• 제목/요약/키워드: The Boltzmann equation

검색결과 219건 처리시간 0.023초

$SF_6$-Ar 혼합기체에서의 전리와부착계수 (Ionization and Attachment Coefficients in Mixtures of $SF_6$ and Ar)

  • 김상남;하성철
    • 한국전기전자재료학회논문지
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    • 제14권9호
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    • pp.773-778
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    • 2001
  • 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$_{6}$ molecule and for Ar atom proposed by other authors. 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 in this work will provide valuable information on the fundamental haviors 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. gas mixtures.

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Reactor core analysis through the SP3-ACMFD approach. Part I: Static solution

  • Mirzaee, Morteza Khosravi;Zolfaghari, A.;Minuchehr, A.
    • Nuclear Engineering and Technology
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    • 제52권2호
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    • pp.223-229
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    • 2020
  • The present work proposes a solution to the static Boltzmann transport equation approximated by the simplified P3 (SP3) on angular, and the analytic coarse mesh finite difference (ACMFD) for spatial variables. Multi-group SP3-ACMFD equations in 3D rectangular geometry are solved using the GMRES solution technique. As the core time dependent analysis necessitates the solution of an eigenvalue problem for an initial condition, this work is hence devoted to development and verification of the proposed static SP3-ACMFD solver. A 3D multi-group static diffusion solver is also developed as a byproduct of this work to assess the improvement achieved using the SP3 technique. Static results are then compared against transport benchmarks to assess the proximity of SP3-ACMFD solutions to their full transport peers. Results prove that the approach can be considered as an acceptable interim approximation with outputs superior to the diffusion method, close to the transport results, and with the computational costs less than the full transport approach. The work would be further generalized to time dependent solutions in Part II.

$ SF_6$가스의 전자에너지 분포함수에 관한 연구 (A Study on the electron energy diffusion function of the sulphur hexaflouride)

  • 김상남;하성철
    • 조명전기설비학회논문지
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    • 제13권2호
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    • pp.95-101
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    • 1999
  • $ SF_6$ 가스의 전자에너지 분포함수를 평균에너지 평형 영역에 대하여 E/N=500~800[Td]에서 해석하였다. 본 논문은 저자들에 의해 결정된 충돌 단면적을 사용하여 몬테칼로 시뮬레이션과 볼쯔만 방정식에 의해 E/N=150~800[Td]범위에서 계산된 $ SF_6$ 가스의 전자 수송 특성과 TOF법에서 구한 전자군 파라미터 값들을 나타냈다. 전자이동속도 전자 이온화 또는 부착계수, 종.횡 방향 확산계수 등의 전자군 파라미터 값들은 E/N 범위에서 실험 치와 이론 치가 일치하였다. 전자사태의 특성은 전자에너지의 비평형 영역에서 고려되었다.

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Effects of the Counter Ion Valency on the Colloidal Interaction between Two Cylindrical Particles

  • Lee, In-Ho;Dong, Hyun-Bae;Choi, Ju-Young;Lee, Sang-Yup
    • Bulletin of the Korean Chemical Society
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    • 제30권3호
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    • pp.567-572
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    • 2009
  • In this study, the effects of counter ion valency of the electrolyte on the colloidal repulsion between two parallel cylindrical particles were investigated. Electrostatic interactions of the cylindrical particles were calculated with the variation of counter ion valency. To calculate the electrical repulsive energy working between these two cylindrical particles, Derjaguin approximation was applied. The electrostatic potential profiles were obtained numerically by solving nonlinear Poission-Boltzmann (P-B) equation and calculating middle point potential and repulsive energy working between interacting surfaces. The electrical potential and repulsive energy were influenced by counter ion valency, Debye length, and surface potential. The potential profile and middle point potential decayed with the counter ion valency due to the promoted shielding of electrical charge. On the while, the repulsive energy increased with the counter ion valency at a short separation distance. These behaviors of electrostatic interaction agreed with previous results on planar or spherical surfaces.

