Development of the WSGGM Using a Gray Gas Regrouping Technique for the Radiative Solution within a 3-D Enclosure Filled with Nonuniform Gas Mixtures

Abstract

A narrow band based WSGGM with a gray gas regrouping technique is proposed for nonhomogeneous and nonisothermal combustion gas mixtures. Applying the multiplication property of narrow band-average transmissivities for gas mixtures of CO 2 -H 2 O, the number of gray gases, required for accurate representation of the absorption characteristics by using the narrow band based WSGGM, is increased drastically. 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 CO 2 -H 2 O gas mixtures in 1-and 3-dimensional enclosures are solved numerically by using the discrete ordinates method. The radiative heat source terms and the radiative heat fluxes obtained by using the proposed method are fairly well compared to those obtained by using the more accurate statistical narrow band model with an excellent computational efficiency.

Numerical solution of radiative transfer within a cubic enclosure filled with nongray gases using the WSGGM

“…All radiative intensities for i-th gray gas in the m Ω direction can be obtained by using Eqs. (6,7), and the radiative inten- …”

“…The equation for the absorption coefficient suggested by Kim and Song [4,5] and Park and Kim [7] expressed the local gray gas absorption coefficient and total weighting factor of CO 2 -H 2 O mixtures as:…”

“…The detailed process of acquiring the parameters of WSGGM is explained in Kim and Song's paper [4]. To improve the computational efficiency of WSGGM for gas mixtures while maintaining accuracy, Park and Kim [7] suggested WSGGM-RG wherein the original number of gray gases was regrouped into a designated number (N G ). As the new weighting factor, W i is obtained by simply summing up the original weighting factors of gray gases in the i-th group as:…”

“…WSGGM was improved in these narrow bands to make it applicable to gas mixtures containing arbitrary substances by Park and Kim [6]. Gray gas regrouping [7], which was also attempted to shorten the calculation time, produced good results. Although several solution methods are suggested for threedimensional enclosures, the applicability and accuracy of these methods have yet to be tested fully, especially for nongray gases.…”

Study on the radiative transfer through non-gray gas mixtures within an irregular 3-D enclosure by using the modified weighted sum of gray gas method

“…Kim and Song [4,5] developed a narrow band based WSGGM to solve radiative transfer through nongray gas media with uniform gas concentrations. Park and Kim [6,7] modified the narrow band based WSGGM for arbitrary mixtures of CO 2 and H 2 O gases and improved the computational efficiency of the WSGGM for gas mixtures by using the gray gas regrouping process which was performed by comparing the magnitudes of the gray gas absorption coefficients.…”