• Title/Summary/Keyword: Second order force

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  • Bhatta, Dambaru
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.45-60
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    • 2008
  • Here we consider the evaluation of the the dynamic component of the second order force due to wave diffraction by a circular cylinder analytically and numerically. The cylinder is fixed, vertical, surface piercing in water of finite uniform depth. The formulation of the wave-structure interaction is based on the assumption of a homogeneous, ideal, incompressible, and inviscid fluid. The nonlinearity in the wave-structure interaction problem arises from the free surface boundary conditions, namely, dynamic and kinematic free surface boundary conditions. We expand the velocity potential and free surface elevation functions in terms of a small parameter and then consider the second order diffraction problem. After deriving the pressure using Bernoulli's equation, we obtain the analytical expression for the dynamic component of the second order force on the cylinder by integrating the pressure over the wetted surface. The computation of the dynamic force component requires only the first order velocity potential. Numerical results for the dynamic force component are presented.

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Second Order Effect Induced by a Forced Heaving

  • Kim, Won-Joong;Kwon, Sun-Hong
    • Journal of Advanced Research in Ocean Engineering
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    • v.2 no.1
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    • pp.12-21
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    • 2016
  • In this paper, the $2^{nd}$ order hydrodynamic force effect of heaving submerged circular cylinder is considered, with the linear potential theory. Boundary value problem (BVP) is expanded up to the $2^{nd}$ order by using of the perturbation method and the $2^{nd}$ order velocity potential is calculated by means of integral equation technique using the classical Green's function expressed in cylindrical coordinates. The method of solving BVP is based on eigenfunction expansions. With different cylinder heights and heaving frequencies, graphical results are presented. As a result of the study, the cause of oscillatory force pattern is analyzed with the occurrence of negative added mass when a top of the cylinder gets closer to the free surface.

RANS CFD simulation for slender floating bodies with forward speed and comparison to BEM with uniform-flow approximation

  • Bakti, Farid P.;Kim, MooHyun
    • Ocean Systems Engineering
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    • v.11 no.2
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    • pp.161-184
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    • 2021
  • The nonlinear wave-uniform current interaction for a slender floating body is investigated by using the commercial CFD (computational fluid dynamics) tool STAR-CCM+ and author-developed simplified BEM (boundary element method) based on potential theory and perturbation approach. The STAR-CCM+ solves the fully non-linear Reynold Averaged Navier Stoke's (RANS) equation for real fluid in the finite volume framework. The viscous effect is accounted for by mesh refinement and the k - ω turbulence closure model. Meanwhile, the fully non-linear body motion and free surface elevation are considered by the overset mesh and volume of fluid method, respectively. Two different input waves with different order of non-linearity are compared to see their effects on ship's motion and added resistance. A detailed step-by-step simulation setup is explained to ensure the reproducibility of the results. Several preliminary simulations such as static tank test, wave calibration, and towing tank case are also conducted for quality assurance. The CFD results show good agreements with both the BEM with Uniform Flow approximation (UF-BEM) and the experimental data by other researchers when the λ/L is large. The CFD simulation also shows that it can properly capture the second-order force (added resistance) and highly nonlinear motion with breaking waves close to the pitch resonance frequency. However, the CFD simulation requires substantially higher computational cost than the UF-BEM. The comparison study shows that the UF-BEM can produce reasonably good results for practical applications with significantly less computational time and human effort. On the other hand, the CFD program can be used for proof computations for special cases.