Gray gas

If the kiln may be considered an enclosure bounding an isothermal gray gas of emissivity, S, with two bounding surfaces consisting of reradiating walls of area, and of bed soHds (the radiation sink) of area, then the expression for R becomes (19)... 

For simplicity, n should be as low as is consistent with small error. The retention of but two terms is feasible when one considers that if Otci is so fitted that the first absorption and the second following surface reflec tion are correct, then further attenuation of the beam by successive surface reflections makes the errors in those absorptions decrease in importance. Let the gas be modeled as the sum of one gray gas plus a clear gas, with the gray gas occupying the energy frac tion a of the blackbody spectrum and the clear gas the frac tion (1 — ). Then... 

Note that these values are specific to the subject problem in which the mean beam length is L, , with gS evaluated from basic data, such as Table 5-8. (1 — in Eq. (5-165) represents the emissivity of a gray gas, which will be called Ec,i. For later use, note that,... 

HEAT AND MASS TRANSFER TABLE 5-10 Total-Exchange Areas for Four Arrangements of Two-Zone-Surface Enclosures of a Gray Gas... 

The simplest application of this simple gray-plus-clear model of gas radiation is the case of a single gas zone surrounded by a single surface zone, Eq. (5-163) for a gray gas. The gray-plus-clear model gives... 

Conversion of (GSi)r to applicabihty to a gray gas comes by making a equal 1, producing the enormous simphfication to... 

An important parameter in RTE that needs modeling is the calculation of the absorption coefficient k(x,A), which depends on the local gas and soot concentrations. In a typical fire CFD, a gray gas is assumed, which means that the spectral dependency of k is not considered instead kx is replaced with an integrated value of k that is obtained by integrating over the entire wavelength... 

Number of surface and volume zones in enclosure Partial pressure of species k, atm Number of WSGG gray gas spectral windows Total radiative flux originating at surface zone t, W Net radiative flux between zone t and zonej, W Temperature, K... 

Radiative transfer with respect to the confined gas is either monochromatic or gray. The gray gas absorption coefficient is denoted here by fC(m-1). In subsequent sections the monochromatic absorption coefficient is denoted by KfX). 

Mean Beam Lengths It is always possible to represent the emissivity of an arbitrarily shaped volume of gray gas (and thus the corre-... 

Energy Balances for Volume Zones—The Radiation Source Term Reconsider a generalized enclosure with N volume zones confining a gray gas. When the N gas temperatures are unknown, an additional set of N equations is required in the form of radiant energy... 

In Eqs. (5-160) the gray gas transmissivity xg is taken to be identical to that obtained for the gas emissivity Eg. The constant agl in Eq. (5-160a) is then obtained with Knowledge of one additional empirical value for agl which may also be obtained from the correlations in Table 5-5. Notice further in the definitions of the three parameters Eg, a 1, and xg l that all the temperature dependence is forced into the two WSGG constants ag and a 1. 

Subject to the restrictions of no scatter and diffuse surface emission and reflection, the above equations are the most general matrix statement possible for the zone method. When P = 1, the directed exchange areas all reduce to the total exchange areas for a single gray gas. If, in addition, K = 0, the much simpler case of radiative transfer in a transparent medium results. If, in addition, all surface zones are black, the direct, total, and directed exchange areas are all identical. 

For the WSGG clear gas components we denote SS ]K 0 = SSQ an( Sf K o = SG0 = 0. Finally the WSGG arrays of directed exchange areas are computed simply from a-weighted sums of the gray gas total exchange areas as... 

Example 12 WSGG Clear plus Gray Gas Emissivity Calculations Methane is burned to completion with 20 percent excess air (50 percent relative humidity at 298 K or 0.0088 mol water/mol dry air) in a furnace chamber of floor dimensions 3 x 10 m and height 5 m. The entire surface area of the enclosure is a gray sink with emissivity of 0.8 at temperature 1000 K. The confined gas is well stirred at a temperature of 1500 K. Evaluate the clear plus gray WSGG constants and the mean effective gas emissivity, and calculate the average radiative flux density to the enclosure surface. 

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