Proceedings of Eurotherm78 omputational hermal Radiation in Participating Media II 5-7 April 00, Poitiers, rance he influence of carbon monoxide on radiation transfer from a mixture of combustion gases and by Vladimir P. SOLOVJOV and Brent W. WEBB Department of Mechanical Engineering, Brigham Young University, Provo, U 840, U.S.A. webb@byu.edu Abstract arbon monoxide and may be present in a wide range of concentrations in combustion applications. Generally speaking, high concentrations in both constituents result from locally fuel-rich conditions. It is known that significantly increases the radiation transfer in combustion applications due to its spectrally continuous emission and high absorption coefficient relative to that of gases. However, it is not generally known how important the contribution from O is to the overall radiation transfer in the system. he purpose of this work is to investigate the role of O in the radiation transfer from a mixture of combustion gases (H O, O, O) with non-gray particles in an idealized combustion environment. alculations of the radiative transfer have been performed for a wide range of possible combinations of the species and concentrations and over a wide range of temperatures in order to characterize conditions under which O is important for accurate prediction of the radiative transfer. Nomenclature I intensity s pathlength N molar density Y concentration absorption cross-section a gray gas weight absorption-line blackbody distribution function volume fraction Greek symbols κ absorption coefficient σ Stefan-Boltzman constant wavenumber Φ fraction of radiation transfer with or without and/or O Subscripts b blackbody wavenumber m number of species n number of gray gases 1. Introduction So-called luminous flames contain not only the mixture of combustion gases (principally water vapor, carbon dioxide and monoxide) but also which consists oery small carbon particles [1,]. he calculation of the radiation field in a luminous flame is more difficult
because of the superposition of band-based gas radiation and the spectrally continuous absorption coefficient. Accurate treatment of the radiation transfer from the combined gases and is a challenge. Simplified gray models for gases and have been shown to yield underpredicted temperatures and, therefore, incorrect prediction of the content of the carbon monoxide and which both are the products of incomplete combustion [3,4]. hus, in reality the radiation transfer and local gas species and concentrations are coupled. It is common in radiation modelling practice to neglect O in scenarios where is known to be present. Under such conditions it is assumed that radiation from dominates that from the O. Indeed, in the case of high concentration radiation transfer from may be dominant relative to that from all gases. However, under typical combustion conditions it is not known under what conditions the presence of O can be neglected. Generally speaking, combustion conditions may yield a very wide range of the ratio of the concentration of O and [1]. Of course, prediction of these concentrations requires detailed modelling of the formation and transport of both species. In this study on the effect of O on radiation transfer from a mixture of combustion gases and, the concentrations are specified over a wide range anticipated in typical combustion systems. Little prior work has specifically explored the influence of O on the radiative transfer in high temperature gas/ mixtures. Bressloff studied the influence of loading on Weighted-Sum-of-Gray-Gases solutions to the radiative transfer equation for mixtures of gases and [5]. As expected, the results revealed that becomes dominant in the radiative transfer as its concentration increases. Modest reviewed techniques for spectral integration of the radiative transfer from mixtures of H O, O, and, revealing the importance of spectral integration. he influence of O was not identified. In the present work, an efficient and accurate method based on the Spectral-Line Weightedsum-of-gray-gases (SLW) model has been used to predict the radiative transfer within mixtures of H O, O, O, and. he method, reported previously [7,8], models as an effective radiating gas, with the Absorption-Line Blackbody Distribution unction (ALBD). he multicomponent gas mixture with is treated as a single gas whose effective ALBD is calculated in a simple way using the ALBDs of individual species present in the mixture. his approach has been shown to yield efficient, accurate calculations for the radiative transfer in mixtures of arbitrary concentrations of gases and, and retains the advantages of SLW model. he spectral properties of O used in the model were presented in [].. Radiative ransfer Equation he radiation field in absorbing, emitting, and non-scattering media along a pathlength s in a direction Ωˆ is described by the spectral intensity of radiation I ( s,ωˆ ), the governing equation for which is a Radiative ransfer Equation (RE) [14]: di ds = κ I + κ I (1) b where I b is the Planck distribution of blackbody intensity, and κ is the spectral absorption coefficient of the medium. 3. Spectral Model he development which follows summarizes in some detail the approach to spectral modelling of mixtures of gas species and presented previously [8]. he spectral absorption coefficient κ is the effective absorption coefficient of the local mixture of m gases and particles, constructed from the individual absorption coefficients of all components included in the combustion process:
