Linearization of Quadratic Drag to Estimate CALM Buoy Pitch Motion in Frequency-Domain and Experimental Validation

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Amir G. Salem ◽  
Sam Ryu ◽  
Arun S. Duggal ◽  
Raju V. Datla
Keyword(s):  
Frequency Domain ◽  
Diffraction Problem ◽  
Wave Theory ◽  
Accurate Estimate ◽  
Linear Wave ◽  
Surface Boundary ◽  
Period Range ◽  
Pitch Motion ◽  
Linearization Methods ◽  
Quadratic Drag

The dynamics of an oil offloading catenary anchor leg mooring (CALM) buoy coupled with mooring and flow lines are directly related to the fatigue life of a mooring system, necessitating an accurate estimate of the buoy hydrodynamic response. Linear wave theory is used for modeling the surface boundary value problem, and the boundary element method is used to solve the fluid-structure interaction between the buoy hull and the incident waves in the frequency-domain. The radiation problem is solved to estimate the added mass and radiation damping coefficients, and the diffraction problem is solved to determine the linear wave exciting loading. The buoy pitch motion is investigated, and linearizations of the quadratic drag/damping term are performed in the frequency-domain. The pitch motion response is calculated by considering an equivalent linearized drag/damping. Quadratic, cubic, and stochastic linearizations of the nonlinear drag term are employed to derive the equivalent drag/damping. Comparisons between the linear and nonlinear damping effects are presented. Time-domain simulations of the buoy motions are performed in conjunction with Morison’s equation to validate the floating buoy response. The time- and frequency-domain results are finally compared with the experimental model test results for validations. The linearization methods applied result in good estimates for the peak pitch response. However, only the stochastic linearization method shows a good agreement for the period range of the incident wave where typical pitch response estimate has not been correctly estimated.

Linearization of Quadratic Drag to Estimate CALM Buoy Pitch Motion in Frequency-Domain and Experimental Validation

2009 ◽  
Author(s):  
Amir G. Salem ◽  
Sam Ryu ◽  
Arun S. Duggal ◽  
Raju V. Datla
Keyword(s):  
Frequency Domain ◽  
Diffraction Problem ◽  
Domain Analysis ◽  
Frequency Domain Analysis ◽  
Linearization Method ◽  
Linear Wave ◽  
Period Range ◽  
Pitch Motion ◽  
Linearization Methods ◽  
Quadratic Drag

Estimate of the pitch motion of an oil offloading Catenary Anchor Leg Mooring (CALM) buoy is presented. Linearization of the quadratic drag/damping term is investigated by the frequency-domain analysis. The radiation problem is solved to estimate the added mass and radiation damping coefficients, and the diffraction problem is solved for the linear wave exciting loading. The equation of motion is solved by considering the linearized nonlinear drag/damping. The pitch motion response is evaluated at each wave frequency by iterative and various linearization methods of the nonlinear drag term. Comparisons between the linear and nonlinear damping effects are presented. Time-domain simulations of the buoy pitch motion were also compared with results from the frequency-domain analysis. Various linearization methods resulted in good estimate of the peak pitch response. However, only the stochastic linearization method shows a good agreement for the period range of the incident wave where typical pitch response estimate has not been correctly estimated.

scholarly journals INVESTIGATIONS ON ORBITAL VELOCITIES AND PRESSURES IN IRREGULAR WAVES

1982 ◽  
Vol 1 (18) ◽  
pp. 20
Author(s):  
K.F. Daemrich ◽  
W.D. Eggert ◽  
H. Cordes
Keyword(s):  
Frequency Domain ◽  
Water Surface ◽  
Wave Theory ◽  
Hydraulic Model ◽  
Irregular Waves ◽  
Linear Wave ◽  
Simulation Methods ◽  
Linear Wave Theory ◽  
Theoretical Results

This paper deals with the results of hydraulic model investigations of orbital velocities and pressures in irregular waves. Different simulation methods in the time and frequency domain were checked or developed, and the theoretical results compared with measurements. Using simulation methods based on linear wave theory, results with good correlation are obtained, at locations near the water surface, however, a tendency towards over- or underestimation exists.

scholarly journals A Coupled Methodology for Wave-Body Interactions at the Scale of a Farm of Wave Energy Converters Including Irregular Bathymetry

