Denison, MK
1996
The Spectral Line Weighted-Sum-of-Gray-Gases Model - A Review
Denison, M.K. and Webb, B.W.
Proceedings of the First International Symposium of Radiative Heat Transfer, 1:193-208, 1996. (Presented at the First International Symposium of Radiative Heat Transfer, Kusadasi, Turkey, August, 1995.) Funded in part by ACERC.
This paper reviews the development and validation of the Spectral-Line Weighted-Sum-of-Gray-Gases (SLW) model for the prediction of radiation transfer in high temperature gases. The parameters in the model are obtained directly from the line-by-line spectra of H2O and CO2. The Model allows the absorption coefficient to be the basic radiative property rather than a transmissivity or band of absorptance etc., and can therefore be used with any arbitrary solution method for the Radiative Transfer Equation (RTE). The model is base on a novel absorption-line blackbody distribution function. Predictions from the model compare well with the spectral line-by-line benchmarks.
The Absorption-Line Blackbody Distribution
Denison, M.K. and Webb, B.W.
Proceedings of the First International Symposium of Radiative Heat Transfer, 1:228-238, 1996. (Presented at the First International Symposium of Radiative Heat Transfer, Kusadasi, Turkey, August, 1995.) Funded in part by ACERC.
The previously published mathematical correlations of the absorption-line blackbody distribution function, central to the spectral-line based weighted-sum-of-gray-gases model (SLW), have been extended to elevate pressures by introducing a dependence on an effective broadening pressure. Comparison between experimentally determined total emissivities and those calculated with the model show good agreement. Agreement at elevated pressure between line-by-line benchmarks and model predictions is also demonstrated.
1994
K-Distributions and Weighted-Sum-of-Gray-Gases - A Hybrid Model
Denison, M.K. and Webb, B.W.
Heat Transfer-1994, 2:19-24, 1994. (Also presented at the 10th International Heat Transfer Conference, Brighton, England, August, 1994.) Funded by ACERC.
The weighted-sum-of-gray-gases (WSGG) model is shown to be related to k-distributions resulting in a hybrid approach that draw on the strengths of each model. The WSGG weights are related to the cumulative k-distributions through an integration of Planck's function over wave number weighted by the cumulative d-distributions. This allows a single quadrature over the absorption cross-section (k-space) of each arbitrarily large band to account for non-gray boundaries or particulates. Predictions from the hybrid model compare well with line-by-line benchmarks.
The Spectral Line-Based Weighted-Sum-of-Gray-Gases Model in Non-Homogeneous Media
Denison, M.K. and Webb, B.W.
ASME Journal of Heat Transfer, 1994 (in press). Funded by ACERC.
An approach is developed to extend the previously developed spectral-line weighted-sum of gray gases (SLW) model to non-isothermal, non-homogeneous media. The distinguishing feature of the SLW gas property model is that it has been developed for use in arbitrary solution methods of the radiaive transfer equation (RTE). A spatial dependence results in significant improvement over the use of spatially uniform gray gas absorption cross-sections in comparisons with line-by-line benchmarks.
Development and Application of an Absorption-Line Blackbody Distribution for CO2
Denison, M.K. and Webb, B.W.
International Journal of Heat Mass Transfer, 1994 (in press). Funded by ACERC.
An absorption-line blackbody distribution function for CO2 is presented which permits efficient and accurate calculation of total heat transfer rates. The model allows the local absorption coefficient to be the basic radiative property permitting its use in arbitrary solution methods of the radiative transfer equation (RE). A mathematical correlation is presented to approximate the function for use in computer codes. Total emissivities calculated with the correlation agree well with Hottel data. Excellent agreement is also demonstrated with line-by-line solutions of the RTE.
The Spectral-Line Weighted-Sum-of-Gray-Gases Model for H2O/CO2 Mixtures
Denison, M.K. and Webb, B.W.
ASME Journal of Heat Transfer, 1994 (in press). Funded by ACERC.
