• Title/Summary/Keyword: Boltzmann equation

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Drift Velocities for Electrons in $SF_6$-Ar Mixtures Gas ($SF_6-Ar$-혼합기체(混合氣體)의 전자(電子) 이동속도(移動速度))

  • Kim, Sang-Nam;Ha, Sung-Chul
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2003.07b
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    • pp.1102-1105
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    • 2003
  • Energy distribution function for electrons in $SF_6$-Ar mixtures gas used by MCS-BEq algorithm has been analysed over the E/N range $30{\sim}300[Td]$ by a two term Boltzmann equation and by a Monte Carlo Simulation using a set of electron cross sections determined by other authors, experimentally the electron swarm parameters for 0.2(%) and 0.5(%) $SF_6$-Ar mixtures were measured by time-of-flight(TOF) method, The results show that the deduced electron drift velocities, Electrons Drift Velocities for a rang of E/N values. As a consequence, it was known that the spatial growth rates and the dielectric behaviors in $SF_6$-Ar mixtures are strongly dependent on the addition rate of $SF_6$ gas but the transport coefficients of electrons are insensitive to the addition rate of $SF_6$ gas. The results obtained from Boltzmann equation method and Monte Carlo simulation have been compared with present and previously obtained data and respective set of electron collision cross sections of the molecules.

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Mean energy of electrons in $SF_6$-Ar Mixtures Gas ($SF_6$-Ar 혼합기체(混合氣體)의 전자(電子) 평균(平均)에너지)

  • Kim, Sang-Nam;Seong, Nak-Jin
    • Proceedings of the KIEE Conference
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    • 2003.07e
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    • pp.75-78
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    • 2003
  • Energy distribution function for electrons in $SF_6$-Ar mixtures gas used by MCS-BEq algorithm has been analysed over the E/N range $30\sim300$[Td] by a two term Boltzmann equation and by a Monte Carlo Simulation using a set of electron cross sections determined by other authors, experimentally the electron swarm parameters for 0.2[%] and 0.5[%] $SF_6$-Ar mixtures were measured by time-of-flight(TOF) method. The results show that the deduced electron drift velocities, the electron ionization or attachment coefficients, longitudinal and transverse diffusion coefficients and mean energy agree reasonably well with theoretical for a rang of E/N values. The transport coefficients for electrons in (0.2[%])$SF_6$-Ar and (0.5[%]$SF_6$ - Ar mixtures were measured by time-of-flight method, and the electron energy distribution function and the parameters of the velocity and the diffusion were determined by the variation of the collision cross-sections with energy. The results obtained from Boltzmann equation method and Monte Carlo simulation have been compared with present and previously obtained data and respective set of electron collision cross sections of the molecules.

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Analysis on Particle Deposition onto a Heated Rotating Disk with Electrostatic Effect (정전효과가 있는 가열 회전원판으로의 입자침착 해석)

  • 유경훈
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.14 no.5
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    • pp.424-432
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    • 2002
  • Numerical analysis has been conducted to characterize deposition rates of aerosol particles onto a heated, rotating disk with electrostatic effect under the laminar flow field. The particle transport mechanisms considered were convection, Brownian diffusion, gravitational settling, thermophoresis and electrophoresis. The aerosol particles were assumed to have a Boltzmann charge distribution. The electric potential distribution needed to calculate local electric fields around the disk was calculated from the Laplace equation. The Coulomb, the image, the dielectrophoretic and the dipole-dipole forces acting on a charged particle near the conducting rotating disk were included in the analysis. The averaged particle deposition vetocities and their radial distributions on the upper surface of the disk were calculated from the particle concentration equation in a Eulerian frame of reference, along with a rotation speed of 0∼1,000rpm, a temperature difference of 0∼5K and a charged disk voltage of 0∼1000V.Finally, an approximate deposition velocity model for the rotating disk was suggested. The present numerical results showed relatively good agreement with the results of the present approximate model and the available experimental data.

