Lunar Base Thermal Analysis with THERMICA
Mr. Timothée SORIANO1
EADS Astrium, Toulouse, France
Thermal analysis of a base or a rover landed on a planet or a moon induces several new
challenges for thermal analysis tools. If the existing capabilities of software to model detailed
geometries and compute temperatures can directly be used to perform thermal analysis of a
rover, some modelling aspects remain complex to handle. This is the case of the external
fluxes (sun, planet IR, Albedo) computation taking into account the relative orientation of
the sun with respect to an object and its moving parts landed on a planet or a moon. This
opens new perspectives in the use of such software to help designing bases and rovers. The
latest generation of THERMICA (THERMICA V4) proposes some solutions to define the
trajectory and pointing of an object landed on a planet and to compute external fluxes.
Using these capabilities, the thermal environment of a lunar base is first studied on a
simplified geometrical model. Some thermal relevant results like direct solar, IR and Albedo
fluxes are analysed and compared with rough estimation. Then, a study of a realistic
geometrical model, where simple estimations are not relevant anymore, is presented.
I. Introduction
T
hermal analysis software have increased their capabilities with the new needs coming from scientific missions.
In the past years, different missions orbiting around Mars, Venus, Mercury and many other planets have been
studied using extended functionalities of the tools for customizing the planet parameters and the solar constant.
Nowadays there are new concerns about landed structures such as bases or rovers. Usually such cases are considered
with hand computed worst conditions. They do not correspond to a real configuration that will occur during the
mission lifetime but they combine all the predictable worst elements. On one hand this approach allows having an
estimation of the worst cases but on the other hands it implies that those worst cases may be over-estimated.
Besides, it may also be necessary to study accurately the mission during a given time range within a realistic
environment. For example, in order to compute the batteries charging from the incident solar fluxes on the solar
panels, an accurate modelling is required.
The latest generation of THERMICA allows analyzing complex missions thanks to a realistic management of the
solar system with the planet’s positions automatically computed. As a consequence, any complex mission can be
studied in their real lifetime conditions.
This paper presents the study of the thermal environment of a lunar base in real conditions. This case shows the
feasibility of landed structures analyses and its conclusions will be generally applicable to any similar case.
The lunar base is composed of a main module, an antenna pointing the Earth and a set of solar panels pointing
the Sun. For this study, it is necessary to set the geometrical model on the moon surface, at a given position in terms
of rotational longitude, latitude and altitude parameters. It will be also necessary to set the correct orientations of the
antenna and the solar panels tracking respectively the Earth and the Sun. The environment will be first studied in
order to understand the real conditions of the base and to compare the observed phenomena to known data. This will
also partially validate the THERMICA computation applied to a landed structure and will demonstrate its accuracy.
1
Numerical & Space Physics Engineer and THERMICA Manager, of the Engineering Tools department (ASG84) in
Astrium Toulouse, [email protected], http://www.systema.astrium.eads.net .
1
American Institute of Aeronautics and Astronautics
II. Trajectory and Kinematics
The latest generation of THERMICA is able to take into account any trajectory in a realistic environment. The
classical orbits such as sun-synchronous, planet-stationary (geo-stationary for the Earth) or any kind of Keplerian
description can be set directly into the software.
For more complex missions, it is possible to get the trajectory directly from a text file describing either a set of
time-position-velocity in the Gamma50 inertial frame with an origin located at the center of any planet, the Moon or
the Sun (the latest is useful to describe interplanetary missions) or a set of time-longitude-latitude-altitude in the
rotational frame of the planet (or Moon) considered. This new kind of trajectory description is particularly useful to
study landed structures with a fixed position or even with a trajectory on the planet’s ground (for example in the
case of a rover).
In our lunar base case, the parameters have been set as shown in figure 1.1.
Fig. 1.1 – Lunar Base Trajectory Setup
This definition references a file called “Lunar_base.xyz” which contains the trajectory in terms of rotational
elements. For a fixed point on the planet only a single interval is required.
