13.3.7 Solution Strategies for Radiation Modeling

For the P-1, DTRM, S2S, and the DO radiation models, there are several parameters that control the radiation calculation. You can use the default solution parameters for most problems, or you can modify these parameters to control the convergence and accuracy of the solution. Iteration parameters that are unique for a particular radiation model are specified in the Radiation Model dialog box (e.g., Flow Iterations Per Radiation Iteration). Spatial Discretization ( this section in the separate Theory Guide) and Under-Relaxation ( this section in the separate Theory Guide) are specified in the Solution Methods and Solution Controls task pages, respectively. The Convergence Criterion (Section  26.13.1) is set in the Residual Monitors dialog box.

There are no solution parameters to be set for the Rosseland model, since it impacts the solution only through the energy equation.

If radiation is the only model being solved in ANSYS FLUENT, and all other equations are switched off, then the Flow Iterations Per Radiation Iteration solution parameter that is available for certain radiation models, is automatically reset to 1.

P-1 Model Solution Parameters

For the P-1 radiation model, you can control the convergence criterion and under-relaxation factor. You should also pay attention to the optical thickness, as described below.

The default convergence criterion for the P-1 model is $10^{-6}$, the same as that for the energy equation, since the two are closely linked. See Section  26.13.1 for details about convergence criteria. You can set the Convergence Criterion for p1 in the Residual Monitors dialog box.

Monitors Residuals Edit...

The under-relaxation factor for the P-1 model is set with those for other variables, as described in Section  26.3.2. Note that since the equation for the radiation temperature ( this equation in the separate Theory Guide) is a relatively stable scalar transport equation, in most cases you can safely use large values of under-relaxation (0.9-1.0).

For optimal convergence with the P-1 model, the optical thickness $(a + \sigma_s)L$ must be between 0.01 and 10 (preferably not larger than 5). Smaller optical thicknesses are typical for very small enclosures (characteristic size of the order of 1 cm), but for such problems you can safely increase the absorption coefficient to a value for which $(a + \sigma_s)L=0.01$. Increasing the absorption coefficient will not change the physics of the problem because the difference in the level of transparency of a medium with optical thickness = 0.01 and one with optical thickness $<$ 0.01 is indistinguishable within the accuracy level of the computation.

DTRM Solution Parameters

When the DTRM is active, ANSYS FLUENT updates the radiation field during the calculation and computes the resulting energy sources and heat fluxes via the ray-tracing technique described in this section in the separate Theory Guide. ANSYS FLUENT provides several solution parameters that control the solver and the solution accuracy. These parameters appear in the expanded portion of the Radiation Model dialog box (Figure  13.3.15).

Figure 13.3.15: The Radiation Model Dialog Box (DTRM)

You can control the maximum number of sweeps of the radiation calculation during each global iteration by changing the Number of DTRM Sweeps. The default setting of 1 sweep implies that the radiant intensity will be updated just once. If you increase this number, the radiant intensity at the surfaces will be updated multiple times, until the tolerance criterion is met or the number of radiation sweeps is exceeded.

The Tolerance parameter (0.001 by default) determines when the radiation intensity update is converged. It is defined as the maximum normalized change in the surface intensity from one DTRM sweep to the next (see Equation  13.3-2).

You can also control the frequency with which the radiation field is updated as the continuous phase solution proceeds. The Flow Iterations Per Radiation Iteration parameter is set to 10 by default. This implies that the radiation calculation is performed once every 10 iterations of the solution process. Increasing the number can speed the calculation process, but may slow overall convergence.

S2S Solution Parameters

For the S2S model, as for the DTRM, you can control the frequency with which the radiosity is updated as the continuous-phase solution proceeds. See the description of Flow Iterations Per Radiation Iteration for the DTRM, above.

If you are using the pressure-based solver and you first solve the flow equations with the energy equation turned off, you should reduce the Flow Iterations Per Radiation Iteration from 10 to 1 or 2. This will ensure the convergence of the radiosity. If the default value of 10 is kept in this case, it is possible that the flow and energy residuals may converge and the solution will terminate before the radiosity is converged. See Section  13.3.7 for more information about residuals for the S2S model.

