• Title, Summary, Keyword: Three-dimensional Discrete Ordinates Method

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COMPUTATIONAL EFFICIENCY OF A MODIFIED SCATTERING KERNEL FOR FULL-COUPLED PHOTON-ELECTRON TRANSPORT PARALLEL COMPUTING WITH UNSTRUCTURED TETRAHEDRAL MESHES

  • Kim, Jong Woon;Hong, Ser Gi;Lee, Young-Ouk
    • Nuclear Engineering and Technology
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    • v.46 no.2
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    • pp.263-272
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    • 2014
  • Scattering source calculations using conventional spherical harmonic expansion may require lots of computation time to treat full-coupled three-dimensional photon-electron transport in a highly anisotropic scattering medium where their scattering cross sections should be expanded with very high order (e.g., $P_7$ or higher) Legendre expansions. In this paper, we introduce a modified scattering kernel approach to avoid the unnecessarily repeated calculations involved with the scattering source calculation, and used it with parallel computing to effectively reduce the computation time. Its computational efficiency was tested for three-dimensional full-coupled photon-electron transport problems using our computer program which solves the multi-group discrete ordinates transport equation by using the discontinuous finite element method with unstructured tetrahedral meshes for complicated geometrical problems. The numerical tests show that we can improve speed up to 17~42 times for the elapsed time per iteration using the modified scattering kernel, not only in the single CPU calculation but also in the parallel computing with several CPUs.

Radiation in axisymmetric cylindrical coordinates with the modified discrete-ordinates method (축대칭 원통좌표계에서 수정된 구분종좌법에 의한 복사열전달 해석)

  • Kim, Man-Yeong;Baek, Seung-Uk
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.22 no.2
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    • pp.213-220
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    • 1998
  • The conventional discrete-ordinates method (DOM) is modified and developed for the analysis of two-dimensional axisymmetric cylindrical enclosure with curved wall. The objective of the present work is to extend the capability of the conventional DOM into a general axisymmetric geometry like nozzle-shaped enclosure, by adopting the arbitrary control angle as was done in the finite-volume method (FVM), while keeping the same two-dimensional solution procedure as in the conventional DOM. The present method is validated by applying it to three different benchmark problems of axisymmetric enclosure containing absorbing, emitting and scattering medium. Results presented in this work not only support the solution accuracy, but also moderate efficiency in the numerical calculation of axisymmetric radiation problem.

Discrete Ordinates Interpolation Method Applied to Irregular Three-Dimensional Geometries (불규칙한 3차원 형상에 응용된 구분종좌표보간법)

  • Cha, Ho-Jin;Song, Tae-Ho
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.24 no.6
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    • pp.814-821
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    • 2000
  • The Discrete Ordinates Interpolation Method (DOIM) is tested in three-dimensional enclosures. The radiative transfer equation (RTE) is solved for a linear source term and the DOIM is formulated for a gray medium. Several interpolation methods can be applied to the DOIM scheme. Among them, the interpolation method applicable to an unstructured grid system is discussed. In a regular hexahedron enclosure, radiative wall heat fluxes are calculated and compared with exact solutions. The enclosure has an absorbing, emitting and nonscattering medium and a constant temperature distribution. These results are obtained with varying optical depths (xD = 0.1, 1.0, 10.0). Also, the same calculations are performed in an irregular hexahedron enclosure. The DOIM is applied to an unstructured grid system as well as a structured grid system for the same regular hexahedron enclosure. They are compared with the exact solutions and the computational efficiencies are discussed. When compared with the analytic solutions, results of the DOIM are in good agreement for three-dimensional enclosures. Furthermore, the DOIM can be easily applied to the unstructured grid system, which proves the reliability and versatility of the DOIM.

An experimental and numerical study on natural convection-radiation conjugate heat transfer in a three-dimensional enclosure having a protruding heat source (돌출 열원을 갖는 3차원 밀폐 공간내에서의 자연대류-복사 복합 열전달에 대한 실험적 및 수치적 연구)

  • Baek, Chang-In;Lee, Gwan-Su;Kim, Woo-Seung
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.20 no.10
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    • pp.3344-3354
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    • 1996
  • An experimental and numerical study on the three-dimensional natural convection-radiation conjugate heat transfer in the enclosure with heat generating chip has been performed. A 3-dimensional simulation model is developed by considering heat transfer phenomena by conduction-convection and radiation. Radiative transfer was analyzed with the discrete ordinates method. Experiments are conducted in order to validate the numerical model. Comparisons with the experimental data show that good agreement is obtained when the radiation effect is considered. The effects of the thermal conductivity of the substrate and power level on heat transfer are investigated. It is shown that radiation is the dominant heat transfer mode and the conductivity of the substrate has important effects on the heat transfer in the enclosure.

Effectiveness of the Discrete Elements Method for the Slab-Geometry Neutron Transport Equation (1차원 평판에서 Discrete Elements Method의 정확도에 대한 연구)

  • Na, Byung-Chan;Kim, ong-Kyung
    • Nuclear Engineering and Technology
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    • v.22 no.2
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    • pp.151-158
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    • 1990
  • The new discrete elements method (DEM) is applied to the one-group neutron transport equation in one-dimensional slab geometry. The fixed source and the criticality problems are treated and three spatial differencing schemes (the DD, the SC, -and the LC schemes) are tested to determine the most computationally efficient in the DEM. In all cases, the accuracy of the results obtained from the DEM shows an improvement over that obtained from the standard discrete ordinates calculations. And the LC scheme gives the most accurate results in the DEM.

