• Title/Summary/Keyword: Boltzmann Equation

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Numerical Analysis of Ultra-Thin Gas Film Lubrication (초박막 기체윤활의 수치해석)

  • Chung C. H.
    • Journal of computational fluids engineering
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    • v.9 no.4
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    • pp.64-70
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    • 2004
  • A kinetic theory analysis is used to study the ultra-thin gas flow field in a gas slider bearing. 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 a flow in a micro-channel between an inclined slider and a moving disk drive platter The results are compared well with those from the DSMC method. The present method does not suffer from statistical noise which is common in particle-based methods and requires much less computational effort.

Numerical Analysis of Ultra-Thin Gas Film Lubrication (초박막 기체윤활의 수치해석)

  • Chung C. H.
    • 한국전산유체공학회:학술대회논문집
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    • 2004.10a
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    • pp.207-213
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    • 2004
  • A kinetic theory analysis is used to study the ultra-thin gas flow field in a gas slider bering, 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 a flow in a micro-channel between an inclined slider and a moving disk drive platter. The results are compared well with those from the DSMC method. The present method does not suffer from statistical noise which is common in particle based methods and requires much less computational effort.

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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.

Efficient Calculation of Gas-kinetic BGK scheme for Analysis of Inviscid and Viscous Flows (점성 및 비점성 유동장 해석을 위한 BGK 수치기법의 효율적 계산)

  • Chae, Dong-Suk;Kim, Chong-Am;Rho, Oh-Hyun
    • Journal of computational fluids engineering
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    • v.3 no.2
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    • pp.65-72
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    • 1998
  • From the Boltzmann equation with BGK approximation, a gas-kinetic BGK scheme is developed and methods for its efficient calculation, using the convergence acceleration techniques, are presented in a framework of an implicit time integration. The characteristics of the original gas-kinetic BGK scheme are improved in order for the accurate calculation of viscous and heat convection problems by considering Osher's linear subpath solutions and Prandtl number correction. Present scheme applied to various numerical tests reveals a high level of accuracy and robustness and shows advantages over flux vector splittings and Riemann solver approaches from Euler equations.

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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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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 Monte-Carlo method and Boltzmann Equation analysis on the electron swarm parameter in SiH$_4$+Ar mixtures gas. ($SiH_4+Ar$ 혼합기체의 전자군 파라미터에 대한 볼츠만 방정식 및 몬테 칼로법 해석)

  • 김대연;하성철
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 1999.05a
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    • pp.387-390
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    • 1999
  • Electron swarm parameterdthe drift velocity and longitudinal diffusion coefficienthn $SiH_4-Ar$ mixtures containing 0.5% and 5% monosilane were measured using over the range of E/N from 0.01 to 300 Td at room temperature. Electron swarm parameters in argon were drastically changed by adding a small amount of monosilane. The electron drift velocity in both mixtures showed unusual behaviour against E/N. It had negative slope in the medium range of E/N, yet the slope was not smooth but contained a small hump. The longitudinal diffusion coefficient also showed a corresponding feature in its dependence on E/N. A two-tern approximation of the Boltzmann equation analysis and Monte Carlo simulation have been used to study electron transport coefficients.

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Electron swarm parameter in $CH_4$ by MCS-BE simulation (시뮬레이션에 의한 $CH_4$ 전자군 파라미터)

  • Kim, Sang-Nam;Seong, Nak-Jin
    • Proceedings of the KIEE Conference
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    • 2005.10a
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    • pp.89-92
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    • 2005
  • Using quantitative simulations of weakly ionized plasma, we can analyze gas characteristic. In this paper, the electron transport characteristic in $CH_4$ has been analysed over the E/N range 0.1${\sim}$ 300(Td), at the 300($_{\circ}$ K) by the two term approximation Boltzmann equation method and Monte Carlo Simulation. The electron energy distribution function has been analysed in $CH_4$ at E/N=10, 100 for a case of the equilibrium region in the mean energy. The result of Boltzmann equation and Monte Carlo Simulation has been compared with experimental data by Ohmori, $Lucas^{[18]}$ 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.

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Electron Transport Characteristics in $SiH_4$ by MCS-BEq (MCS-BEq에 의한 $SiH_4$ 전자수송특성(電子輸送特性))

  • Seong, Nak-Jin;Kim, Sang-Nam
    • Proceedings of the KIEE Conference
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    • 2005.10a
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    • pp.97-100
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    • 2005
  • This paper describes the electron transport characteristics in SiH4 has been analysed over the E/N range 0.5${\sim}$300[Td] and Pressure value 0.5, 1, 2.5 [Torr] by a two-term approximation Boltzmann equation method and by a Monte Carlo simulation. The motion has been calculated to give swarm parameters for the electron drift velocity, diffusion coefficient, electron ionization, mean energy and the electron energy distribution function. The electron energy distribution function has been analysed in $SiH_4$ at E/N=30, 50[Td] for a case of the equilibrium region in the mean electron energy and respective set of electron collision cross sections. The results of Boltzmann equation and Monte carlo simulation have been compared with experimental data by Pollock, Ohmori, cottrell and Walker.

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