a Space Mission
Vincent Still
Space Engineering, master's level (120 credits) 2018
Luleå University of Technology
Department of Computer Science, Electrical and Space Engineering
Mission
Master’s Thesis for M.Sc. Spacecraft Design
Department of Computer Science, Electrical and Space Engineering at
Vincent STILL
External Supervisor:
Florian RUESS
External Co-Supervisor:
Luca POMPA
Examiner:
Leonard FELICETTI
November 15, 2018
Vincent Still
ALL RIGHTS RESERVED
The following document describes an example mission, which originated from a real life concept of an imaging satellite in a Sun Synchronous Orbit (SSO) around Earth. This report takes the reader through the thermal analysis and evaluation of space equipment performed with Airbus Space & Defence’s Sys- tema/Thermica tool, atSpace Structures GmbH. It details the full process of designing a thermal control system for a space project. The project started from a CAD file which was converted into a Geometric Mathematical Model (GMM) inside Thermica. This process requires an extensive knowledge of not only the software, but also the technical background behind what happens to a satellite in such an extreme environment. This thesis addresses this by showing a step-by-step approach of a full thermal evaluation, starting with the required theoretical background of the thermal environment and the dif- ferent passive and active thermal design techniques. The next step involves gathering the required input information for the software; such as defining the conductance values between the components and calculating the per node power dissipation for each component considering each operational mode. The final step includes the designing, simulation, iteration and presentation of the temperature results across the spacecraft thermal model. The results of the initial simulation showed that some sensitive components were not within the specified temperature requirements, and therefore both radiators and heaters were sized and introduced to the model. After the third iteration of thermal control, the sensitive components’ temperatures were observed to be within the allowable margins of an ECSS Phase A study. This thesis can serve as a guide and complete document for future missions which plan the design of a Thermal Control System of a satellite in orbit around Earth.
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Firstly, I would like to thank Florian Ruess and Leonard Felicetti for supervising me throughout this thesis, with a special thanks to Luca Pompa, who dedicated so much of his own time in order to help me get things right.
I would also like to thank everyone else at Space Structures GmbH, and my Berlin friends who either directly or indirectly gave me help or generally made my time in Berlin a truly unforgettable experience.
Next, I would like to thank all of my close friends and family from all across Europe for always encouraging me to do my best, and supporting me from wherever they were.
Finally, I would like to thank both my girlfriend and my mother for always being by my side through thick and thin, making sure my life always stays on track.
VINCENT STILL
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Abstract . . . i
Acknowledgements . . . iii
List of Tables . . . vi
List of Figures . . . vi
List of Acronyms . . . ix
List of Symbols . . . x
1 Introduction 1 2 Heat Transfer Mechanisms 2 2.1 Convection . . . 3
2.2 Thermal Conduction . . . 3
2.2.1 Thermal Conductance . . . 3
2.3 Thermal Radiation . . . 4
3 The Thermal Environment 5 3.1 Spacecraft Orbital Parameters . . . 5
3.1.1 a Semi Major-Axis . . . . 6
3.1.2 e Eccentricity . . . . 6
3.1.3 i Inclination . . . . 7
3.1.4 ω Longitude of the Ascending Node . . . 7
3.1.5 β Beta Angle . . . . 7
3.1.6 Reentry Environment . . . 8
3.2 Perturbations . . . 8
3.3 Radiation Flux Sources . . . 10
3.3.1 Solar Flux . . . 10
3.3.2 Albedo Flux . . . 11