1 + κ + + κ m κ () κ = κ + where κ is the spectral absorption coefficient of, and κ m is the spectral absorption coefficient of gas species m. he spectral absorption coefficient κ m can be expressed in terms of the gas absorption cross-section mn and molar density N m by the relation κ m = N (3) Let N be the molar density of the gas mixture. hen the absorption coefficient may be expressed as m m 1 + κ + + κ m + κ = N (4) κ = κ Equation (4) presents a relation for the absorption coefficient of a single gas whose absorption cross-section is defined as = Y1 1 + Y + + Ymm + (5) his formulation provides the utility of using the conventional formulation of the SLW model for a single gas. he absorption cross-section of, included in Eqs. (4) and (5) is artificially constructed by dividing the absorption coefficient by the molar density. It depends on the local thermodynamic properties of the gas mixture. 4. SLW Modelling he radiative transfer equation of the SLW model obtained by the integration of the RE (1) with respect to wavenumber and subdivision of the absorption cross-section into gray gases has the form [9] di j = κ j I j + a jκ j Ib, j = 0, 1,, n () ds where n is the number of gray gases in the model, I j is the intensity of gray gas j, and j N j 1 j κ = (7) is the absorption coefficient of the gray gas j defined by the supplemental cross-sections j-1 and j and the weight of the gray gas j ( ) ( ) a (8) j = j j 1 In the SLW model s modification of the classical WSGG model, gray gas weights are calculated with the aid of the Absorption-Line Blackbody Distribution unction (), which is 4 defined as that portion of the radiative blackbody energy σ which corresponds to wavenumbers for which absorption cross-section is less than the arbitrary value. Solving Eq. () for each gray gas j, one obtains the integrated intensity of radiation I by the simple summation over all gray gases I = Id = I (9) = 0 In the calculation of the ALBD for the mixture (), the ALBDs of individual species m () will be used. hese are readily calculated from spectroscopic data, and can be correlated for more efficient use [,10,11]. urther, the ALBD of () may be calculated treating as an equivalent gas. he multiplication approach is then used for calculation of () [7,8]. he multiplication approach to the calculation of the ALBD of the mixture through the ALBDs of individual species is based on the assumption that absorption cross- n j= 1 j
sections of different species included in the mixture are statistically independent. or gas mixtures without particles this assumption is discussed in [7,8]. he absorption cross-section of is a smooth, almost-linear function which is obviously statistically independent of any line molecular gas spectrum. According to this approach, the ALBD ( ) of the composite absorption cross-section is obtained as a product of ALBDs of individual contributors to this absorption cross-section: ( ) ( ) ( ) ( ) ( ) = (10) Y 1 1 Y where m is a number of species in gas mixture. As derived previously [7,8], the dependence of the ALBD on the mole fraction for the gas species allows the calculation of the ALBD for arbitrary mole fraction through the ALBD of the pure gas applied to Eq. (10), which yields Y ( ) = m m 1 Y 1 Y Y Ym m m ( ) = ( ) 1 m Y m Equation (11) provides a simple and efficient method of calculation of the ALBD of the gas mixture with particles. 5. ALBDs he Absorption-Line Blackbody Distribution unctions for H O and O were introduced and correlated in engineering form previously in [10,11]. he ALBD for O was calculated by Solovjov and Webb []. he ALBD of non-gray is calculated directly in the model as follows. he volume fraction is the ratio of concentration c to density ρ : f v c (11) = ρ (1) he value of density may be approximated as the density of carbon, approximately 000 kg/m 3. A simple model of absorption coefficient with linear dependence on wavenumber was proposed by Hottel and Sarofim [1]: κ = c (13) where c is a constant for each fuel. Hottel and Sarofim assumed c to be equal to 7 for any fuel. or typical hydrocarbon flames the volume fraction varies in the range 10-8 10 - [1]. Using Eq. (13) for the absorption cross-section defined in Eq. (4), one finds = cf N = Y (14) v where Y s has the sense of molar ratio which depends on the thermodynamic state of the medium. In a fashion similar to the definition of the ALBD for absorption cross-sections of gases, one can define the blackbody radiation distribution function of absorption crosssection of by the following ( ) = E ( ) { : < } he blackbody radiation distribution function of through the Planck blackbody radiation distribution function () is calculated by the following relationship [8]: b s d σ 4 (15)
