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.

INTRINSIC MAGNETIZATION RELAXATION PROPERTIES OF Y1:2:3

1991 ◽  
Vol 05 (04) ◽  
pp. 277-284 ◽  
Author(s):  
Y.Y. XUE ◽  
Z.J. HUANG ◽  
L. GAO ◽  
P.H. HOR ◽  
R.L. MENG ◽  
...  
Keyword(s):  
High Temperature ◽  
Critical State ◽  
Flux Pinning ◽  
High Temperature Superconductors ◽  
Distribution Model ◽  
Magnetization Relaxation ◽  
Pinning Potential ◽  
Monotonically Increasing Function ◽  
Monotonically Decreasing Function ◽  
Increasing Function

The intrinsic magnetization relaxation rate R(T)≡dM(t, T)/d ln t and the pinning potential U0(T) have been determined for single crystalline and melt-textured YBa2Cu3O7 (Y1:2:3) high temperature superconductors of different sizes in their critical state. In contrast to previous reports, R(T) is a monotonically decreasing function and U0(T), deduced from R(T), a monotonically increasing function of temperature. The unusual temperature dependence of U0 is qualitatively explained in terms of a collective flux pinning. The U0-distribution model previously proposed for HTS’s is not consistent with certain experimental observations.

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.

Prediction of Radiative Transport in Nonhomogeneous Combustion Gas Mixtures With a Wide Band G(K) Model

2013 ◽  
Author(s):  
Liping Liu ◽  
Jing He
Keyword(s):  
Radiative Transfer ◽  
Narrow Band ◽  
Gaussian Quadrature ◽  
Wide Band ◽  
Gas Mixtures ◽  
Source Distribution ◽  
Distribution Model ◽  
Band Model ◽  
Radiative Transport ◽  
Combustion Gas

A wide band cumulative absorption coefficient distribution, g(k), model is adopted to predict radiative transport in combustion gas mixtures. Prior research has demonstrated similar accuracy of the model to the statistical narrow-band model and superiority to the exponential wideband model under isothermal and homogeneous conditions. This study aims to assess its usefulness in nonhomogeneous media. Sample calculations are performed in a 1D planar slab containing H2O/CO2 mixtures. The six-flux discrete ordinate method (S6-DOM) is employed to solve the radiative transfer equation (RTE), followed by an eight-point Gaussian quadrature of moments with zeroth-order fit. Predictions on the radiative source distribution along the slab and the net radiative flux at the walls are compared to the benchmark line-by-line calculation (LBL) and the statistical narrow-band correlated-k distribution model using the 7-point Gauss-Lobatto quadrature scheme (SNBCK-7). The differences between the g(k) model and LBL are below 5% for a large domain of the layer, with a CPU reduction by a factor of over 30 compared to SNBCK-7 and on the order of 104∼105 compared to LBL. The wide band g(k) model shows significant promise as an accurate and efficient tool to predict radiative transfer in nonhomogenerous media for combustion and fire simulations.

On the First-Passage Distribution for the Envelope of a Nonstationary Narrow-Band Stochastic Process

1974 ◽  
Vol 41 (3) ◽  
pp. 793-797 ◽  
Author(s):  
W. C. Lennox ◽  
D. A. Fraser
Keyword(s):  
Stochastic Process ◽  
Hypergeometric Functions ◽  
Narrow Band ◽  
First Passage Time ◽  
Wide Band ◽  
Passage Time ◽  
First Passage ◽  
Eigenvalues And Eigenfunctions ◽  
One Dimensional ◽  
Backward Equation

A narrow-band stochastic process is obtained by exciting a lightly damped linear oscillator by wide-band stationary noise. The equation describing the envelope of the process is replaced, in an asymptotic sense, by a one-dimensional Markov process and the modified Kolmogorov (backward) equation describing the first-passage distribution function is solved exactly using classical methods by reducing the problem to that of finding the related eigenvalues and eigenfunctions; in this case degenerate hypergeometric functions. If the exciting process is white noise, the analysis is exact. The method also yields reasonable approximations for the first-passage time of the actual narrow-band process for either a one-sided or a symmetric two-sided barrier.

The Full-Spectrum Correlated-k Distribution for Thermal Radiation From Molecular Gas-Particulate Mixtures

2001 ◽  
Vol 124 (1) ◽  
pp. 30-38 ◽  
Author(s):  
Michael F. Modest ◽  
Hongmei Zhang
Keyword(s):  
Radiative Transfer ◽  
Solution Method ◽  
Radiative Transfer Equation ◽  
Distribution Model ◽  
Molecular Gas ◽  
Gas Mixture ◽  
Spectral Absorption ◽  
Full Spectrum ◽  
One Dimensional ◽  
Molecular Gases

A new Full-Spectrum Correlated-k Distribution has been developed, which provides an efficient means for accurate radiative transfer calculations in absorbing/emitting molecular gases. The Full-Spectrum Correlated-k Distribution can be used together with any desired solution method to solve the radiative transfer equation for a small number of spectral absorption coefficients, followed by numerical quadrature. It is shown that the Weighted-Sum-of-Gray-Gases model is effectively only a crude implementation of the Full-Spectrum Correlated-k Distribution approach. Within the limits of the Full-Spectrum Correlated-k Distribution model (i.e., an absorption coefficient obeying the so-called “scaling approximation”), the method is exact. This is demonstrated by comparison with line-by-line calculations for a one-dimensional CO2-N2 gas mixture as well as a two-dimensional CO2-H2O-N2 gas mixture with varying temperature and mole fraction fields.

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.

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.

scholarly journals The Full-Spectrum Correlated-K Distribution and Its Relationship to the Weighted-Sum-of-Gray-Gases Method

2000 ◽  
Author(s):  
Michael F. Modest ◽  
Hongmei Zhang
Keyword(s):  
Radiative Transfer ◽  
Solution Method ◽  
Distribution Model ◽  
Weighted Sum ◽  
Full Spectrum ◽  
One Dimensional ◽  
Molecular Gases ◽  
Transfer Equations ◽  
Gray Medium ◽  
Radiative Transfer Equations

Abstract A new Full-Spectrum correlated-k distribution has been developed, which provides an efficient means for accurate radiative transfer calculations in absorbing/emitting molecular gases. The Full-Spectrum correlated-k distribution can be used together with any desired solution method to solve gray-medium radiative transfer equations for a small number of gray absorption coefficients, followed by numerical quadrature. It is shown that the Weighted-Sum-of-Gray-Gases model is effectively only a crude implementation of the Full-Spectrum correlated-k distribution approach. Within the limits of the Full-Spectrum correlated-k distribution model (i.e., an absorption coefficient obeying the so-called “scaling approximation”), the method is exact. This is demonstrated by comparison with line-by-line calculations for a one-dimensional CO2-N2 gas mixture with varying temperature and concentration fields.

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