$SF_{6+}Ar$혼합기체의 전자수송특성 개선에 관한 연구 (A Study on the Improvement of the Electron Transport Properties in $SF_{6+}Ar$ Mixtures Gas)

  • 하성철;김상남;유회영;서상현;임상원;전병훈
    • 한국전기전자재료학회논문지
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    • 제11권1호
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    • pp.67-73
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    • 1998
  • In this paper, the electron swarm parameters in the 0.5% and 0.2% SF\ulcorner+Ar mixtures are measured by time of flight method over the E/N(Td) range from 30 to 300(Td). The measurements have been carried out by the double shutter drift tube with variable drift distance from the cathod. A two-term approximation of the boltzmann equation analysis and Monte Carlo simulation have been also used to study electron transport coefficients. We have calculated W, $ND_L,\;ND_T,\;\alpha,\;\eta,\;\alpha-\eta$, and the limiting breakdown electric field to gas mixtures ratio in pure $SF_6$+Ar mixtures. The electron energy distribution function has been analysed in $SF_6$+Ar mixtures at E/N : 200(Td) for a case of the equilibrium region in the mean electron energy. The measured results and the calculated results have been compared each other.

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전자충돌과정을 통한 SF6 혼합기체의 절연특성 분석 (The Analysis of Insulation Properties with Electron Collision Processes on SF6 Mixture Gases)

  • 소순열
    • 전기학회논문지P
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    • 제59권2호
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    • pp.197-201
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    • 2010
  • $SF_6$ gas would be used in power transformer, GIS (Gas insulated switchgear) and so on because of its electrically superior insulation and chemically stable structure. Recently, the reduction of $SF_6$ is required to avoid global warming and the researches on the dilution of $SF_6$ with other gases have been carried out. $SF_6$ mixture gases with $N_2$ and $C_xF_y$ have drawn attention to the synergy effect. However, in order to understand the mechanism of the synergy effect, it is important to analyze and evaluate properties of mixture gases quantitatively. In this paper, we investigated the mechanism of synergy effect from electron collision processes and electron energy distribution by solving Boltzmann equation with propagator method. Three kinds of gases for dilution of $SF_6$ ($SF_6/N_2$, $SF_6/CF$4 and $SF_6/C_4F_8$) are considered in this simulation. On the properties of $SF_6/N_2$ mixture gas, the variation of reduced electric field was shown highly within 0%~40% mixtures of $SF_6$. And the more low-level electron energy has been distributed, the higher insulation capability has appeared.

Kr과 Xe 원자기체의 전자수송계수의 해석 (The Analysis of Electron Transport Coefficients in Kr and Xe Atom Gas)

  • 전병훈
    • 조명전기설비학회논문지
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    • 제22권8호
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    • pp.104-108
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    • 2008
  • 플라즈마 현상의 정량적 이해를 위해서는 원자나 분자기체가 가지고 있는 정확한 전자충돌단면적과 그 전자수송 계수의 값을 필요로 한다. 본 연구에서 사용하고 있는 Kr과 Xe 원자기체는 PDP와 무전각램프 등 다양한 산업 응용분야에 이용되고 있다. 따라서 2항 근사 볼츠만 해석에 의해 기체압력 1[torr]의 조건에 $0.001{\sim}500$[Td]의 광범위한 E/N에서 순수 Kr과 Xe 원자기체의 전자이동속도 W, 종 횡축확산계수 $ND_L$$ND_T$, 전리계수 $\alpha$/N의 전자수송 계수를 계산하고 물성 해석하였다.

