Chairman: S. Maruyama
MACRO-RANDOM MODEL FOR DESCRIBING OF RADIATIVE HEAT TRANSFER WITH VIBRATIONAL BAND STRUCTURE
Institute for Problems in Mechanics Russian Academy of Sciences, Moscow, Russia
The problem of calculation of selective radiative heat transfer in gas volumes, containing
such optically active components as CO2, H2O, CH4, CO demands development of effective
economic methods, allowing to refuse from uneconomical multigroup spectral models.
The following computing models of selective radiative heat transfer are in common use:
"line-by-line" integration, multigroup models of a spectrum, wide-band and narrow-band
models of a spectrum. In each of these models the investigated spectral range is broken into
finer spectral regions, in limits of which the equation of radiation is solved. Integrated
absorptivity (emissivity) in a full spectral range is determined by summation of integrated
absorptivity (emissivity) in separate ranges.
In the study a macro-random computing model, intended for determination of integrated
radiating characteristics without division of the spectral region into finer spectral region is
presented. The basic idea of the macro-random model is that the vibrational band averaged
on rotational structure is considered as an isolated line of absorption.
The opportunity of application of such model to calculation of averaged spectral
characteristics in a range is checked by comparison with results of "line by line"
calculations in which the spectral range = 1000-10000 cm-1 is broken on 1000 spectral
ranges. The half-moment method is used for calculation of radiative heat transfer in both
To use the random model, formulated by Goody, Plass, Pennerl-4, it is necessary to set a
contour function of band absorption, , where intensity S and half-width is
necessary to understand as parameters, specifying integrated absorption coefficient and half-
width of the vibrational band. It is necessary also to fulfil the following condition: the band
half-width should be much less, than size of the spectral range .
In the study the approximation of function of vibrational bands absorption offered by
Edwards5 is used: where is the centre of the band of
absorption, C1=O.5S and C2= are parameters, determining intensity and half-width of the
band. If to assume, that a probability density of intensities distribution of vibrational bands
has the same kind, as well as for rotational lines in vibrational bands, i.e.
, then equivalent width may be dctermined as following:
Thus, average transmission of the spectral range , containing G vibrational bands can be
calculated under the formula
For calculation of average transmission of a non-uniform optical paths the Curtis-Godson6,7
method is used.
The macro-random model of vibrational bands of molecules H2O and CO2 was applied for
calculation of radiative characteristics in flat non-uniform layers with different parameters
(Fig.1 ). Spectral absorption coefficients on two points inside the layer are shown in Fig.2.
Analysis of presented calculated data of numerical investigation allows to make a conclusion
about satisfactory accuracy of the macro-random model and its high efficiency. The given
model can be recommended for realization of engineering calculations of radiatīve heat
transfer, and especially for solution of radiative gas dynamic problems.
- Goody, R.M., Atmospheric Radiation. I. Theoretical Basis. Oxford , 1964.
- Plass, G.N., J.Opt.Soc.Am., 1958, Vol.48, p.690.
- Goody, R.M., Quart.J.Roy.Meteorol. Soc., 1952, Vol.78, p.l65.
- Penner, S.S., Quantitative Molecular Speetroscopy and Gas Emissivities. Reading, Mass., Addison-Wesley, 1959.
- Edwards,D.K., Advances in Heat Transfer, 1976, Vol.l2. Academic Press, New York
- Curtis,A.R., Quart. J. Roy. Meteorol. Soc., 1952, V.78, p.638.
- Godson,W.L., J. Roy. Meteorol. Soc., 1953, V.79, p.367.
Figure 1. Distributions of temperatures (solid line, scale at the left), and relative molar concentrations of H2O (long dashed line; scale at the right) CO2 (short dashed line; scale at the right) in the plane layer.
Figure 2. Spectral absorption coefficient, averaged on rotational structure in points of the layer with coordinates x = 0 (1) and x = H = 200 cm (2)
AN IMPROVED SPECTRAL WSGGM OF WATER VAPOR USING A NARROW BAND MODEL
Ook Joong KIM*, Tae-Ho SONG**
*Department of Thermal and Fluid Systems
Korea Institute of Machinery and Materials, Taejon, Korea
**Department of Mechanical Engineering
Korea Advanced Institute of Science and Technology, Taejon, Korea
ABSTRACT. A WSGGM-based low resolution spectral modeling of radiative
properties of water vapor using a narrow band model has been presented. For a given
narrow band, models of gray gas absorption coefficients vs. temperature relation have
been reviewed and an improved model is suggested. The modeled gray gas absorption
coefficients become the basic radiative property which can be used for any solution
methods for Radiative Transfer Equation (RTE). Comparisons between the modeled
emissivity and the 'true' emissivity generated from a high temperature statistical narrow
band parameters are made for a few typical bands. Application of the model to
nonuniform gas layer is also made. Low resolution spectral intensities at the boundary
are obtained for uniform, parabolic and boundary layer type temperature profiles using
the obtained WSGGM's with 15 gray gases. The results are compared with the narrow
band spectral intensities as obtained by a narrow band model-based code with the
Curtis-Godson approximation. Good agreement is found between them. Local heat
source strength and total wall heat flux are also compared for the reference cases, which
again produced acceptable agreement.
