• 제목/요약/키워드: Boltzmann equation

검색결과 221건 처리시간 0.025초

천이영역의 희박기체 압축성 경계층 해석 (Analysis of rarefied compressible boundary layers in transition regime)

  • 최서원
    • 대한기계학회논문집B
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    • 제21권4호
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    • pp.509-517
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    • 1997
  • Results of flat plate compressible boundary layer calculation, based on discrete formulation of DSMC method, are presented in low Mach number and low Knudsen number range. The free stream is a uniform flow of pure nitrogen at various Mach numbers in low pressures (i.e. rarefied gas). Complete thermal accommodation and diffuse molecular reflections are used as the wall boundary condition, replacing unreal no-slip condition used in continuum calculations. In the discrete formulation of DSMC method, there is no need to use ad hoc assumptions on transport properties like viscosity and thermal conductivity, instead viscosity is calculated from values of other field variables (velocity and shear stress). Also the results are compared with existing self-similar continuum solutions. In all Mach number cases computed, velocity slip is most pronounced in regions near the leading edge where continuum formulation renders the solution singular. As the boundary layer develops further downstream, velocity slips asymptote to values that are between 10 to 20% of the magnitude of free stream velocity. When the free stream number density is reduced, so the gas more rarefied, the velocity slip increases as expected.

펄스코로나 방전에서 프로핀($C_3H_6$)이 NO-$NO_2$ 변환에 미치는 영향에 관한 연구 (Effect of Propene($C_3H_6$) ON NO-$NO_2$ Conversion Process in a Pulsed Corona Discharge)

  • 박광서;전배혁;전광민
    • 한국자동차공학회논문집
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    • 제8권5호
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    • pp.67-77
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    • 2000
  • Investigated was the effect of propene(C3H6) on the NO-NO2 conversion in dry exhaust gases from lean burn engine using a pulsed corona discharge. A kinetic model was developed to characterize the plasma chemistry in simulated exhausts containing propene. The model uses ELENDIF program to solve Boltzmann equation for electron energy distribution function, and CHEMKIN-II program to solve stiff ODE(ordinary differential equation) problems for species concentrations. The corona discharge energy per pulse and the time-space averaged E/N were obtained by fitting the model to experimental data. The model calculation shows good agreement for NO and NO2 concentrations with the experimental data, and predicts the formation of byproducts such as CH2O, CH3HCO, CO AND CH3NO2 Propene enhances the NOx conversion enormously at lower energy density and the NOx conversion increases with the increase of initial propene and oxygen concentration, and temperature.

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Numerical analysis of particle transport in low-pressure, low-temperature plasma environment

  • Kim, Heon Chang
    • 한국입자에어로졸학회지
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    • 제5권3호
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    • pp.123-131
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    • 2009
  • This paper presents simulation results of particle transport in low-pressure, low-temperature plasma environment. The size dependent transport of particles in the plasma is investigated with a two-dimensional simulation tool developed in-house for plasma chamber analysis and design. The plasma model consists of the first two and three moments of the Boltzmann equation for ion and electron fluids respectively, coupled to Poisson's equation for the self-consistent electric field. The particle transport model takes into account all important factors, such as gravitational, electrostatic, ion drag, neutral drag and Brownian forces, affecting the motion of particles in the plasma environment. The particle transport model coupled with both neutral fluid and plasma models is simulated through a Lagrangian approach tracking the individual trajectory of each particle by taking a force balance on the particle. The size dependant trap locations of particles ranging from a few nm to a few ${\mu}m$ are identified in both electropositive and electronegative plasmas. The simulation results show that particles are trapped at locations where the forces acting on them balance. While fine particles tend to be trapped in the bulk, large particles accumulate near bottom sheath boundaries and around material interfaces, such as wafer and electrode edges where a sudden change in electric field occurs. Overall, small particles form a "dome" shape around the center of the plasma reactor and are also trapped in a "ring" near the radial sheath boundaries, while larger particles accumulate only in the "ring". These simulation results are qualitatively in good agreement with experimental observation.

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Simulation of Capacitively Coupled RF Plasma; Effect of Secondary Electron Emission - Formation of Electron Shock Wave

  • Park, Seung-Kyu;Kim, Heon-Chang
    • 반도체디스플레이기술학회지
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    • 제8권3호
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    • pp.31-37
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    • 2009
  • This paper presents one and two dimensional simulation results with discontinuous features (shocks) of capacitively coupled rf plasmas. The model consists of the first two and three moments of the Boltzmann equation for the ion and electron fluids respectively, coupled to Poisson's equation for the self-consistent electric field. The local field and drift-diffusion approximations are not employed, and as a result the charged species conservation equations are hyperbolic in nature. Hyperbolic equations may develop discontinuous solutions even if their initial conditions are smooth. Indeed, in this work, secondary electron emission is shown to produce transient electron shock waves. These shocks form at the boundary between the cathodic sheath (CS) and the quasi-neutral (QN) bulk region. In the CS, the electrons emitted from the electrode are accelerated to supersonic velocities due to the large electric field. On the other hand, in the QN the electric field is not significant and electrons have small directed velocities. Therefore, at the transition between these regions, the electron fluid decelerates from a supersonic to a subsonic velocity in the direction of flow and a jump in the electron velocity develops. The presented numerical results are consistent with both experimental observations and kinetic simulations.