3.3.3 IR Flux . . . 11
3.3.4 Radiation into Space . . . 12
3.3.5 Black & Grey Bodies . . . 12
3.4 Radiative View Factor . . . 13
4 Thermal Control Techniques 15 4.1 Passive Control . . . 15
4.1.1 Radiators . . . 15
4.1.2 Surface Coating . . . 16
4.1.3 Reflective Mirrors . . . 16
4.1.4 Multi-Layer Insulation (MLI) . . . 17
4.1.5 Heat Pipes . . . 18
4.1.6 Thermal Filler . . . 19
4.2 Active Control . . . 20
4.2.1 Heaters . . . 20
4.2.2 Cryogenic Coolers . . . 21
4.2.3 Peltier Element . . . 22
4.2.4 Louvres . . . 23
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5 Method 25
5.1 Assumptions . . . 25
5.1.1 Universal Constants . . . 25
5.1.2 Coldest Case Scenario . . . 26
5.1.3 Hottest Case Scenario . . . 26
5.1.4 Software Boundary Conditions . . . 26
5.2 Thermal Design Process . . . 27
5.3 Phase 1: Background Information & Set Up . . . 28
5.3.1 Mission Orbital Parameters and Perturbations . . . 28
5.3.2 The Model . . . 28
5.3.3 Modes of Operation . . . 29
5.3.4 Component Analysis . . . 31
5.3.5 Preliminary Model Calculations . . . 36
5.3.6 Temperature Requirements . . . 38
5.4 Phase 2: Thermica Modelling . . . 38
5.4.1 Node Definitions . . . 38
5.4.2 MLI Modelling . . . 40
5.4.3 Thermal Mass Check . . . 42
6 Results & Analysis 43 6.1 Case 1 - Preliminary Model . . . 43
6.2 Case 2 - Adding Radiators . . . 45
6.3 Case 3 - Adding Heaters . . . 49
6.4 Initial Conclusion . . . 52
7 Discussion 53 7.1 Conclusion . . . 53
7.2 Improvements & Future Work . . . 54
A Appendix 55 A.1 Additional Tables . . . 55
A.2 MATLAB Code . . . 58
A.2.1 Temperature Equations . . . 58
A.2.2 MLI Equations . . . 60
A.2.3 Radiator Sizing Equations . . . 61
A.3 Excel Workbook . . . 62
A.3.1 Summary Sheet . . . 62
A.3.2 Conduction Sheet . . . 63
A.3.3 Radiation Sheet . . . 64
A.3.4 Steady State Temperatures Sheet . . . 65
A.3.5 Heat Dissipation Sheet . . . 66
A.4 Extra Figures . . . 67
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3.1 List of Orbital Parameters. . . 6
3.2 Different Orbital Eccentricities. . . 6
3.3 Summary of Forces Acting on a Spacecraft in Earth Orbit [17]. . . 9
3.4 Table showing a range of approximated Albedo values around the Earth [6]. 11 4.1 Cryocooler Technology Temperature Ranges [25]. . . 22
4.2 Price/Performance Characteristics of Common Thermal Control Techniques. 24 5.1 Sun-Synchronous Orbit Parameters. . . 28
5.2 The different modes of operation the satellite will experience. . . 30
5.3 Thermal Conductance Design Guideline from TRW Inc. [14]. . . 33
5.4 Table to show the properties of the materials used in the Solar Panel, in order to calculate the GL value. . . 34
5.5 The different Reaction Wheels, their mounting elements and their GL values. 36 5.6 Steady State Temperatures for both the Hot and Cold case of the Spherical Basic Model Simulation. . . 37
5.7 Thermal Requirements of Each Component. All units in r°Cs. . . 38
5.8 Temperature Tolerances from ECSS-E-19-3A. . . 38
5.9 The list of components with their respective node count. . . 39
5.10 MLI Modelling Trade Off. . . 40
5.11 Table to compare the estimated mass of the components from data-sheets to the thermal mass used within the Thermica software. . . 42
6.1 Different Power Dissipation choice for each of the Heaters. . . 49
A.1 Albedo and IR Emission of the Planets. This table shows representative values of the Albedo and the IR emission of our Solar Systems planets. Perihelion and Aphelion represent the points in the orbits of Mercury and Mars where they are the closest and the furthest from the Sun [36]. . . 55
A.2 Properties of Common Finishes. The absorptivity and emissivity of typical spacecraft finishes are shown here. Note that a combination of finishes can be made to create the desired absorptibity to emissivity ratios [36]. For a more complete list of standard material thermal properties see [16]. . . 56
