SESSION 11

GAS MIXTURES

Chairman: S. Maruyama

MACRO-RANDOM MODEL FOR DESCRIBING OF RADIATIVE HEAT TRANSFER WITH VIBRATIONAL BAND STRUCTURE

S.T. Surzhikov
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 cases.

To use the random model, formulated by Goody, Plass, Penner^l-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-Godson^6,7 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 radiatïve heat transfer, and especially for solution of radiative gas dynamic problems.

REFERENCES

1. Goody, R.M., Atmospheric Radiation. I. Theoretical Basis. Oxford , 1964.
2. Plass, G.N., J.Opt.Soc.Am., 1958, Vol.48, p.690.
3. Goody, R.M., Quart.J.Roy.Meteorol. Soc., 1952, Vol.78, p.l65.
4. Penner, S.S., Quantitative Molecular Speetroscopy and Gas Emissivities. Reading, Mass., Addison-Wesley, 1959.
5. Edwards,D.K., Advances in Heat Transfer, 1976, Vol.l2. Academic Press, New York
6. Curtis,A.R., Quart. J. Roy. Meteorol. Soc., 1952, V.78, p.638.
7. 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

L.A.Kuznetsova, S.T.Surzhikov
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: w_J'J" is the wave number of the line centre; and are the vibrational wave functions of upper and lower electronic states accordingly; R_e(r) is the electronic transition moment, dependent on the internuclear distance; N_J' is the population of the rotational level J", S_J'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 [1], accepted as conventional at present, on the definition of rotational line, electronic transition moment and sum rule for the S_J'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[2], and the RADEN data bank on fundamental radiative and spectroscopic parameters of diatomic molecules was produced at the Chemical Department of Moscow State University[3]). 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.

REFERENCES

1. 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.
2. Surzhikov,S.T., Computational Radiation Models for Low Temperature Plasma. AIAA Paper No.96-2313, 1996.
3. 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.
4. Huber,K.P., Herzberg, G., Molecular Spectra und Molecular Structure, Van Nostrand Reinhold Company, 1979.
5. Kuzmenko, N.E., Kuznetcova, L.A., Kuzyakov, Yu. Ya., Frunck-Condon Factors of Diatovnic Molecules, Moscow State University, 1984 (in Russian)
6. Kuzmenko,N.E., Kuznetcova,L.A., Matveev,V.K., Optics and Spectroscopy, 1982, Vo1.53, No.2, p.235 (in Russian)