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NTP-ERSN verification with C5G7 1D extension benchmark and GUI development

  • Lahdour, M.;El Bardouni, T.;El Hajjaji, O.;Chakir, E.;Mohammed, M.;Al Zain, Jamal;Ziani, H.
    • Nuclear Engineering and Technology
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    • 제53권4호
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    • pp.1079-1087
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    • 2021
  • NTP-ERSN is a package developed for solving the multigroup form of the discrete ordinates, characteristics and collision probability of the Boltzmann transport equation in one-dimensional cartesian geometry, by combining pin cells. In this work, C5G7 MOX benchmark is used to verify the accuracy and efficiency of NTP-ERSN package, by treating reactor core problems without spatial homogenization. This benchmark requires solutions in the form of normalized pin powers as well as the vectors and the eigenvalue. All NTP-ERSN simulations are carried out with appropriate spatial and angular approximations. A good agreement between NTP-ERSN results with those obtained with OpenMC calculation code for seven energy groups. In addition, our studies about angular and mesh refinements are carried out to produce better quality solution. Moreover, NTP-ERSN GUI has also been updated and adapted to python 3 programming language.

Quasi-static responses of time-dependent sandwich plates with viscoelastic honeycomb cores

  • Nasrin Jafari;Mojtaba Azhari
    • Structural Engineering and Mechanics
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    • 제88권6호
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    • pp.589-598
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    • 2023
  • This article addresses the quasi-static analysis of time-dependent honeycomb sandwich plates with various geometrical properties based on the bending analysis of elastic honeycomb sandwich plates employing a time function with three unknown coefficients. The novel point of the developed method is that the responses of viscoelastic honeycomb sandwich plates under static transversal loads are clearly formulated in the space and time domains with very low computational costs. The mechanical properties of the sandwich plates are supposed to be elastic for the faces and viscoelastic honeycomb cells for the core. The Boltzmann superposition integral with the constant bulk modulus is used for modeling the viscoelastic material. The shear effect is expressed using the first-order shear deformation theory. The displacement field is predicted by the product of a determinate geometrical function and an indeterminate time function. The simple HP cloud mesh-free method is utilized for discretizing the equations in the space domain. Two coefficients of the time function are extracted by answering the equilibrium equation at two asymptotic times. And the last coefficient is easily determined by solving the first-order linear equation. Numerical results are presented to consider the effects of geometrical properties on the displacement history of viscoelastic honeycomb sandwich plates.

레이저유도 플라즈마분광법을 이용한 방사성폐기물 유리의 현장분석 시스템 개발 (Development of in-situ Analysis System for Radwaste Glass Using Laser Induced Breakdown Spectroscopy)

  • 김천우;박종길;신상운;하종현;송명재;이계호
    • 한국방사성폐기물학회:학술대회논문집
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    • 한국방사성폐기물학회 2004년도 학술논문집
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    • pp.137-146
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    • 2004
  • 방사성폐기물 유리화 공전 중 용융로 내에서 유리시료를 직접분석 하기 위한 레이저유도 플라즈마분광법(LIBS: Laser Induced Breakdown Spectroscopy)을 개발 중이다. LIBS 시스템을 구성하기 위하여 분광기, 검출기, 레이저 등의 장비들을 구축하였다. 분광기는 CCD(charge coupled device)가 보정되어 내장되어있는 ESA 3000을 레이저는 Q-switched Nd-YAG인 Brilliant로 구매하여 분석시스템을 구축하였다. 구축된 분석시스템 분야별 성능들을 확인하였으며 최적화 연구를 수행하였다. 첫 번째 단계로 Fe가 함유된 시료에 레이저를 주사하였을 때 발광스펙트럼을 측정하였으며 검출기의 지연시간을 변화시켰을 때의 발광스펙트럼의 특성과 이를 이용한 여기온도를 Einstein-Boltzmann 식을 이용하여 계산하였다. 시료에 532nm Nd-YAG 레이저를 주사하고 검출기의 지연시간을 500, 1000, 1500, 2000ns로 변화시켰을 때의 분광선의 intensity 및 여기온도 변화를 분석하였다. 그 결과 검출시간이 1500㎱ 일 때 여기온도는 7820k로 가장 최적의 상태를 확인하였다. 향후 이 시스템은 유리화 실증시설에 적용되어 용융로 외부로의 유리시료 이송 없이 현장에서 유리성분들의 정량분석을 수행할 예정이다.