You can control the maximum number of sweeps of the radiation calculation during each global iteration by changing the Number of S2S Sweeps. The default setting of 1 sweep implies that the radiosity will be updated just once. If you increase this number, the radiosity at the surfaces will be updated multiple times, until the tolerance criterion is met or the number of radiation sweeps is exceeded.

The Tolerance parameter (0.001 by default) determines when the radiosity update is converged. It is defined as the maximum normalized change in the radiosity from one S2S sweep to the next (see Equation  13.3-3).

DO Solution Parameters

For the discrete ordinates model, as for the DTRM, you can control the frequency with which the surface intensity is updated as the continuous phase solution proceeds. See the description of Flow Iterations Per Radiation Iteration for the DTRM, above.

For most problems, the default under-relaxation of 1.0 for the DO equations is adequate. For problems with large optical thicknesses ( $aL>10$), you may experience slow convergence or solution oscillation. For such cases, under-relaxing the energy and DO equations is useful. Under-relaxation factors between 0.9 and 1.0 are recommended for both equations.

Running the Calculation

Once the radiation problem has been set up, you can proceed as usual with the calculation. Note that while the P-1 and DO models will solve additional transport equations and report residuals, the DTRM and the Rosseland and S2S models will not (since they impact the solution only through the energy equation). Residuals for the DTRM and S2S model sweeps are reported by ANSYS FLUENT every time a DTRM or S2S model iteration is performed, as described below.

Residual Reporting for the P-1 Model

The residual for radiation as calculated by the P-1 model is updated after each iteration and reported with the residuals for all other variables. ANSYS FLUENT reports the normalized P-1 radiation residual as defined in Section  26.13.1 for the other transport equations.

Residual Reporting for the DO Model

After each DO iteration, the DO model reports a composite normalized residual for all the DO transport equations. The definition of the residuals is similar to that for the other transport equations (see Section  26.13.1).

Residual Reporting for the DTRM

ANSYS FLUENT does not include a DTRM residual in its usual residual report that is issued after each iteration. The effect of radiation on the solution can be gathered, instead, via its impact on the energy field and the energy residual. However, each time a DTRM iteration is performed, ANSYS FLUENT will print out the normalized radiation error for each DTRM sweep. The normalized radiation error is defined as

where the error $E$ is the maximum change in the intensity ( $I$) at the current sweep, normalized by the maximum surface emissive power, and $N$ is the total number of radiating surfaces. Note that the default radiation convergence criterion, as noted in Section  13.3.7, defines the radiation calculation to be converged when $E$ decreases to $10^{-3}$ or less.

Residual Reporting for the S2S Model

ANSYS FLUENT does not include an S2S residual in its usual residual report that is issued after each iteration. The effect of radiation on the solution can be gathered, instead, via its impact on the energy field and the energy residual. However, each time an S2S iteration is performed, ANSYS FLUENT will print out the normalized radiation error for each S2S sweep. The normalized radiation error is defined as

where the error $E$ is the maximum change in the radiosity ( $J$) at the current sweep, normalized by the maximum surface emissive power, and $N$ is the total number of radiating surface clusters. Note that the default radiation convergence criterion, as noted in Section  13.3.7, defines the radiation calculation to be converged when $E$ decreases to $10^{-3}$ or less.

Disabling the Update of the Radiation Fluxes

Sometimes, you may wish to set up your ANSYS FLUENT model with the radiation model active and then disable the radiation calculation during the initial calculation phase. For the P-1 and DO models, you can turn off the radiation calculation temporarily by deselecting P1 or Discrete Ordinates in the Equations list, which is accessed via the Solution Controls task page. For the DTRM and the S2S model, there is no item in the Equations. You can instead set a very large number for Flow Iterations Per Radiation Iteration in the expanded portion of the Radiation Model dialog box.

If you turn off the radiation calculation, ANSYS FLUENT will skip the update of the radiation field during subsequent iterations, but will leave in place the influence of the current radiation field on energy sources due to absorption, wall heat fluxes, etc. Turning the radiation calculation off in this way can thus be used to initiate your modeling work with the radiation model inactive and/or to focus the computational effort on the other equations if the radiation model is relatively well converged.