The weighted-sum-of-gray-gases model, first introduced by Hottel and Sarofim (1967) for expressing total gas emissivities and in e context of the zone method, has recently been extended to the general form of the radiative transfer equation (RTE). The fundamental radiative property of the model is the locally defined absorption coefficient that permits the use of arbitrary solution methods of the RTE. Denison and Webb developed a spectral line-based weighted-sum-of-gray-gases (SLW) model by constructing a histogram representation of the high-resolution spectra of H2O. Subsequently, a novel absorption-line blackbody distribution function was developed which easily allows the blackbody weights of aj of any desired number of gray gases to be determined by simple differencing rather than accessing detailed spectral line information. The distribution function also provides the means of incorporating a spatial dependence of the gray gas absorption cross-sections on temperature, pressure and species mole in non-isothermal, non-homogeneous problems.
The development of the SLW model in the above references has only considered individual species (H2O and CO2) independent of one another. In most practical gas flames a mixture of gases must be considered. Previous treatment of gas mixtures with the weighted-sum-of-gray-gases models has involved either determining a single set of absorption coefficients and blackbody weights from emissivities of the mixture or determining the weights of the mixture as a product of the weights of the individual species under the assumption of random positions of absorption-lines. In this paper the SLW model is formulated for H2O/CO2 mixtures.
Radiation Heat Transfer in a Laboratory-Scale, Pulverized Coal-Fired Reactor
Butler, B.W.; Denison, M.K. and Webb, B.W.
Experimental Thermal and Fluid Science, 9:69-79, 1994. Funded by ACERC and US Department of Energy.
This article reports local gas and particle temperature and radiant and total heat flux measurements made in a 0.8 m diameter cylindrical down-fired laboratory-scale reactor fired at approximately 0.1 MWt with a high-volatile bituminous coal pulverized to a mass mean diameter of 55µm. Spatially resolved gas temperatures were measured using a triple-shielded suction pyrometer and particle cloud temperatures with a specially designed two-color pyrometer. Hemispherical wall radiant heat fluxes were measured using an ellipsoidal radiometer and total (convective plus radiative) heat fluxes with a plug-type heat flux meter. The particle and gas temperature profiles exhibit a strong spatial dependence on reactor fluid dynamics. Additionally, the difference between the gas and particle temperatures varies significantly with location relative to the burner inlet streams and recirculation zones. Maximum radiant fluxes of 110 kW/m² were observed, with differences between radiative and total heat flux being less than 10% at all axial locations. Maximum heat fluxes occur downstream from the location of the maximum gas and particle temperatures and exhibit a generally decreasing trend as distance from the flame increases. Predictions of the radiation heat transfer in the reactor were carried out using the discrete ordinates method. Both spectral and gray radiative transfer calculations were performed. Predicted radiant fluxes agree well with the experimental data. The sensitivity of the model predictions to the uncertainties in the input data is explored.
Spectral-Line Based WSGG Model for Arbitrary RTE Solvers
Denison, M.K.
Spectral-Line Based WSGG Model for Arbitrary RTE Solvers, Ph.D./BYU, August 1994. Advisor: Webb
1993
An Absorption-Line Blackbody Distribution Function for Efficient Calculation of Total Gas Radiative Transfer
Denison, M.K. and Webb, B.W.
J. Quant. Spectrosc. Radiat. Transfer, 50 (5) 499-510, 1993. Funded by ACERC.
An absorption-line blackbody distribution function for H2O that provides an efficient means for total radiative transfer calculations is presented. The function eliminates the need to specify a path-length required by current narrow and wide bank models since the basic radiative property is the locally defined absorption coefficient. This allows the model to be used with arbitrary solution methods of the radiative transfer equation that requires the absorption coefficient as input. A simple mathematical correlation is presented for use in computer algorithms. A few sample calculations of total emissivity as well as numerical solutions to the radiative transfer equation with the use of the distribution function are performed. The model shows good agreement with Hottel's total emissivity data. There is also very good agreement between the model and computationally intensive line-by-line calculations in isothermal media of uniform composition. The function may also be used for approximate calculations in non-uniform media.
