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Code Manual for CONTAIN 2.0 - Federation of American Scientists

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cases in which only water vapor is present, a Cess-Lian correlation maybe specified with the CESS<br />

keyword in the R4D-HEAT input block. [Ces76] If this option is chosen, CO and COZ(if present)<br />

are assumed to be transparent and do not contribute to the gas mixture emissivity.<br />

Section 10.3.1 describes the net enclosure radiation model, and Section 10.3.2 discusses the direct<br />

radiation model. The gas mixture emissivity models used in <strong>CONTAIN</strong> are presented in Section<br />

10.3.3.<br />

10.3.1 Net Enclosure Radiation Model<br />

The net enclosure model in <strong>CONTAIN</strong> is a treatment <strong>of</strong> radiative transfer involving a participating<br />

gas-aerosol-debris mixture and the surrounding surfaces that takes secondary reflections into account<br />

automatically. This model was adapted from a <strong>for</strong>mulation <strong>for</strong> diffuse gray surfaces in Reference<br />

Sie81 (see the derivation in Reference Ber85b). A basic assumption is that the atmosphere is<br />

completely surrounded by the inner surfaces <strong>of</strong> heat transfer structures and the uppermost layer <strong>of</strong><br />

the lower cell, if present. The surrounding surfaces can be at different temperatures with automatic<br />

accounting <strong>for</strong> secondary (surface-to-surface) reflections. Since the method requires the gas in the<br />

enclosure to be isothermal, only one cell is modeled at a time. In addition, each cell is treated as a<br />

complete enclosure. When a participating medium is not present in the cell (i.e., when water vapor,<br />

CO, COZ,aerosols, and core debris are absent), the radiation model reduces to the surface radiative<br />

exchange problem with a transparent nonattenuating gas medium.<br />

According to Kirchh<strong>of</strong>f’s law, the radiation flux ~~J to surface j is given by<br />

‘@j = * (’l’, “ ‘j)<br />

s,j<br />

(10-58)<br />

where &,,jis the emissivity <strong>of</strong> surface j, ~j is the radiosity <strong>of</strong> surface j (W/m2), and Bj is the Planck<br />

blackbody radiation flux <strong>for</strong> surface j (W/m2)<br />

B,=GT4 w,<br />

(lo-59)<br />

where o is the Stefan-Boltzmann constant (W/m2-K4),and TW,jis the surface node temperature <strong>for</strong><br />

surface j (see Figure 10-9).<br />

The radiosity, ~j in Equation (10-58), is calculated by solving a series <strong>of</strong> linear equations<br />

simultaneously.<br />

N N<br />

~j - (1 - ‘S,j) ~ ‘jk (1 - ‘m,jk) Vk = ‘s,j ‘j + (1 - ‘$j) k~l ‘jk ‘m,jk ‘g (10-60)<br />

k=l<br />

Rev O 10-37 6/30/97

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