• Title/Summary/Keyword: 해석적 미분

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Numerical Modeling of Current Density and Water Behavior at a Designated Cross Section of the Gas Diffusion Layer in a Proton Exchange Membrane Fuel Cell (고분자전해질 연료전지의 동작압력에 대한 가스 확산층의 위치 별 전류밀도 및 수분거동에 대한 수치해석)

  • Kang, Sin-Jo;Kim, Young-Bae
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.36 no.2
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    • pp.161-170
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    • 2012
  • There are many factors to consider when attempting to improve the efficiency of fuel cell operation, such as the operation temperature, humidity, stoichiometry, operation pressure, geometric features, etc. In this paper, the effects of the operation pressure were investigated to find the current density and water saturation behavior on a cross section designated by the design geometry. A two-dimensional geometric model was established with a gas channel that can provide $H_2$ to the anode and $O_2$ and water vapor to the cathode gas diffusion layer (GDL). The results from this numerical modeling revealed that higher operation pressures would produce a higher current density than lower ones, and the water saturation behavior was different at operation pressures of 2 atm and 3 atm in the cathode GDL. In particular, the water saturation ratios are higher directly below the collector than in other areas. In addition, this paper presents the dependence of the velocity behavior in the cathode on pressure changes, and the velocity fluctuations through the GDL are higher in the output area than in inlet area. This conclusion will be utilized to design more efficient fuel cell modeling of real fuel cell operation.

A Study on Shape Optimization of Distributed Actuators using Time Domain Finite Element Method (시간유한요소법을 이용한 분포형 구동기의 형상최적화에 관한 연구)

  • Suk, Jin-Young;Kim, You-Dan
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.33 no.9
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    • pp.56-65
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    • 2005
  • A dynamic analysis method that freezes a time domain by discretization and solves the spatial propagation equation has a unique feature that provides a degree of freedom on spatial domain compared with the space discretization or space-time discretization finite element method. Using this feature, the time finite element analysis can be effectively applied to optimize the spatial characteristics of distributed type actuators. In this research, the time domain finite element method was used to discretize the model. A state variable vector was used in the discretization to include arbitrary initial conditions. A performance index was proposed on spatial domain to consider both potential and vibrational energy, so that the resulting shape of the distributed actuator was optimized for dynamic control of the structure. It is assumed that the structure satisfies the final rest condition using the realizable control scheme although the initial disturbance can affect the system response. Both equations on states and costates were derived based on the selected performance index and structural model. Ricatti matrix differential equations on state and costate variables were derived by the reconfiguration of the sub-matrices and application of time/space boundary conditions, and finally optimal actuator distribution was obtained. Numerical simulation results validated the proposed actuator shape optimization scheme.

Hybrid Algorithm for Interpolation Based on Macro-block Gray Value Gradient under H.264 (H.264하에서 마크로 블록 그레이 값의 미분을 사용한 인터폴레이션)

  • Wang, Shi;Chen, Hongxin;Yoo, Hyeon-Joong;Kim, Hyong-Suk
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.10 no.2
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    • pp.274-279
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    • 2009
  • H.264 suggests applying a 2-D 6-tap wiener filter to realize the interpolation for half-pixel positions, followed by a bilinear interpolation to get the data of quarter-pixels precision. This method is comparatively simpler; however, it only considers the affection of 4-connection neighborhood ignoring the influence that comes from the changing rate between respective neighborhoods. As a result, it has the characteristics of a Low-pass filter under the risk of losing high-frequency weights. The Cubic interpolation uses the gray-values within the larger regions of points to be sampled for interpolation. Nevertheless, the cubic interpolation is more complicated and computational. We give a deep analysis on the features while applying both bilinear and cubic interpolation in H.264 presenting a proper selection of interpolation algorithm with respect to specific distribution of gray-value in a certain grand block. The experiments point out that load far motion searching and interpolation are reduced when promoting the precision of interpolation simultaneously.

Numerical Dispersion and Its Control for 1-D Finite Element Simulation of Stress Wave Propagation (응력파 전파 수치모의를 위한 일차원 유한요소모형의 분산 특성 및 제어)

  • 이종세;유한규;윤성범
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.17 no.1
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    • pp.75-82
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    • 2004
  • With an aim at eliminating the numerical dispersion error arising from the numerical simulation of stress wave propagation, numerical dispersion characteristics of the wave equation based one-dimensional finite element model are analyzed and some dispersion control scheme are proposed in this paper The dispersion analyses are carried out for two types of mass matrix, namely the consistent and the lumped mass matrices. Based on the finding of the analyses, dispersion correction techniques are developed for both the implicit and explicit schemes. For the implicit scheme, either the weighting factor for the spatial derivatives of each time level or the lumping coefficient for mass matrix is adjusted to minimize the numerical dispersion. In the case of the explicit scheme an artificial dispersion term is introduced in the governing equation. The validity of the dispersion correction techniques proposed in this study is demonstrated by comparing the numerical solutions obtained using the Present techniques with the analytical ones.