Radiation Heat Transfer in a Laboratory-Scale, Pulverized Coal-Fired Reactor: Experiment and Analysis
Butler, B.W., Denison, M.K. and Webb, B.W.
Experimental Thermal and Fluid Science, 1993 (in press). (Also presented at the Experimental Heat Transfer, Fluid Mechanics and Thermodynamics Conference, Honolulu, HI, 1993.) Funded by US Department of Energy and ACERC.
This paper reports local gas and particle temperature and radiant and total heat flux measurements made in a 0.8 m diameter cylindrical down-fired laboratory-scale reactor fired at approximately 0.1 MWt with a high-volatile bituminous coal pulverized to a mass mean diameter of 55µm. Spatially resolved gas temperatures were measured using a triple-shielded suction pyrometer and particle cloud temperatures with a specially designed two-color pyrometer. Hemispherical wall radiant heat fluxes were measured using an ellipsoidal radiometer and total (convective plus radiative) heat fluxes with a plug-type heat flux meter. The particle and gas temperature profiles exhibit a strong spatial dependence on reactor fluid dynamics. Additionally, the difference between the gas and particle temperatures varies significantly with location relative to the burner inlet streams and recirculation zones. Maximum radiant fluxes of 110 kW/m² were observed, with differences between radiative and total heat flux being less than 10% at all axial locations. Maximum heat fluxes occur downstream from the location of the maximum gas and particle temperatures and exhibit a generally decreasing trend as distance from the flame increases. Predictions of the radiation heat transfer in the reactor were carried out using the discrete ordinates method. Both spectral and gray radiative transfer calculations were performed. Predicted radiant fluxes agree well with the experimental data. The sensitivity of the model predictions to the uncertainties in the input data is explored.
A Spectral Line-Based Weighted-Sum-of-Gray-Gases Model for Arbitrary RTE Solvers
Denison, M.K. and Webb, B.W.
ASME Heat Transfer, 115, 1004-1012, 1993. (Also presented at the William Maxwell Reed Seminar, Department of Mechanical Engineering Conference, Lexington, KY, April 1993. Funded by ACERC.
This paper presents an approach for generating weighted-sum-of-gray gases (WSGG) models directly from the line-by-line spectra of H2O. Emphasis is placed on obtaining detailed spectral division among the gray gases. Thus, for a given model spectrum, the gray gas weights are determined as blackbody fractional functions for specific subline spectral regions at all temperatures. The model allows the absorption coefficient to be the basic radiative property rather than a transmissivity or band absorptance, etc., and can be used with any arbitrary solution method for the Radiative Transfer Equation (RTE). A single absorption cross section spectrum is assumed over the entire spatial domain in order to fix the subline spectral regions associated with a single spectral calculation. The error associated with this assumption is evaluated by comparison with line-by-line benchmarks for problems of nonisothermal and nonhomogeneous media.
A Hybrid Spectral-Line Based Weighted-Sum-of-Gray-Gases Model
Denison, M.K. and Webb, B.W.
Proceedings from the National Science Foundation Joint US-Russian Workshop on Radiative Heat Transfer in Highly Coupled Physical Systems, Austin, TX, October, 1993. Funded by ACERC.
This paper presents a hybrid spectral-line-based weighted-sum-of-gray-gases (SLWSGG) model obtained directly from the line-by-line spectra of H2O and CO2. The model allows the absorption coefficient to be the basic radiative property rather than a transmissivitiy or band absorptance etc., and can therefore be used with any arbitrary solution method for the Radiative Transfer Equation (RTE). The model is based on a novel absorption-line blackbody distribution function. Predictions from the hybrid model compare well with line-by-line benchmarks.
