• 제목/요약/키워드: Boltzmann Equation

검색결과 221건 처리시간 0.025초

시뮬레이션에 의한 $SF_6-N_2$ 혼합기체의 전자수송특성 (Electron Transport Characteristic in $SF_6-N_2$ Mixture Gases by MCS-BEq Simulation)

  • 김상남
    • 한국전기전자재료학회:학술대회논문집
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    • 한국전기전자재료학회 2006년도 하계학술대회 논문집 Vol.7
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    • pp.507-508
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    • 2006
  • $SF_6$ gas is widely used in industrial of insulation field. In this paper, $N_2$ is mixed to improve pure $SF_6$ gas characteristics. Electron transport coefficients in $SF_6-N_2$ mixture gases are simulated in range of E/N values from 70 to 400 [Td] at 300K and 1 Torr by using Boltzmann equation method. 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. 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.

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SF6+Ar혼합기체의 MCS-BEq에 의한 전자분포함수 (Energy Distribution Function for Electrons in SF6+Ar Mixtures Gas used by MCS-BEQ Algorithm)

  • 김상남
    • 전기학회논문지P
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    • 제51권1호
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    • pp.28-32
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    • 2002
  • Energy distribution function for electrons in $SF_6+Ar$ mixtures gas used by MCS-BEq algorithm bas been analysed over the E/N range 30-300[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, 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.

Electric double layers interactions under condition of variable dielectric permittivity

  • Payam, Amir Farrokh;Fathipour, Morteza
    • Interaction and multiscale mechanics
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    • 제3권2호
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    • pp.157-171
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    • 2010
  • In this paper, a theoretical method has been developed for the electric double layer interaction under condition of the variable dielectric permittivity of water. Using Poisson-Boltzmann equation (PBE), for one plate and two plates having similar or dissimilar constant charge or constant potential, we have investigated the electric double layer potential, its gradient and the disjoining pressure as well as the effect of variation of dielectric permittivity on these parameters. It has been assumed that plates are separated by a specific distance and contain a liquid solution in between. It is shown that reduction of the dielectric permittivity near the interfaces results in compression of electric double layers and affects the potential and its gradient which leads to a decreased electrostatic repulsion. In addition, it is shown that variation of dielectric permittivity in the case of higher electrolyte concentration, leads to a greater change in potential distribution between two plates.

반복적 Cumulant 모멘트 방법에 의한 Boltzmann 방정식의 해법과 충격파구조에 관한 연구 (Iterative Cumulant Moment Method for solution of Boltzmann Equation and its Application to Shock Wave Structure)

  • 오영기
    • 대한화학회지
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    • 제42권4호
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    • pp.398-410
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    • 1998
  • Boltzmann 방정식의 비선형 해법으로서 cumulant 모멘트 방법을 연구하였으며, Maxwell 분자모형 단원자분자 기체계의 정상충격파 문제에 대하여 적용하였다. 모멘트 방정식의 해는 Maxwell-Ikenberry-Truesdell(MIT) 반복법을 사용하였다. 원래의 MIT 반복법은 초기값을 평형분포함수로부터 구하지만, 본 연구에서는 반복계산의 초기값을 Mott-Smith의 두방식(bimodal)함수로부터 구하였다. 모멘트 계산은 2차 반복단계까지 수행하였으며, 강한 충격파에 대한 밀도, 온도, stress, heat flux 등의 윤곽과 충격파의 두께, 그리고 마하수 1.4 미만의 약한 충격파의 두께를 계산하였다. 1차 반복계산에서 충격파 윤곽에 대한 간단한 형태의 해석적 표현을 얻었으며, 이로부터 도출한 약한 충격파 두께에 대한 극한법칙은 Navier-Stokes 이론과 정확히 일치한다. 2차 반복계산에 의한 결과는 강한 충격파의 윤곽곡선 및 충격파 두께가 Monte Carlo 문헌값과 정량적으로 일치함을 보인다.

