• 제목/요약/키워드: eigenfunction expansion method

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사각형형상 수중방파제의 반사에 관한 수리실험 (Hydraulic Experiments on Reflection of Regular Waves due to Rectangular Submerged Breakwaters)

  • 조용식;이종인;김영택
    • 한국수자원학회논문집
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    • 제35권5호
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    • pp.563-573
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    • 2002
  • 본 연구에서는 일정수심상에 사각형형상의 불투과성 수중방파제를 설치한 후 파랑의 반사를 수리실험을 통해 조사하였다. 입사파는 규칙파를 사용하였으며, 고유함수전개법을 이용하여 예측한 반사율을 본 연구에서 수행한 수리모형실험 결과와 비교하였다. 예측된 결과와 수리실험에서 관측한 결과는 비교적 잘 일치하였으며, 수리실험에 의한 반사율이 고유함수전개법에 의한 결과보다 다소 작았다.

폭 변화에 따른 다열 불투과성 수중방파제를 통과하는 다방향 불규칙파랑 해석 (Analysis of Multi-directional Random Waves Propagating over Multi Arrayed Submerged Breakwaters as Varying Crown Widths)

  • 강규영;정재상;정태화;조용식
    • 한국수자원학회:학술대회논문집
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    • 한국수자원학회 2007년도 학술발표회 논문집
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    • pp.2113-2116
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    • 2007
  • In this study, transmission and reflection of multi-directional random waves propagating over multi-arrayed submerged breakwaters are investigated using eigenfunction expansion method. The numerical analysis on the wave energy reflection of submerged breakwaters with various crown widths is carried out. Strong wave reflection is occurred at the Bragg reflection condition of the peak frequency. When relative heights and crown widths of breakwaters are equal to 0.6 and 0.4h, respectively, more than 25% of wave energy is reflected to off shore.

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Diffraction of water waves by an array of vertical barriers and heterogeneous bottom

  • Mondal, R.;Alam, Md. Mahbub
    • 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.

Effect of Internal Fluid Resonance on the Performance of a Floating OWC Device

  • Cho, Il Hyoung
    • 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.

유한한 깊이의 투수층에 의한 파랑의 감쇠 (Damping of Water Waves over Permeable Bed of Finite Depth)

  • 김건우;이명은
    • 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.

파일 방파제의 소파성능 해석 (Analysis on Wave Absorbing Performance of a Pile Breakwater)

  • 조일형;고혁준
    • 한국해양공학회지
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    • 제21권4호
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    • pp.1-7
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    • 2007
  • Based on the eigenfunction expansion method, the wave-absorbing performance of a square or circular pile breakwater was investigated. Flow separation resulting from sudden contraction and expansion is generated and is the main cause of significant energy loss. Therefore, evaluation of an exact energy loss coefficient is critical to enhancing the reliability of the mathematical model. To obtain the energy loss coefficient, 2-dimensional turbulent flow is analyzed using the FLUENT commercial code, and the energy loss coefficient can be obtained from the pressure difference between upstream and downstream. It was found that energy loss coefficient of circular pile is 20% that of a square pile. To validate the fitting equation for the energy loss coefficient, comparison between the analytical results and the experimental results (Kakuno and Liu, 1993) was made for square and circular piles with good agreement. The array of square piles also provides better wave-absorbing efficiency than the circular piles, and the optimal porosity value is near P=0.1.

Analytical Solutions of Unsteady Reaction-Diffusion Equation with Time-Dependent Boundary Conditions for Porous Particles

  • Cho, Young-Sang
    • 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.

Catenary 계류된 부방파제의 3차원 파랑변형에 관한 수치해석 (Numerical Analysis of Three-Dimensional Wave Transformation of Floating Breakwater Moored by Catenary)

  • 김도삼;최낙훈;윤희면;손병규
    • 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.

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2차원 경계요소법을 이용한 Bragg반사 해석 (Analysis of Bragg Reflection using Two-Dimensional Boundary Element Method)

  • 김영택;조용식;이정규
    • 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.

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2차원 유한요소법을 이용한 불투과성 사각형 수중방파제의 Bragg 반사 해석 (Analysis of Bragg Reflection of Waves due to Rectangular Impermeable Submerged Breakwaters with Two-Dimensional Finite Element Method)

  • 조용식;정우창
    • 한국수자원학회논문집
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    • 제36권3호
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    • pp.447-454
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    • 2003
  • 본 연구에서는 유한요소법을 이용하여 일정 수심상에서 사각형 형상의 불투과성 수중방파제에 의한 파랑의 Bragg 반사를 수치적으로 고찰하였다. 유한요소법에 의해 계산된 반사율은 수리모형실험을 통해 얻어진 결과와 비교하였을 때 비교적 잘 일치하였으며, 고유함수전개법에 의한 결과와도 좋은 일치를 나타내었다. 그밖에 본 연구에서 개발된 모형은 불투과성 수중방파제의 폭과 길이의 변화에 따른 반사율 계산에 적용되었다.