• Title/Summary/Keyword: The Boltzmann equation

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NUMERICAL SIMULATION ON PHASE SEPARATION BY 2D LATTICE-BOLTZMANN METHOD (LBM을 이용한 2차원 상분리 시뮬레이션)

  • Jung, Rho-Taek
    • 한국전산유체공학회:학술대회논문집
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    • 2009.11a
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    • pp.109-114
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    • 2009
  • As one of the promising model on the multiphase fluid mixtures, the Lattice-Boltzmann Method(LBM) is being developed to simulate flows containing two immisible components which are different mass values. The equilibrium function in the LBM can have a nonideal gas model for the equation of state and use the interfacial energy for the phase separation effect. An example on the phase separation has been carried out through the time evolution. The LBM based on the statistic mechanics is appropriate to solve very complicated flow problems and this model gives comparative merits rather than the continuum mechanics model.

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SIMULATION OF FREE SURFACE FLOW OVER TRAPEZOIDAL OBSTACLE WITH LATTICE BOLTZMANN METHOD (격자볼츠만법을 이용한 장애물 월반 자유수면 시뮬레이션)

  • Korkmaz, Emrah;Jung, Rho-Taek
    • Journal of computational fluids engineering
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    • v.19 no.2
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    • pp.79-85
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    • 2014
  • An air-water free surface flow simulation by using the Lattice Boltzmann Method(LBM) has not been studied a lot compared with the done by the Navier-Stoke equation. This paper shows the LBM is as one of the application tools for the free surface movement over an obstacle. The Mezo scaled application tool has been developed with two dimensional and nine discretized velocity direction using conventional lattice Bhatnagar-Gross-Krook model. Boundary conditions of a halfway-based for solid wall and a kinematic-based for interface are adopted. A validation case with a trapezoidal shape bump to make a comparison between freesurface movements from computational results and experimental ones was described with grid size dependency.

Determination of an Inelastic Collision Cross Sections for C3F8 Molecule by Electron Swarm Method (전자군 방법에 의한 C3F8분자가스의 비탄성충돌단면적의 결정)

  • Jeon Byung-Hoon
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.19 no.3
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    • pp.301-306
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    • 2006
  • The electron drift velocity W and the product of the longitudinal diffusion coefficient and the gas number density $ND_{L}$ in the $0.525\;\%$ and $5.05\;\%$ $C_{3}F_8-Ar$ mixtures were measured by using the double shutter drift tube with variable drift distance over the E/N range from 0.03 to 100 Td and gas pressure range from 1 to 915 torr. And we determined the electron collision cross sections set for the $C_{3}F_8$ molecule by STEP 1 of electron swarm method using a multi-term Boltzmann equation analysis. Our special attention in the present study was focused upon the vibrational excitation and new excitations cross sections of the $C_{3}F_8$ molecule.

Electron Swarm Drift Velocity and Characteristic Energy in e$^{[-10]}$ -CF$_4$Scattering (e ̄-CF$_4$산란의 전자이동속도 및 특성에너지 연구)

  • 임상원;유회영;김상남;하성철
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 1996.11a
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    • pp.169-174
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    • 1996
  • In this paper, the electron transport characteristic in CF$_4$has been analysed over the E/N range 1~300(Td) by a two-term approximation Boltzmann equation method and by a Monte Carlo simulation. The alteration of cross sections from the literature is avoided as much as possible in the analysis. The motion has been calculated to give swarm parameters for the electron drift velocity(W), diffusion coefficient(D$_{L}$), the ratio of the diffusion coefficient to the mobility(D$_{L}$/$\mu$), mean energy($\varepsilon$), the electron energy distribution function. The electron energy distribution function has been analysed in CF$_4$at E/N=50, 100 and 200(Td) for a case of the equilibrium region in the mean electron energy. The results of Boltzmann equation and Monte Carlo simulation have been compared with experimental data by Y. Nakamura and M. Hayashi.shi.

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A Simulation of the Energy Distribution Function for Electron in $CF_4$-Ar Mixtures Gas ($CF_4$ 혼합기체(混合氣體)에서 전자(電子)에너지분포함수)

  • Kim, Sang-Nam;Seong, Nak-Jin
    • Proceedings of the KIEE Conference
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    • 2004.07e
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    • pp.37-40
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    • 2004
  • Electron swarm parameters in pure $CF_4$ and mixtures of $CF_4$ and Ar, have been analyzed over a range of the reduced electric field strength between 0.1 and 350[Td] by the two-term approximation of the Boltzmann equation(BEq.) method and the Monte Carlo simulation(MCS) The results of the Boltzmann equation and the Monte Carlo simulation have been compared with the data presented by several workers. The deduced transport coefficients for electrons agree reasonably well with the experimental and simulation data obtained by Nakamura and Hayashi. The energy distribution function of electrons in $CF_4$-Ar mixtures shows the Maxwellian distribution for energy. That is, f(${\varepsilon}$) has the symmetrical shape whose axis of symmetry is a most probably energy

