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), this equation in the separate Theory Guide , 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

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 Create/Edit Materials dialog box. (Select constant in the drop-down list first if it is not already selected.)

Inputs for a Composition-Dependent Absorption Coefficient

ANSYS FLUENT also allows you to input a composition-dependent absorption coefficient, where the local value of $a$ is a function of the local mass fractions of water vapor and carbon dioxide. This modeling option can be useful for the simulation of radiation in combustion applications. The variable-absorption-coefficient model used by ANSYS FLUENT is the weighted-sum-of-gray-gases model (WSGGM) described in this section in the separate Theory Guide. 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 Create/Edit Materials dialog box. 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 this equation in the separate Theory Guide. You can use the characteristic cell size or the mean beam length (computed by the solver or defined by you). See this section in the separate Theory Guide 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.

• If you choose wsggm-cell-based, the characteristic-cell-size approach will be used and no further inputs are required.

• If you choose wsggm-domain-based, the mean-beam-length approach will be used for the calculation of $a$ and ANSYS FLUENT will compute the mean beam length based on an average dimension of the domain; no further inputs are required.

• If you choose wsggm-user-specified, the mean-beam-length approach will be used, but you will set the mean beam length yourself in the Path Length field in the WSGGM User Specified dialog box. This dialog box will open when you choose wsggm-user-specified, and since it is a modal dialog box, you must tend to it immediately.

Inputs for a Non-Gray Radiation Absorption Coefficient

If you are using the non-gray DO model (see this section in the separate Theory Guide and 13.3.4), 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 dialog box. (Note that, since this is a modal dialog box, you must tend to it immediately.)

Effect of Particles and Soot on the Absorption Coefficient

ANSYS 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 dialog box (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 Soot-Radiation Interaction in the Soot Model dialog box. 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.