DEVELOPMENT OF A 2-D GAS-KINETIC BGK SOLVER FOR CONTINUUM AND TRANSITIONAL FLOWS ON UNSTRUCTURED MESHES (비정렬 격자계에서 연속체 및 천이 영역 유동 해석을 위한 2차원 Gas-Kinetic BGK 해석자 개발)

  • Yang, T.H.;Kwon, O.J.
    • Journal of computational fluids engineering
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    • v.19 no.2
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    • pp.49-57
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    • 2014
  • In the present study, 2-D gas-kinetic flow solver on unstructured meshes was developed for flows from continuum to transitional regimes. The gas-kinetic BGK scheme is based on numerical solutions of the BGK simplification of the Boltzmann transport equation. In the initial reconstruction, the unstructured version of the linear interpolation is applied to compute left and right states along a cell interface. In the gas evolution step, the numerical fluxes are computed from the evaluation of the time-dependent gas distribution function around a cell interface. Two-dimensional compressible flow calculations were performed to verify the accuracy and robustness of the current gas-kinetic approach. Gas-kinetic BGK scheme was successfully applied to two-dimensional steady and unsteady flow simulations with strong contact discontinuities. Exemplary hypersonic viscous simulations have been conducted to analyze the performances of the gas-kinetic scheme. The computed results show fair agreement with other standard particle-based approaches for both continuum part and transitional part.

Analysis on the Mean energy of electrons in $SF_6-Ar$ Mixtures Gas used by MCS-BEq Algorithm ($SF_6-Ar$ 혼합기체(混合氣體)의 MCS-BEq알고리즘에 의한 전자(電子) 평균(平均)에너지 해석(解析))

  • Kim, Sang-Nam;Ha, Sung-Chul
    • Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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    • 2004.05a
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    • pp.281-284
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    • 2004
  • Mean energy of electrons in $SF_6-Ar$ Mixtures Gas used by MCS-BEq algorithm has been analysed over the E/N range $30{\sim}300[Td]$ by a two term Boltzmann equation and by a Monte Carlo Simulation using a set of electron cross sections determined by other authors, experimentally the electron swarm parameters for 0.2[%] and 0.5[%] $SF_6-Ar$, 0.1[%] and 5.0[%], $SF_6-Ar$ mixtures were measured by time-of-flight(TOF) method. The transport Coefficients for electrons in (100[%])$SF_6$. (100[%])Ar, (0.2[%])$SF_6-Ar$ and (0.5[%]) $SF_6-Ar$, (5.0[%]) $SF_6-Ar$, (0.1[%])$SF_6-Ar$ mixtures were measured by time-of-flight method, and the electron energy distribution function and the parameters of the velocity and the diffusion were determined by the variation of the collision cross-sections with energy. The results obtained from Boltzmann equation method and Monte Carlo simulation have been compared with present and previously obtained data and respective set of electron collision cross sections of the molecules.

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The analysis on the Energy Distribution Function for Electron in SiH4-Ar Gas Mixtures (SiH4-Ar혼합기체의 전자분포함수 해석)

  • Kim, Sang-Nam
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.53 no.2
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    • pp.65-69
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    • 2004
  • This paper calculates and gives the analysis of electron swarm transport coefficients as described electric conductive characteristics of pure Ar, pure $SiH_4$, Ar-$SiH_4$ mixture gases($SiH_4$-0.5%, 2.5%, 5%) over the range of E/N = 0.01~300[Td], P = 0.1, 1, 5.0 [Torr] by Monte Carlo the backward prolongation method of the Boltzmann equation using computer simulation without using expensive equipment. The results have been obtained by using the electron collision cross sections by TOF, PT, SST sampling, compared with the experimental data determined by the other author. It also proved the reliability of the electron collision cross sections and shows the practical values of computer simulation. Electron swann parameters in argon were drastically changed by adding a small amount of mono-silane. The electron drift velocity in these 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-tenn approximation of the Boltzmann equation analysis and Monte Carlo simulation have been used to study electron transport coefficients.

