Surface Radiation Exchange Reference
Surface radiation exchange simulations concern only the radiating and absorbing surfaces, not any intervening medium.
The medium that fills the space between the surfaces is non-participating. That is, it does not absorb, emit, or scatter radiation. Under these circumstances, the radiation properties and the thermal boundary conditions that are imposed on each surface uniquely define the amount of radiation that a surface receives and emits. The surface properties are quantified in terms of emissivity, reflectivity, transmissivity, and radiation temperature. These properties are not dependent on direction; however, they can be dependent on radiation wavelength with the Multiband Radiation model. Surface radiative properties are available for various boundary types, such as walls, outlets, inlets, and interface boundaries. A notable exception are the interface boundaries corresponding to the mixing plane interfaces.
Surface-to-Surface Radiation simulation can have regions connected by mixing plane interfaces. Mixing planes are non-participating boundaries and so, like transparent boundaries, do not take part in emission, absorption, or reflection. However, unlike the radiation passing through a fully transparent boundary or interface, radiation passing through a mixing plane gets radially averaged coming out on the other side. Use of the mixing plane interface is not compatible with the Solar Loads model or the Circumferential Flux Averaging model.
Fully developed interfaces are not considered in radiation calculations. The corresponding interface boundaries are not present in Surface-to-Surface calculations, and radiation goes uninterrupted through those boundaries.
The boundaries at an interface need to be coincident. Since meshing is not perfect, a very small tolerance is allowed between the two sides of the interface. The ray tracing procedure ignores this separation and treats the geometries as coincident. If the two boundaries are not coincident with a too large distance between them, the ray tracing algorithm stops giving meaningful results.
Symmetry plane and periodic boundaries contribute to the radiation heat transfer only by reflecting or periodically transforming the radiative energy in the correct direction.
There are two models for surface radiation exchange simulations: Surface-to-Surface Radiation and Surface Photon Monte Carlo. Surface-to-Surface (S2S) is a deterministic model that uses view factors (computed beforehand) to compute radiative exchange between surfaces. Surface Photon Mote Carlo (SPMC) is a statistical model and solves for the RTE via ray tracing.
Patches
The surface radiation exchange models rely on the spatial discretization of the boundary surfaces into patches. Patches can be formed, for instance, from aggregating the boundary faces from the underlying mesh.
Patches allow you to make trade-offs between accuracy and computational cost. See Impact of Patch and Angular Resolution in the Surface-to-Surface Model.
View Factors
The S2S model relies on the view factors that quantify the proportion of surface area in each patch that the other patches illuminate. This model operates in two steps:
- Calculate view factors using ray tracing.
- Apply view factors to compute radiosity and irradiation fields on all surfaces.
In the view factor calculation step, deterministic ray tracing is applied to compute the factors. Rays are traced into the hemisphere above each patch using a fixed distribution of directions over this hemisphere. By default, a distribution of 1024 rays per patch is used.
The view factors must be calculated only when the geometry and radiative properties such as transmissivity and specular reflectivity change. Therefore, they generally can be calculated once and then reused during the combined-mode heat transfer solution to update the radiative fluxes from the surface emissive powers (that is temperatures).
An advantage of the two-step approach is computational efficiency gained from doing relative infrequent ray tracing. The trade-off is that view factors must be stored, often requiring considerable amount of memory.
| Note | View factors are calculated from non-diffuse surfaces to other partially diffuse surfaces, but not the other way round. |
Patches and view factors are explained in further detail in the Theory Guide—S2S (Surface-to-Surface) Radiation section.
Impact of Patch and Angular Resolution in the Surface-to-Surface Model
View factors are considered computationally efficient for combined-mode problems. However, the number of degrees of freedom (that is, the number of patches) is often limited. The limitation is because the view factors count can be O(N2) in the limit, where N is the number of patches. The Simcenter STAR-CCM+ approach provides flexibility through patch and angular resolution to help address the computation time and memory issues that are associated with view factors. This approach makes it is possible to run cases having a million patches or so.
With the deterministic ray tracing approach of the Surface-to-Surface (S2S) model, the number of rays per patch limits the view factor count. Therefore, with reciprocity you can get a maximum of 2L view factors per patch, where L is the number of rays per patch. Thus, 1 million patches with 1024 rays/patch could produce a maximum of about 2 billion view factors. This number is manageable in Simcenter STAR-CCM+ in terms of both computation time and memory with parallel ray tracing and S2S algorithms. The resolution of the ray-tracing can be increased to increase accuracy, but at the expense of computation time and memory. There is thus a classic trade-off between accuracy and required computational resources (time and memory).
For some combined-mode problems, the resolution of the underlying mesh for the advection/diffusion transport can be prohibitively high when using its boundary faces directly as patches in the S2S calculations. For instance, some simulations can have tens of millions of boundary faces, making a 1-to-1 ratio between the S2S patches and the boundary faces intractable. Additionally, this fine patch resolution is not always needed with respect to accuracy, especially when the surface topology and surface temperatures do not change rapidly. Simcenter STAR-CCM+ therefore provides the flexibility to use a patch resolution that is coarser than the boundary face resolution. Patches can be formed, for instance, from aggregating the boundary faces from the underlying mesh. For high-resolution meshes, you can generally use 1 patch for every 10 or so faces from the underlying mesh. There is again a trade-off between accuracy and required computational resources. A finer patch resolution generally provides better accuracy, but also requires more computational resources. You can find a balance that provides the needed accuracy within the given time and hardware constraints. In the end, most methods for solving the radiative transfer equations are constrained in a similar trade-off between performance and accuracy due to the nature of the physics (transfer at a distance).
Use of Shells
For the highest possible accuracy, each boundary belonging to a shell must be coincident and be as similarly meshed as possible—that is, have non-conformal meshes as seldom as possible. When non-conformal meshes are unavoidable, the meshes should be as similar as possible.
Patching Considerations with Surface Photon Monte Carlo
The patching considerations here are similar to that for the S2S model. The patch resolution in the SPMC model offers a trade-off between accuracy and required computational resources. For more details, see Impact of Patch and Angular Resolution in the Surface-to-Surface Model.