• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.5
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• pp.628-636
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• 1999

This work describes the low-resolution spectral modeling of the water vapor, carbon dioxide and their mixtures by applying the weighted-sum-of-gray-gas-gases model (WSGGM) to each narrow band. Proper modeling scheme of gray gas absorption coefficients vs temperature relation is suggested. Comparison between the modeled emissivity calculated from this relation and the 'true' emissivity obtained from the high temperature statistical narrow band parameters is made for a few typical narrow bands. Low resolution spectral intensities from one-dimensional layers are also obtained and examined for uniform, parabolic and boundary layer type temperature profiles using the obtained WSGGM's with several gray gases. The results are compared with the narrow band spectral intensities obtained by a narrow band model-based code with Curtis-Godson approximation. Good agreement is found between them. Data bases including optimized modeling parameters and total and low-resolution spectral weighting factors are developed for water vapor, carbon dioxide and their mixtures. This model and obtained data bases, available from the authors' Internet site, can be appropriately applied to any radiative transfer equation solver.

• Journal of Mechanical Science and Technology
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• v.16 no.12
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• pp.1725-1732
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• 2002

Combined convection and radiation heat transfer in a circular tube with circumferential fins and circular disks is investigated for various operating conditions. Using a finite volume technique for steady laminar flow, the governing equations are solved in order to study the flow and temperature fields. The P- 1 approximation and the weighted sum of gray gases model (WSGGM) are used for solving the radiation transport equation. The results show that the total Nusselt number of combined convection and radiation is higher than that of pure convection. If the temperatures of the combustion gas and the wall in a tube are high, radiation becomes dominant. Therefore, it is necessary to evaluate the effect of radiation on the total heat transfer.

• Journal of the Korean Society of Combustion
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• v.10 no.2
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• pp.9-17
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• 2005

WSGGM with gray gas regrouping is successfully applied to study the flame structure of opposed flow flames including effect of radiative transfer. The statistical narrow band model is used to obtain the benchmark solutions. Results obtained by using the optically thin model are shown to overestimate the emission and to predict the flame structures inadequately especially for optically thick and low stretch rate flames. Computed results by using the WSGGM with 10 gray gases and SNB model show reasonable agreements with each other, and the required calculation time for the WSGGM is acceptable for engineering applications.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.2 s.245
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• pp.101-109
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• 2006

The narrow band-averaged transmissivity of $CO_2-H_2O$ mixtures is expressed by multiplying the transmissivities of $CO_2\;and\;H_2O$. Applying the multiplication property of narrow band transmissivities for gas mixtures of $CO_2-H_2O$ of the narrow band based WSGGM (weighted sum of gray gases model), the number of gray gases, required for accurate representation of the absorption characteristics by using the narrow band based WSGGM, is significantly increased. To reduce the computational loads by reducing the number of gray gases, we propose a gray gas regrouping process where the gray gases used for .the WSGGM are regrouped into a specified number of groups according to the magnitudes of absorption coefficients. To evaluate the proposed WSGGM for gas mixtures, the radiative transfer problems through 3-dimensional gas media are considered. The radiative source terms and the radiative heat fluxes obtained by using the proposed method are fairly well compared to previous results obtained by using the SNB model and other models. The regrouping technique results in an excellent computational efficiency with minor loss of accuracy.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1652-1660
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• 1990

Combined radiative-convective heat transfer in a hot gas tube flow has been investigated numerically and experimentally. In the numerical analysis, a standard k-.epsilon. model is used for the evaluation of turbulent shear stresses and spherical harmonics method with the Weighted Sum of Gray Gases Model for the solution of radiative transfer equation. In the experimental study measured are the velocity and temperature of the hot gas flow generated by the propane gas combustion, and tude wall heat flux distribution. Numerical results are compared with experimental ones and it is confirmed that P-3 provides quite reliable results in the analysis of the combined radiation-convection system.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.10
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• pp.3371-3380
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• 1996