Diffusion Coefficients in $SF_6-Ar$ Gas used by MCS-BE Algorithm (MCS-BEq 알고리즘에 의한 $SF_6-Ar$ 혼합기체의 확산계수)

  • Kim, Sang-Nam
    • Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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    • 2006.05a
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    • pp.298-301
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    • 2006
  • This paper describes the electron energy distribution function characteristics in $SF_6-Ar$ gas calculated for range of E/N values from $50\sim700[Td]$ by the Monte Carlo simulation(MCS) and Boltzmann equation(BE) method using a set of electron collision cross sections determined by the authors and the values of electron swarm parameters are obtained by time of flight(TOF) method. In this dissertation the results of the combined experimental and theoretical studies designed to understand and predict the spatial growth and transport coefficients for electrons in $SF_6$ and $SF_6-Ar$ mixtures have described. The ionization and attachment coefficients in pure $SF_6$ and $SF_6-Ar$ mixtures have been calculated over the range of 10$SF_6$ molecule and for Ar atom proposed by other authors. The results obtained in this work will provide valuable information on the fundamental behaviors of electrons in weakly ionized gases and the role of electron attachment in the choice of better gases and unitary gas dielectrics or electro negative components in dielectric gas mixtures.

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Electron Collision Cross Sections for the TRIES Molecule and Electron Transport Coefficients in TRIES-Ar and TRIES-O2 Mixtures

  • Tuoi, Phan Thi;Tuan, Do Anh;Hien, Pham Xuan
    • Journal of the Korean Physical Society
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    • v.73 no.12
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    • pp.1855-1862
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    • 2018
  • A reliable set of low-energy electron collision cross sections for the triethoxysilane (TRIES) molecule was derived based on the measured electron transport coefficients for a pure TRIES molecule by using an electron swarm method and a two-term approximation of the Boltzmann equation. The electron transport coefficients calculated using the derived set are in good agreement with experimental value over a wide range of E/N values (ratio of the electric field E to the neutral number density N). The present electron collision cross section set for the TRIES molecule, therefore, is the most reliable so far for plasma discharges and for materials processing using the TRIES molecule. Moreover, the electron transport coefficients for the TRIES-Ar and the $TRIES-O_2$ mixtures were also calculated and analyzed over a wide range of E/N for the first time.

An Analysis of Dynamic Characteristics of Air-Lubricated Slider Bearing by Using Perturbation Method (섭동법을 이용한 공기윤활 슬라이더 베어링의 동특성 해석)

  • Gang, Tae-Sik;Choe, Dong-Hun;Jeong, Tae-Geon
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.6 s.177
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    • pp.1520-1528
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    • 2000
  • This study presents a method for determining bearing stiffness and damping coefficients of air-lubricated slider bearing, and shows influences of air-bearing surface geometry(recess depth, crown an d pivot location) on flying attitude and dynamic characteristics. To derive the dynamic lubrication equation, the perturbation method is applied to the generalized lubrication equation which based on linearized Boltzmann equation. The generalized lubrication equation and the dynamic lubrication equation are converted to a control volume formulation, and then, the static and dynamic pressure distributions are calculated by finite difference method. The recess depth and crown of the slider show significantly influence on flying attitude and dynamic characteristics comparing with those of pivot location.

Investigation of Hg free Electrodeless inductively capacitive tubular discharge (무수은 무전극 유도-용량형 직관형 램프 방전에 관한 연구)

  • 이태일;박해일;백홍구
    • Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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    • 2002.11a
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    • pp.191-196
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    • 2002
  • In this paper we introduce novel electrode structure for high efficiency discharge. We operate discharge tube under the 0.16 torr pure Xe and apply the sinusoidal wave power to the lamp with 60kHz. We measure the electric power dissipation, plasma parameters, and 828 nm IR intensity. From these data we determine the discharge efficiency, IR intensity/watt, EEDF(Electron energy distribution function). As a result we obtain that the novel electrode structure has better performance in efficiency than that of conventional external electrode system. Also we determine the EEDF for each type of electrode structure by Boltzmann stover, EELNDIF code. The result of Boltzmann equation solving show that the noble electrode system has many high energy electrons compared with the conventional system.

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