• Wind and Structures
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• 제29권1호
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• pp.33-41
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• 2019

The interaction of head waves with an infinite row of identical, equally spaced, rectangular breakwaters is investigated in the presence of uneven bottom topography. Using linear water wave theory and matched eigenfunction expansion method, the boundary value problem is transformed into a system of linear algebraic equations which are numerically solved to know the velocity potentials completely. Utilizing this method, reflected and transmitted wave energy are computed for different physical parameters along with the wave field in the vicinity of breakwaters. It is observed that the wave field becomes more complicated when the incoming wavelength becomes smaller than the channel width. A critical ratio of the gap width to the channel width, corresponding to the inflection point of the transmitted energy variation, is identified for which 1/3 of the total energy is transmitted. Similarly, depending on the incident wavelength, there is a critical breakwater width for which a minimum energy is transmitted. Further, the accuracy of the computed results is verified by using the derived energy relation.

• Korean Chemical Engineering Research
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• 제57권5호
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• pp.652-665
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• 2019

Analytical solutions of the reactant concentration inside porous spherical catalytic particles were obtained from unsteady reaction-diffusion equation by applying eigenfunction expansion method. Various surface concentrations as exponentially decaying or oscillating function were considered as boundary conditions to solve the unsteady partial differential equation as a function of radial distance and time. Dirac delta function was also used for the instantaneous injection of the reactant as the surface boundary condition to calculate average reactant concentration inside the particles as a function of time by Laplace transform. Besides spherical morphology, other geometries of particles, such as cylinder or slab, were considered to obtain the solution of the reaction-diffusion equation, and the results were compared with the solution in spherical coordinate. The concentration inside the particles based on calculation was compared with the bulk concentration of the reactant molecules measured by photocatalytic decomposition as a function of time.

• International Journal of Naval Architecture and Ocean Engineering
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• 제12권1호
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• pp.468-478
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• 2020

The wave interaction problem with a vertical slotted breakwater, consisting of impermeable upper, lower parts and a permeable middle part, has been studied theoretically. An analytical model was presented for the estimation of reflection and transmission of monochromatic waves by a slotted breakwater. The far-field solution of the wave scattering involving nonlinear porous boundary condition was obtained using eigenfunction expansion method. The empirical formula for drag coefficient in the near-field, representing energy dissipation across the slotted barrier, was determined by curve fitting of the numerical solutions of 2-D channel flow using CFD code StarCCM+. The theoretical model was validated with laboratory experiments for various configurations of a slotted barrier. It showed that the developed analytical model can correctly predict the energy dissipation caused by turbulent eddies due to sudden contraction and expansion of a slotted barrier. The present paper provides a synergetic approach of the analytical and numerical modelling with minimum CPU time, for better estimation of the hydrodynamic performance of slotted breakwater.

• 한국해양공학회지
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• 제35권3호
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• pp.216-228
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• 2021

In the present study, the performance of a floating oscillating water column (OWC) device has been studied in regular waves. The OWC model has the shape of a hollow cylinder. The linear potential theory is assumed, and a matched eigenfunction expansion method(MEEM) is applied for solving the diffraction and radiation problems. The radiation problem involves the radiation of waves by the heaving motion of a floating OWC device and the oscillating pressure in the air chamber. The characteristics of the exciting forces, hydrodynamic forces, flow rate, air pressure in the chamber, and heave motion response are investigated with various system parameters, such as the inner radius, draft of an OWC, and turbine constant. The efficiency of a floating OWC device is estimated in connection with the extracted wave power and capture width. Specifically, the piston-mode resonance in an internal fluid region plays an important role in the performance of a floating OWC device, along with the heave motion resonance. The developed prediction tool will help determine the various design parameters affecting the performance of a floating OWC device in waves.