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On-line monitoring system 개발에 관한 음극 액상 글로우 방전의 기초 연구 (Fundamental study of electrolyte cathode atomic discharge for development of on-line monitoring system)

  • 김경미;우영아;조원보;김효진
    • 분석과학
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    • 제15권6호
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    • pp.496-501
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    • 2002
  • Electrolyte cathode atomic discharge (ELCAD)는 용액 중에 포함된 미량 중금속을 연속 자동적으로 측정하기 위한 새로운 광학 측정기로서 플라스마에 의한 중금속들의 방출 강도를 측정하는 원자방출 분광법의 하나이다. 특히 이 방법은 검액을 전처리하지 않고 직접 분석할 수 있기 때문에 온라인 (on-line) 현장분석이 가능하다. ELCAD에서는 분위기 가스로 공기를 이용하고, 양극부분에 백금 전극을 사용하며, 음극에서는 연속적으로 전해질 시료를 주입하면서 플라스마를 형성하면서 미량의 중금속을 분석할 수 있다. 액상 글로우 방전의 기초 특성 연구로는 철의 원자 방출선 세기를 구한 다음 Einstein-Boltzmann식을 사용하여 플라스마 온도를 구한 다음 구리, 납, 철 및 니켈의 미량 분석 및 간섭 현상에 대해서 연구하였고, 검출 한계를 구하였다.

Characteristics of K+ Outward Currents in the Cochlear Outer Hair Cells of Circling Mice within the First Postnatal Week

  • Ahn, Ji Woong;Kang, Shin Wook;Ahn, Seung Cheol
    • The Korean Journal of Physiology and Pharmacology
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    • 제19권4호
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    • pp.383-388
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    • 2015
  • $K^+$ outward currents in the outer hair cells (OHCs) of circling mice (homozygous (cir/cir) mice), an animal model for human deafness (DFNB6 type), were investigated using a whole cell patch clamp technique. Littermate heterozygous (+/cir) mice of the same age (postnatal day (P) 0-P6) were used as controls. Similar slow rising $K^+$ currents were observed in both genotypes, but their biophysical and pharmacological properties were quite different. The values of Vhalf for activation were significantly different in the heterozygous (+/cir) and homozygous (cir/cir) mice ($-8.1{\pm}2.2mV$, heterozygous (+/cir) mice (n=7) and $-17.2{\pm}4.2mV$, homozygous (cir/cir) mice (n=5)). The inactivation curve was expressed by a single first order Boltzmann equation in the homozygous (cir/cir) mice, while it was expressed by a sum of two first order Boltzmann equations in the heterozygous (+/cir) mice. The $K^+$ current of homozygous (cir/cir) mice was more sensitive to TEA in the 1 to 10 mM range, while the 4-AP sensitivities were not different between the two genotypes. Removal of external $Ca^{2+}$ did not affect the $K^+$ currents in either genotype, indicating that the higher sensitivity of $K^+$ current to TEA in the homozygous (cir/cir) mice was not due to an early expression of $Ca^{2+}$ activated $K^+$ channels. Our results suggest that the $K^+$ outward current of developing homozygous (cir/cir) mice OHCs is different in both biophysical and pharmacological aspects than that of heterozygous (+/cir) mice.

1 차원 과도 전도와 정전기 방전 현상에 관한 포논 전달의 몬테 카를로 모사 (Monte Carlo Simulation of Phonon Transport in One-Dimensional Transient Conduction and ESD Event)

  • 오장현;이준식
    • 대한기계학회:학술대회논문집
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    • 대한기계학회 2007년도 춘계학술대회B
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    • pp.2165-2170
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    • 2007
  • At nanoscales, the Boltzmann transport equation (BTE) can best describe the behavior of phonons which are energy carriers in crystalline materials. Through this study, the phonon transport in some micro/nanoscale problems was simulated with the Monte Carlo method which is a kind of the stochastic approach to the BTE. In the Monte Carlo method, the superparticles of which the number is the weighted value to the actual number of phonons are allowed to drift and be scattered by other ones based on the scattering probability. Accounting for the phonon dispersion relation and polarizations, we have confirmed the one-dimensional transient phonon transport in ballistic and diffusion limits, respectively. The thermal conductivity for GaAs was also calculated from the kinetic theory by using the proposed model. Besides, we simulated the electrostatic discharge event in the NMOS transistor as a two-dimensional problem by applying the Monte Carlo method.

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