Hydrodynamic analysis of wave interactions with a moored floating breakwater using the element-free Galerkin method

Abstract

This paper deals with a numerical investigation of incident wave interactions with a moored pontoon-type floating breakwater. The element-free Galerkin method, in which only nodal data are required to analyze the problem, is employed to solve the diffraction and radiation boundary value problems addressed by the modified Helmholtz equation. The numerical model includes the hydrodynamic and mooring analyses, and it is validated by previous numerical and experimental results. Using the numerical model, we are able to assess the hydrodynamic performance of a moored pontoon-type floating breakwater in regular waves. Numerical results are presented to show the effects of wave conditions and mooring system configuration. This paper also presents the simple forms of stiffness coefficients of a slack mooring line. The influence of mooring line condition on the performance of a floating breakwater is highlighted.Résumé : Cet article présente une étude numérique des interactions des ondes incidentes sur un brise-lames flottant amarré de type ponton. La méthode sans maillage de Galerkin, dans laquelle uniquement les données nodales sont requises pour analyser le problème, est employée pour résoudre les problèmes de valeur de diffraction et de rayonnement aux limites tels qu'abordés par l'équation d'Helmholtz modifiée. Le modèle numérique comprend les analyses hydrodynamiques et d'amarrage et il est validé par les résultats numériques et expérimentaux antérieurs. En utilisant le modèle numérique, nous pouvons évaluer la performance hydrodynamique d'un brise-lames flottant amarré de type ponton avec des conditions de vagues régulières. Les résultats numériques sont présentés afin de montrer les effets des conditions de vagues et de la configuration d'amarrage. Cet article présente également les formes simples des coefficients de rigidité d'une ligne d'amarrage à tension variable. L'influence de l'état de la ligne d'amarrage sur le rendement d'un brise-lames flottant est soulignée.Mots clés : brise-lames flottant amarré, méthode sans maillage de Galerkin, condition de la ligne d'amarre.[Traduit par la Rédaction]

Stiffness of mooring lines and performance of floating breakwater in three dimensions

“…The numerical models described above are compared to the experimental and the numerical results of Sannasiraj et al [20] and the numerical results of Lee and Cho [14]. The experiments of Sannasiraj et al [20] refer to the case of a floating breakwater with a single rectangular-section pontoon moored with four mooring lines as shown in Fig.…”

“…With regard to the hydrodynamic analysis of the floating body, linear two-dimensional models describing the complete hydrodynamic problem (diffraction and radiation) have been developed by Isaacson and Nwogu [11], Isaacson [6], Isaacson and Bhat [9], Williams and Abul-Azm [23], Bhat and Isaacson [2], Sannasiraj et al [20], Williams et al [24] and Lee and Cho [14]. Most of these models are based on the finite element method (FEM) or the boundary integral equation method (BIEM) utilizing Green's theorem, while Lee and Cho [14] use the element-free Galerkin method. Isaacson and Nwogu [11] and Bhat [1] properly modified a two-dimensional hydrodynamic model in order to take into account the effect of finite floating body length.…”

“…Williams and Abul-Azm [23] and Williams et al [24] modified the hydrodynamic equations by using appropriate values of the mooring lines' stiffness coefficients. On the contrary, Sannasiraj et al [20] and Lee and Cho [14] derived analytically the stiffness coefficients of the mooring lines for taut and slack conditions, respectively, using the basic catenary equation for the cable equilibrium. However, in those investigations, the derivations of the stiffness coefficients were restricted to two dimensions (stiffness coefficients in sway, heave and roll modes only), following the procedure given by Jain [12]; furthermore, it was assumed that the stiffness components remain unaffected by the motions of the structure, i.e.…”

The effect of axial stiffness of mooring lines on the horizontal motion of FDPSO

“…[1] and Lee et al [2] derived analytically the stiffness coefficients of the mooring lines for taut and slack conditions, respectively. Through the differential changes of the mooring lines' tensions caused by the static motions of floating bodies, Eva et al [3] derived the stiffness coefficient of a mooring line in six degrees of freedom of the breakwater.…”

“…incident wave amplitude, heading and water depth, respectively; k is the wave number, determined by the dispersion equation2 tanh( ) gk kh ω = . ρ and g are the density of fluid and the acceleration due to gravity, respectively.…”