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 ChâtenayMalabry 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
H_{2}ON_{2} planar geometry. The studied models are: (i) the
linebyline (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 H_{2}O data base which contains line positions,
intensities, Lorentz broadening parameters and level energies. (ii) The
statistical narrowband (SNB) model with the exponential tailedinverse
distribution of line intensities. The CurtisGodson approximation is used for
nonhomogeneous paths. The considered spectral resolutions of the SNB model are
25 cm_{1} and an optimized variable resolution. (iii) The correlatedk
(CK) model with an optimized variable spectral resolution. (iv) The
correlatedk 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 nonisothermal 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
linebyline 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 nonhomogeneous and nonisothermal
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 H_{2}ON_{2} 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 multidimensional 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 semianalytical formulation with the exponential integral functions
since this formulation cannot be generalized to multidimensional 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.
Absorptioncoefficient 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 WEIGHTEDSUMOFGRAYGASES 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 SpectralLine
WeightedSumofGrayGasrs (SLW) model for the prediction of radiation transfer
in high temperature gases. The parameters in the model are obtained directly
from the linebyline spectra of the primary radiating species in combustion
environments, H_{2}O and CO_{2}. 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 absorptionline
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,
nonisothermal/nonhomogeneous media, binary gas mixtures, and nongray
boundaries and particulates. Sample problems using the model are compared with
spectral linebyline integrations. Predictions from the model compare well
with spectral linebyline 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 ChâtenayMalabry 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 longrange sensing. This increase is
significant when the shift is at least of the same order of magnitude as a
characteristic midheight halfwidth of both emission and transmission profiles
of representative lines. This effect has been systematically studied using a
linebyline approach based on the EM2C high temperature data bases related to
H_{2}O and CO_{2}. 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 narrowband containing a
few wellseparated 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 (CO_{2} near 2.7 and 4.3
m, H_{2}O 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
H_{2}O than for CO_{2} since the absorption lines of
H_{2}O are more separated than those of CO_{2}. 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 ABSORPTIONLINE 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 absorptionline
blackbody distribution function, central to the spectralline based
weightedsumofgraygases 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
linebyline variation in absorption crosssection 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
linebyline benchmarks and model predictions is also demonstrated.