( ) ( ) = ( Y ) = (1) Y s Now, if one applies the property defined by Eq. (1) to Eq. (11), it may be shown that the multiplication approach for the mixture of m gases with particles yields the following expression for the calculation of the effective ALBD of gas/ mixtures ( ) ( Y ) ( Y ) ( Y ) ( Y ) 1 1 m s = (17) Equation (17) will be employed in the calculation of the ALBD for the prediction of radiation field in the multicomponent gas mixtures with particles with the SLW model.. Results and Discussion he impact of the presence of O on the radiative transfer from a mixture of H O, O (at atmospheric pressure), and in an isothermal plane layer of thickness L = 1.0 m bounded by black, non-emitting walls is considered. he RE was solved using the discrete ordinate method using the procedure described elsewhere [7, 8]. Medium temperatures between 800 K and 1400 K, and volume fractions between 10-8 and 10 - (in addition to vanishing volume fraction) are explored. he total radiative flux divergence Q(x) (W/m 3 ), total radiative flux q(x) (W/m ), and total radiative flux at the boundary q w = q(x=0) = q(x=l) (W/m ) are calculated. he impact of O on the radiative transfer is quantified by definition of two parameters. he contribution from O to the total boundary flux at fixed volume fraction is examined by defining the parameter Φ q q with O w/ o O O = q with O m 100% Similarly, the contribution from to the total boundary flux at fixed O volume fraction Y O is defined as Φ q = with q q with w/ o 100% he magnitude of the deviation of Φ from a zero value indicates contribution of either O or to the radiative transfer from the respective constituent. Both Φ O and Φ are calculated as functions of Y O and at different temperatures and mole fractions of H O and O. igure 1 illustrates the variation in local dissipation source Q(x) for a medium temperature = 1000 K, Y = Y 0. 1. Predictions are presented for vanishing volume fraction O for Y O in the range 0 0.3, and for vanishing O concentration for in the range 0 10 -. he figure demonstrates why conventional radiative modelling wisdom is that O be neglected. Over the range of parameters explored, the local dissipation source is significantly more sensitive to volume fraction than O concentration. However, the several-orderof-magnitude range in volume fraction studied should be noted. or low to moderate volume fractions (e.g., mildly ing flames), the contribution of O to the radiative transfer can be comparable to that from the. igure presents three-dimensional surface contours of Φ O and Φ, quantifying contribution of O and to the boundary radiative flux for Y H 0. 1 O = YO = at three different temperatures, 800 K, 1000 K, and 1400 K. As expected, at all temperatures Φ O rises with increases in Y O and decreases in. Likewise, Φ is observed to increase with increases in and decreases in Y O. he significantly higher slope of the Φ surface in the figures confirms the observation made relative to ig. 1 that radiative transfer predictions are more sensitive to volume fraction than to O concentration (over the wide range of volume s (18) (19)
-0-0 -40-40 Q, W/m 3-0 Q, W/m 3-0 Y O =0 Y O =0.1 =0-80 Y O =0. Y O =0.3-80 =10-8 =10-7 =10 - -100 0 0. 0.4 0. 0.8 1 x, m -100 0 0. 0.4 0. 0.8 1 x, m (a) (b) ig. 1 otal dissipation radiative source Q(x), W/m 3 for = 1000 K, Y H 0. 1 O = YO = : a) = 0, and b) Y O = 0. fraction anticipated in flames). he intersection in surface contours for Φ O and Φ indicate the values of and Y O where the two constituents ( and O) contribute equally to the wall radiative flux, i.e., Φ O = Φ. he predictions show that the contribution of O to the radiative transfer is equal to that of for in the range 10-8 10-7. Only at lower volume fraction does the contribution of O to the radiative transfer exceed that of. As expected, O and are equal contributors at higher volume fractions as the O concentration Y O increases. It is also observed that O becomes a significant player in the radiative transfer at lower volume fraction as the medium temperature increases. igure 3 shows surface contours of Φ O and Φ for Y = Y 0. 1at the three tempera- O tures investigated. It is seen from ig. 3a that the contribution of O does not change significantly with temperature. he dependence of Φ on temperature is only moderately greater than Φ O, increasing as temperature increases. An increase in temperature thus favors the radiative contribution of relative to the contribution of O. urther, ig. 3 illustrates that while Φ O is strongly dependent on both and Y O, Φ is only weakly dependent on Y O. he influence of H O and O concentration on the contributions of O and to radiation = 800K = 1000K = 1400K O O O 8 YO 8 YO 8 YO ig. omparison of contributions of O and to wall radiation flux in the mixture with Y = Y 0. 1 at temperatures = 800 K, 1000 K, and 1400 K. O
Φ O, % = 800K = 1400K Φ, % = 1400K = 1000K O = 1000K = 800K f v 8 YO f v 8 YO (a) (b) ig. 3 ontributions of O and to wall radiation flux in the mixture with Y = Y 0.1 at temperatures = 800 K, 1000 K, and 1400 K. O transfer is illustrated for a medium temperature of 1000 K by ig. 4, where Φ O and Φ are plotted for H O and O concentrations Y H 0. 1 O = YO = (reproduced from ig. b) and Y H 0. O = YO =. It is interesting to note that an increase in H O and O concentration (for otherwise unchanged Y O ) results in an increase in the contribution of O relative to that of. 7. onclusions he influence of O on the radiation heat transfer from a one-dimensional layer of a homogeneous, isothermal mixture of H O, O, and has been explored for a range of species and volume fractions. he results reveal that the conditions under which the contribution to the radiative flux by O is higher or comparable to that of is significant in all cases, and that O should be accounted for to provide accurate prediction of the radiation field in combustion systems with low or moderate concentration of (10-8 10-7 ). O O 8 YO 8 YO (a) (b) ig. 4 omparison of contributions of O and to radiation in the mixture with = 1000 K for a) Y = Y 0. 1, and b) Y = Y 0.. O O
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