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Code Manual for CONTAIN 2.0 - Federation of American Scientists

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10.3.3 Radiative Properties<br />

Both the net enclosure and direct radiation models, discussed in Sections 10.3.1 and 10.3.2,<br />

respectively, require the emissivity and absorptivity <strong>of</strong> the atmosphere gas mixture. These quantities<br />

are a function <strong>of</strong> the gas composition, pressure, temperature, and the average optical depth <strong>of</strong> the gas.<br />

The average optical depth is also referred to as the beam length. The present section discusses the<br />

methods available to calculate the emissivity e. <strong>of</strong> a gas mixture from the emissivities <strong>of</strong> the<br />

individual active gas species (CO, COZ,and H20) and the aerosols present in the gas.<br />

The Modak radiative property model is used by default to calculate these properties. [Mod79] If<br />

only water vapor and/or aerosols are present to an appreciable extent in the atmosphere, the user can<br />

invoke the Cess-Lian water vapor radiative property model [Ces76] by specifying the CESS keyword<br />

in the IL4D-HEAT input block. This model assumes that CO and COZ,if present, are transparent<br />

and do not affect radiative heat transfer.<br />

The gas absorptivity ct. is calculated from either the Modak model or the Cess-Lian correlation by<br />

using Kirchh<strong>of</strong>f’s law <strong>of</strong> radiation, which states that spectral emissivity <strong>for</strong> the emission <strong>of</strong> radiation<br />

at temperature T is equal to the spectral absorptivity <strong>for</strong> radiation coming from a blackbody at the<br />

same temperature T. This law maybe considered valid whether or not thermal equilibrium prevails.<br />

Its proper application greatly simplifies the calculation <strong>of</strong> radiative transfer.<br />

The Modak radiative property model is described in Section 10.3.3.1. The Cess-Lian radiative<br />

property model is described in Section 10.3.3.2.<br />

10.3.3.1 Modak Radiative Prom rtv Model. The default Modak radiative property model calculates<br />

the total gas mixture emissivity and absorptivity, taking into account the active gases HZO,CO, and<br />

C02 and aerosols.<br />

The gas mixture emissivity e. and absorptivity a. are given by<br />

and<br />

Em =&p+&-&&<br />

g Pg<br />

am =ap+a– aa<br />

g Pg<br />

where &Pand aP are, respectively,<br />

respectively, the gas emissivity and<br />

(10-69)<br />

(10-70)<br />

the aerosol emissivity and absorptivity, and s~ and a~ are,<br />

absorptivity.

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