Sum-and Difference-Frequency Wave Loads on a Body in Unidirectional Gaussian Seas

1991 ◽  
Vol 35 (02) ◽  
pp. 127-140 ◽  
Author(s):  
M. H. Kim ◽  
Dick K. P. Yue
Keyword(s):  
Volterra Series ◽  
Extreme Values ◽  
Large Body ◽  
Wave Force ◽  
Second Order ◽  
Difference Frequency ◽  
Approximation Methods ◽  
Wave Loads ◽  
Frequency Wave ◽  
Incident Waves

When nonlinear effects are included in the diffraction of waves by a large body, there are, at second order, interactions at the sums and differences of the component frequencies of the incident waves. In this paper, the complete deterministic and stochastic solutions of second-order (sum-and difference-frequency) wave loads in unidirectional Gaussian waves are considered. The deterministic result, namely the wave force quadratic transfer function (QTF) in bichromatic incident waves, is complete in the context of second-order diffraction theory in that all the relevant components including those due to the exact second-order potentials are obtained. Statistical properties of second-order wave excitations are then investigated using the QTF results and a two-term Volterra series model. For illustration, the exact second-order force spectra and probability distributions for the simple geometry of a truncated vertical cylinder are obtained and compared with those based on a number of existing approximation methods. It is found that second-order exciting force variances and probability of extreme values may be significantly underestimated by existing approximation methods.

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

1990 ◽  
Vol 211 ◽  
pp. 557-593 ◽  
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.

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

2017 ◽  
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.

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

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.

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

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.

Approximation of Second-Order Low-Frequency Wave Loading in Multi-Directional Waves

2010 ◽  
Author(s):  
Flavia C. Rezende ◽  
Xiao-bo Chen
Keyword(s):  
Low Frequency ◽  
Second Order ◽  
Wave Loads ◽  
Wave Loading ◽  
Frequency Wave ◽  
New Developments ◽  
Directional Waves ◽  
Novel Method ◽  
The Difference ◽  
Accurate Scheme

Further to the studies by Chen & Rezende (OMAE2009) on the quadratic transfer function (QTF) of low-frequency wave loading in which the QTF is developed by the series expansion associated with the difference-frequency up to the order-Δω2, new formulations have been developed in order to take into account the effect of interactions between waves of different headings. It provides a novel method to evaluate the low-frequency second-order wave loads in a more accurate than usual order-Δω approximation (often called Newman approximation) and more efficient way comparing to the computation of complete QTF in multi-directional waves. New developments including numerical results of different components of QTF are presented here. Furthermore, the time-series reconstruction of excitation loads by quadruple sums in the motion simulation of mooring systems is analyzed and a new efficient and accurate scheme using only a triple sum is demonstrated.

Efficient Computations of Second-Order Low-Frequency Wave Load

2009 ◽  
Author(s):  
Xiao-Bo Chen ◽  
Fla´via Rezende
Keyword(s):  
Low Frequency ◽  
Second Order ◽  
Wave Loads ◽  
Wave Loading ◽  
Wave Load ◽  
Frequency Wave ◽  
New Developments ◽  
Novel Method ◽  
The Difference ◽  
New Formulation

As the main source of resonant excitations to most offshore moored systems like floating LNG terminals, the low-frequency wave loading is the critical input to motion simulations which are important for the design. Further to the analysis presented by Chen & Duan (2007) and Chen & Rezende (2008) on the quadratic transfer function (QTF) of low-frequency wave loading, the new formulation of QTF is developed by the series expansion of the second-order wave loading with respect to the difference-frequency upto the order-2. It provides a novel method to evaluate the low-frequency second-order wave loads in a more accurate than usual order-0 approximation (often called Newman approximation) and more efficient way comparing to the computation of complete QTF. New developments including numerical results of different components of QTF are presented here. Furthermore, the time-series reconstruction of excitation loads in the motion simulation of mooring systems is analyzed and a new efficient and accurate scheme is demonstrated.

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