• Title/Summary/Keyword: Boltzmann equation

Search Result 221, Processing Time 0.026 seconds

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

  • Mirzaee, Morteza Khosravi;Zolfaghari, A.;Minuchehr, A.
    • Nuclear Engineering and Technology
    • /
    • v.52 no.2
    • /
    • pp.223-229
    • /
    • 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.

Strong Correlation Effect by the Rare Earth Substitution on Thermoelectric Material Bi2Te3 ; in GGA+U Approach

  • Quang, Tran Van;Kim, Miyoung
    • Proceedings of the Korean Magnestics Society Conference
    • /
    • 2013.05a
    • /
    • pp.19-20
    • /
    • 2013
  • Thermoelectic properties of the typical thermoelectric host materials, the tellurides and selenides, are known to be noticeably changed by their volume change due to the strain [1]. In the bismuth telluride ($Bi_2Te_3$) crystal, a substitution of rare-earth element by replacing one of the Bi atoms may cause the change of the lattice parameters while remaining the rhombohedral structure of the host material. Using the first-principles approach by the precise full potential linearized augmented plane wave (FLAPW) method [2], we investigated the Ce substitution effect on the thermoelectric transport coefficients for the bismuth telluride, employing Boltzmann's equation in a constant relaxation-time approach fed with the FLAPW wave-functions within the rigid band approximation. Depending on the real process of re-arrangement of atoms in the cell to reach the equilibrium state, $CeBiTe_3$ was found to manifest a metal or a narrow bandgap semiconductor. This feature along with the strong correlation effect originated by the 4f states of Ce affect significantly on the thermoelectric properties. We showed that the position of the strongly localized f-states in energy scale (Fig. 1, f-states are shaded) was found to alter critically the transport properties in this material suggesting an opportunity to improve the thermoelectric efficiency by tuning the external strain which may changing the location of the f-sates.

  • PDF

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

  • 김상남;하성철
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
    • /
    • v.14 no.9
    • /
    • pp.773-778
    • /
    • 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.

  • PDF

Analysis on particle deposition onto a heated, horizontal free-standing wafer with electrostatic effect (정전효과가 있는 가열 수평웨이퍼로의 입자침착에 관한 해석)

  • Yoo, Kyung-Hoon;Oh, Myung-Do;Myong, Hyon-Kook
    • Transactions of the Korean Society of Mechanical Engineers B
    • /
    • v.21 no.10
    • /
    • pp.1284-1293
    • /
    • 1997
  • The electrostatic effect on particle deposition onto a heated, Horizontal free-standing wafer surface was investigated numerically. The deposition mechanisms considered were convection, Brownian and turbulent diffusion, sedimentation, thermophoresis and electrostatic force. The electric charge on particle needed to calculate the electrostatic migration velocity induced by the local electric field was assumed to be the Boltzmann equilibrium charge. The electrostatic forces acted upon the particle included the Coulombic, image, dielectrophoretic and dipole-dipole forces based on the assumption that the particle and wafer surface are conducting. The electric potential distribution needed to calculate the local electric field around the wafer was calculated from the Laplace equation. The averaged and local deposition velocities were obtained for a temperature difference of 0-10 K and an applied voltage of 0-1000 v.The numerical results were then compared with those of the present suggested approximate model and the available experimental data. The comparison showed relatively good agreement between them.

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
    • /
    • v.30 no.3
    • /
    • pp.567-572
    • /
    • 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.

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

  • Jeon, Byung-Hoon
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
    • /
    • v.22 no.8
    • /
    • pp.104-108
    • /
    • 2008
  • Accurate sets of electron collision cross sections and the electron transport coefficients for atoms and molecules are necessary for quantitative understanding of plasma phenomena Kr and Xe atom are used in many industrial applications, such as in PDP and fluorescent induction lamps(FILs). Therefore, we analysed and calculated the electron transport coefficients, the electron drift velocity W, the longitudinal and transverse diffusion coefficient $ND_L$ and $ND_T$, and the ionization coefficient $\alpha$/N in pure Kr and Xe gases over the wide E/N range from 0.001 to 500[Td] at 1[Torr] by two-tenn approximation of the Boltzmann equation.

Airborne Remote Sensing of Evapotranspiration over Rice Paddy

  • Chen, Y.Y.;Liou, Yuei-An
    • Proceedings of the KSRS Conference
    • /
    • 2003.11a
    • /
    • pp.351-353
    • /
    • 2003
  • We present a retrieval scheme for the remote sensing of evapotranspiration (ET) over rice paddy. To perform the retrieval, high-resolution airborne imagery of multi-spectral visible and thermal infrared data, and ground-based meteorological measurements are utilized. Our ET retrieval scheme is based on the basic principal of surface energy budget, which is a result of balance in longwave and shortwave radiation, latent heat, sensible heat, and energy flux into the ground. To partition the latent and sensible heat fluxes of interest from the energy balance equation, three basic parameters are of most concern, including albedo, surface temperature, and normalized difference vegetation index (NDVI). The NDVI and albedo can be easily derived from the visible and near infrared spectral data, while the surface tem-perature can be determined through the analysis of the infrared data with the Stefan Boltzmann law. From the airborne imagery taken on 28 April 2003, we observe very good dry and wet pixels that can be easily corre-sponded to the radiation and evaporation controlled crite-ria, respectively, and, hence, for the further use in defin-ing the evaporative fraction needed to partition sensible and latent heat fluxes from the net energy flux. The de-rived ET is compared with the in situ measurements.

  • PDF

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

  • 하성철;김상남;유회영;서상현;임상원;전병훈
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
    • /
    • v.11 no.1
    • /
    • pp.67-73
    • /
    • 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.

  • PDF

Microflow of dilute colloidal suspension in narrow channel of microfluidic-chip under Newtonian fluid slip condition

  • Chun Myung-Suk;Lee Tae Seok;Lee Kangtaek
    • Korea-Australia Rheology Journal
    • /
    • v.17 no.4
    • /
    • pp.207-215
    • /
    • 2005
  • We present a finite difference solution for electrokinetic flow in rectangular microchannels encompassing Navier's fluid slip phenomena. The externally applied body force originated from between the nonlinear Poisson-Boltzmann field around the channel wall and the flow-induced electric field is employed in the equation of motion. The basic principle of net current conservation is applied in the ion transport. The effects of the slip length and the long-range repulsion upon the velocity profile are examined in conjunction with the friction factor. It is evident that the fluid slip counteracts the effect by the electric double layer and induces a larger flow rate. Particle streak imaging by fluorescent microscope and the data processing method developed ourselves are applied to straight channel designed to allow for flow visualization of dilute latex colloids underlying the condition of simple fluid. The reliability of the velocity profile determined by the flow imaging is justified by comparing with the finite difference solution. We recognized the behavior of fluid slip in velocity profiles at the hydrophobic surface of polydimethylsiloxane wall, from which the slip length was evaluated for different conditions.

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

  • Cho, Hui Jae;Kim, You Sub;Jung, Yong Chan;Lee, Soo Yeol
    • Korean Journal of Materials Research
    • /
    • v.29 no.6
    • /
    • pp.378-384
    • /
    • 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.