Gas Emissivity and Absorptivity

Each spectral line is characterized by an absorption coefficient kp which exhibits a maximum at some central characteristic wavelength or wave number r 0 = l/ o and is described by a Lorentz probability distribution. Since the widths of spectral lines are dependent on collisions with other molecules, the absorption coefficient will also depend upon the composition of the combustion gases and the total system pressure. This brief discussion of gas spectroscopy is intended as an introduction to the factors controlling absorption coefficients and thus the factors which govern the empirical correlations to be presented for gas emissivities and absorptivities. 

Total Emissivities and Absorptivities Total emissivities and absorptivities for water vapor and carbon dioxide at present are still based on data embodied in the classical Hottel emissivity charts. These data have been adjusted with the more recent measurements in RADCAL and used to develop the correlations of emissivities given in Table 5-5. Two empirical correlations which permit hand calculation of emissivities for water vapor, carbon dioxide, and four mixtures of the two gases are presented in Table 5-5. The first section of Table 5-5 provides data for the two constants b and n in the empirical relation 

In both cases the empirical constants are given for the three temperatures of 1000,1500, and 2000 K. Table 5-5 also includes some six values for the partial pressure ratios pw/pc of water vapor to carbon dioxide, namely 0, 0.5, 1.0, 2.0,3.0, and . These ratios correspond to composition values of pc / (pc + pw) =1/(1+ pw tyc) of 0, 1/3, 1/2, 2/3, 3/4, and unity. For emissivity calculations at other temperatures and mixture compositions, linear interpolation of the constants is recommended. 

The absorptivity can be obtained from the emissivity with aid of Table 5-5 by using the following functional equivalence. 

Verbally, the absorptivity computed from Eq. (5-141) by using the correlations in Table 5-5 is based on a value for gas emissivity Eg calculated at a temperature 7 and at a partial-pressure path-length product of (pc+pw)L7y77. The absorptivity is then equal to this value of gas emissivity multiplied by (Tg/Tj). It is recommended that spectrally based models such as RADCAL (loc. cit.) be used particularly when extrapolating beyond the temperature, pressure, or partial-pressure-length product ranges presented in Table 5-5. 

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These temperatures, partial pressures, and dimensions were used in Example 6 to determine gas emissivity and absorptivity, .q = 0.145 OCci = 0.210. The approximate effective emissivity of the boundary is (0.8 -I-1)72 = 0.9. Then from Eq. (5-155), modified to allow for sink emissivity and for the presence of a small amount of refractory boundary,... 

Example 11 Calculations of Gas Emissivity and Absorptivity Consider a slab of gas confined between two infinite parallel plates with a distance of separation of L = 1 m. The gas pressure is 101.325 kPa (1 atm), and the gas temperature is 1500 K (2240°F). The gas is an equimolar mixture of C02 and H20, each with a partial pressure of 12 kPa (pc = pw = 0.12 atm). The radiative flux to one of its bounding surfaces has been calculated by using RADCAL for two cases. For case (a) the flux to the bounding surface is 68.3 kW/m2 when the emitting gas is backed by a black surface at an ambient temperature of 300 K (80°F). This (cold) back surface contributes less than 1 percent to the flux. In case (b), the flux is calculated as 106.2 kW/m2 when the gas is backed by a black surface at a temperature of 1000 K (1340°F). In this example, gas emissivity and... 

It is clear that transfer from the gas to the surface and transfer from the surface into the gas are characterized by two different constants of proportionality, g and agi. To allow for the difference between gas emissivity and absorptivity, it proves convenient to introduce a single... 

The gas emissivities and absorptivities are then calculated from the two constant correlation in Table 5-5 (column 5 with pjpc - 2.0) as follows ... 

Total Emissivity and Absorptivity Models. For many engineering applications, spectrally integrated gas emission and absorption are needed. The total emissivity is defined as the ratio of the total radiation emitted from a path of length X to the maximum possible emission ... 

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