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A Simulation of the Energy Distribution Function for Electron in Gas Mixtures (시뮬레이션을 이용한 혼합기체(混合氣體)에서 전자(電子)에너지분포함수)

  • Kim, Sang-Nam;Yu, Heoi-Young;Ha, Sung-Chul
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2002.05c
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    • pp.194-198
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    • 2002
  • Energy Distribution Function in pure $CH_4$, $CF_4$ and mixtures of $CF_4$ and Ar, have been analyzed over a range of the reduced electric field strength between 0.1 and 350[Td] by the two-tenn approximation of the Boltzmann equation (BEq.) method and the Monte Carlo simulation (MCS). The results of the Boltzmann equation and the Monte Carlo simulation have been compared with the data presented by several workers. The deduced transport coefficients for electrons agree reasonably well with the experimental and simulation data obtained by Nakamura and Hayashi. The energy distribution function of electrons in $CF_4-Ar$ mixtures shows the Maxwellian distribution for energy. That is, f(${\varepsilon}$) has the symmetrical shape whose axis of symmetry is a most probably energy

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The Dependence on the Gas Pressure in SF6 Molecular Gas (SF6분자가스의 압력 의존도)

  • Jeon, Byung-Hoon
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.20 no.9
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    • pp.816-820
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    • 2007
  • We measured the electron drift velocity, W, in 0.5% $SF_6-Ar$ mixture over the E/N range from 30 Td to 300 Td and gas pressure range from 0.1 to 0.5 Torr by the double shutter drift tube with a variable drift distance, and calculated over the same E/N and gas pressure range by using the two-term approximation of the Boltzmann equation. The measured and calculated values at different gas pressure at each E/N was appreciable dependence in the results on the gas pressure.

Kinetic Theory Analysis for Thin-Film Bearings (기체분자운동론을 이용한 박막 베어링 해석)

  • Chung Chan Hong
    • Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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    • 2004.11a
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    • pp.162-170
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    • 2004
  • A kinetic theory analysis is used to study the ultra-thin gas flow field in gas slider hearings. The Boltzmann equation simplified by a collision model is solved by means of a finite difference approximation with the discrete ordinate method. Calculations are made for the flow field inside stepped and straight slider bearings. The results are compared well with those from the DSMC method. Special attention has been paid to the effect of the pressure build-up in front of a hearing, which has never been assessed before. It has been shown that the pressure build-up at the inlet is about $4.5\%$ of the operating pressure and the resulting load capacity is about $25\%$ higher for the case considered in the present study.

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The analysis of dependence on the gas number density in $SF_{6}$-Ar mixtures ($SF_{6}$-Ar혼합가스에서의 압력 의존도 해석)

  • 전병훈;하성철
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2002.07a
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    • pp.248-251
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    • 2002
  • We measured the electron drift velocity, W, in 0.5% $SF_{6}$-Ar mixture over the E/N range from 30 Td to 300 Td and gas pressure range from 0.1 to 8 Torr by the double shutter drift tube with a variable drift distance. This coefficient in the mixture was calculated over the same E/N and gas pressure range by using the two-term approximation of the Boltzmann equation. And the measured and calculated values at different gas number density at each E/N was appreciable dependence in the results on the gas number density,

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Electron Energy Distribution Function in SF6-He Gas by Simulation (시뮬레이션에 의한 SF6-He 혼합기체에서 전자에너지 분포함수)

  • Kim, Sang-Nam
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.63 no.1
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    • pp.19-23
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    • 2014
  • This paper describes the electron transport characteristics in $SF_6$-He gas calculated E/N values 0.1~700[Td] by the Monte Carlo simulation and Boltzmann equation method using a set of electron collision cross sections determined by the authors and the values of electron swarm parameters obtained by TOF method. This study gained the values of the electron swarm parameters such as the electron drift velocity, the electron ionization or attachment coefficients, longitudinal and transverse diffusion coefficients for $SF_6$-He gas at a range of E/N. A set of electron collision cross section has been assembled and used in Monte Carlo simulation to predict values of swarm parameters. The result of Boltzmann equation and Monte Carlo Simulation has been compared with experimental data by Ohmori, Lucas and Carter. The swarm parameter from the swarm study are expected to sever as a critical test of current theories of low energy scattering by atoms and molecules.