• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.341-348
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• 1991

An efficient tool to deal with a multi-dimensional radiative heat transfer is in strong demand to analyze various thermal problems combined either with other modes of heat transfer or with combustion phenomena. The current study examined the discrete ordinates method (DOM) for a coupled radiative and conductive heat transfer in rectangular enclosures in which either nonscattering or scattering medium is present. The results were compared with the other benchmarked approximate solution. The efficiency and accuracy of the DOM were thus validated.

• 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.

• Journal of the Korean Society of Propulsion Engineers
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• v.9 no.3
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• pp.85-91
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• 2005

Radiative heating of a liquid rocket base plane due to plume emission is numerically investigated. Calculation of flow and temperature fields around rocket nozzle precedes and thereby realistic plume shape and temperature distribution inside the plume are obtained. Based on the calculated temperature field, radiative transfer equation is solved by discrete ordinate method. With the sample rocket plume, the averaged radiative heat flux reaching the base plane is calculated about 5 kw/m$^{2}$ at the flight altitude of 10.9 km. This value is small compared with radiative heat flux caused by constant-temperature (1500 K) plume emission, but it is not negligibly small. At higher. altitude (29.8km), view factor between the base plane and the exhaust plume is increased due to the increased expansion angle of the plume. Nevertheless, the radiative heating disappears since the base plane is heated to high temperature (above 1000 K due to convective heat transfer.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.32 no.2
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• pp.149-157
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• 2008

During CVD process of semiconductor wafer fabrication, maintaining the uniformity of temperature distribution at wafer top surface is one of the key factors affecting the quality of final products. Effect of contact conductance between wafer and hot plate on predicted temperature of wafer was investigated. The validity of opaque wafer assumption was also examined by comparing the predicted results with Discrete Ordinate solutions accounting for semitransparent radiative characteristics of silicon. As the contact conductance increases predicted wafer temperature increases and the differences between maximum and minimum temperatures within wafer and between wafer and hot plate top surface temperatures decrease. The opaque assumption always overpredicted the wafer temperature compared to semitransparent calculation. The influences of surrounding reactor inner wall temperature and hot plate configuration are then discussed.

• Journal of computational fluids engineering
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• v.9 no.2
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• pp.43-51
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• 2004

Interaction between fluid flow and thermal radiation has received considerable attention due to its numerous applications in engineering field. In this case the thermofluid properties of radiating fluid vary with the variation of temperature field caused by absorption and emission of radiant heat. To analyze the radiation heat transfer in radiating fluid, the simultaneous solution of the radiative transfer equation (RTE) and the fluid dynamics equations is required. This means that the numerical procedure used for the RTE must be computationally efficient to permit its inclusion in the other submodels, and must be compatible with the other transport equations. The finite volume method (FVM) and the discrete ordinates method (DOM) are usually employed to simulate radiation problems in generalized coordinates. These two representative methods are examined and compared, especially in view of the numerical integration of the radiation intensity over solid angle. The FVM shows better accuracy than the DOM owing to less constraints of the selection of control angle.

• 한국전산유체공학회:학술대회논문집
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• 2004.03a
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• pp.62-70
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• 2004

Interaction between fluid flow and thermal radiation has received considerable attention due to its numerous applications in engineering field. In this case the thermofluid properties of radiating fluid vary with the variation of temperature field caused by absorption and emission of radiant heat. To analyze the radiation heat transfer in radiating fluid, the simultaneous solution of the radiative transfer equation (RTE) and the fluid dynamics equations is required. This means that the numerical procedure used for the RTE must be computationally efficient to permit its inclusion in the other submodels, and must be compatible with the other transport equations. The finite volume method (FVM) and the discrete ordinates method (DOM) are usually employed to simulate radiation problems in generalized coordinates. These two representative methods are examined and compared, especially in view of the numerical integration of the radiation intensity over solid angle. The FVM shows better accuracy than the DOM owing to less constraints of the selection of control angle.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.10
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• pp.2582-2589
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• 1993

Transient heat transfer characteristics of cooling of a spherical body were investigated in the radiatively active spherical medium. Initially the spherical body and the medium were maintained at their constant temperatures. Then heat transfer begins from spherical body t medium. The heat transfer mode inside the spherical body is just conduction. But heat is transferred by both conduction and radiation inside the medium. All thermodynamic properties were held constant in time. Spherical symmetry is assumed. DOM was adopted to solve RTE. The effect of characteries-tic optical thickness, conduction to radiation parameters, and solid surface emissivity has been studied.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.5
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• pp.620-627
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• 2003

Radiative heat transfer in an axisymmetric enclosure with absorbing, emitting, and scattering medium is studied here by using the different methods such as MDOM, FVM, and FVM2 with emphasis on the treatment of angular derivative term, which appears in a curvilinear coordinates due to angular redistribution. After final discretization equation for FVM2 is introduced by using the step scheme and directional weights, present approach is validated by applying it to three different benchmarking problems with absorbing, emitting, and scattering medium.

• 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.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.1341-1346
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• 2004

Detailed flame structures of the opposed flames formed for different oxidant compositions are studied numerically. The detailed chemical reactions are modeled by using the CHEMKIN code. Only the $CO_{2}$ and $H_{2}O$ are assumed to participate by absorbing the radiative energy while all other gases are assumed to be transparent. The discrete ordinates method and a narrow band based WSGGM with a gray gas regrouping technique are applied for modeling the radiative transfer through non-homogeneous and non-isothermal combustion gas mixtures generated by the opposed flow flames. The results show that the different radiation model can cause different results for flame structures and the WSGGM with gray gas regrouping is successful in modeling the opposed flames with non-gray gas mixture. The results also show that a reasonable information on the flame structure can be obtained from the modeling by considering different chemical compositions of the oxidant.