송전선로 ACSR 케이블의 산화에 따른 결빙 특성 평가 (Evaluation of Ice Adhesion Strength on the Oxidation of Transmission Line ACSR Cable)

  • 조희재;김유섭;정용찬;이수열
    • 한국재료학회지
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    • 제29권6호
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    • pp.378-384
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    • 2019
  • Ice accumulation on Aluminum Conductor Steel Reinforced(ACSR) cable during winter is an important matter in terms of safety, economy, and efficient power supply. In this work, the ice adhesion strengths of ACSR cable oxidized during different periods(7 years oxidized and 15 years oxidized) are evaluated. At first, a plate type dry oxidation standard specimen, whose surface characteristics are similar to those of ACSR cable, is prepared. Dry oxidation standard specimens are heat-treated at $500^{\circ}C$ for 20, 60, and 120 minutes in order to obtain different degrees of oxidation. After the dry oxidation, surface properties are analyzed using contact angle analyzer, atomic force microscopy, spectrophotometer, and gloss meter. The ice adhesion strengths are measured using an ice pull-off tester. Correlations between the surface properties and the ice adhesion strength are obtained through a regression analysis indicating a Boltzmann equation. It is revealed that the ice adhesion strength of 15-year oxidized ACSR cable is approximately 8 times higher than that of ACSR-bare.

곡선경계처리법을 이용한 주기적으로 진동하는 실린더주위의 유동해석 (Numerical Study on Flow Over Oscillating Circular Cylinder Using Curved Moving Boundary Treatment)

  • 김형민
    • 대한기계학회논문집B
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    • 제31권11호
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    • pp.895-903
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    • 2007
  • CMBT(Curved Moving Boundary Treatment) is a newly developed scheme for the treatment of a no slip condition on the curved solid wall of moving obstacle in a flow field. In our research CMBT was used to perform LBM simulation of a flow over a moving circular cylinder to determine the flow feature and aerodynamics characteristic of the cylinder. To ascertain the applicability of CMBT on the complex shape of the obstacle, it was first simulated for the case of the flow over a fixed circular cylinder in a channel and the results were compared against the solution of Navier-Stokes equation with deforming mesh technique. The simulations were performed in a moderate range of reynolds number at each moving cylinder to identify the flow feature and aerodynamic characteristics of circular cylinder in a channel. The drag coefficients of the cylinder were calculated from the simulation results. We have numerically confirmed that the critical reynolds number for vortex shedding is ar Re=250 and the result is the same as the case of fixed cylinder. As the cylinder approaching to one wall, the 2nd vortex is developed by interacting with the wall boundary-layer vorticity. As the velocity ratio increase the third vortex are generated by interacting with the 2nd vortexes developed on the upper and lower wall boundary layer. The resultant $C_d$ decrease as reynolds number increasing and the Cd approached to a value when Re>1000.

Electronic properties of graphene nanoribbons with Stone-Wales defects using the tight-binding method

  • M.W. Chuan;S.Z. Lok;A. Hamzah;N.E. Alias;S. Mohamed Sultan;C.S. Lim;M.L.P Tan
    • Advances in nano research
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    • 제14권1호
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    • pp.1-15
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    • 2023
  • Driven by the scaling down of transistor node technology, graphene became of interest to many researchers following the success of its fabrication as graphene nanoribbons (GNRs). However, during the fabrication of GNRs, it is not uncommon to have defects within the GNR structures. Scaling down node technology also changes the modelling approach from the classical Boltzmann transport equation to the quantum transport theory because the quantum confinement effects become significant at sub-10 nanometer dimensions. The aim of this study is to examine the effect of Stone-Wales defects on the electronic properties of GNRs using a tight-binding model, based on Non-Equilibrium Green's Function (NEGF) via numeric computation methods using MATLAB. Armchair and zigzag edge defects are also implemented in the GNR structures to mimic the practical fabrication process. Electronic properties of pristine and defected GNRs of various lengths and widths were computed, including their band structure and density of states (DOS). The results show that Stone-Wales defects cause fluctuation in the band structure and increase the bandgap values for both armchair GNRs (AGNRs) and zigzag GNRs (ZGNRs) at every simulated width. In addition, Stone-Wales defects reduce the numerical computation DOS for both AGNRs and ZGNRs. However, when the lengths of the structures increase with fixed widths, the effect of the Stone-Wales defects become less significant.