A Narrow Band-Based Multiscale Multigroup Full-Spectrum k-Distribution Method for Radiative Transfer in Nonhomogeneous Gas-Soot Mixtures

2009 ◽  
Vol 132 (2) ◽  
Author(s):  
Gopalendu Pal ◽  
Michael F. Modest
Keyword(s):  
Heat Transfer ◽  
Narrow Band ◽  
Computational Cost ◽  
Single Species ◽  
Full Spectrum ◽  
Participating Media ◽  
Distribution Method ◽  
Molecular Gases ◽  
Combustion Gases ◽  
Inhomogeneous Gas

The full-spectrum k-distribution (FSK) approach has become a promising method for radiative heat transfer calculations in strongly nongray participating media, due to its ability to achieve high accuracy at a tiny fraction of the line-by-line (LBL) computational cost. However, inhomogeneities in temperature, total pressure, and component mole fractions severely challenge the accuracy of the FSK approach. The objective of this paper is to develop a narrow band-based hybrid FSK model that is accurate for radiation calculations in combustion systems containing both molecular gases and nongray particles such as soot with strong temperature and mole fraction inhomogeneities. This method combines the advantages of the multigroup FSK method for temperature inhomogeneities in a single species, and the modified multiscale FSK method for concentration inhomogeneities in gas-soot mixtures. In this new method, each species is considered as one scale; the absorption coefficients within each narrow band of every gas scale are divided into M exclusive spectral groups, depending on their temperature dependence. Accurate and compact narrow band multigroup databases are constructed for combustion gases such as CO2 and H2O. Sample calculations are performed for a 1D medium and also for a 2D axisymmetric combustion flame. The narrow band-based hybrid method is observed to accurately predict heat transfer from extremely inhomogeneous gas-soot mixtures with/without wall emission, yielding close-to-LBL 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.

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.

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.

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.

Treatment of Wall Emission in the Narrow-Band Based Multiscale Full-Spectrum k-Distribution Method

2006 ◽  
Vol 129 (6) ◽  
pp. 743-748 ◽  
Author(s):  
Liangyu Wang ◽  
Michael F. Modest
Keyword(s):  
Heat Transfer ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Narrow Band ◽  
Inhomogeneous Media ◽  
Spectral Absorption ◽  
Full Spectrum ◽  
Distribution Method ◽  
Boundary Wall ◽  
Distribution Scheme

The multiscale full-spectrum k-distribution (MSFSK) method has become a promising method for radiative heat transfer in inhomogeneous media. In this paper a new scheme is proposed to extend the MSFSK’s ability in dealing with boundary wall emission by distributing this emission across the different gas scales. This scheme pursues the overlap concept of the MSFSK method and requires no changes in the original MSFSK formulation. A boundary emission distribution function is introduced and two approaches of evaluating the function are outlined. The first approach involves line-by-line integration of the spectral absorption coefficients and is, therefore, impractical. The second approach employs a narrow-band k-distribution database to calculate all parameters as in the original narrow-banded based MSFSK formulation and is, therefore, efficient. This distribution scheme of wall emission 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.

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.

Reverse Monte-Carlo Ray-Tracing Method Combined With Full-Spectrum K-Distribution Method for Radiative Heat Transfer

2008 ◽  
Author(s):  
Xiaojing Sun ◽  
Philip J. Smith
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Ray Tracing ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Radiative Transfer Equation ◽  
Computational Effort ◽  
Simulation Methods ◽  
Full Spectrum ◽  
Distribution Method

Accurate prediction of radiative heat transfer plays a key role in many high temperature applications, such as combustion devices and fires. Among various simulation methods, the Monte-Carlo Ray-Tracing (MCRT) has the advantage of solving the radiative transfer equation (RTE) for real gas mixtures with almost no approximations; however, it has disadvantage of requiring a large computational effort. The MCRT method can be carried out with either the Forward MCRT or the Reverse MCRT, depending on the direction of ray tracing. The RMCRT method has advantages over the FMCRT method in that it uses less memory, and in a domain decomposition parallelization strategy, it can explicitly obtain solutions for the domain of interest without the need for the solution on the entire domain.

Sign in / Sign up

Export Citation Format

Share Document