COMPUTING MODELS OF THE AVERAGE ABSORPTION COEFFICIENTS IN DIATOMIC ELECTRONIC SPECTRA
Moscow State University, Moscow, Russia
Institute for Problems in Mechanics
Russian Academy of Sciences, Moscow, Russia
Spectral coefficients of absorption and emission are used for solving a wide class of the
problems on radiative transfer. In these problems the radiative characteristics (density of
emission energy, density of radiative flows, divergence of radiative flows), integrated in
rather wide spectral ranges, can be simulated by using the averaged absorption or emission
coefficients. The aim of present report is co classificate the models used for calculation of
absorption coefficients in electronic spectra of diatomic molecules.
The starting point for many models is equation for integrated absorption coefficient of
rotational line. For electric-dipole allowed transition in Born-Oppenheimer approximation it
can be written:
where: wJ'J" is the wave number of the line centre; and are the vibrational wave
functions of upper and lower electronic states accordingly; Re(r) is the electronic transition
moment, dependent on the internuclear distance; NJ' is the population of the rotational level
J", SJ'J" is the Hoenle-London factor.
It should be stressed that there is an interdependence between the electronic transition
moment and the Hoenle-London factors. We use the recommendations of Whiting et al ,
accepted as conventional at present, on the definition of rotational line, electronic transition
moment and sum rule for the SJ'J" values.
In the report the following computing models for spectral averaged absorption coefficients
are presented in detail: model of "line-by-line" calculation (1), "just-overlapping line"
model (2), model with analytical representation of vibrational band profile (3), model of a
"grey" vibrational band (4). For some electronic systems we compared absorption coefficients
obtained with different models of averaging over the rotational structure. Results of such
comparison for the Swan system of C2 molecule are given in Fig.l. As it can be seen, the
simplified second and third models and the more reliable first model give rather close results.
The classification of computing models was carried out in connection with the fact that
the authors of the present report begin work on creation of application-oriented information-
computing system MSRT-RADEN (computing system "Mathematical Simulation of Radiative:
Transfer" was developed in Institute of Problem in Mechanics of Russian Academic of
Science, and the RADEN data bank on fundamental radiative and spectroscopic parameters
of diatomic molecules was produced at the Chemical Department of Moscow State
University). The MSRT-RADEN system includes:
- the base of computing models for absorption coefficients in diatomic electronic spectra;
- thu base of model parameters, the spectroscopic and radiative characteristics;
- the base of recommended average absorption coefficients.
Figure 1. C2 molecule, the Swan system. Comparison of absorption coefficients obtained with different computing models. The model numbers are the same as in the text
The bases will be regularly updated according to the newly published or calculated data. We
plan also that the third base will be available on the WWW, wich has become the de facto
standard for electronic exchange of information.
Creation of the system requires to conduct an extensive complex of studies. The aim of
these studies discussed in the report is to estimate the influence of models and their
parameters on results of radiative transfer calculation. Specifically, it was shown that
absorption coefficients averaged over the rotational structure are correct only for optically-thin
layers. For other cases the errors introduced into results should be estimated.
In the report the average spectral absorption coefficients for 28 electronic band systems are
given in the form of graphs. The calculations were carried out for the temperatures: l000,
4000, 8000, and 12000 K. Results were received by using the more reliable computing model,
"line by line" calculation. The following input data were used: spectroscopic constants from
Ref.4, the Franck-Condon factors from Ref.5, the spectral dependence of electronic transition
strengths was approximated by equations from Ref.6.
- Whiting, E.E., Schadee, A., Tatum, J.B., Hougen, J.T., and Nicholls, R.W., "Recommended conventions for defining transition moments and intensity factors in diatomic molecular spectra," J.Mol.Spec., Vo1.80, p. 249, 1980.
- Surzhikov,S.T., Computational Radiation Models for Low Temperature Plasma. AIAA Paper No.96-2313, 1996.
- Kuznetsova, L.A., Pazyuk, E.A., and Stolyarov, A.V., "Radiation and Energy Characteristics of Diatomic molecules (Data Bank)," Russ.J. Phys.Chem..Vol.67, pp.2046-2049, 1993.
- Huber,K.P., Herzberg, G., Molecular Spectra und Molecular Structure, Van Nostrand Reinhold Company, 1979.
- Kuzmenko, N.E., Kuznetcova, L.A., Kuzyakov, Yu. Ya., Frunck-Condon Factors of Diatovnic Molecules, Moscow State University, 1984 (in Russian)
- Kuzmenko,N.E., Kuznetcova,L.A., Matveev,V.K., Optics and Spectroscopy, 1982, Vo1.53, No.2, p.235 (in Russian)