A.3 A table showing different working fluids in heat pipes, and their useful temperature ranges [28]. . . 57
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2.1 Conduction, convection, and radiation heat transfer methods [13]. . . 2
3.1 Diagram showing the orbital parameters relevant for the TCS [35]. . . 5
3.2 Beta angle over a year for a 400 rkms, 70° inclination orbit [17]. . . 7
3.3 Different Sources of Radiation [8]. . . 10
3.4 View factor associated with radiation exchange between elemental surfaces of area dAi and dAj [12]. . . 13
4.1 Thermal Radiator [33]. . . 16
4.2 Surface Coating on board the Space Shuttle Discovery [26]. . . 16
4.3 The 18 first mirrors on the JWST [22]. . . 17
4.4 Figures showing different forms of external insulation. . . 18
4.5 Heat Pipes on board the SAM instrument [28]. . . 19
4.6 Thermal Filler in an orbiter tile - the filler can be seen in brown [2]. . . 20
4.7 Thermal Heater on the XRT instrument [11]. . . 21
4.8 Cryocooler designed for the MIRI mission [15], which uses three stage pulse- tube cooling [23]. . . 22
4.9 Example Peltier Element in a Thermoelectric cooling application [20]. . . . 23
4.10 Thermal Louvres for ESA’s Rosetta Mission [10]. . . 23
5.1 Full Model to show the main dimensions, the name of the faces and the major components within. . . 29
5.2 Simple model view showing the orientation in connection with table 5.2. . . 29
5.3 Diagrams denoting the two analytical methods used to discretise the thermal conduction between two components. . . 32
5.4 Cross Section of the Solar Panel used in the Thermica model. . . 33
5.5 Payload Photo vs. Thermal Model. . . 35
5.6 Basic Model in Thermica to verify the MATLAB® model. . . 37
5.7 Schematic cross section depicts the key elements of an MLI blanket. Not all elements need be present in every design. Courtesy NASA [9]. . . 40
5.8 This shows how the two node model is represented within the Thermica software. . . 41
6.1 Graph showing the temperature range of the electronic components for simulation Case 1. . . 44
6.2 Case 1 Cold Case Temperatures on the spacecraft model . . . 44
6.3 Case 1 Hot Case Temperatures on the spacecraft model. . . 45
6.4 Figure showing the radiator panels in Thermica. The radiators are the two yellow panels. . . 47
6.5 Graph showing the temperature range of the electronic components for the simulation Case 2. . . 47
6.6 Case 2 Cold Case Temperatures on the spacecraft model. . . 48
6.7 Case 2 Hot Case Temperatures on the spacecraft model. . . 48
6.8 Figure showing the added heaters in Thermica. The heaters are the three red panels seen inside the satellite. . . 50
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6.11 Case 3 Hot Case Temperatures on the spacecraft model. . . 52 A.1 Thermal Design Development Process. This diagram Illustrates the general
thermal design process, showing the many iterative loops Involved In the process. [36]. . . 67 A.2 Table to show the materials used inside Thermica when simulating. . . 67
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AIT Assembly, Integration & Testing.
AOCS Attitude and Orbit Control System.
APG Annealed Pyrolytic Graphite.
BOL Beginning-Of-Life.
CAD Computer Aided Design.
CDR Critical Design Review.
CoI Centre of Inertia.
CoM Centre of Mass.
ECSS European Cooperation for Space Standardiza- tion.
EOL End-Of-Life.
EPS Electrical Power System.
ESA European Space Agency.
FEM Finite Element Method.
FSM First Surface Mirror.
GEO Geostationary Earth Orbit.
GMAT General Mission Analysis Tool.
GmbH Gesellschaft mit beschränkter Haftung.
GMM Geometric Mathematical Model.
GMT Greenwich Mean Time.
GUI Graphical User Interface.
HVAC Heating, Ventilation and Air Conditioning.
IR Infrared.
ISS International Space Station.
JWST James Webb Space Telescope.
LEO Low Earth Orbit.
MIRI Mid-InfraRed Instrument.
MLI Multi-Layer Insulation.
MMOD Micro-Meteoroids & Orbital Debris.
NASA National Aeronautics and Space Administra- tion.
