A MULTI-SCALE FULL-SPECTRUM k-DISTRIBUTION METHOD FOR RADIATIVE TRANSFER IN NONHOMOGENEOUS GAS-SOOT MIXTURES WITH WALL EMISSION

2008 ◽  
Author(s):  
Gopalendu Pal
Keyword(s):  
Radiative Transfer ◽  
Full Spectrum ◽  
Distribution Method ◽  
Multi Scale

Multi-Scale Full-Spectrum k-Distribution Method for Radiative Transfer in Inhomogeneous Gas Mixtures With Wall Emission

2005 ◽  
Author(s):  
Liangyu Wang ◽  
Michael F. Modest
Keyword(s):  
Heat Transfer ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Inhomogeneous Media ◽  
Full Spectrum ◽  
Distribution Method ◽  
Multi Scale ◽  
Original Distribution ◽  
Distribution Scheme ◽  
Inhomogeneous Gas

The multi-scale full-spectrum k-distribution (MSFSK) method has become a promising method for radiative heat transfer in inhomogeneous media. In this paper an original distribution scheme is proposed to extend the MSFSK’s ability in dealing with boundary wall emission. This scheme pursues the overlap concept of the MSFSK method and requires no changes in the original MSFSK formulation. A boundary emission overlap coefficient is introduced and two approaches of evaluating the coefficient are outlined. The distribution scheme is evaluated and the two approaches are compared by conducting sample calculations for radiative heat transfer in strongly inhomogeneous media using both the MSFSK method and the line-by-line method.

Scalable Multi-Group Full-Spectrum Correlated-K Distributions for Radiative Transfer Calculations

2002 ◽  
Author(s):  
Hongmei Zhang ◽  
Michael F. Modest
Keyword(s):  
Radiative Transfer ◽  
Absorption Coefficient ◽  
Partial Pressure ◽  
Atmospheric Pressure ◽  
Full Spectrum ◽  
Distribution Method ◽  
Numerical Efficiency

A new full-spectrum k-distribution method has been developed, in which spectral locations are sorted into M spectral groups, according to their absorption coefficient dependence on (partial) pressure and temperature. Calculating correlated-k full-spectrum k-distributions for each of the M groups, LBL accuracy can be obtained with M ≤ 32. Database values have been assembled for CO2 mixtures at atmospheric pressure. The method is fully scalable, i.e., spectral groups from the database can be combined to obtain coarser group models (M = 1,2,4,···) for greater numerical efficiency (accompanied by slight loss in accuracy).

Scalable Multi-Group Full-Spectrum Correlated-k Distributions for Radiative Transfer Calculations

2003 ◽  
Vol 125 (3) ◽  
pp. 454-461 ◽  
Author(s):  
Hongmei Zhang ◽  
Michael F. Modest
Keyword(s):  
Radiative Transfer ◽  
Absorption Coefficient ◽  
Partial Pressure ◽  
Atmospheric Pressure ◽  
Full Spectrum ◽  
Distribution Method ◽  
Numerical Efficiency

A new full-spectrum k-distribution method has been developed, in which spectral locations are sorted into M spectral groups, according to their absorption coefficient dependence on (partial) pressure and temperature. Calculating correlated-k full-spectrum k-distributions for each of the M groups, LBL accuracy can be obtained with M⩽32. Database values have been assembled for CO2 mixtures at atmospheric pressure. The method is fully scalable, i.e., spectral groups from the database can be combined to obtain coarser group models M=1,2,4,… for greater numerical efficiency (accompanied by slight loss in accuracy).

Hybrid Full-Spectrum Correlated k-Distribution Method for Radiative Transfer in Nonhomogeneous Gas Mixtures

2008 ◽  
Vol 130 (8) ◽  
Author(s):  
Gopalendu Pal ◽  
Michael F. Modest ◽  
Liangyu Wang
Keyword(s):  
Heat Transfer ◽  
Radiative Transfer ◽  
Computational Cost ◽  
Gas Mixtures ◽  
New Method ◽  
Gas Temperature ◽  
Full Spectrum ◽  
Participating Media ◽  
Distribution Method ◽  
Combustion Gases

The full-spectrum k-distribution (FSK) approach is a promising model for radiative transfer calculations in participating media. FSK achieves line-by-line (LBL) accuracy for homogeneous media at a tiny fraction of LBL’s high computational cost. However, inhomogeneities in gas temperature, total pressure, and component-gas mole fractions change the spectral distribution of the absorption coefficient and can cause inaccuracies in the FSK approach. In this paper, a new hybrid FSK method is proposed that combines the advantages of the multigroup FSK (MGFSK) method for temperature inhomogeneities in a single gas species and the multiscale FSK (MSFSCK) method for concentration inhomogeneities in gas mixtures. In this new hybrid method, the absorption coefficients of each gas species in the mixture are divided into M spectral groups depending on their temperature dependence. Accurate MGFSK databases are constructed for combustion gases, such as CO2 and H2O. This paper includes a detailed mathematical development of the new method, method of database construction, and sample heat transfer calculations for 1D inhomogeneous gas mixtures with step changes in temperature and species mole fractions. Performance and accuracy are compared to LBL and plain FSK calculations. The new method achieves high accuracy in radiative heat transfer calculations in participating media containing extreme inhomogeneities in both temperature and mole fractions using as few as M=2 spectral groups for each gas species, accompanied by several orders of magnitude lower computational expense as compared to LBL solutions.