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다중완화시간 가상경계볼쯔만법을 이용한 실린더 주위의 난류유동해석 (NUMERICAL STUDY ON TURBULENT FLOW OVER CYLINDER USING IMMERSED BOUNDARY LATTICE BOLTZMANN METHOD WITH MULTI RELAXATION TIME)

  • 김형민
    • 한국전산유체공학회지
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    • 제15권2호
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    • pp.21-27
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    • 2010
  • Immersed boundary lattice Boltzmann method (IBLBM) has been applied to simulate a turbulent flow over circular cylinder in a flow field effectively. Although IBLBM is very effective method to simulate the flow over a complex shape of obstacle in the flow field regardless of the constructed grids in the calculation domain, the results, however, become numerically unstable in high reynolds number flow. The most effective suggestion to archive the numerical stability in high Reynolds number flow is applying the multiple relaxation time (MRT) model instead of single relaxation time(SRT) model in the collision term of lattice Boltzmann equation. In the research MRT model for IBLBM was introduced and comparing the numerical results obtained by applying SRT and MRT. The hydraulic characteristic of cylinder in a flow field between two parallel plate at the range of $Re{\leqq}2000$represented and it is also compared the drag and lifting coefficients of the cylinder calculated by IBLBM with SRT and MRT model.

Modeling of Degenerate Quantum Well Devices Including Pauli Exclusion Principle

  • 이은주
    • 대한전자공학회논문지SD
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    • 제39권2호
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    • pp.14-26
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    • 2002
  • Pauli 배타 원리를 적용한 축퇴 상태의 양자 우물 소자 모델링을 제안하였다. 양자 우물에서의 다중 에너지 부준위 각각에 대한 Boltzmann 방정식의 collision 항들을 Pauli 배타 원리를 적용하여 전개하고 이들을 Schrodinger 방정식과 Poisson 방정식과 결합하여 비선형적인 시스템의 모델을 설정하였다. 시스템의 해를 직접적으로 구하기 위하여 유한 차분법과 Newton-Raphson method를 적용하여 양자 우물의 다중 에너지 부준위 각각에 대한 캐리어 분포 함수를 구하였다. Si MOSFET의 inversion 영역에 본 모델을 적용하여 전자 밀도의 증가에 따라 양자 우물의 에너지 분포 함수가 Boltzmann 분포 함수의 형태로부터 Fermi-Dirac 분포 함수의 형태로 변화함을 제시하고, 소자 크기가 감소할수록 소자 모델링에 있어서의 Pauli 배타 원리의 중요성과 함께 본 모델의 정당함과 그 해석 방법의 효율성을 보여주었다.

Analysis of Airflow Pattern and Particle Dispersion in Enclosed Environment Using Traditional CFD and Lattice Boltzmann Methods

  • Inoguchi, Tomo;Ito, Kazuhide
    • 국제초고층학회논문집
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    • 제1권2호
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    • pp.87-97
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    • 2012
  • The indoor environments in high-rise buildings are generally well enclosed by defined boundary conditions. Here, a numerical simulation method based on the Lattice Boltzmann method (LBM), which aims to model and simulate the turbulent flow accurately in an enclosed environment, and its comparison with traditional computational fluid dynamics (CFD) results, are presented in this paper. CFD has become a powerful tool for predicting and evaluating enclosed airflows with the rapid advance in computer capacity and speed, and various types of CFD turbulence modeling and its application and validation have been reported. The LBM is a relatively new method; it involves solving of the discrete Boltzmann equation to simulate the fluid flow with a collision model instead of solving Navier-Stokes equations. In this study, the LBM-based scheme of flow pattern and particle dispersion analyses are validated using the benchmark test case of two- and three-dimensional and isothermal conditions (IEA/Annex 20 case); the prediction accuracy and advantages are also discussed by comparison with the results of CFD.