Denison, MK
1996
The Spectral Line Weighted-Sum-of-Gray-Gases Model - A Review
Denison, M.K. and Webb, B.W.
Proceedings of the First International Symposium of Radiative Heat Transfer, 1:193-208, 1996. (Presented at the First International Symposium of Radiative Heat Transfer, Kusadasi, Turkey, August, 1995.) Funded in part by ACERC.
This paper reviews the development and validation of the Spectral-Line Weighted-Sum-of-Gray-Gases (SLW) model for the prediction of radiation transfer in high temperature gases. The parameters in the model are obtained directly from the line-by-line spectra of H2O and CO2. The Model allows the absorption coefficient to be the basic radiative property rather than a transmissivity or band of absorptance etc., and can therefore be used with any arbitrary solution method for the Radiative Transfer Equation (RTE). The model is base on a novel absorption-line blackbody distribution function. Predictions from the model compare well with the spectral line-by-line benchmarks.
The Absorption-Line Blackbody Distribution
Denison, M.K. and Webb, B.W.
Proceedings of the First International Symposium of Radiative Heat Transfer, 1:228-238, 1996. (Presented at the First International Symposium of Radiative Heat Transfer, Kusadasi, Turkey, August, 1995.) Funded in part by ACERC.
The previously published mathematical correlations of the absorption-line blackbody distribution function, central to the spectral-line based weighted-sum-of-gray-gases model (SLW), have been extended to elevate pressures by introducing a dependence on an effective broadening pressure. Comparison between experimentally determined total emissivities and those calculated with the model show good agreement. Agreement at elevated pressure between line-by-line benchmarks and model predictions is also demonstrated.
1994
K-Distributions and Weighted-Sum-of-Gray-Gases - A Hybrid Model
Denison, M.K. and Webb, B.W.
Heat Transfer-1994, 2:19-24, 1994. (Also presented at the 10th International Heat Transfer Conference, Brighton, England, August, 1994.) Funded by ACERC.
The weighted-sum-of-gray-gases (WSGG) model is shown to be related to k-distributions resulting in a hybrid approach that draw on the strengths of each model. The WSGG weights are related to the cumulative k-distributions through an integration of Planck's function over wave number weighted by the cumulative d-distributions. This allows a single quadrature over the absorption cross-section (k-space) of each arbitrarily large band to account for non-gray boundaries or particulates. Predictions from the hybrid model compare well with line-by-line benchmarks.
The Spectral Line-Based Weighted-Sum-of-Gray-Gases Model in Non-Homogeneous Media
Denison, M.K. and Webb, B.W.
ASME Journal of Heat Transfer, 1994 (in press). Funded by ACERC.
An approach is developed to extend the previously developed spectral-line weighted-sum of gray gases (SLW) model to non-isothermal, non-homogeneous media. The distinguishing feature of the SLW gas property model is that it has been developed for use in arbitrary solution methods of the radiaive transfer equation (RTE). A spatial dependence results in significant improvement over the use of spatially uniform gray gas absorption cross-sections in comparisons with line-by-line benchmarks.
Development and Application of an Absorption-Line Blackbody Distribution for CO2
Denison, M.K. and Webb, B.W.
International Journal of Heat Mass Transfer, 1994 (in press). Funded by ACERC.
An absorption-line blackbody distribution function for CO2 is presented which permits efficient and accurate calculation of total heat transfer rates. The model allows the local absorption coefficient to be the basic radiative property permitting its use in arbitrary solution methods of the radiative transfer equation (RE). A mathematical correlation is presented to approximate the function for use in computer codes. Total emissivities calculated with the correlation agree well with Hottel data. Excellent agreement is also demonstrated with line-by-line solutions of the RTE.
The Spectral-Line Weighted-Sum-of-Gray-Gases Model for H2O/CO2 Mixtures
Denison, M.K. and Webb, B.W.
ASME Journal of Heat Transfer, 1994 (in press). Funded by ACERC.
