Anouar Soufiani

Gas IR radiative properties : From spectroscopic data to approximate models

Abstract Different IR gas radiative property models suitable for a wide range of engineering applications (statistical narrowband, correlated- k :, correlated- k -fictitious gases, and models based on global absorption coefficient distribution functions, such as WSGG, SLW, ADF, and ADFFG) are presented. High-temperature properties, especially with CO 2 and H 2 O as active species, are emphasized. The accuracy of the different models is discussed by comparing their results with those of a line-by-line (LBL) approach, considered as a reference. This last model is introduced step by step, and the effects of the properties of the molecular states of the absorbing and emitting species on the properties of the corresponding spectra are discussed. The main physical features of complex IR spectra of CO 2 and H 2 O are presented in order to explain important phenomena occuring in different applications. The key point in the use of an LBL approach is the development of a complete and accurate spectroscopic database suitable for high-temperature applications. The parameters of approximate models are generated from the LBL approach in order to provide accurate predictions of radiative properties of uniform media. The intrinsic accuracy of these models applied to radiative transfer in nonuniform media is then studied. The implementation of the models is discussed on the basis of their formulations in terms of absorption coefficients or in terms of averaged transmissivities, and on the basis of their classification into band models and global models. Different methods for the treatment of mixtures of absorbing species are discussed.

Accuracy of narrow-band and global models for radiative transfer in H2O, CO2, and H2OCO2 mixtures at high temperature

The accuracy of several narrow-band (SNB, CK, CKFG) and global (WSGG, SLW, ADF, ADFFG) gas infrared radiative property models applied to radiative transfer in a planar geometry with different types of temperature profiles is studied. The considered gaseous mixtures are H2ON2, CO2N2 and H2OCO2N2. Reference solutions are provided by line-by-line (LBL) calculations. All model parameters are based on the same spectroscopic data bases so that only the intrinsic accuracy of each model is tested. All narrow-band models lead in most cases to accurate results, but errors induced by the transmissivity-based models SNB and CKFG increase with wall reflectivity if the reflected radiation is assumed spectrally uncorrelated with gaseous transmissivity. Global models are less time consuming than narrow-band models but are generally less accurate and limited to media with gray boundaries and/or participating particles. The WSGG model leads in many cases to very important errors. The relative accuracy of the SLW and ADF models is typically about 10–20% but care must be taken in the choice of the reference temperature. The ADFFG model is the most accurate global model but requires greater computing times than the ADF and SLW models. For long range sensing of hot gases, only the fictitious-gas based models CKFG and ADFFG lead to accurate results. In the case of mixtures containing H2O and CO2, the spectral uncorrelation assumption is accurate for narrow-band models and its implementation results only in greater computing times for the CK model. On the contrary, this assumption is not generally accurate for the whole spectra and specific parameters must be generated from the joint distribution function of the absorption coefficients in the case of global models.

Validity of band-model calculations for CO2 and H2O applied to radiative properties and conductive-radiative transfer

Abstract A previously presented line-by-line (LBL) calculation is used to test the validity of various approximate models. Narrow-band model parameters are generated from the lines used by the LBL approach in the 150–8000 cm -1 and 300–1500 K ranges. The accuracy of narrow-band models and of approximations for nonuniform paths applied to transmissivities and intensities of columns is studied. Random-statistical models give good results for the transmissivities but inaccurate results for the emitted intensities. Applications to combined conductive-radiative transfer in one-dimensional media are then presented. The temperature and flux distributions predicted by wide-band models are accurate when radiative transfer is preponderant; narrow-band models must be used in the case of optically thin media (e.g. in boundary layers).

Correlated-k and fictitious gas methods for H2O near 2.7 μm

Abstract The correlated-k distribution (CK) method is extended with a fictitious gas approach in order to account for strong temperature-gradient effects. The correlated-k fictitious gas (CKFG) method involves consideration of the absorbing gas as a mixture of fictitious gases, each characterized by real gas lines with a lower level energy belonging to a fixed range. CK and CKFG parameters have been obtained from a line-by-line (LBL) approach for H2O between 2900 and 4200 cm-1 in the 300–1500 K temperature and 0.2–3 atm pressure ranges. Results obtained from CK, CKFG and narrow-band statistical (NBS) models are compared under various conditions with LBL results. The CK approach yields accurate results for isothermal and slightly nonisothermal media. But for large temperature gradients, only CKFG results agree well with LBL calculations. It is shown that the CK approach leads to an underestimation of more than 50% under some conditions of the radiation emitted by a hot medium and transmitted through a cold medium. For practical use, the variations of the CK and CKFG model parameters with temperature and pressure are approximated by analytical functions with few coefficients fitted from LBL calculations. It is shown that this fitting procedure does not degrade the accuracy of either model. Finally, the utility of each of the models is discussed for use under various radiative transfer situations.

