, the resonance can take place, which results in adverse effects on the platform. In this paper, the second-order difference frequency wave load on the wind-wave hybrid platform is numerically assessed and time domain simulation by coupled platform-mooring dynamic analysis is carried out. As a result, the horizontal motions of the platform was highly excited and the increased motions led higher top tension of the mooring lines compared with the case of linear wave environment. Especially, the combination of the wind and wave loads excited the horizontal motions more and made the mooring top tension far higher than wave load was only applied. With regards to the second-order difference frequency wave load, the result with the Quadratic Transfer Function (QTF) is compared to the one with Newman’s approximation. As the simulation results between them was insignificant, the Newman’s approximation can be used instead of the complete QTF to reduce the computational effort.

Download Full-text

Second Order Difference Frequency Wave-Current Loading Using Kelvin-Newman Approximation

Volume 6A: Ocean Engineering ◽

10.1115/omae2020-18901 ◽

2020 ◽

Author(s):

Farid P. Bakti ◽

Moo-Hyun Kim

Keyword(s):

Second Order ◽

The Body ◽

Difference Frequency ◽

Computational Time ◽

Forward Speed ◽

Frequency Wave ◽

Order Difference ◽

First Order ◽

Current Interaction ◽

Current Loading

Abstract Kelvin & Newman introduced a linearization method to include the current (or forward speed) effect into the diffraction & radiation wave field for large-slender floating bodies. The K-N method assumes a steady far-field current while disregarding the steady potential field due to the presence of the body. The method is proven to be reliable when the Froude number is relatively small, the body shape is relatively slender (∂∂x≪∂∂y,∂∂z), and the sea condition is mild. This requirement is fulfilled for typical FPSOs and ship-shaped vessels in a typical current (or forward speed) condition. Several studies suggested that the presence of the current might change the first order hydrodynamic coefficients such as the first order diffraction force, added mass, and radiation damping. Currents also contributed to a change in the second-order slowly-varying drift force. However, the effect of current in the second-order difference-frequency force is yet to be investigated. By expanding the Kelvin-Newman approximation up to the second order, and solving the problem in the frequency domain, we can save computational time while expanding the accuracy of the scheme. The second order quadratic force is the main focus of this study, since it is the main contributor to the total second order difference frequency forces especially near the diagonal. By implementing the Kelvin-Newman wave current interaction approach up to the wave’s second order, we can assess the performance of the Kelvin-Newman wave current interaction formulation in various sea conditions.

Download Full-text