Nonlinear Wave Disturbance Around a Vertical Circular Column

2002 ◽  
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.

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

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.

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.

Air-Gap Analysis of a Semi-Submersible Considering Full Second Order Effects

2019 ◽  
Author(s):  
Zhiyuan Pan ◽  
Torgeir Kirkhorn Vada ◽  
Arne Nestegård
Keyword(s):  
Gap Analysis ◽  
Low Frequency ◽  
Vertical Motion ◽  
Second Order ◽  
Surface Elevation ◽  
Asymmetry Factor ◽  
Order Effects ◽  
Short Term ◽  
Sea State ◽  
Sum Frequency

Abstract In the present paper, a complete and consistent second-order computation of airgap for a semi-submersible is presented. The second-order sum and difference frequency upwell will be calculated and combined with the linear upwell statistically to find the short-term extremes. The phasing of the low frequency surface elevation with respect to the low frequency vertical motion will be considered. The asymmetric characteristics of the surface elevation will be taken care of by the sum frequency surface elevation. By comparing the maximum and minimum extremes of surface elevation in a given sea state at specified off-body points, the “asymmetry factor” up to the second order can be obtained.

Aspects of Nonlinear Random Wave Kinematics

2002 ◽  
Author(s):  
Dag Myrhaug ◽  
Carl Trygve Stansberg ◽  
Hanne Therese Wist
Keyword(s):  
Free Surface ◽  
Second Order ◽  
Difference Frequency ◽  
Stokes Wave ◽  
Frequency Effect ◽  
Random Wave ◽  
Sum Frequency ◽  
Wave Kinematics ◽  
Nonlinear Random Wave ◽  
Nonlinear Free Surface

Statistics of the nonlinear free surface elevation as well as the nonlinear random wave kinematics in terms of the horizontal velocity component in arbitrary water depth are addressed. Two different methods are considered: a simplified analytical approach based on second-order Stokes wave theory including the sum-frequency effect only, and a second-order random wave model including both sum-frequency and difference-frequency effects. The paper compares results for the statistics of the nonlinear free surface, and the consequences of neglecting the difference-frequency effect in the first method are discussed.

Springing Analysis of Elastic Vessels in Head and Oblique Seas Including Nonlinear Effects Due to Second Order Diffraction Pressures

2004 ◽  
Author(s):  
Haiping He ◽  
Armin W. Troesch ◽  
Yung Sup Shin ◽  
Boo-Ki Kim
Keyword(s):  
Theoretical Calculations ◽  
Bending Moment ◽  
Nonlinear Effects ◽  
Diffraction Theory ◽  
Ocean Waves ◽  
Second Order ◽  
Sea State ◽  
Zero Crossing ◽  
Sum Frequency ◽  
State Dependent

The wave-induced vibration of the ship hull, commonly called springing, may not produce extreme stresses, but it is likely to have a direct effect on fatigue-life estimates due to its high frequency content. This research investigates the second order contribution to the springing bending moment from the sum frequency of incident ocean waves in both head and oblique seas. The computer program developed here extends the ABS SSRS (Ship Spring Response System) program to oblique seas using Troesch’s oblique sea linear diffraction theory [1]. The theoretical calculations for forward speed are modified by an empirical factor to correlate more closely with experimental results. An example calculation on a Bulk Carrier was performed for different heading angles. For one such representative sea state, the overall increase to the total bending moment from the nonlinear, sum-frequency excitation is found to be less than 12%. However, the nonlinear springing (RMS) increases the total RMS springing over the linear springing by more than 5 times in some stations, which has significant implications for fatigue studies. A sea state sweep study (using ITTC spectrum) also shows the springing effects are highly sea state dependent. Overall, springing effects decrease as zero crossing periods increase, which indicates springing is important in sea states with short waves and becomes less significant in sea states with long waves.