A comparison between weighted sum of gray gases and statistical narrow-band radiation models for combustion applications

Abstract The weighted sum of gray gases (WSGG) and the statistical narrow-band (SNB) models are implemented for radiative transfer calculations in realistic combustion gas mixtures and their results are compared. The WSGG model parameters are generated from SNB emissivity calculations in the [300, 2500 K] temperature range for a partial pressure ratio p w p c = 2 . In addition, the same methods are used for the resulution of the transfer equation associated with both models. Comparisons are made for the cases of planar geometry and an axisymmetrical methaneoxygen furnace. When the gas mixture is practically isothermal and surrounded by cold walls, small errors are introduced by the use of the WSGG model. On the other hand, in the case of significant temperature gradients, the inaccurate representation of gas absorptivities by the WSGG model leads to important errors.

Study of radiative effects on laminar counterflow H2/O2N2 diffusion flames

Abstract: The effects of radiative transfer on the structure and extinction limits of counterflow H-2/O-2/N-2 diffusion flames are studied numerically using detailed kinetics and transport properties. The radiative properties of the main emitting species, H2O and OH in these flames, are represented using a statistical narrow-band model. The radiative transfer equation and flow governing equations are solved in a coupled manner. The model is first validated by comparing numerical results with Rayleigh temperature and total flame radiative emission measurements. It is then applied to the numerical study of radiative effects on flame structure and properties. These effects, i.e., a decrease in flame temperature, flame width and production of minor species, are found to be the most important for high values of inlet H-2 mass fraction and for low strain rates. Quantitative values of radiative low strain rate extinction limits are given. The limits of validity and the discrepancies due to the optically thin medium approximation are also investigated.

Spectral correlated and non-correlated radiative transfer in a finite axisymmetric system containing an absorbing and emitting real gasparticle mixture

Abstract Radiative transfer in a finite axisymmetric enclosure is investigated for a non-isothermal, inhomogeneous, absorbing, emitting but non-scattering gas-particle mixture. A random statistical narrow band model and the Curtis-Godson approximation are used to calculate the real gas radiative properties. High resolution spectral correlations between the transmissivities of homogeneous and isothermal discretization column elements are treated by an ellipse correlation model which is validated. A discretedirection method is applied to solve the geometrical part of the radiative transfer problem. Applications to planar and finite axisymmetric geometries show that spectral correlations significantly modify, typically 30–50%, the radiative flux and radiative dissipation in practical systems. Non-correlated models may lead to inaccurate qualitative predictions (e.g. the radiative flux sign may be reversed).

AIR MIXTURE RADIATIVE PROPERTY MODELLING IN THE TEMPERATURE RANGE 10,000-40,000 K

Abstract A model based on the distribution functions of the absorption coefficients is used to describe the radiative properties of an air plasma at atmospheric pressure between 10,000 and 40,000 K. In order to account for spectral fine structure effects on radiative transfer in nonuniform media, fictitious species whose spectra reasonably satisfy the scaling approximation are introduced. The absorption spectra of these fictitious species are assumed to be spectrally uncorrelated. Radiative properties are described in terms of absorption coefficients and the model can be used with arbitrary radiative transfer equation solvers. Model parameters are generated from spectral high resolution calculations. The different approximations required to implement the model are discussed and their validity is checked by comparisons with line-by-line benchmarks. It is shown that the model can predict radiative transfer along strongly nonisothermal columns within a few percent.

Contributions of diatomic molecular electronic systems to heated air radiation

Abstract A spectroscopic database has been constructed for all the contributing electronic systems of air diatomic molecules for elevated temperatures (up to 15,000 K ). The electronic systems which have been investigated are N2 first- and second-positive, Birge–Hopfield 1 and 2, Carroll–Yoshino, Worley and Worley–Jenkins, N2+ Meinel, first- and second-negative, O2 Schumann–Runge and NO γ,β,δ,e,γ′,β′,11,000 A and infrared. The RKR potentials have been reconstructed in order to calculate the vibrational wavefunctions, and the electronic-vibrational part of line intensities has been computed with up-to-date ab-initio electronic transition moment functions. The results of our calculated vibrational band strengths are in good agreement with the available measurements. The positions and intensities of the rotational lines have been determined in intermediate a/b Hunds coupling case with up-to-date molecular constants, and the lambda doubling has been resolved when related parameters were available in the literature. Absorption spectra and the optically thin radiation source strengths of the studied electronic systems are presented and discussed in terms of their comparative contribution to emission and absorption.

Radiative transfer in LTE air plasmas for temperatures up to 15,000 K

Abstract Radiative transfer in local thermodynamic and chemical equilibrium N2–O2 plasmas is analyzed in this study using a line-by-line approach. The contributions of line absorption by atoms, ions and of continuous absorption by atoms, ions and molecules to the absorption coefficient of heated air are calculated. These data combined to our previous work on the contribution of molecular electronic systems to heated air radiation (J. Quant. Spectrosc. Radiat. Transfer 72 (2002) 503) lead to a reliable and exhaustive spectroscopic data base for radiative transfer in air plasmas and for temperatures up to 15,000 K . Line-by-line radiative transfer calculations are carried out for a simple planar geometry with prescribed temperature profiles. The spectral distribution of radiative fluxes and volumetric powers is analyzed and the relative contributions of continuum and line radiation are discussed.