• Title/Summary/Keyword: Boltzmann equation

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

  • Kim, Sang-Nam
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2006.06a
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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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Energy Distribution Function for Electrons in SF6+Ar Mixtures Gas used by MCS-BEQ Algorithm (SF6+Ar혼합기체의 MCS-BEq에 의한 전자분포함수)

  • Kim, Sang-Nam
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.51 no.1
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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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    • v.3 no.2
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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.

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

  • Ohr, Young Gie
    • Journal of the Korean Chemical Society
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    • v.42 no.4
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    • pp.398-410
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    • 1998
  • For non-linear solution of the Boltzmann equation, the cumulant moment method has been studied. To apply the method to the normal shock wave problem, we restricted ourselves to the monatomic Maxwell molecular gases. The method is based on the iterative approach developed by Maxwell-Ikenberry-Truesdell (MIT). The original MIT approach employs the equilibrium distribution function for the initial values in beginning the iteration. In the present work, we use the Mott-Smith bimodal distribution function to calculate the initial values and follow the MIT iteration procedure. Calculations have been carried out up to the second iteration for the profiles of density, temperature, stress, heat flux, and shock thickness of strong shocks, including the weak shock thickness of Mach range less than 1.4. The first iteration gives a simple analytic expression for the shock profile, and the weak shock thickness limiting law which is in exact accord with the Navier-Stokes theory. The second iteration shows that the calculated strong shock profiles are consistent with the Monte Carlo values quantitatively.

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

  • Kim, Hyung-Min
    • Journal of computational fluids engineering
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    • v.15 no.2
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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

  • Lee, Eun-Ju
    • Journal of the Institute of Electronics Engineers of Korea SD
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    • v.39 no.2
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    • pp.14-26
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    • 2002
  • A new model for degenerate semiconductor quantum well devices was developed. In this model, the multi-subband Boltzmann transport equation was formulated by applying the Pauli exclusion principle and coupled to the Schrodinger and Poisson equations. For the solution of the resulted nonlinear system, the finite difference method and the Newton-Raphson method was used and carrier energy distribution function was obtained for each subband. The model was applied to a Si MOSFET inversion layer. The results of the simulation showed the changes of the distribution function from Boltzmann like to Fermi-Dirac like depending on the electron density in the quantum well, which presents the appropriateness of this modeling, the effectiveness of the solution method, and the importance of the Pauli -exclusion principle according to the reduced size of semiconductor devices.

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

  • Inoguchi, Tomo;Ito, Kazuhide
    • International Journal of High-Rise Buildings
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    • v.1 no.2
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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.