Multispectral band radiation analysis

The thermal solver converts wavelength-dependent thermo-optical properties into equivalent values for each spectral band to use in radiative heating and radiation exchange calculations.

A common assumption in thermal analysis is that radiating surfaces are gray bodies. This means that their emissivity does not depend on wavelength. This approximation is usually reasonable when the absolute temperatures of the radiating surfaces are relatively similar, since the spectral distribution of the emitted radiation remains comparable throughout the system. The main advantage of this assumption is that it greatly simplifies radiation calculations. By assuming gray behavior, the radiation exchange between surfaces can be included directly in the thermal model equations.

In practice, the gray-body approximation is often a necessary simplification that reduces the computational complexity of numerical radiation analysis while still giving acceptable results for many engineering problems.

Use non-gray radiation when the gray-body approximation is not accurate enough because surface properties vary significantly with wavelength. This is especially important when:

Radiating surfaces have very different temperatures.
Solar radiation is involved.
Materials exhibit selective optical properties.

In these cases, a single emissivity value cannot represent the radiation behavior accurately, so the radiation exchange must be modeled over separate spectral bands.

Spectral bands

In a gray-body radiation run, the solver uses two broad spectral regions: solar and infrared (IR). In a multispectral radiation run, the solver divides the radiation spectrum into several wavelength bands. Spectral bands allow the radiation calculation to account for wavelength-dependent behavior. Instead of treating radiation as a single gray quantity, the solver performs the calculation separately over defined wavelength ranges.

In a multispectral analysis, the solver:

Creates a separate radiative coupling matrix for each band in the IR spectrum.
Creates separate radiative heat loads for each band in the total spectrum.
Computes equivalent optical properties for each spectral band and uses those values to calculate radiative heat loads and radiative couplings.

Within each band, the solver replaces the wavelength-dependent optical property with one equivalent value. This value is obtained by averaging the property over the wavelength range of the band.

where:

P_i is the property in band i such as absorptivity, reflectivity, transmissivity or emissivity.
λ_i,1 is the lower wavelength boundary of band i.
λ_i,2 is the upper wavelength boundary of band i.
P(λ) is the wavelength-dependent optical property.

Because each optical property is averaged over the band, the accuracy of a multispectral analysis depends on how the bands are defined. If the bands are too wide, important wavelength-dependent variations—such as sharp absorption peaks, changes in reflectivity or transmissivity, or peaks in lamp intensity—may be averaged out. As a result, the model may not capture where and how much radiation is actually absorbed, which can reduce the accuracy of the predicted heat absorption and temperatures.

A good practice is to use narrower bands in wavelength regions where the lamp intensity or material optical properties change rapidly. After defining the bands, perform a sensitivity study by increasing the number of bands until the temperatures or absorbed heat values no longer change significantly.

Solar to IR transition wavelength

The Solar to IR transition wavelength defines the wavelength that separates shortwave radiation from longwave thermal radiation. It is a simplified two-band spectral model used to distinguish between solar and infrared (IR) behavior.

Radiation below the transition wavelength is treated as part of the solar band. This band usually represents shortwave radiation, such as sunlight or lamp radiation in the visible and near-infrared range.

Radiation above the transition wavelength is treated as part of the IR band. This band usually represents longwave thermal radiation emitted by surfaces because of their temperature.

This split is useful because many materials behave very differently when exposed to shortwave incoming radiation than they do when emitting longwave thermal radiation. For example, a material may absorb strongly in the solar range but emit weakly in the IR range, or vice versa.

Radiative enclosure exchange is generally calculated only in the IR range, above the transition wavelength. Radiative heat loads, however, can be applied over all wavelengths defined by the source spectrum.

Many models contain a combination of gray and non-gray properties. For gray bodies, the Solar/IR transition defines which spectral bands use solar properties and which bands use IR properties. If a spectral band contains wavelengths on both sides of the transition, the solver computes an equivalent property for that band using the appropriate solar and IR values.

The transition wavelength also affects the creation of radiative couplings. Radiative couplings for enclosure heat transfer are not calculated below the transition wavelength, because thermal emission in the solar range is generally negligible.

Radiative heating and radiation enclosures

Radiative heating and radiation enclosure exchange use different spectral ranges.

Radiative heating comes from an imposed source, such as a lamp or solar load. It follows the wavelength range of the defined source spectrum and may occur below or above the Solar/IR transition wavelength.

Radiation enclosures represent element-to-element thermal radiation exchange between model surfaces. This exchange is normally treated as longwave IR radiation and is calculated only above the Solar/IR transition wavelength, unless the Full Multi-Bands option is used.

For Earth radiation, the spectral distribution is determined from the specified planetary heat load per unit area leaving the planet, assuming an Earth emissivity of 0.612. This distribution is then used to assign the Earth radiative heat load across the applicable spectral bands.