The trajectory is given by the following parameters:
- longitude: 90° west
- latitude: 60° south
- altitude: 1 m
- time range: 1st of January 2015 to 31st of December 2055
2
American Institute of Aeronautics and Astronautics
Content of the Lunar_base.xyz file:
# Date : From the 1st of january of 2015 (duration 40 years)
# Gamma50
X(deg)
Y (deg)
Z (km)
23741.
270.
-60.0
0.001
38341.
270.
-60.0
0.001
The 0 degree of longitude in the Moon rotational frame corresponds to the mean Earth direction. The 90° west
longitude localization is then explain in figure 1.2.
Out of eclipse
Base
located at
90°
90° west
0°
Earth
180°
Moon
To eclipse
Fig. 1.2 – Lunar base position and Moon eclipse
Finally, we get a realistic view of the trajectory shown in figure 1.3. This 3D view is fully interactive and can be
also animated with time motion which is helpful to understand the behavior of the trajectory within its environment.
Fig. 1.3 – Lunar Base Orbit view from THERMICA
3
American Institute of Aeronautics and Astronautics
About the model’s orientation and kinematics, a dedicated module of THERMICA deals with frames,
mechanical connections, pointing rules and attitude laws. In this module it is possible to target the real position of
any planet, the Sun or Moon. This is very convenient for moving an antenna in the Earth direction on any kind of
trajectory and at any time.
In our case, the orientation of the lunar base can be set with a direction to the velocity (in inertial frame),
corresponding to the Moon’s east direction, and a second one to the Moon north. Then it will be necessary to have
the antenna pointing the Earth and the solar panels pointing the Sun. For this latest, we will also set some restrictions
on one axis to enable the rotation further than -60 or +60 degrees (see figure 1.4).
Fig. 1.4 – Kinematic description of the Solar Panel
4
American Institute of Aeronautics and Astronautics
III. Solar Environment
The thermal environment of a lunar base may be complex to understand especially if we need to know its real
conditions in time. We propose to study the thermal environment on a cube placed at the base.
The cube has been oriented with the following convention:
- + X: Velocity (West)
- +Y: North
- +Z: Space
- -X: Anti-velocity (East)
- -Y: South
- -Z: Ground
The solar fluxes computed on a single Moon orbit (see figure 2.1) shows that the sides oriented from/to
velocities (east and west sides) receive the maximum fluxes. The one oriented to the north direction has the most
important flux in time but with a maximum bellow the one seen by the previous one. The face oriented to space
receives even less flux. This behavior is conform to what we could have expected: the velocity sides get exactly
oriented to the Sun direction when leaving/entering into the eclipse cone leading to a maximum incoming solar flux
equal to the Sun constant. Due to the latitude much lower than -45° it is also normal to get lower solar fluxes on the
space direction than on the north one. However it would have been difficult to manually quantify the ratio between
the sun constant and the received flux without knowing exactly the position of the Sun in the rotational frame of the
Moon.
Fig. 2.1 – Solar Fluxes over 1 moon orbit
As the Moon rotates around the Earth, we expect to have incident solar fluxes maximized around the earth
perihelion and minimized around its aphelion. This will be true over an earth year. However there are also variations
through the years. If we look at the fluxes on the +Z direction (oriented to space) during a time range of 10 years
between 2015 and 2025, we get the profile in figure 2.2.
5
American Institute of Aeronautics and Astronautics
Fig. 2.2 – Solar Fluxes on +Z over 10 years
This graph shows that three kinds of variations have to be taken into account:
- Moon’s rotation viewed from the Sun:
This variation was clearly seen in figure 2.1. The period of this variation is about 27 days.
- Earth’s orbit around the Sun:
In figure 2.2 we see that the maximum flux received describes a sinusoidal function with a period of
an Earth’s year (1 maximum and 1 minimum per year).
