• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.5
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• pp.543-552
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• 2003

The effects of a directionally emitting and reflecting dielectric surface on the wall heat flux and medium temperature distribution are studied. The system is an infinite square duct enclosing an absorbing and emitting medium. The emissivity and reflectivity of opaque and gray wall vary with direction. Combined effect of conductive and radiative heat transfer is analyzed using finite difference and the direct discrete-ordinates method. The parameters under study are conduction to radiation parameter, optical depth, refractive index ratio. The results with directional and diffuse properties deviate each other when the conduction to radiation parameter is less than around 0.01. The wall heat flux differs fur optical thickness less than around 0.1. However, the medium temperature profiles differ for optical thickness greater than around 1. Deviations from diffuse property calculations are larger for hot wall with directional property than cold wall with directional property. As n increases from 1.5, the trend changes are observed fur refractive index ratio about n=6.10

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.10
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• pp.1451-1458
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• 2001

The effects of a specularly reflecting surface on the wall heat flux and medium temperature distribution are studied. The system is an infinite square duct enclosing an absorbing and emitting medium. The walls are opaque, and black or gray. The walls emit diffusely but reflect diffusely or speculary. Heat is transferred by the combined effect of conduction and radiation. The radiative heat transfer is analyzed using direct discrete-ordinates method. The parameters under study are conduction, to radiation parameter, optical depth, wall emissivity, and reflection characteristics. The specular reflection and diffuse reflection show sizeable differences when the conduction to radiation parameter is less than around 0.01. The differences appear only either on the side wall heat flux or on the medium temperature profiles for the range of this study. The differences on the side wall heat flux are observed for optical thickness less than around 0.1 However the differences on the medium temperate profiles are found for optical thickness greater than around 1. The difference increase with increasing reflectance. The specular reflection increases the well heat flux gradient along the side wall.

• 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.

• Journal of Mechanical Science and Technology
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• v.20 no.2
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• pp.242-250
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• 2006

Detailed structures of the counterflow flames formed for different inlet fluid temperatures and different amount of additives are studied numerically. The detailed chemical reactions are modeled by using the CHEMKIN-II code. The discrete ordinates method and the narrow band based WSGGM with a gray gas regrouping technique (WSGGM-RG) are applied for modeling the radiative transfer through non-homogeneous and non-isothermal combustion gas mixtures generated by the counterflow flames. The results compared with those obtained by using the SNB model show that the WSGGM-RG is very successful in modeling the counterflow flames with non-gray gas mixture. The numerical results also show that the addition of $CO_2\;or\;H_2O$ to the oxidant lowers the peak temperature and the NO concentration in flame. But preheat of fuel or oxidant raises the flame temperature and the NO production rates. $O_2$ enrichment also causes to raise the temperature distribution and the NO production in flame. And it is found that the $O_2$ enrichment and the fuel preheat were the major parameters in affecting the flame width.

• Journal of Energy Engineering
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• v.15 no.4 s.48
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• pp.250-255
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• 2006

In this study, the discrete ordinates method which has been widely used in the solution of neutron transport equation is applied to the solution of the time dependent radiative transfer equation. The self-adjoint form of the second order radiation intensity equation is used to enhance the stability of the solution, and a new multi-step linearization method is developed to avoid the nonlinearity in the material temperature equation. This new solution method is applied to the well known Marshak wave problem, and the numerical result is compared with that of the conventional Monte-Carlo method.

• 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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.9
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• pp.2353-2364
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• 1995

The ignition phenomena of a solid fuel plate of polymethyl-methacrylate(PMMA), which is vertically positioned and exposed to a thermal radiation source, is numerically studied here. A two-dimensional transient model includes such various aspects as thermal decomposition of PMMA, gas phase radiation absorption, gas phase chemical reaction and air entrainment by natural convection. Whereas the previous studies considers the problem approximately in a one-dimensional form by neglecting the natural convection, the present model takes account of the two-dimensional effect of radiation and air entrainment. The inert heating of the solid fuel is also taken into consideration. Radiative heat transfer is incorporated by th Discrete Ordinates Method(DOM) with the absorption coefficient evaluated using gas species concentration. The thermal history of the solid fuel plate shows a good agreement compared with experimental results. Despite of induced natural convective flow that induces heat loss from the fuel surface, the locally absorbed radiant energy, which is converted to the internal energy, is found to play an important role in the onset of gas phase ignition. The ignition is considered to occur when the rate of variation of gas phase reaction rate reaches its maximum value. Once the ignition takes place, the flame propagates downward.

• Proceedings of the Korean Nuclear Society Conference
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• 2004.10a
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• pp.151-152
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• 2004

An acceleration technique combined with the discrete ordinates method which has been widely used in the solution of neutron transport phenomena is applied to the solution of radiative transfer equation. The self-adjoint form of the second order radiation intensity equation is used to enhance the stability of the solution, and a new linearization method is developed to avoid the nonlinearity of the material temperature equation. This new acceleration method is applied to the well known Marshak wave problem, and the numerical result is compared with that of a non-accelerated calculation

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.11
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• pp.2995-3002
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• 1995

The cooling problem of the hot internal pipe flow has been investigated. Simultaneous conduction, convection, and radiation were considered with azimuthally varying convective heat loss at the pipe wall. A complex, nonlinear integro-differential radiative transfer equation was solved by the discrete ordinates method (or called S$_{N}$ method). The energy equation was solved by control volume based finite difference technique. A parametric study was performed by varying the conduction-to-radiation parameter, optical thickness, and scattering albedo. The results have shown that initially the radiatively active medium could be more efficiently cooled down compared with the cases otherwise. But even for the case with dominant radiation, as the medium temperature was lowered, the contribution of conduction became to exceed that of radiation.n.

• 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.