Characteristics of Steep Second-Order Random Waves in Finite and Shallow Water

2011 ◽  
Author(s):  
Carl Trygve Stansberg
Keyword(s):  
Time Series ◽  
Shallow Water ◽  
Frequency Component ◽  
Second Order ◽  
Difference Frequency ◽  
Nonlinear Interactions ◽  
Random Waves ◽  
Theoretical Formulation ◽  
Sum Frequency ◽  
The Difference

The theoretical formulation of second-order random waves in deep and finite water is reviewed. In particular, the increased nonlinear interactions with decreasing depth are addressed, including both the sum-frequency as well as the slowly varying difference-frequency components. Depth-defined limitations in the valid range for random waves are suggested based on the Ursell number. Numerical time series realizations at various depths and for two sea states are obtained by an efficient bifrequency summation procedure. Resulting time series show moderate average second-order energy contents, except for the steep sea state Hs = 15m, Tp = 14s in depths of 30m and 20m which are outside the suggested valid second-order range. The two largest wave events from the simulations are studied in particular for the different depths. Nonlinear interactions increase significantly with decreasing depth. Still, within the valid range, extreme second-order crests and peak particle velocities are only moderately increased with decreasing depth, while the negative peaks increase significantly. This is because the difference-frequency component almost compensates for the sum-frequency part at crests, while it is opposite at troughs. Maximum slopes, however, are clearly increased in shallow water, eventually leading to increased breaking (which is beyond second order of course). Velocity profiles under the crests are also shown, confirming the findings from the elevation.

Determination of Combined and Second Order Factor Effects for Simultaneous Optimization of Physical and Mechanical Properties of NR/BR Blend System

2014 ◽  
Vol 42 (4) ◽  
pp. 290-304
Author(s):  
Rajarajan Aiyengar ◽  
Jyoti Divecha
Keyword(s):  
Physical And Mechanical Properties ◽  
Second Order ◽  
Simultaneous Optimization ◽  
Order Effects ◽  
Elongation At Break ◽  
Five Factors ◽  
Rubber Compounds ◽  
Polybutadiene Rubber ◽  
Contour Plots

ABSTRACT The blends of natural rubber (NR), polybutadiene rubber (BR), and other forms of rubbers are widely used for enhancing the mechanical and physical properties of rubber compounds. Lots of work has been done in conditioning and mixing of NR/BR blends to improve the properties of its rubber compounds and end products such as tire tread. This article employs response surface methodology designed experiments in five factors; high abrasion furnace carbon black (N 330), aromatic oil, NR/BR ratio, sulfur, and N-oxydiethylene-2-benzothiazole sulfenamide for determination of combined and second order effects of the significant factors leading to simultaneous optimization of the NR/BR blend system. One of the overall optimum of eight properties existed at carbon 44 phr, oil 6.1 phr, NR/BR 78/22 phr with the following values of properties: tensile strength (22 MPa), elongation at break (528%), tear resistance (30 kg/mm), rebound resilience (67%), moderate hardness (68 International rubber hardness degrees) with low heat buildup (17 °C), permanent set (12%), and abrasion loss (57 mm3). More optimum combinations can easily be determined from the NR/BR blend system models contour plots.

Bulk Contributions Modulate the Sum-Frequency Generation Spectra of Interfacial Water on Model Sea-Spray Aerosols

2018 ◽  
Author(s):  
Sandeep K. Reddy ◽  
Raphael Thiraux ◽  
Bethany A. Wellen Rudd ◽  
Lu Lin ◽  
Tehseen Adel ◽  
...  
Keyword(s):  
Single Layer ◽  
Sum Frequency Generation ◽  
Second Order ◽  
Interfacial Structure ◽  
Sea Spray ◽  
Third Order ◽  
Systematic Analysis ◽  
Sum Frequency ◽  
Structure Of Water ◽  
Frequency Generation

Vibrational sum-frequency generation (vSFG) spectroscopy is used to determine the molecular structure of water at the interface of palmitic acid monolayers. Both measured and calculated spectra display speci c features due to third-order contributions to the vSFG response which are associated with nite interfacial electric potentials. We demonstrate that theoretical modeling enables to separate the third-order contributions, thus allowing for a systematic analysis of the strictly surface-sensitive, second-order component of the vSFG response. This study provides fundamental, molecular-level insights into the interfacial structure of water in a neutral surfactant system with relevance to single layer bio-membranes and environmentally relevant sea-spray aerosols. These results emphasize the key role that computer simulations can play in interpreting vSFG spectra and revealing microscopic details of water at complex interfaces, which can be difficult to extract from experiments due to the mixing of second-order, surface-sensitive and third-order, bulk-dependent contributions to the vSFG response.

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