Study on Real Time Control of Robot Manipulator Using Sliding Mode (슬라이딩 모드를 이용한 로보트 매니퓰레이터의 실시간 제어에 관한 연구)

  • ;靑島伸治
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.11
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    • pp.2011-2020
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    • 1992
  • This paper discusses about real time control applying sliding mode to robot manipulators whose nonlinear terms, which are inertia term, Corilis term and centrifugal force mterm, are regarded as disturbances. We could simplify the dynamic equations of a manipulator and servo system, which are composed of linear elements and nonlinear elements, by assuming that non-linear terms are external disturbance. By simplifying that equation, we could easily obtain a control input which satisfy sliding mode. We proposed a new control input algorithm to decrease chattering in the application of sliding mode control of manipulator whose nonlinear elements are regarded as disturbances. We could take impulse response of linear elements of dynamic equations of a robot manipulator and servo system by Signal Compression Method. So then, we could obtain the unknown parametes of its linear lements, which are used to obtain switching parameter satisfying sliding mode, by Signal Compression Method. In this experiments, we used DSP(Digital Signal Processor) controller to suppress chattering by obtaining a switching speed and to carry out real time control.

Study on the Prediction of Lateral and Yawing Behaviors of a Leading Vehicle in a Train Collision (철도차량 충돌 시 선두차량의 횡 및 요잉 거동 예측 연구)

  • Kim, Jun Woo;Jeong, Eui Cheol;Koo, Jeong Seo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.41 no.2
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    • pp.95-101
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    • 2017
  • In this study, we derived theoretical equations for the zigzag movement of a leading vehicle, which is the most frequent behavior in train accidents, by using a simplified spring-mass model for the rolling stock. In order to solve the equations of motion, we applied the Runge-Kutta method, which is the typical numerical analysis method used for differential equations. Furthermore, the lateral displacement of the wheel-set at the wheel-rail interface was estimated using kinetic energy. In order to verify the derived equations, we compared the theoretical and simulated results under various collision conditions. The maximum relative deviations of the lateral displacements were 0.8 [%] ~ 4.7 [%] in light collisions and 0.6 [%] ~ 5.1 [%] under derailment conditions. When an accident is simulated, these theoretical equations can be used to predict the overall behavior and obtain the offset of the body-to-body link as the initial perturbation.

A Numerical Analysis of the Shallow Water Equations Using the Multi-slope MUSCL (다중 경사 MUSCL을 이용한 천수방정식의 수치해석)

  • Hwang, Seung-Yong;Lee, Sam-Hee
    • Proceedings of the Korea Water Resources Association Conference
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    • 2011.05a
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    • pp.158-158
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    • 2011
  • 천수방정식과 같은 쌍곡선형 미분방정식의 불연속 해에 대한 Riemann 해법은, 1950년대 말 공기동역학 분야에서 S. K. Godunov의 선구적인 시도 이후, 다양한 영역에서 성공적으로 적용되고 있다. 당초 제안된 해법은 공간에 대해 1차 정도였으나, 2차의 정도를 얻을 수 있는 기법이 1970년대 말 B. van Leer에 의해 제안되었으며, MUSCL로 불린다. 서로 인접한 격자의 보존변수가 고려된 경사가 도입되어 두 격자에 의해 공유되는 변의 좌 우에서 선형으로 보존변수가 재구축되는 MUSCL은 제한자와 함께 이용될 때, 구조 격자 체계에서 비교적 단순하면서도 효과적인 적용성이 입증되었다. 그런데, 이 기법을 2차원의 비구조 격자 체계에 적용하는 경우, 인접한 모든 격자의 보존변수를 고려한 평면의 경사를 결정해야 하는 어려움이 따른다. 특히, 삼각형 비구조 격자에 적용할 경우 최적의 평면을 결정하기 위해 Green-Gauss 적분식이나 최소-자승법 등을 이용하게 된다. 이에 비해, 2010년 T. Buffard와 S. Clain이 제안한 다중경사 기법은 격자의 각 변에서 경사가 각각 결정되는 방법으로 계산량이 많은 Green-Gauss 적분식이나 최소자승법을 피할 수 있는 장점이 있는 것으로 알려져 있다. 정확해가 알려진 두 경우에 대해 몇 가지 제한자를 적용한 결과를 1차 정도의 해와 함께 비교하였으며, superbee 제한자에 의한 결과가 우수하였으나, 희유파와 충격파가 맞닿는 곳에서 수치 분산이 나타났다. minmod 제한자의 결과가 대체로 무난하였으며, 이를 2차원 댐 붕괴 문제에 적용하여 1차 정도의 해와 비교하였다. 마찰이 없고 초기 수심이 댐 상류에서 10 m, 하류에서 5 m로서 물이 차 있는 경우, 1차 정도의 해에서 나타나는 수치 소산이 2차 정도에서는 발생되지 않았다. 댐 하류에서 초기에 수심이 영으로 바닥이 드러난 경우에서 마찰의 영향을 검토하였다. 마찰이 있는 경우, 마찰 경사 항의 Manning 계수를 0.04로 두었으며, 마찰에 의한 영향이 잘 드러났다. 수심이 50 mm 보다 작은 경우에는 마찰을 적용하지 않았다. 이 연구는 환경부 '차세대 핵심환경기술개발 사업'의 지원에 의한 것이다.