Low resolution spectral modeling of water vapor is carried out by applying the weighted-sum-of-gray-gases model (WSGGM) to a narrow band. For a given narrow band, focus is placed on proper modeling of gray gas absorption coefficients vs. temeprature relation used for any solution methods for the Radiative Transfer Equation(RTE). Comparison between the modeled emissivity and the "true" emissivity obtained from a high temperatue statistical narrow band parameters is made ofr the total spectrum as well as for a few typical narrow bands. Application of the model to nonuniform gas layers is also made. Low resolution spectral intensities at the boundary are obtained for uniform, parabolic and boundary layer type temeprature profiles using the obtained for uniform, parabolic and boundary layer type temperature profiles using the obtained WSGGM's with 9 gray gases. The results are compared with the narrow band spectral intensities as obtained by a narrow band model-based code with the Curtis-Godson approximation. Good agreement is found between them. Local heat source strength and total wall heat flux are also compared for the cases of Kim et al, which again gives promising agreement.

• 한국연소학회:학술대회논문집
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• 1999.10a
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• pp.155-163
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• 1999

A numerical study for simulating a swirling pulverized coal combustion in axisymmetric geometry is done here by applying the weighted sum of gray gases model (WSGGM) approach with the discrete ordinate method (DOM) to model the radiative heat transfer equation. In the radiative transfer equation, the same polynomial equation and coefficients for weighting factors as those for gas are adopted for the coal/char particles as a function of partial pressure and particle temperature. The Eulerian balance equations for mass, momentum, energy, and species mass fractions are adopted with the standard ${\kappa}-{\varepsilon}$ turbulence model, whereas the Lagrangian approach is used for the particulate phase for soot. The eddydissipation model is employed for the reaction rate for gaseous mixture, and the single-step first-order reaction model for the devolatilization process for coal. By comparing the numerical results with experimental ones, the models used here are confirmed and found to be one of good alternatives for simulating the combustion as well as radiative characteristics.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.10
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• pp.1363-1370
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• 1997

Single liquid droplet combustion processes including heating, evaporation, droplet burning and flame radiation were theoretically investigated by adopting nongray gas radiation model for the radiative transfer equation (RTE). n-Heptane was chosen as a fuel and the numerical results were compared with the experimental data available in the literature. The discrete ordinate method (DOM) was employed to solve the radiative transfer equation and the weighted sum of gray gases model (WSGGM) was applied to account for nongray effect by CO$_{2}$, and H$_{2}$0. Therefore, detailed effects by nongray gas and its comparison with the gray gas model could be figured out in the results. It is found that the radiative heat flux is higher when the nongray model is used, thereby reducing the maximum gas temperature and the flame thickness, but the total burning time increases due to the deceased conductive heat flux in nongray model. Consequently, a better agreement with experimental data could be obtained by using nongray model.

• 한국연소학회:학술대회논문집
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• 2006.10a
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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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.10
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• pp.1955-1962
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• 1992

The purpose of this study is to identify the radiative heat transfer augmentation by a coaxial cylinder introduced in the infinite cylindrical pipe enclosing a participating gas. The gas is either a mixture of water vapor and carbon dioxide or gray. The gas is assumed to be homogeneous at a constant temperature, and has a refractive index of unity. All of the surfaces are opaque and gray, diffusely emitting and reflecting at a constant temperature, The effect of system diameter, diameter ratio, wall emittances, gas and surface temperatures, mixture component on heat transfer augmentation are studied by using the zone method with participating gas radiative properties evaluated from the weighted sum of gray gases model. From the radiative equilibrium condition, the installed wall temperature is formulated and calculated by the iteration method. If the medium is a gray gas, the augmentation observed are negligible. For the range of values studied for a real gas, if the system diameter is larger than about 0.1m the augmentation parameter increases up to about 1.2 as the system diameter increases. The augmentation parameter have a maximum value at a certain diameter ratio. The augmentation parameters decreases as the emittance of the installed wall decreases. If the gas temperature is higher than about 1273 k, the augmentation parameter decreases as the gas temperature increases.