- Sun’s inclination in the Moon reference:
Still in figure 2.2 we observe that the amplitude of the annual variation is not constant but varies
through the years.
By suppressing the variation due to the Moon’s rotation, the flux envelops induced by the Earth and Moon orbits
between the years 2015 and 2055 are shown in figure 2.3. Those curves have been obtained by setting in
THERMICA a period of analysis of 14400 days with a time-step of 600 minutes. Then the fluxes tables have been
processed by THERMISOL (temperature solver of THERMICA) in order to export in a text file the maximum
fluxes for each moon period (see figure 2.4).
6
American Institute of Aeronautics and Astronautics
1500
1400
1300
1200
1100
+X: Velocity
+Y: North
+Z: Space
-X: Anti-Velocity
1000
900
800
700
600
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Years from 2015 to 2055
Fig. 2.3 – Solar Fluxes Variations over 40 years
The solar fluxes variations on the different sides of the cube show that the multi-annual variations are not so
simple to understand. The analysis performed with THERMICA leads to the following remarks:
-
The velocity sides have a constant behavior through the years. They have a maximum and a minimum
incident flux at the Earth’s perihelion and aphelion. Due to the longitude of the base at 90° west, the base
goes out of eclipse when the Moon is the furthest to the Sun and goes back into eclipse when the Moon
is the closest to the Sun. This is conformed to the explanation given in figure 1.2. As a consequence, the
+X and –X curves present a shift corresponding to the solar constant variation between the extreme
positions of the Moon
-
The North direction (+Y) presents decreasing then increasing amplitudes of the flux variation as the
space direction (+Z) has increasing then decreasing amplitudes. This behavior shows that the Sun’s
inclination is changing through the year with a period of 18 to 19 years. This multi-annual variation
observed corresponds in fact to the variation of the ascending node longitude which is regressing by one
revolution in 18.6 years. This variation is equivalent to a precession of the Moon’s axis toward the Sun.
This kind of effect would be very difficult to take into account without an accurate modelling of the solar
system.
In conclusion of this study, it has been possible to compute accurately the solar fluxes with THERMICA with
only a few requirements: where (at 90° west, 60° south on the moon), which orientation (+X velocity, +Y north) and
when (from year 2015 to 2055).
7
American Institute of Aeronautics and Astronautics
Fig. 2.4 – Example of THERMISOL input file to post-process the solar fluxes
8
American Institute of Aeronautics and Astronautics
IV. IR and Albedo Fluxes
The fluxes coming from the planet are also automatically computed by THERMICA. The mathematical formulas
used are true for any altitude and even for landed structures. The approach of this computation in the latest versions
of the software is basically the same as it has always been: first it computes Gebhart factors in IR and UV from all
the elements of the geometrical model with a discretization of space. Then it integrates the incoming planet fluxes
from each space element.
The planet flux is then computed with the following formula:
p
(s ) = As
Fs,b
b
b
Where:
Φp(s) is the power received a surface s of the geometrical model
As
is the area of the surface s
Fs,b is the Gebhart factor (in IR or in UV) between the surface s and the box element (i.e. element of the
space discretization)
Φb
is the incoming IR or Albedo flux from the Moon crossing the space box element
The incoming flux is the result of the following integration:
Φb =
Where:
Ωb
f
Ωb
f dΩ
Ωb
is the solid angle of the space box element
is the incoming flux from a specific direction of Ωb
By default, the number of space elements is 2400. The fluxes crossing the elements are numerically integrated by
subdividing them between 1 and 256 depending on the variability of the function f.