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Geopotentinl Field in Nonlinear Balance with the Sectoral Mode of Rossby-Haurwitz Wave on the Inclined Rotation Axis (섹터모드의 로스비하우어비츠 파동과 균형을 이루는 고도장)

  • Cheong, Hyeong-Bin;Park, Ja-Rin
    • Journal of the Korean earth science society
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    • v.28 no.7
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    • pp.936-946
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    • 2007
  • Analytical geopotential field in balance with the sectoral mode (the first symmetric mode with respect to the equator) of the Rossby-Haurwitz wave on the inclined rotation axis was derived in presence of superrotation background flow. The balanced field was obtained by inverting the divergence equation with the time derivative being zero. The inversion consists of two steps, i.e., the evaluation of nonlinear forcing terms and the finding of analytical solutions based on the Poisson's equation. In the second step, the forcing terms in the from of Legendre function were readily inverted due to the fact that Legendre function is the eigenfunction of the spherical Laplacian operator, while other terms were solved either by introducing a trial function or by integrating the Legendre equation. The balanced field was found to be expressed with six zonal wavenumber components, and shown to be of asymmetric structure about the equator. In association with asymmetricity, the advantageous point of the balanced field as a validation method for the numerical model was addressed. In special cases where the strength of the background flow is a half of or exactly the same as the rotation rate of the Earth it was revealed that one of the zonal wavenumber components vanishes. The analytical balanced field was compared with the geopotential field which was obtained using a spherical harmonics spectral model. It was found that the normalized difference lied in the order of machine rounding, indicating the reliability of the analytical results. The stability of the sectoral mode of Rossby-Haurwitz wave and the associated balanced field was discussed, comparing with the flrst antisymmetric mode.

Modeling of Magnetotelluric Data Based on Finite Element Method: Calculation of Auxiliary Fields (유한요소법을 이용한 MT 탐사 자료의 모델링: 보조장 계산의 고찰)

  • Nam, Myung-Jin;Han, Nu-Ree;Kim, Hee-Joon;Song, Yoon-Ho
    • Geophysics and Geophysical Exploration
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    • v.14 no.2
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    • pp.164-175
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    • 2011
  • Using natural electromagnetic (EM) fields at low frequencies, magnetotelluric (MT) surveys can investigate conductivity structures of the deep subsurface and thus are used to explore geothermal energy resources and investigate proper sites for not only geological $CO_2$ sequestration but also enhanced geothermal system (EGS). Moreover, marine MT data can be used for better interpretation of marine controlled-source EM data. In the interpretation of MT data, MT modeling schemes are important. This study improves a three dimensional (3D) MT modeling algorithm which uses edge finite elements. The algorithm computes magnetic fields by solving an integral form of Faraday's law of induction based on a finite difference (FD) strategy. However, the FD strategy limits the algorithm in computing vertical magnetic fields for a topographic model. The improved algorithm solves the differential form of Faraday's law of induction by making derivatives of electric fields, which are represented as a sum of basis functions multiplied by corresponding weightings. In numerical tests, vertical magnetic fields for topographic models using the improved algorithm overcome the limitation of the old algorithm. This study recomputes induction vectors and tippers for a 3D hill and valley model which were used for computation of the responses using the old algorithm.

Computational Simulation of Hydrocarbon Adsorption in a Packed Column (탄화수소 흡착 컬럼의 전산모사 특성)

  • Yoo, Kyung-Seun;Lee, Su-Jung;Kim, Ji-Eun
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.21 no.3
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    • pp.10-16
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    • 2020
  • Computational simulations of adsorption columns were carried out to investigate the removal characteristics of VOCs from a laundry shop. n-Decane was selected as the representative component among the VOCs emitted, and the activity of the adsorbents, such as activated carbon, was evaluated using commercial CFD code. The mathematical framework was composed of continuity and Navier-stokes equations, and the simulation was performed using the Matlab program. The adsorption isotherms of LDF, Freundlich, and Langmuir were evaluated, and the adsorption amount of the adsorption isotherms with the adsorption parameter was compared. The simulation was carried out using a particle porosity, dispersion coefficient, particle density, bed diameter, and bed length of 0.79, 42.4 ㎠/min, 485 g/L, 2.0 cm, and 2.5 cm, respectively. The effect of the gas velocity, dispersion coefficient, and voidage on the adsorption amount was compared in the Langmuir adsorption isotherm. The simulation was carried out in the velocity range of 50 to 200 cm/min, dispersion coefficient range of 100 to 400 ㎠/min, and particle porosity range of 0.66 to 0.79. The simulation results of activated carbon with benzene coincided with the Langmuir isotherm. Three types of adsorption isotherm were compared under similar conditions, and the simulation results showed the efficient adsorption condition for hydrocarbons.