The weighted-sum-of-gray-gases model, first introduced by Hottel and Sarofim (1967) for expressing total gas emissivities and in e context of the zone method, has recently been extended to the general form of the radiative transfer equation (RTE). The fundamental radiative property of the model is the locally defined absorption coefficient that permits the use of arbitrary solution methods of the RTE. Denison and Webb developed a spectral line-based weighted-sum-of-gray-gases (SLW) model by constructing a histogram representation of the high-resolution spectra of H2O. Subsequently, a novel absorption-line blackbody distribution function was developed which easily allows the blackbody weights of aj of any desired number of gray gases to be determined by simple differencing rather than accessing detailed spectral line information. The distribution function also provides the means of incorporating a spatial dependence of the gray gas absorption cross-sections on temperature, pressure and species mole in non-isothermal, non-homogeneous problems.
The development of the SLW model in the above references has only considered individual species (H2O and CO2) independent of one another. In most practical gas flames a mixture of gases must be considered. Previous treatment of gas mixtures with the weighted-sum-of-gray-gases models has involved either determining a single set of absorption coefficients and blackbody weights from emissivities of the mixture or determining the weights of the mixture as a product of the weights of the individual species under the assumption of random positions of absorption-lines. In this paper the SLW model is formulated for H2O/CO2 mixtures.
Radiation Heat Transfer in a Laboratory-Scale, Pulverized Coal-Fired Reactor
Butler, B.W.; Denison, M.K. and Webb, B.W.
Experimental Thermal and Fluid Science, 9:69-79, 1994. Funded by ACERC and US Department of Energy.
This article reports local gas and particle temperature and radiant and total heat flux measurements made in a 0.8 m diameter cylindrical down-fired laboratory-scale reactor fired at approximately 0.1 MWt with a high-volatile bituminous coal pulverized to a mass mean diameter of 55µm. Spatially resolved gas temperatures were measured using a triple-shielded suction pyrometer and particle cloud temperatures with a specially designed two-color pyrometer. Hemispherical wall radiant heat fluxes were measured using an ellipsoidal radiometer and total (convective plus radiative) heat fluxes with a plug-type heat flux meter. The particle and gas temperature profiles exhibit a strong spatial dependence on reactor fluid dynamics. Additionally, the difference between the gas and particle temperatures varies significantly with location relative to the burner inlet streams and recirculation zones. Maximum radiant fluxes of 110 kW/m² were observed, with differences between radiative and total heat flux being less than 10% at all axial locations. Maximum heat fluxes occur downstream from the location of the maximum gas and particle temperatures and exhibit a generally decreasing trend as distance from the flame increases. Predictions of the radiation heat transfer in the reactor were carried out using the discrete ordinates method. Both spectral and gray radiative transfer calculations were performed. Predicted radiant fluxes agree well with the experimental data. The sensitivity of the model predictions to the uncertainties in the input data is explored.
Spectral-Line Based WSGG Model for Arbitrary RTE Solvers
Denison, M.K.
Spectral-Line Based WSGG Model for Arbitrary RTE Solvers, Ph.D./BYU, August 1994. Advisor: Webb
1993
An Absorption-Line Blackbody Distribution Function for Efficient Calculation of Total Gas Radiative Transfer
Denison, M.K. and Webb, B.W.
J. Quant. Spectrosc. Radiat. Transfer, 50 (5) 499-510, 1993. Funded by ACERC.
An absorption-line blackbody distribution function for H2O that provides an efficient means for total radiative transfer calculations is presented. The function eliminates the need to specify a path-length required by current narrow and wide bank models since the basic radiative property is the locally defined absorption coefficient. This allows the model to be used with arbitrary solution methods of the radiative transfer equation that requires the absorption coefficient as input. A simple mathematical correlation is presented for use in computer algorithms. A few sample calculations of total emissivity as well as numerical solutions to the radiative transfer equation with the use of the distribution function are performed. The model shows good agreement with Hottel's total emissivity data. There is also very good agreement between the model and computationally intensive line-by-line calculations in isothermal media of uniform composition. The function may also be used for approximate calculations in non-uniform media.
