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8.8.1 Absorption Coefficient

To define the absorption coefficient, you can specify a constant value, a temperature-dependent function (see Section  8.2), a composition-dependent function, or a user-defined function. The absorbing and emitting parts of the radiative transfer equation (RTE), Equation  13.3-1, is a function of the absorption coefficient. The absorbing or emitting effects depend on the chosen radiation model. If there are only absorption effects,then Lambert's Law of absorption applies

 I = I_o\exp{(-ax)} (8.8-1)

where $I$ is the radiation intensity, $a$ is the absorption coefficient, and $x$ is the distance through the material.

If you are modeling non-gray radiation with the DO radiation model, you also have the option to specify a constant absorption coefficient in each of the gray bands. The absorption coefficient is requested in units of 1/length. Along with the scattering coefficient, it describes the change in radiation intensity per unit length along the path through the fluid medium. Absorption coefficients can be computed using tables of emissivity for CO $_2$ and H $_2$O, which are generally available in textbooks on radiation heat transfer.



Inputs for a Constant Absorption Coefficient


To define a constant absorption coefficient, simply enter the value in the field next to Absorption Coefficient in the Materials panel. (Select constant in the drop-down list first if it is not already selected.)



Inputs for a Composition-Dependent Absorption Coefficient


FLUENT also allows you to input a composition-dependent absorption coefficient, with the local value of $a$ a function of the local mass fractions of water vapor and carbon dioxide. This modeling option can be useful for simulation of radiation in combustion applications. The variable-absorption-coefficient model used by FLUENT is the weighted-sum-of-gray-gases model (WSGGM) described in Section  13.3.8. To activate it, select wsggm-cell-based, wsggm-domain-based, or wsggm-user-specified in the drop-down list to the right of Absorption Coefficient in the Materials panel. The three WSGGM options differ in the method used to compute the path length, as described below.

(Remember that you must first enable the species calculation in order to see the wsggm choices in the list, and CO $_2$ and H $_2$O must be present in the mixture.)

Path Length Inputs

When the WSGGM is used to compute the absorption coefficient, you will have a choice of methods used to calculate the path length $s$ in Equation  13.3-81. You can use the characteristic cell size or the mean beam length (computed by the solver or defined by you). See Section  13.3.8 to determine which method is appropriate for your case.

You will select the path length method when you choose the property input method for Absorption Coefficient as described above.



Inputs for a Non-Gray Radiation Absorption Coefficient


If you are using the non-gray DO model (see Sections  13.3.6 and 13.3.13), you can specify a different constant absorption coefficient for each of the bands used by the gray-band model. Select gray-band in the Absorption Coefficient drop-down list, and then define the absorption coefficient for each band in the Gray-Band Absorption Coefficient panel. (Note that, since this is a modal panel, you must tend to it immediately.)



Effect of Particles and Soot on the Absorption Coefficient


FLUENT will include the effect of particles on the absorption coefficient if you have turned on the Particle Radiation Interaction option in the Discrete Phase Model panel (only for the P-1 and DO radiation models).

If you are modeling soot formation and you want to include the effect of soot formation on the absorption coefficient, turn on the Generalized Model for Soot-Radiation Interaction in the Soot Model panel. The soot effects can be included for any of the radiation models, as long as you are using the WSGGM to compute a composition-dependent absorption coefficient.


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