Narrow-Band Based Multiscale Full-Spectrum k-Distribution Method for Radiative Transfer in Inhomogeneous Gas Mixtures

2004 ◽  
Vol 127 (7) ◽  
pp. 740-748 ◽  
Author(s):  
Liangyu Wang ◽  
Michael F. Modest
Keyword(s):  
Radiative Transfer ◽  
Narrow Band ◽  
Computational Cost ◽  
Inhomogeneous Media ◽  
Full Spectrum ◽  
Participating Media ◽  
Distribution Method ◽  
Practical Applications ◽  
Mixing Problem ◽  
Overlap Coefficient

The full-spectrum k-distribution (FSK) method has become the most promising model for radiative transfer in participating media since its introduction a few years ago. It achieves line-by-line (LBL) accuracy for homogeneous media with only a tiny fraction of LBL’s computational cost. Among the variants of the FSK method for dealing with inhomogeneous media, the multiscale FSK (MSFSK) method not only provides a strategy to treat the inhomogeneity problem by introducing an overlap coefficient, it also accommodates a solution to the so-called mixing problem (mixing of k-distributions for different gas species). The evaluation of MSFSK parameters, however, is tedious and excludes the MSFSK method from practical applications. In this paper a new scheme of evaluating k-distributions and overlap coefficients from a database of narrow-band k-distributions is formulated, treating each gas specie as a single scale. The new scheme makes the MSFSK method efficient and convenient for practical applications, and ready to accommodate nongray absorbing particles (such as soot) in the medium. The method virtually eliminates errors caused by uncorrelatedness due to independently varying species concentrations. It was also found that, in addition, breaking up a gas mixture into gas scales reduces the error caused by temperature inhomogeneities. The mathematical development of the new scheme is described and validated; the concept and the implication of the overlap coefficient are discussed. Sample calculations for inhomogeneous media with step changes in species mole fraction and temperature are performed to demonstrate the accuracy of the new scheme by comparison with LBL calculations.

A Hybrid Multi-Scale Full-Spectrum k-Distribution Method for Radiative Transfer in Inhomogeneous Gas Mixtures

2005 ◽  
Author(s):  
Liangyu Wang ◽  
Michael F. Modest
Keyword(s):  
Radiative Heat ◽  
Single Species ◽  
Gas Mixtures ◽  
Great Accuracy ◽  
New Method ◽  
Full Spectrum ◽  
Participating Media ◽  
Distribution Method ◽  
Multi Scale ◽  
Inhomogeneous Gas

A new full-spectrum k-distribution (FSK) method has been developed, which integrates the advantage of the multi-group FSK method in dealing with temperature inhomogeneities for single-species media with the advantages of the multi-scale FSK method in dealing with partial pressure inhomogeneities for gas mixtures. The new method can achieve great accuracy for radiative heat tranfer calculations in participating media with inhomogeneities in both temperature and gas concentrations. The mathematical development of the new method is described, and several sample calculations are performed to demonstrate the accuracy the new method by comparison with line-by-line calculations.

A New Hybrid Full-Spectrum Correlated k-Distribution Method for Radiative Transfer Calculations in Nonhomogeneous Gas Mixtures

2007 ◽  
Author(s):  
Gopalendu Pal ◽  
Michael F. Modest
Keyword(s):  
Heat Transfer ◽  
Radiative Transfer ◽  
Computational Cost ◽  
Gas Mixtures ◽  
New Method ◽  
Gas Temperature ◽  
Full Spectrum ◽  
Participating Media ◽  
Distribution Method ◽  
Combustion Gases

The full-spectrum k-distribution (FSK) approach is a promising model for radiative transfer calculations in participating media. FSK achieves line-by-line (LBL) accuracy for homogeneous media at a tiny fraction of LBL’s high computational cost. However, inhomogeneities in gas temperature, total pressure and component-gas mole fractions change the spectral distribution of the absorption coefficient and can cause inaccuracies in the FSK method. In this paper, a new hybrid FSK method is proposed that combines the advantages of the multi-group FSK (MGFSK) method for temperature inhomogeneities in a single gas specie and the multi-scale FSK (MSFSK) method for concentration inhomogeneities in gas mixtures. In this new hybrid method the absorption coefficients of each gas specie in the mixture are divided into M spectral groups depending on their temperature dependence. New and accurate MGFSK databases are constructed for combustion gases, such as CO2 and H2O. This paper includes a brief mathematical development of the new method, method of database construction and sample heat transfer calculations for 1-D inhomogeneous gas mixtures with step changes in temperature and species mole-fractions. Performance and accuracy are compared to LBL and traditional FSK calculations. The new method achieves high accuracy in radiative heat transfer calculations in participating media containing extreme inhomogeneities in both temperature and mole fractions using as few as M = 2 spectral groups for each gas specie, accompanied by several orders of magnitude lower computational expense as compared to LBL solutions.

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