In the 4th generation of THERMICA, the ability of taking into account planet fluxes with low altitudes comes
from mainly two improvements. The first one is the use of non-approximated formula which allows computing the
real size of the visibility cone of the planet (which tends to 2 steradian when the altitude tends to 0) and the correct
visible location of the planet ground in any direction. The second one is the possibility to model non-uniform planet
properties using either maps or simply night / sub-solar point temperatures. This latest definition automatically
creates a temperature profile commonly used for planets without atmosphere (figure 3.1)
9
American Institute of Aeronautics and Astronautics
T (θ ) =
4
Uniform Night
Temperature
cos θ .TS4 + (1 − cos θ ).TN4
θ
TN
Sub-Solar
Temperature
TS
Fig. 3.1 – Moon Temperature Profil
The Albedo flux is integrated in the same manner as for the IR but takes into account the Sun reflection on the
planet ground. In both case the knowledge of the sun direction is required.
In order to study the feasibility of an automatic analysis on a planet with THERMICA, we have to analyze the
planet flux received by the cube computed with THERMICA.
Moon IR flux
The temperatures of the Moon have been set to -233°C for the night side and 123°C for the sub-solar point. For
60° south latitude, the previous formula gives a local maximum ground temperature of 90°C which correspond to a
maximum flux of 986 W/m². This is an approximation considering that the Moon’s equator is in the ecliptic plane
(which is more or less true by 5.8°). The computation of the real angle depending on the Sun’s direction at the
current simulation date – January 2015 – it is not easy to determine it.
The computation performed with THERMICA gives the following flux profiles for a single Moon’s orbit:
Fig. 3.2 – Moon IR fluxes computed by THERMICA
10
American Institute of Aeronautics and Astronautics
This graph presents a maximum flux of 981 W/m² on the side oriented to the ground which is approximately
what we predicted considering a local and uniform temperature of 90°C. For the other sides, the ground
temperatures seen are different. Besides expecting a north flux higher and a south flux lower, it is difficult to predict
the level of fluxes received since the temperature profile depends on the Sun’s real direction.
Moon Albedo flux
The estimation of the Moon Albedo flux is also complex due to the Sun direction. With the hypothesis of a Sun
constant of 1400 W/m² and a Sun direction in the equatorial plane of the Moon, we can roughly estimate that the
flux received by the -Z side shall be 1400 x cos(60°) x 0.12 (Moon Albedo coefficient) = 84 W/m².
To evaluate the quality of the Albedo flux integration, we propose to compare the following results:
- From the planet flux module with the methodology explained (integration on discretized space elements)
- From the solar flux module (by ray-tracing) with the addition of a very large square representing the
Moon ground which will diffuse the solar flux on the cube sides (as the Moon Albedo coefficient was set
0.12, the ground was then set with an alpha of 0.88).
Fig. 3.3 – Moon Albedo fluxes computed by THERMICA
(Direct computation from the Planet Fluxes module – Indirect computation by Solar Flux reflections)
The maximum flux received in both cases is about 83 W/m² which is quite closed to the estimated value. The
indirect computation (on the right of figure 3.3) presents irregularities due to the ray-tracing accuracy with an
insufficient density of rays on the ground which involves diffusive reflections.
This comparison shows that the Albedo flux is naturally well taken into account with the THERMICA planet
fluxes module. Moreover the use of a planet ground included in the geometrical model to compute the Albedo flux
with classical ray-tracing techniques leads to accuracy problems.
11
American Institute of Aeronautics and Astronautics
V. Lunar Base
In the case of the cube, we have seen that THERMICA was able to compute realistic flux levels. Generally, the
maximum and the flux profile can be approximated with hand computation (this was for example the case of the
planet fluxes on the -Z side). However on a more complex model these estimations are insufficient and the flux
integration on all the surface elements may be almost impossible without the help of software.
To study the external flux on the lunar base model, we use the same trajectory and the kinematics defined in
paragraph 2. THERMICA proposes a realistic view of the mission as shown in figure 4.1. This is particularly
interesting to understand the environment of the mission, to visualize the shadowing effects or even to present a
picture or video (via the recording function) of the scene.
Fig. 4.1 – Lunar base view from THERMICA
The external fluxes from the Sun, planet IR and planet Albedo are computed on detailed models as it was done
on the cube presented in the previous paragraphs. Complex kinematics definitions are also automatically solved.
