By Stefan Braun and Ingo Cremer, Fluent Germany

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Heat transfer is a major component of most CFD applications. In addition to common transport mechanisms like convection and conduction, radiation plays an important role in many of these cases. Radiation is an electromagnetic wave that interacts with its surroundings. The interaction includes absorption and reflection at walls, and absorption and scattering within the fluid medium. Absorption and scattering are important effects in optically thick (or participating) media, such as exhaust gases. In FLUENT there are several models available for simulating radiation. The appropriateness of one model over another is determined by the problem definition, fluid properties, and solution needs.

Eight people enjoy a raclette party in a heated room

The Rosseland (and P-1, not shown) models predict similar temperatures on all people

The S2S model predicts warmer temperatures than the Rosseland or P-1 models

The Rosseland approach is the simplest. Designed for optically thick media, it accounts for radiation losses through the use of a diffusive source term in the energy equation. The P-1 approach requires the solution of a radiation transport equation (RTE), based on the assumption that radiation is continuous throughout the domain. It works best with participating media. While the P-1 model accounts for scattering, it does not allow wavelength dependence. For optically thin or non-participating media, three models are available. A view-factor method is implemented in the surface-to-surface (S2S) model, which is designed for enclosures with nonparticipating media. Alternatively, a Lagrangian approach can be followed to calculate discrete rays departing from surfaces. The discrete transfer radiation model (DTRM) is based on this approach, and can be applied to a range of optical thicknesses. It tends to be computationally expensive, however, with an accuracy that is proportional to the number of rays computed. The discrete ordinate method (DOM) combines continuous and Lagrangian elements. Space is divided into discrete segments (solid angles), each covered by its own transport equation for radiation energy. By increasing the number of spatial divisions, accuracy can be enhanced quite naturally. The model can be used for all optical thicknesses, and can include wavelength-dependent interactions with the media.

The DTRM (top) and DO (bottom) models predict warmer temperatures on the people closest to the grill

To compare and contrast the various radiation models in FLUENT, a dinner party in a heated room has been studied. The room contains a tiled stove in one corner that serves as a heat source. Three directional lamps stand in the corners and point to the ceiling. Eight people are seated around a table with a heat-emitting raclette grill (used to heat individual portions of cheese and toppings) positioned in the middle. The outer boundary conditions correspond to an autumn evening in a wooden house. Since it is warm inside, the door is open. The room air is not optically thick, but the radiative properties of air are included in the calculations, when possible. Using GAMBIT, a hybrid mesh of 800,000 cells was created for the simulations.

The P-1 model captures the plume from the grill, despite an economical calculation scheme

The DO (shown), DTRM, and S2S models also predict a plume rising from the grill with weaker currents elsewhere in the room

The parameters in the radiation models employed were chosen to balance calculation effort and accuracy. Volumetric heat sources were chosen for the lamps, stove, grill, and people.

The temperatures on the surfaces of the people at the table and objects in the room were found to differ among the radiation models tested. The diffusive Rosseland and P-1 models predicted the same temperature distribution on all people seated at the table, with warmer faces than bodies. The S2S, DTRM, and DOM methods were the only ones to predict warmer temperatures on the faces of the people closest to the grill, because they take into account the distance between all surfaces. The DOM model resulted in smoother, yet asymmetric temperature profiles on the faces of the people at the table. The asymmetry is likely a feature of the radiation energy, which is greatest near the center of the table. The surfaces of the people that are closest to the raclette grill are directly confronted with the radiation energy of the grill. Since the sides of the people don’t have direct exposure to the radiation, the smoothing of the profiles is most likely due to heat conduction. The S2S model gives similar results, despite the fact that the view-factor calculation for this example was done with low resolution. For all of the radiation models studied, the foot temperatures, near the cold floor, are lowest.

Because the flow field in the room is the result of natural convection, the temperature solution is a governing factor in the flow field. For this reason, the flow fields predicted by the various radiation models were found to differ. The Rosseland model, which predicted nearly uniform temperatures on the people seated at the table, did not predict a strong plume rising above the grill. It did, however, predict a strong recircuclation across the cold floor leading to the warm people and hot stove, a result which is incorrect. The P-1 and S2S models both predicted a plume, and weaker circulation elsewhere in the room. The results of the P-1 model are surprisingly good, and better than expected, considering the modest calculation effort.

Following the temperature results, the flow predicted by the DTRM and DOM calculations were again similar. Compared to the P-1 and S2S results, there was a stronger plume predicted above the grill, which led to stronger recirculation zones in front of the tiled stove and in the back of the sitting people.

The outcome of the different models tested leads to some clear guidelines for modeling this type of flow. The Rosseland model neglects directional dependence while assuming that all energy is directly converted into radiation energy. These assumptions are wrong for this type of problem, with a non-participating medium. The predicted temperature field from this model is almost uniform and, subsequently, the flow field fails to capture certain anticipated features. The goal of the CFD simulation influences the choice between the remaining models. If just the global flow field is of interest, all four models will provide sufficient results. For general flow field studies, therefore, the one with the lowest computational effort - the P-1 model - should be chosen. If the temperature distribution is important, the P-1 model should be avoided, since it, too, lacks the geometric dependence that is captured by the S2S, DTRM, and DO models. For a parameter study or an unsteady calculation, the S2S model may be the model of choice, since the computational effort is low once the view factor calculation has been done at the start of the simulation. If the details of the temperature distribution are of interest, the DTRM and DO models are the best choices, and the results are even more accurate when these models are used with proper discretization. Since the DTRM performs best on a fine mesh with a sufficient number of rays, it is not the most cost-effective. The DO model, on the other hand, is more generally applicable, since the number of discrete ordinates can be increased to meet the desired solution accuracy. Indeed, it is possible to start with a coarse DO discretization and make refinements during the simulation until a smooth solution is obtained.

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