The surface-to-surface radiation model can be used to account for the radiation exchange in an enclosure of gray-diffuse surfaces. The energy exchange between two surfaces depends in part on their size, separation distance, and orientation. These parameters are accounted for by a geometric function called a "view factor".
The main assumption of the S2S model is that any absorption, emission, or scattering of radiation can be ignored; therefore, only "surface-to-surface" radiation need be considered for analysis.
For information about setting up the model, see Setting Up the S2S Model in the User's Guide.
Ansys Fluent’s S2S radiation model assumes the surfaces to
be gray and diffuse. Emissivity and absorptivity of a gray surface
are independent of the wavelength. Also, by Kirchoff’s law [447], the emissivity equals the absorptivity (
). For a diffuse surface, the reflectivity is independent of the
outgoing (or incoming) directions.
The gray-diffuse model is what is used in Ansys Fluent. Also, as
stated earlier, for applications of interest, the exchange of radiative
energy between surfaces is virtually unaffected by the medium that
separates them. Thus, according to the gray-body model, if a certain
amount of radiant energy (
) is incident on a surface, a fraction (
) is reflected,
a fraction (
) is absorbed, and a fraction
(
) is transmitted. Since for most
applications the surfaces in question are opaque to thermal radiation
(in the infrared spectrum), the surfaces can be considered opaque.
The transmissivity, therefore, can be neglected. It follows, from
the conservation of energy, that 
,
since 
(emissivity), and 
.
The energy flux leaving a given surface is composed of directly
emitted and reflected energy. The reflected energy flux is dependent
on the incident energy flux from the surroundings, which then can
be expressed in terms of the energy flux leaving all other surfaces.
The energy leaving from surface 
is
 | (5–97) |
where 
is the energy flux
leaving the surface, 
is the emissivity, 
is the Stefan-Boltzmann
constant, and 
is the energy flux
incident on the surface from the surroundings.
The amount of incident energy upon a surface from another surface
is a direct function of the surface-to-surface "view factor,"
. The view factor 
is
the fraction of energy leaving surface 
that is incident on surface 
. The surfaces used in the
calculation of a view factor can be mesh faces or (for 3D cases only)
clusters of faces; see Clustering and View Factors for
details about clusters. The incident energy flux 
can be expressed
in terms of the energy flux leaving all other surfaces as
 | (5–98) |
where 
is the area of surface 
and 
is
the view factor between surface 
and surface 
. For 
surfaces, using the view factor reciprocity relationship
gives
 | (5–99) |
so that
 | (5–100) |
Therefore,
 | (5–101) |
which can be written as
 | (5–102) |
where 
represents the energy that
is given off (or radiosity) of surface 
, and 
represents
the emissive power of surface 
. This represents 
equations, which can be recast
into matrix form as
 | (5–103) |
where 
is an 
matrix, 
is the radiosity vector, and 
is the emissive power vector.
Equation 5–103 is referred to as the
radiosity matrix equation. The view factor between two finite surfaces 
and 
is given by
 | (5–104) |
where 
is determined
by the visibility of 
to 
. 
= 1 if 
is visible to 
and 0 otherwise.
The S2S radiation model is computationally very expensive when you calculate the radiation and view factors for a large number of surfaces. To reduce the computational time as well as the storage requirement, the number of surfaces is reduced by creating surface "clusters". The surface clusters are made by starting from a face and adding its neighbors and their neighbors until a specified number of faces per surface cluster is collected.
By default, view factors are calculated using a face to face basis, in which clustering is used in a limited way only. The boundary faces act as the surfaces for the view factor calculation, and then a cluster view factor is obtained by taking the area-weighted average of the view factors of the faces within the cluster.
For 3D cases, you have the option of using the cluster to cluster
basis instead of the face to face basis, which can reduce the computational
expense and storage requirements. In this approach, Ansys Fluent internally
creates polygon faces by combining all of the faces from non-polyhedral
cells in each cluster, and these are then used as the surfaces for
the view factor calculation. The .s2s file
will contain the connectivity information of the cluster itself instead
of the individual faces in the cluster, and the coarser, polyhedral
mesh that is written requires less disk space. Note that accuracy
can be impacted by the use of the cluster to cluster basis, because
of the following reasons:
Clusters are assumed to be planar for view factor computation, even though they may not be exactly planar. This discrepancy reduces the accuracy, especially as the surface becomes more convex / concave, and as the number of faces per surface clusters for the boundary zones increases.
The option of dividing faces into subfaces as part of the hemicube algorithm (which increases accuracy) is not available with the cluster to cluster basis.
The radiosity, 
, is calculated for the surface clusters. These values
are then distributed to the faces in the clusters to calculate the
wall temperatures. Since the radiation source terms are highly nonlinear
(proportional to the fourth power of temperature), care must be taken
to calculate the average temperature of the surface clusters and distribute
the flux and source terms appropriately among the faces forming the
clusters.
The surface cluster temperature is obtained by area averaging as shown in the following equation:
 | (5–105) |
where 
is the temperature
of the surface cluster, and 
and 
are the area
and temperature of face 
. The summation is carried over all faces of a surface
cluster.