Understanding view factors

When you create a Radiation simulation object, within an enclosure, the solver computes the view or partial view between each element and all other elements.

• The black body view factor is the view or partial view an element has of another element.

• The gray body view factor is the fraction of total energy leaving one element that is absorbed by another, including the element's emissivity and the effect of reflections.

Black body view factor definition

A black body view factor (also called a radiation form factor) represents that fraction of the total diffuse radiative energy emitted from a particular element which arrives at a second element assuming no intermediate reflections. Black body view factors are functions of surface geometry only; surface properties do not enter into their calculation. The solver calculates black body view factors between each pair of elements in an enclosure.

Black body view factors are defined mathematically by:

where F ij is the black body view factor from surface i to surface j.

Black body view factor calculation

The solver uses one of two methods for computing radiation view factors based on a blockage criterion. The solver first determines if a surface pair has an unobstructed view, that is, if every point on one surface can be seen from any point on the other without obstruction (or "shadowing") by intervening surfaces. Where it is established that there is an unobstructed view, the solver computes the view factor using the exact contour integral technique. This method is very fast, and gives accurate results regardless of surface geometry or size ratio.

For surface pairs whose view is partially shadowed by other elements, shadowing checks must be performed, and the solver uses the Nusselt sphere technique.

Black body view factor precision

When modeling radiation, elements simulate the surfaces of an enclosure. If the geometry of the model itself does not form a physical enclosure, or if it radiates to the environment, select the Include Radiative Environment option in the Radiation dialog box.

In an enclosure, the sum of any element's view factors is equal to 1. Each view factor represents a fraction of the energy an element radiates in the enclosure. Since all the energy the element radiates either reaches other elements that are inside the enclosure or escapes to the radiative environment, the sum of the fractions is 1.

Although the view factor sum of each element should be to equal 1, it is not always the case, usually because of imprecision in the calculation of partial views. Shadowing checks are used to determine which elements have an obstructed view of other elements and a subdivision method is then used to calculate the partial view.

You can control the precision of this calculation with the options in the Radiation dialog box.

Gray body view factor definition

The gray body view factor is the fraction of total energy leaving one element that is absorbed by another. It includes direct and reflected paths. It is a function of the element's Thermo-Optical Properties and the geometry of all elements in the enclosure, since they may participate in reflection. If you change the geometry of one element, it can affect the gray body view factors of the others to a greater or lesser degree. The solver calculates gray body view factors for each element and uses this data to calculate radiative exchange in the enclosure.

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