Radiation Heat Transfer in a Laboratory-Scale, Pulverized Coal-Fired Reactor: Experiment and Analysis
Butler, B.W., Denison, M.K. and Webb, B.W.
Experimental Thermal and Fluid Science, 1993 (in press). (Also presented at the Experimental Heat Transfer, Fluid Mechanics and Thermodynamics Conference, Honolulu, HI, 1993.) Funded by US Department of Energy and ACERC.
This paper reports local gas and particle temperature and radiant and total heat flux measurements made in a 0.8 m diameter cylindrical down-fired laboratory-scale reactor fired at approximately 0.1 MWt with a high-volatile bituminous coal pulverized to a mass mean diameter of 55µm. Spatially resolved gas temperatures were measured using a triple-shielded suction pyrometer and particle cloud temperatures with a specially designed two-color pyrometer. Hemispherical wall radiant heat fluxes were measured using an ellipsoidal radiometer and total (convective plus radiative) heat fluxes with a plug-type heat flux meter. The particle and gas temperature profiles exhibit a strong spatial dependence on reactor fluid dynamics. Additionally, the difference between the gas and particle temperatures varies significantly with location relative to the burner inlet streams and recirculation zones. Maximum radiant fluxes of 110 kW/m² were observed, with differences between radiative and total heat flux being less than 10% at all axial locations. Maximum heat fluxes occur downstream from the location of the maximum gas and particle temperatures and exhibit a generally decreasing trend as distance from the flame increases. Predictions of the radiation heat transfer in the reactor were carried out using the discrete ordinates method. Both spectral and gray radiative transfer calculations were performed. Predicted radiant fluxes agree well with the experimental data. The sensitivity of the model predictions to the uncertainties in the input data is explored.
A Spectral Line-Based Weighted-Sum-of-Gray-Gases Model for Arbitrary RTE Solvers
Denison, M.K. and Webb, B.W.
ASME Heat Transfer, 115, 1004-1012, 1993. (Also presented at the William Maxwell Reed Seminar, Department of Mechanical Engineering Conference, Lexington, KY, April 1993. Funded by ACERC.
This paper presents an approach for generating weighted-sum-of-gray gases (WSGG) models directly from the line-by-line spectra of H2O. Emphasis is placed on obtaining detailed spectral division among the gray gases. Thus, for a given model spectrum, the gray gas weights are determined as blackbody fractional functions for specific subline spectral regions at all temperatures. The model allows the absorption coefficient to be the basic radiative property rather than a transmissivity or band absorptance, etc., and can be used with any arbitrary solution method for the Radiative Transfer Equation (RTE). A single absorption cross section spectrum is assumed over the entire spatial domain in order to fix the subline spectral regions associated with a single spectral calculation. The error associated with this assumption is evaluated by comparison with line-by-line benchmarks for problems of nonisothermal and nonhomogeneous media.
A Hybrid Spectral-Line Based Weighted-Sum-of-Gray-Gases Model
Denison, M.K. and Webb, B.W.
Proceedings from the National Science Foundation Joint US-Russian Workshop on Radiative Heat Transfer in Highly Coupled Physical Systems, Austin, TX, October, 1993. Funded by ACERC.
This paper presents a hybrid spectral-line-based weighted-sum-of-gray-gases (SLWSGG) model obtained directly from the line-by-line spectra of H2O and CO2. The model allows the absorption coefficient to be the basic radiative property rather than a transmissivitiy or band absorptance etc., and can therefore be used with any arbitrary solution method for the Radiative Transfer Equation (RTE). The model is based on a novel absorption-line blackbody distribution function. Predictions from the hybrid model compare well with line-by-line benchmarks.