SESSION 5

RADIATIVE PROPERTIES OF GASES


ACCURACY OF VARIOUS GAS IRRADIATIVE PROPERTY MODELS APPLIED TO RADIATIVE TRANSFER IN PLANAR MEDIA

Laurent PIERROT, Anouar SOUFIANI, Jean TAINE
Laboratoire d'Energétique Moléculaire et Macroscopique, Combustion, UPR 288 du CNRS et de l'ECP.
Ecole Centrale Paris, 92295 Châtenay-Malabry Cedex, France

Radiative transfer calculations which take into account each absorption line, i.e. the fine structure of the molecular spectrum, need very important computational times. Several models have been developed to predict gas radiative properties averaged over a spectral range of a finite width varying from a few cm-1 to a few hundred cm-1 (band models) or over the whole spectrum (global models). The aim of this paper is to compare the accuracy of these models and the computational times required when they are applied to radiative transfer calculations in a simple H2O-N2 planar geometry. The studied models are: (i) the line-by-line (LBL) approach which is used as a reference for benchmark comparisons. The spectral resolution is typically 10-2 cm-1. LBL calculations are based on the EM2C high temperature spectroscopic H2O data base which contains line positions, intensities, Lorentz broadening parameters and level energies. (ii) The statistical narrow-band (SNB) model with the exponential tailed-inverse distribution of line intensities. The Curtis-Godson approximation is used for non-homogeneous paths. The considered spectral resolutions of the SNB model are 25 cm-1 and an optimized variable resolution. (iii) The correlated-k (CK) model with an optimized variable spectral resolution. (iv) The correlated-k fictitious gas (CKFG) model in which the real gas is considered as a mixture of fictitious gases characterized by lines of similar transition lower state energies. The CK approach is then applied to each gas. This model has been developed especially for highly non-isothermal paths. (v) The weighted sum of gray gases (WSGG) model which is global, contrary to the three previous models. The parameters of the approximate models are adjusted to fit line-by-line transmissivity calculations for various optical paths. Radiative properties of homogeneous and isothermal columns are then practically the same when predicted from all models. In this manner, we compare only the ability of each model to treat radiative transfer in non-homogeneous and non-isothermal paths and avoid discrepancies resulting from the use of different basical data. For this reason, we do not include the exponential wide band model in the comparison since Edwards' parameters are not originated from the same spectroscopic data.

The accuracies of the models are compared on the basis of wall radiative fluxes and volumetric radiative power in a planar geometry with prescribed temperature and composition profiles. The medium is an absorbing, emitting but nonscattering H2O-N2 mixture and different temperature profiles are tested. Numerical methods for the resolution of the radiative transfer equation (RTE) in association with each radiative property model have been chosen in order to provide a consistent comparison of CPU times required in multi-dimensional geometries. When the model is based on an absorption coefficient formulation (LBL, CK, WSGG), the differential form of the RTE is used and the directional integrations are performed numerically instead of using the semi-analytical formulation with the exponential integral functions since this formulation cannot be generalized to multi-dimensional problems. For the models based on column transmissivities (SNB and CKFG), the integral form of the RTE is used.

The results are discussed from several points of view. The use of a mean transmissivity based model with a deterministic method for the resolution of the RTE resolution requires a noncorrelation approximation to treat reflection at a wall or more generally radiation scattering. The errors due to this approximation reach 15% in the applications considered in this study. Absorption-coefficient based models are more suited to treat problems where reflection and scattering are important. For applications where gas emitted radiation is mostly absorbed by a long cold medium before reaching a wall, only the CKFG model provides accurate wall fluxes. The corresponding computational times are very important but they could be reduced with optimized spectral resolutions and quadratures. The WSGG model is the less expensive one but it yields generally very important and sometimes unpredictable discrepancies. Absorption by gases at a temperature different from the emitting temperature cannot be accurately predicted from this model. Another limitation of this model is that it can only be applied when wall or particle radiative properties are gray. For instance, its extension to the case of selective walls requires the subdivision of the spectrum into wide bands and the use of the WSGG model for each band. Model parameters are then no more universal and should be calculated for each particular application.