• 해양환경안전학회지
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• 제18권3호
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• pp.199-205
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• 2012

본 연구에서는 유한한 깊이의 투수층에 의한 에너지 감쇠효과를 고려한 파랑의 변형을 해석하였다. 파의 에너지 감쇠율과 상대수심의 관계식을 제시하였으며, 에너지 감쇠율을 고유함수전개법에 사용하여 투수층에 의한 에너지 감쇠를 계산하였다. 투수성이 있는 수중둔덕에 대해서, 수치실험 결과는 해석해로 간주할 수 있는 적분방정식의 결과와 비교하여 잘 일치하였다. 또한, 투수경사에 의한 반사율을 다양한 주파수에 대해서 실험하였으며, 수치실험 결과, 수심이 매우 커서 수면파가 투수층의 영향을 받을 정도가 아닌 경우에는 상대적으로 파장이 짧은 파랑일수록 투수층의 영향을 크게 받는 것으로 나타났다.

• Kyungpook Mathematical Journal
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• 제28권2호
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• pp.221-226
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• 1988

Using the method of eigenfunction expantion of self adjoint operators, we establish the necessary and sufficient conditions for a reflection positive generalized matrix kernel to be represented in an integral form. This integral converges in the cosidered spaces.

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2004년도 학술대회지
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• pp.241-248
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• 2004

In general, the salient features if the floating breakwater have excellent regulation of sea-water keeping the marine a1ways clean, up and dorm free movement with the incoming and outgoing tides, capable of being installed without considering the geological condition of sea-bed at any water depth, This study discusses the three dimensional wave transformation of the floating breakwater moored by catenary. Numerical method is based at the Green function method and eigenfunction expansion method. The validity of the present is confirmed by comparing it with the result of Ijima et a1.(1975) fer tensile maxed floating breakwater. According to the numerical results, drift and width of the floating breakwater affect at the wave transformation greatly, and incident wave of long period is well transmitted to the rear of the floating breakwater.

• 한국해양공학회지
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• 제28권5호
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• pp.474-483
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• 2014

The majority of existing WECs (wave energy converters) are designed to achieve maximum power at a resonance condition. In the case of a single WEC, its size must be large enough for tuning, and it has high efficiency only within a limited frequency band. Recently, wave power extraction by deploying many small buoys in a compact array has been studied under the assumption that the buoy's size and separation distance are much smaller than the water depth, wave length, and size of the array. A boundary value problem involving the macro-scale boundary condition on the mean surface covered by an infinite strip of buoys is solved using the eigenfunction expansion method. The energy extraction efficiency (${\varepsilon}=1-R^2_f-T^2_r$), where $R_f$ and $T_r$ are the reflection and transmission coefficients for a strip array of buoys, is assessed for various combinations of packing ratio, strip width, and PTO damping coefficient.

• 한국해양공학회지
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• 제31권3호
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• pp.208-218
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• 2017

The performance of a wave energy converter (WEC) that uses the rolling motion of a partially submerged pendulum plate in front of a quay wall was analyzed. The wave exciting moment and hydrodynamic moment were obtained using a matched eigenfunction expansion method (MEEM) based on the linear potential theory, and then the roll motion response of a pendulum plate, time averaged extracted power, and efficiency were investigated. The optimal PTO damping coefficient was suggested to give the optimal extracted power. The peak value of the optimal extracted power occurs at the resonant frequency. The resonant peak and its width increase as the submergence depth of the pendulum plate decreases and thickness of the pendulum plate increases. An increase in the wave incidence angle reduces the efficiency of the wave energy converter. In addition, the WEC using a rolling pendulum plate contributes not only to the extraction of the wave energy, but also to a reduction in the waves reflected from the quay wall, which helps to stabilize ships going near the quay wall.

• 한국수자원학회논문집
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• 제33권6호
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• pp.805-814
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• 2000

본 연구에서는 경계요소법을 이용하여 수심이 변하는 지형을 통과할 때 발생하는 파랑의 회절을 수치해석하였다. 먼저, 트렌치지형을 통과하는 파랑의 반사율과 통과율을 계산하였으며 고유함수전개법에 의한 결과와 비교하여 본 모형을 검증하였다. 아울러, 경계요소법을 정현파형 지형에 적용하여 반사율 및 Bragg 반사를 연구하였다. 수치해석에 의한 반사율은 수리모형실험에 의한 관측결과 및 고유함수전개법에 의한 결과와 비교하였다. 전체적으로 본 연구의 결과는 기존의 자료와 잘 일치하였다.