2014 ◽  
Author(s):  
François Charrayre ◽  
Christophe Peyrard ◽  
Michel Benoit ◽  
Aurélien Babarit
Keyword(s):  
Wave Energy ◽  
Diffraction Problem ◽  
Wave Theory ◽  
Field Approximation ◽  
Coupling Scheme ◽  
Linear Wave ◽  
Wave Energy Converters ◽  
Mild Slope Equation ◽  
Wave Farm ◽  
Energy Converters

Knowledge of the wave perturbation caused by an array of Wave Energy Converters (WEC) is of great concern, in particular for estimating the interaction effects between the various WECs and determining the modification of the wave field at the scale of the array, as well as possible influence on the hydrodynamic conditions in the surroundings. A better knowledge of these interactions will also allow a more efficient layout for future WEC farms. The present work focuses on the interactions of waves with several WECs in an array. Within linear wave theory and in frequency domain, we propose a methodology based on the use of a BEM (Boundary Element Method) model (namely Aquaplus) to solve the radiation-diffraction problem locally around each WEC, and to combine it with a model based on the mild slope equation at the scale of the array. The latter model (ARTEMIS software) solves the Berkhoff’s equation in 2DH domains (2 dimensional code with a z-dependence), considering irregular bathymetries. In fact, the Kochin function (a far field approximation) is used to propagate the perturbations computed by Aquaplus into Artemis, which is well adapted for a circular wave representing the perturbation of an oscillating body. This approximation implies that the method is only suitable for well separated devices. A main advantage of this coupling technique is that Artemis can deal with variable bathymetry. It is important when the wave farm is in shallow water or in nearshore areas. The methodology used for coupling the two models, with the underlying assumptions is detailed first. Validations test-cases are then carried out with simple bodies (namely heaving vertical cylinders) to assess the accuracy and efficiency of the coupling scheme. These tests also allow to analyze and to quantify the magnitude of the interactions between the WECs inside the array.

A Second Order Lagrangian Model for Irregular Ocean Waves

2005 ◽  
Vol 128 (3) ◽  
pp. 177-183 ◽  
Author(s):  
Sébastien Fouques ◽  
Harald E. Krogstad ◽  
Dag Myrhaug
Keyword(s):  
Specular Reflection ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Wave Theory ◽  
Ocean Waves ◽  
Second Order ◽  
Lagrangian Model ◽  
Lagrangian Description ◽  
Linear Wave ◽  
Irregular Solution

Synthetic aperture radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, slope, and mean curvature are studied.

scholarly journals Multivariate analysis of Kelvin wave seasonal variability in ECMWF L91 analyses

2018 ◽  
Author(s):  
Marten Blaauw ◽  
Nedjeljka Žagar
Keyword(s):  
Seasonal Variability ◽  
Wave Theory ◽  
Fast Response ◽  
Linear Wave ◽  
Kelvin Wave ◽  
Vertical Projection ◽  
Northern Summer ◽  
Eastern Hemisphere ◽  
Function Decomposition ◽  
Vertically Propagating

Abstract. The paper presents the seasonal variability of Kelvin waves (KWs) in 2007–2013 ECMWF analyses on 91 model levels. The waves are filtered using the normal-mode function decomposition which simultaneously analyses wind and mass field based on their relationships from linear wave theory. Both spectral as well as spatiotemporal features of the KWs are examined in terms of their seasonal variability in comparison with background wind and stability. Furthermore, a differentiation is made using spectral bandpass filtering between the slow horizontal barotropic KW response and the fast vertical projection response observed as vertically-propagating KWs. Results show a clear seasonal cycle in KW activity which is predominantly at the largest zonal scales (wavenumber 1–2) where up to 50 % more energy is observed during the solstice seasons in comparison with spring and autumn. The spatiotemporal structure of the KW reveals the slow response as a robust Gill-type structure with its position determined by the location of the dominant convective outflow winds throughout the seasons. Its maximum strength occurs during northern summer when easterlies in the Eastern Hemisphere are strongest. The fast response in the form of free traveling KWs occur throughout the year with seasonal variability mostly found in the wave amplitudes being dependent on background easterly winds.

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