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).

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).

Multi-Group Full-Spectrum k-Distribution Database for Water Vapor Mixtures in Radiative Transfer Calculations

2003 ◽  
Author(s):  
Hongmei Zhang ◽  
Michael F. Modest
Keyword(s):  
Water Vapor ◽  
Radiative Transfer ◽  
Absorption Coefficient ◽  
Mixture Model ◽  
Atmospheric Pressure ◽  
Distribution Model ◽  
Full Spectrum ◽  
Temperature And Pressure ◽  
Vapor Mixtures ◽  
Combustion Problem

A thorough investigation of the absorption coefficient dependence on temperature and pressure has been performed for water vapor and a 32-group database has been assembled for H2O mixtures at atmospheric pressure, based on the Multi-Group Full-Spectrum Correlated k-distribution model. The method is fully scalable, i.e., spectral groups from the database can be combined to obtain coarser group models (N = 1, 2, 4, …) for greater numerical efficiency (accompanied by slight loss in accuracy). The databases for CO2 and H2O, together with the random-overlap mixture model have been used to simulate a practical combustion problem.

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 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.

Full-Spectrum k-Distribution Model for Radiation in Gas Based on Multi-Group Methods

2014 ◽  
Vol 1008-1009 ◽  
pp. 839-845
Author(s):  
Yue Zhou ◽  
Qiang Wang ◽  
Hai Yang Hu
Keyword(s):  
Narrow Band ◽  
Wide Band ◽  
Distribution Model ◽  
Full Spectrum ◽  
Distribution Method ◽  
One Dimensional ◽  
Group Methods ◽  
Monotonically Increasing Function ◽  
Homogeneous Media ◽  
Increasing Function

The k-distribution method applied in narrow band and wide band is extended to the full spectrum based on spectroscopic datebase HITEMP, educing the full-spectrum k-distribution model. Absorption coefficents in this model are reordered into a smooth,monotonically increasing function such that the intensity calculations are performed only once for each absorption coefficent value and the resulting computations are immensely more efficent.Accuracy of this model is examined for cases ranging from homogeneous one-dimensional carbon dioxide to inhomogeneous ones with simultaneous variations in temperature. Comparision with line-by-line calculations (LBL) and narrow-band k-distribution (NBK) method as well as wide-band k-distribution (WBK) method shows that the full-spectrum k-distribution model is exact for homogeneous media, although the errors are greater than the other two models. After dividing the absorption coefficients into several groups according to their temperature dependence, the full-spectrum k-distribution model achieves line-by-line accuracy for gases inhomogeneous in temperature, accompanied by lower computational expense as compared to NBK model or WBK model. It is worth noting that a new grouping scheme is provided in this paper.

Sign in / Sign up

Export Citation Format

Share Document