Tech Briefs Magazine - October 2023 - Comsol-24A

DESIGN OPTIMIZATION
FIGURE 2 Imported CAD
geometry and the resultant
finite element mesh after some
defeaturing and simplification.
Computers used to be relatively slow, so
having the numerical analyst spend time
semimanually reducing the computational
complexity was important for getting
results quickly. This approach is still
relevant for the modeling of very large
structures like the International Space
Station, but for small satellites - especially
as computational costs continue to drop -
it is now becoming increasingly attractive
to start at the other end of the modeling
spectrum.
In practice, a thermal analyst will want
to work somewhere on the spectrum
between a wholly simplified and a fullfidelity
model. For example, it might be
desirable to replace the CAD description
of each screw and fastener with a lumped
thermal resistance at the surface between
the joined components. Similarly, it
might make sense to reduce an electronic
component such as a chip or battery
to a block of material with averaged
properties and internal dissipation.
» IMPORTANT MODELING
CONSIDERATIONS
Regardless of the modeling approach
taken, certain aspects need to be
considered. Let's explore these points in
more detail.
The geometric description of the
satellite. The CAD design and thermal
properties (thermal conductivity, density,
and specific heat) of the materials being
used in each component determine the
24a COMSOL NEWS
FIGURE 3 A visualization of
a satellite in orbit, showing the
position and orientation relative
to the Sun and Earth as well as
the irradiation onto the satellite's
exposed faces. Earth image credit:
Visible Earth and NASA.
total thermal mass of the satellite as well
as the conductive heat transfer between
parts. The relative orientation of the
satellite faces also determines the view
factors, describing how well one surface
can see another surface. This is needed
when computing radiative heat transfer.
Along with the CAD design, there is
additional information that is related to
the geometry. For example, the mating
surfaces between two parts might have a
thin coating, or a bonding material, that
alters the thermal contact resistance. The
total resistance can also be a function of
contact pressure, as determined by the
mounting hardware.
The emissivities of all exposed
surfaces. Emissivity (or absorptivity)
is a measure of how well a surface
emits and absorbs thermal radiation.
It can be a function of wavelength,
temperature, and angle of incidence.
The combination of the view factors
and surface emissivities is used to
compute the radiative heat exchange.
There is radiation both on the exterior
surfaces of the satellite and within
the interior. The exterior surfaces also
experience environmental heat loads,
such as the thermal irradiations from the
Sun and Earth. It is particularly worth
understanding the topic of wavelengthdependent
emissivities. The Sun is the
primary source of heating and the only
source of electrical energy, via solar
cells. The light from the Sun is classified
as short-wavelength light, with peak
intensity at the 500-nm wavelength
and with most energy in the sub-5µm
wavelength range. The satellite
itself is much colder than the Sun and
emits thermal radiation at much longer
wavelengths, primarily at wavelengths
greater than 2 µm. Because of this, it is
very common to use thermal coatings
that are strongly wavelength dependent.
A coating with low emissivity at shorter
wavelengths will reduce solar heating,
but if that same coating has higher
emissivity at longer wavelengths, it will
radiate heat more effectively.
The satellite orbit. Defined by the
standard Keplerian orbital elements,
the satellite orbit determines how the
satellite travels around Earth and when
it goes into and out of eclipse. When
the satellite goes into eclipse, there is
no longer any solar irradiation, which
usually leads to significant drops in
temperature on the exterior surfaces. For
thermal modeling purposes, the orbit
itself can typically be treated as periodic,
especially in the context of small
satellites in low Earth orbits.
The satellite orientation. This
information determines which faces
see the Sun, Earth, or deep space. The
satellite may be pointing in a particular
direction, spinning about its axes, or
even have parts of the structure that
are rotating and moving relative to the
satellite frame. This information affects
the irradiation onto the exposed faces.
The orientation, unlike the orbit, might
not be periodic. For example, a satellite
antenna might be pointed toward a
ground station only every few orbits.
The radiative properties of Earth and
Sun. The solar flux varies throughout
the year, and this solar flux is both
directly incident on the satellite and
also diffusely reflected from Earth. The
magnitude of this reflection, known as
the albedo, can vary over the planet
surface. Earth itself is also a radiator of
infrared light, and this radiated flux can
be a function of latitude and longitude.
Although solar flux is well known, the
albedo and Earth infrared radiation
also vary significantly over the planet's
surface and over time.
The electrical dissipations of the
components. The solar cells convert
Tech Briefs Magazine - October 2023

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