The Radiosity Method for Diffuse-Spectral Surfaces
For a general diffuse-spectral surface:
where
•
ε(λ, T) and ρd(λ, T) are is the hemispherical spectral surface emissivity and diffuse reflectivity, dimensionless quantities in the range [0,1]. Diffuse-spectral surface corresponds to a surface properties are dependent on the radiation wavelength and surface temperature.
•
T is the surface temperature (SI unit: K).
•
eb, λ(λ, T) is the blackbody hemispherical emissive power (SI unit: W/(m3·sr)) defined in Equation 4-106.
The Surface-to-Surface Radiation Interface assumes that the surface emissivity and opacity properties are constant per spectral band. It defines N spectral bands (N = 2 when solar and ambient radiation model is used),
so that the radiosity has a custom definition in each interval:
The surface properties can then be defined per spectral band:
•
Surface emissivity on Bi: εi(T) = ε(λ, T) for λ in the interval Bi
•
Surface diffuse reflectivity on Bi: ρd,i(T) = ρd(λ, T) for λ in the interval Bi
•
Ambient irradiation on Bi, assuming that the ambient fractional emissive power corresponds to the one of a blackbody at temperature Tamb:
•
External radiation sources on Bi with q0, s, i and Ps, i the external radiation source heat flux and heat rate, respectively, over Bi:
or
When the external source fractional emissive power corresponds to the one of a blackbody at Text, external radiation sources on Bi can be defined from the external radiation source heat flux, q0, s, and heat rate, Ps, over all wavelengths:
or
The Surface-to-Surface Radiation Interface includes the following radiation types:
•
Diffuse Surface (Surface-to-Surface Radiation Interface) is the default radiation type. The incident radiation over the Bi spectral band at one point of the boundary is a function of the radiosity, Ji (SI unit: W/m2), at every other point in view. The radiosity, in turn, is a function of Gm, i, which leads to an implicit radiation balance:
(4-111)
•
Diffuse Mirror (Surface-to-Surface Radiation Interface) is a variant of the Diffuse Surface radiation type with εi = 0. Reradiation surfaces are common as an approximation of a surface that is well insulated on one side and for which convection effects can be neglected on the opposite (radiating) side (see Ref. 21). It resembles a mirror that absorbs all irradiation and then radiates it back in all directions.
•
Prescribed Radiosity (Surface-to-Surface Radiation Interface) makes it possible to specify the surface radiation for each spectral band. Using the graybody radiation definition, the radiosity is then . A user-defined surface radiosity expression can also be defined.
•
Opaque Surface (Surface-to-Surface Radiation Interface) is available with Ray shooting as Surface-to-surface radiation method. It accounts for specular reflection. The conservation equation reads
and the radiosity reads as in Equation 4-111.
•
Semitransparent Surface (Surface-to-Surface Radiation Interface) is available with Ray shooting as Surface-to-surface radiation method. It accounts for reflection, transmission and the conservation equation reads
and the radiosities read
(4-112)
(4-113)
The Surface-to-Surface Radiation interface handles the radiosity Ji as a shape function unless Ji is prescribed.
Whereas diffuse and specular reflectivities are handled by the different features of the Surface-to-Surface Radiation interface, only diffuse emissivity is considered.