THE SPECTRAL LINE WEIGHTED-SUM-OF-GRAY-GASES MODEL -- A REVIEW

Martin K. Denison*, Brent W. Webb**
* Advanced Combustion Engineering Research Center
Brigham Young University
Provo, Utah, U.S.A.
** Department of Mechanical Engineering
Brigham Young University
Provo, Utah, U.S.A.

This paper reviews the development and validation of the Spectral-Line Weighted-Sum-of-Gray-Gasrs (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 the primary radiating species in combustion environments, H2O and CO2. The model allows the absorption coefficient to be the basic radiative property rather than a transmissivity or band absorptance etc., and can therefore be used with any arbitrary solution method for the Radiative Transfer Equation (RTE), and for multidimensional situations. The model is based on a novel absorption-line blackbody distribution function, which is generated and fit empirically from detailed spectral line data. The model has been formulated for applications of increasing complexity including isothermal/homogeneous media, non-isothermal/non-homogeneous media, binary gas mixtures, and non-gray boundaries and particulates. Sample problems using the model are compared with spectral line-by-line integrations. Predictions from the model compare well with spectral line-by-line benchmarks.

EFFECTS OF LINE DOPPLER SHIFT ON INFRARED RADIATION IN HIGH VELOCITY FLOWS

Laurent PIERROT, Anouar SOUFIANI, Jean TAINE
Laboratoire d'Energétique Moléculaire et Macroscopique, Combustion, UPR 288 du CNRS et de l'ECP
Ecole Centrale Paris 92295 Châtenay-Malabry Cedex, France

The emission lines of a gaseous medium at a given velocity are shifted by Doppler effect with respect to their initial position. The effect of this line Doppler shift is an increase in the radiative intensity emitted by a gaseous jet and transmitted through gaseous columns at rest. This is expected to occur for instance in applications involving long-range sensing. This increase is significant when the shift is at least of the same order of magnitude as a characteristic mid-height half-width of both emission and transmission profiles of representative lines. This effect has been systematically studied using a line-by-line approach based on the EM2C high temperature data bases related to H2O and CO2. Simulations have been carried out in the case of two columns, one at 1000 K ana a given velocity V, the other at 216 K and at rest; both columns are at the same pressure. The line Doppler shift effect is considered for an isolated line, for a narrow band and for a whole absorption band successively. It is shown that for a given isolated line, there are precise optical path conditions for which the Doppler shift effect on transmitted radiative intensity is maximum. Apart from these conditions, the Doppler shift effect decreases quickly. In the case of narrow-band containing a few well-separated lines, it can be significant but is however about two times less important than in the case of an isolated line. Our simulations show that for a global absorption band (CO2 near 2.7 and 4.3 m, H2O near 2.7 m), the line Doppler shift can increase the transmitted radiative intensity by up to 15% for a pressure of 0.1 atm and a velocity V of 2000 m/s. This phenomenon is more important for H2O than for CO2 since the absorption lines of H2O are more separated than those of CO2. The maximum Doppler shift effect decreases as the spectral band width over which radiative intensities are integrated increases. Indeed, for a wide spectral band and given thermophysical conditions, there are very few lines for which the Doppler shift effect is important. For velocities lower than 1000 m/s and pressures greater than 0.1 atm, the increase in the transmitted intensity is limited to 4%.

THE ABSORPTION-LINE BLACKBODY DISTRIBUTION FUNCTION AT ELEVATED PRESSURE

Martin K. Denison*, Brent W. Webb**
* Advanced Combustion Engineering Research Center
Brigham Young University
Provo, Utah, U.S.A.
** Department of Mechanical Engineering
Brigham Young University
Provo, Utah, U.S.A.

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 elevated pressures by introducing a dependence on an effective broadening pressure. The distribution function attempts to capture the spectral information of the line-by-line variation in absorption cross-section in an empirical form. Effective pressures ranging from 0.32 to 100 atm. This extends accepted previous theoretical approaches to the distribution function. Comparisons between experimentally determined total emissivities and those calculated with the model show good agreement. Very good agreement at elevated pressure between line-by-line benchmarks and model predictions is also demonstrated.

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