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SOME OUTSTANDING PROBLEMS IN NEUTRON TRANSPORT COMPUTATION

  • Cho, Nam-Zin;Chang, Jong-Hwa
    • Nuclear Engineering and Technology
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    • v.41 no.4
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    • pp.381-390
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    • 2009
  • This article provides selects of outstanding problems in computational neutron transport, with some suggested approaches thereto, as follows: i) ray effect in discrete ordinates method, ii) diffusion synthetic acceleration in strongly heterogeneous problems, iii) method of characteristics extension to three-dimensional geometry, iv) fission source and $k_{eff}$ convergence in Monte Carlo, v) depletion in Monte Carlo, vi) nuclear data evaluation, and vii) uncertainty estimation, including covariance data.

Study of the Radiation Effect by Equivalence ratio change on the 3-D Turbulent Combustion (당량비 변화에 따른 복사 특성이 3차원 난류 연소에 미치는 영향 연구)

  • Kim, Tea-Kuk;Yoon, Kyung-Beom;Min, Dong-Ho;Chang, Hee-Chul;Kim, Jin-Soo
    • 한국연소학회:학술대회논문집
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    • pp.79-85
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    • 2006
  • Radiative heat transfer is very important in many combustion systems since they are operated in high temperature. Fluid flows in most of the combustion systems are turbulent to promote fast mixing of the hydrocarbon fuel and oxidant. Major combustion products are $CO_2$ and $H_2O$. The turbulent flow is modeled by using the standard ${\kappa}-{\epsilon}$ model and the radiation transfer is modeled by using the discrete ordinates method where the radiative gas properties are calculated by using the weighted sum of gray gases model with a gray gas regrouping(WSGGM-RG). Effect of the radiation on the combustion characteristics in a three-dimensional rectangular enclosure is studied by changing the equivalence ratio. Results show that the radiation plays a significant role on the heat transfer in the combustion systems by resulting in a temperature drop of 16% as compared to that obtained without radiation. The equivalence ratio also affects the combustion by different contribution of the radiative transfer with different gas compositions.

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A Numerical Study of the Heat Transfer Characteristics in a Printed Circuit Board (PCB내의 열전달특성에 관한 수치적 연구)

  • Pak, H.Y.;Park, K.W.;Lee, J.H.
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.7 no.3
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    • pp.461-472
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    • 1995
  • The interaction of laminar mixed convection and surface radiation in a two-dimensional channel with an array of rectangular blocks is analyzed numerically. Three blocks are maintained at high temperature and the other bottom and top horizontal walls are insulated. Discrete ordinate method(DOM) is introduced to analyze the radiative heat transfer. The effects of the variations of Reynolds number and channel specifications on the heat transfer characteristics are investigated. The average Nusselt numbers along the block surfaces are correlated and presented in terms of Reynolds number and dimensionless geometric parameters such as the block spacing, height and channel spacing. For the conditions considered in this study, average Nusselt numbers along the block surfaces are strongly influenced by the channel spacing and Reynolds number but weakly influenced by the block spacing and block height.

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A Numerical Study on the Effect of PCB Structure Variation on the Electronic Equipment Cooling (PCB 구조변화가 전자장비 냉각에 미치는 영향에 관한 수치적 연구)

  • ;;Park, Kyoung-Woo
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.12
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    • pp.3329-3343
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    • 1995
  • The interaction of mixed convection and surface radiation in a printed circuit board(PCB) is investigated numerically. The electronic equipment is modeled by a two-dimensional channel with three hot blocks. In order to calculate the turbulent flow characteristics, the low Reynolds number k-.epsilon. model which is proposed by Launder and Sharma is applied. The S-4 approximation is used to solve the radiative transfer equation. The effects of the Reynolds number and geometric configuration variation of PCB on the flow and heat transfer characteristics are analyzed. As the results of this study, it is found that the thermal boundary layer occured at adiabatic wall in case with thermal radiation included, and the effect of radiation is also found to be insignificant for high Reynolds numbers. It is found, as well, that the heat transfer increases as the Reynolds number and block space increase and the channel height decreases and the heat transfer of vertical channel is greater than that of horizontal channel.

Development of Radiation Shielding Analysis Program Using Discrete Elements Method in X-Y Geometry (2차원 직각좌표계에서 DEM을 이용한 방사선차폐해석 프로그램개발)

  • Park, Ho-Sin;Kim, Jong-Kyung
    • Nuclear Engineering and Technology
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    • v.25 no.1
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    • pp.51-62
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    • 1993
  • A computational program [TDET] of the particle transport equation is developed on radiation shielding problem in two-dimensional cartesian geometry based on the discrete element method. Not like the ordinary discrete ordinates method, the quadrature set of angles is not fixed but steered by the spatially dependent angular fluxes. The angular dependence of the scattering source term in the particle transport equation is described by series expansion in spherical harmonics, and the energy dependence of the particles is considered as well. Three different benchmark tests are made for verification of TDET : For the ray effect analysis on a square absorber with a flat isotropic source, the results of TDET calculation are quite well conformed to those of MORSE-CG calculation while TDET ameliorates the ray effect more effectively than S$_{N}$ calculation. In the analysis of the streaming leakage through a narrow vacuum duct in a shield, TDET shows conspicuous and remarkable results of streaming leakage through the duct as well as MORSE-CG does, and quite better than S$_{N}$ calculation. In a realistic reactor shielding situation which treats in two cases of the isotropic scattering and of linearly anisotropic scattering with two groups of energy, TDET calculations show local ray effect between neighboring meshes compared with S$_{N}$ calculations in which the ray effect extends broadly over several meshes.eshes.

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