• Title/Summary/Keyword: mixed Eulerian-Lagrangian

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Fully nonlinear time-domain simulation of a backward bent duct buoy floating wave energy converter using an acceleration potential method

  • Lee, Kyoung-Rok;Koo, Weoncheol;Kim, Moo-Hyun
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.5 no.4
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    • pp.513-528
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    • 2013
  • A floating Oscillating Water Column (OWC) wave energy converter, a Backward Bent Duct Buoy (BBDB), was simulated using a state-of-the-art, two-dimensional, fully-nonlinear Numerical Wave Tank (NWT) technique. The hydrodynamic performance of the floating OWC device was evaluated in the time domain. The acceleration potential method, with a full-updated kernel matrix calculation associated with a mode decomposition scheme, was implemented to obtain accurate estimates of the hydrodynamic force and displacement of a freely floating BBDB. The developed NWT was based on the potential theory and the boundary element method with constant panels on the boundaries. The mixed Eulerian-Lagrangian (MEL) approach was employed to capture the nonlinear free surfaces inside the chamber that interacted with a pneumatic pressure, induced by the time-varying airflow velocity at the air duct. A special viscous damping was applied to the chamber free surface to represent the viscous energy loss due to the BBDB's shape and motions. The viscous damping coefficient was properly selected using a comparison of the experimental data. The calculated surface elevation, inside and outside the chamber, with a tuned viscous damping correlated reasonably well with the experimental data for various incident wave conditions. The conservation of the total wave energy in the computational domain was confirmed over the entire range of wave frequencies.

LES of breakup and atomization of a liquid jet into cross turbulent flow (비정상 난류 유동장에서 수직 분사 액주의 분열 및 기화에 관한 LES)

  • Yang, Seung-Joon;Sung, Hong-Gye
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2009.05a
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    • pp.99-102
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    • 2009
  • LES(Large eddy simulation) of breakup and atomization of a liquid jet into cross turbulent flow was performed. Two phase flow between a gas phase and a liquid phase was modeled by a mixed numerical scheme of both Eulerian and Lagrangian methods for gas and liquid phases respectively. The first and second breakup of liquid column was observed. The penetration depth in cross flow was comparable with experimental data for several variant of a liquid-gas momentum flux ratio by varying liquid injection velocities. SMD(Sauter Mean Diameter) distribution downstream of jet was analyzed.

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Spatial Modulation of Nonlinear Waves due to Bragg Reflection (Bragg 반사에 의한 비선형파의 공간적 파형변조해석)

  • Choi, Ka-Ram;Koo, Weon-Cheol
    • Journal of Ocean Engineering and Technology
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    • v.24 no.6
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    • pp.34-40
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    • 2010
  • Bragg reflection of nonlinear waves is simulated by a 2D fully nonlinear numerical wave tank (NWT). The developed NWT was based on the Boundary Element Method (BEM) with potential theory and the mixed Eulerian-Lagrangian (MEL) time marching scheme with Runge-Kutta 4th-order time integration. A spatial variation of wave elevations and their Fourier amplitudes of each component are compared to investigate the effect of sea bottom ripples and their relative heights. The incident waves over an undulated sea bottom are partially reflected and changed to partial standing waves due to Bragg reflection. The present results are verified with linear calculations and experimental data. It is found that the 1st-order wave component is mainly affected by Bragg reflection and its spatial modulation is significant in front of the bottom ripples.

Wave propagation in a 3D fully nonlinear NWT based on MTF coupled with DZ method for the downstream boundary

  • Xu, G.;Hamouda, A.M.S.;Khoo, B.C.
    • Ocean Systems Engineering
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    • v.4 no.2
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    • pp.83-97
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    • 2014
  • Wave propagation in a three-dimensional (3D) fully nonlinear numerical wave tank (NWT) is studied based on velocity potential theory. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing algorithm, B-spline, is applied to eliminate the possible saw-tooth instabilities. The artificial wave speed employed in MTF (multi-transmitting formula) approach is investigated for fully nonlinear wave problem. The numerical results from incorporating the damping zone (DZ), MTF and MTF coupled DZ (MTF+DZ) methods as radiation condition are compared with analytical solution. An effective MTF+DZ method is finally adopted to simulate the 3D linear wave, second-order wave and irregular wave propagation. It is shown that the MTF+DZ method can be used for simulating fully nonlinear wave propagation very efficiently.

Numerical Study on Wave Run-up of a Circular Cylinder with Various Diffraction Parameters and Body Drafts

  • Jeong, Ho-Jin;Koo, Weoncheol;Kim, Sung-Jae
    • Journal of Ocean Engineering and Technology
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    • v.34 no.4
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    • pp.245-252
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    • 2020
  • Wave run-up is an important phenomenon that should be considered in ocean structure design. In this study, the wave run-up of a surface-piercing circular cylinder was calculated in the time domain using the three-dimensional linear and fully nonlinear numerical wave tank (NWT) techniques. The NWT was based on the boundary element method and the mixed Eulerian and Lagrangian method. Stokes second-order waves were applied to evaluate the effect of the nonlinear waves on wave run-up, and an artificial damping zone was adopted to reduce the amount of reflected and re-reflected waves from the sidewall of the NWT. Parametric studies were conducted to determine the effect of wavelength, wave steepness, and the draft of the cylinder on the wave run-up of the cylinder. The maximum wave run-up value occurred at 0°, which was in front of the cylinder, and the minimum value occurred near the circumferential angle of 135°. As the diffraction parameter increased, the wave run-up increased up to 1.7 times the wave height. Furthermore, the wave run-up was 4% higher than the linear wave when the wave steepness was 1/35. In particular, the crest height of the wave run-up increased by 8%.

Development and Application of Two-Dimensional Numerical Tank using Desingularized Indirect Boundary Integral Equation Method (비특이화 간접경계적분방정식방법을 이용한 2차원 수치수조 개발 및 적용)

  • Oh, Seunghoon;Cho, Seok-kyu;Jung, Dongho;Sung, Hong Gun
    • Journal of Ocean Engineering and Technology
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    • v.32 no.6
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    • pp.447-457
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    • 2018
  • In this study, a two-dimensional fully nonlinear transient wave numerical tank was developed using a desingularized indirect boundary integral equation method. The desingularized indirect boundary integral equation method is simpler and faster than the conventional boundary element method because special treatment is not required to compute the boundary integral. Numerical simulations were carried out in the time domain using the fourth order Runge-Kutta method. A mixed Eulerian-Lagrangian approach was adapted to reconstruct the free surface at each time step. A numerical damping zone was used to minimize the reflective wave in the downstream region. The interpolating method of a Gaussian radial basis function-type artificial neural network was used to calculate the gradient of the free surface elevation without element connectivity. The desingularized indirect boundary integral equation using an isolated point source and radial basis function has no need for information about the element connectivity and is a meshless method that is numerically more flexible. In order to validate the accuracy of the numerical wave tank based on the desingularized indirect boundary integral equation method and meshless technique, several numerical simulations were carried out. First, a comparison with numerical results according to the type of desingularized source was carried out and confirmed that continuous line sources can be replaced by simply isolated sources. In addition, a propagation simulation of a $2^{nd}$-order Stokes wave was carried out and compared with an analytical solution. Finally, simulations of propagating waves in shallow water and propagating waves over a submerged bar were also carried and compared with published data.