The analyses are performed with optimized ray-tracing techniques taking into account the thermo-optical
properties. Specular effects are also handled as it has been done for more than 20 years in THERMICA and many
other software. The outputs are then dedicated to thermal solvers such as THERMISOL, ESATAN or SINDA so the
complete analysis of a lunar base can be performed with the processes already in used for standard
telecommunication or observation programs.
An example of Albedo flux results is shown in figure 4.2 to illustrate the possibility of studying a complete
model.
12
American Institute of Aeronautics and Astronautics
Fig. 4.2 – Absorbed Albedo flux – 3D view
VI. Discussion
In this study, we have seen that THERMICA allows an accurate computation of the external fluxes (solar, planet
IR and Albedo) in realistic conditions. This is particularly important in the following cases:
-
-
Analyses of specific conditions taking into account accurate shadowing effects (especially at the poles
where the solar flux has a very low inclination), night and day durations (which are also particularly
variable at the poles) or any phenomena linked with the true positions of the planets, Sun and Moon into
the solar system.
Minimization the margins using real computed worst conditions rather than over-estimated external
fluxes. In order to find such worst cases, THERMICA can be parameterized and run in batch command
which allows serial parametric computations and sensitive analyses.
Computation of the generated power from the solar gear by integration of the solar flux in realistic
conditions.
However the accurate solar system management of THERMICA may not be sufficient to accurately perform a
thermal analysis in realistic conditions. Some phenomena have not yet been taken into account.
-
-
Residual atmosphere: the presence of an atmosphere may have three kinds of effects. First of all, the
temperature of the environment can be higher than the space temperature of 4K. To deal with this effect,
it is possible to change this temperature with either a constant temperature or a variable one (but in this
case the temperature profile of the atmosphere needs to be computed in order to be set in the temperature
solver). Secondly, the Sun constant may be attenuated by a given ratio. In the current version of
THERMICA it is only possible to set a constant value or an automatically computed Sun constant. The
addition of a ratio on the automatic Sun constant would be necessary. Finally, there can be convective
fluxes that would need to be computed with another tool or by hand.
Planet relief: some advanced study on lunar missions have used accurate 3D map of the ground. The
relief may also have different impacts on the thermal environment. On one hand there can be shadowing
effects on the structure. To model this behavior it would be necessary to add in the geometrical model
13
American Institute of Aeronautics and Astronautics
-
the significant part of the relief (thanks to the Thales theorem a reasonable ratio can be applied). On the
other hand, the shadowing effects on the ground itself also modify the Albedo flux and the ground
temperature. For the IR flux, the ground temperature may be input by the thermal engineer as a map (but
its knowledge is then required). For the Albedo flux, the relief will have an impact only when the Sun is
very low on the skyline which also means that the Albedo flux becomes not significant.
Presence of dust: the dust can degrade temporally or definitively the coating properties. This behavior
needs to be taken into account by the engineer in the definition of the thermo-optical properties.
VII. Conclusion
The complex thermal environment of a landed structure on the Moon was successfully studied with
THERMICA. The celestial bodies being automatically well positioned and oriented into the solar system at all time
makes it easier to study and understand the thermal environment.
This management of the solar system is a great progress of thermal analysis software which opens many
possibilities for accurate modelling. It can be of a real interest for any scientific mission and at any development
stage; preliminary design, advanced analysis or even for investigating specific cases. Rather than trying to guess the
external conditions at a given time or for worst cases, its automatic computation into THERMICA is also helpful
and brings an integrated solution (management of the environment plus fluxes integration) to problems that usually
required the use of different tools and even hand computed estimations.
Acknowledgements
The author would like to gratefully acknowledge the valuable contributions made by C. Theroude who designed
the lunar base model and G. Chanteperdrix for its analyses and remarks.
14
American Institute of Aeronautics and Astronautics