Gebhardt method

The radiative conductances can be calculated using the Gebhardt method.

Gray body view factors between the elements are calculated by Gebhardt method. This method assumes that the radiation emitted by i and absorbed by j after multiple diffuse reflections is equal to the absorbed portion of the radiation directly incident upon j, plus the radiation reflected by all surfaces:

The reflected radiation is assumed to be reflected perfectly diffusely, i.e. it is reflected in proportion to the view factors of the element. If only geometric view factors are present on the VUFF file, then even if an element has specular reflectivity, its reflectivity is treated as perfectly diffuse.

If ray-traced view factors are present on VUFF through the use of the VFTRACE option, the equivalent reduced diffuse properties of the view factor matrix are used for elements that have specular or transmissive surface properties. In this case, the specular and transmissive effects have been accounted for during the ray-tracing procedure.

Eliminating insignificant radiative conductances

Excessively weak radiative conductances calculated with Gebhardt method may be eliminated or connected to element through the use of a non-zero RK parameter. For each element i and j the largest gray body view factors not connected to a space element VF_Gimax and VF_Gimax are found, and only those radiative conductances whose gray body view factors fulfill the two inequalities are considered:

All others are considered insignificant.

The double inequality is necessary because when A_i << A_j the conductance may be insignificant for j but very important for i.

If RK > 0 the insignificant radiative conductances are not considered, unless the coupling is to space.

If RK < 0 and the element number is not equal to zero, each insignificant coupling is replaced by two equivalent couplings, one from element i and one from element j, to element number, provided element number is not a space element.

The gray body view factor matrices are not affected by RK.

It is necessary to exercise care with RK > 0 to avoid eliminating an excessive number of radiative couplings. RK = 1 eliminates all radiative couplings.

RK = 0 defaults to RK = 1.E-4.