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PCDU Power Control and Distribution Unit.
PDR Preliminary Design Review.
PRR Preliminary Requirements Review.
PTFE Polytetrafluoroethylene.
SAM Sample Analysis at Mars.
SLI Single-Layer Insulation.
SNR Signal-to-Noise Ratio.
SSO Sun Synchronous Orbit.
TCS Thermal Control System.
TMM Thermal Mathematical Model.
TPS Thermal Protection System.
TT& C Tracking, Telemetry, & Command.
UV Ultra-Violet.
XRT Swift’s X-Ray Telescope.
List of Symbols
Symbol Description Unit
A Area [m2]
GL Thermal Conductance [WK]
S Solar Flux Constant [mW2]
T Temperature [K{˝C]
α Absorptivity [´]
ρ Reflectivity [´]
τ Transmissivity [´]
ε Albedo Factor [´]
ε Emissivity [´]
hc Thermal Contact Conductance [mW2K]
k Thermal Conductivity [mKW ]
t Thickness [m]
x Distance [m]
x
Introduction
Thermal design is one of the main critical phases during the design cycle of a spacecraft.
It ensures the correct function of all elements in every supportive subsystem including the payload of a potential mission, many of them needing to be kept within very strict operating temperature margins.
This thesis work was based on an example mission put forward by Space Structures GmbH, combining background information from previously completed missions within the company.
In detail, the thermal environment and satellite model was analysed and simulated in Airbus Defence and Space’sSystema and Thermica software. It follows different studies in relevant literature, with the main text being the Thermal Handbook [14], and describes the entire process of developing a thermal model for a satellite, and simulating in order to ensure that what is simulated and modelled, designed represents reality. It explains the full methodology behind a thermal simulation using Thermica, from describing the thermal control techniques that are used in satellites, to describing how conductive links are calculated and then describing the input into the software itself.
The ultimate goal of this thesis is to accurately analyse the thermal behaviour of an imaging satellite in the defined Sun Synchronous Orbit (SSO). The primary objectives include the complete analysis of the thermal environment of the current mission, by taking into account all the necessary assumptions made throughout the design, and the simulation.
The first chapter provides an extensive background knowledge to many of the elements that are important in a thermal analysis. It covers the heat transfer mechanisms, the harsh thermal environment and the basics of orbital mechanics, specifying the relevance to the thermal case.
The next chapter describes the method that is followed in this thermal analysis. It is separated into three main sections, the first to define all the assumptions followed in the simulation, the second to state all the background information needed to set up the software, and the third to show exactly how it is modelled within Thermica itself.
The third chapter presents the results from all the simulations performed. It shows them following the order of a thermal analysis; starting at a the basic model then adding different control techniques to iterate to the final solution.
The last chapter concludes the thesis by giving a full evaluation of the final result. It explains whether further work is need and highlights any source of potential error. Any additional calculations or information can be found in the Appendix.
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Heat Transfer Mechanisms
The temperature of deep space is very close to absolute zero which does not occur naturally anywhere in the Earth’s atmosphere. This means the thermal environment in space is incredibly unique, and equally harsh. It is for this reason the thermal design of the spacecraft is so important and must be carefully planned in coordination with the other subsystems.
There are very important components that need to be analysed before any calculations can be initiated. If the components are not kept within their operating temperatures during mission it could result in catastrophic consequences. A good example is the failure of the Thermal Protection System (TPS) on board the STS-107 Space Shuttle mission launched in 2003. A piece of insulating foam broke off during launch and caused the damaged wing to burn up on reentry into the atmosphere. This, in turn caused the shuttle to fail and it was completely destroyed, killing all seven crew members. During the seven month investigation into the failure, around 38% of the Columbia orbiter was found and collected [24].
Without a correct and fully tested Thermal Control System (TCS) to endure the harsh thermal environment both through our atmosphere and beyond, a space mission would be doomed to fail before it even launched.
The first step in any thermal analysis is to fully understand the heat transfer mechanisms.
Heat transfer on Earth includes the processes of convection, thermal conduction and thermal radiation, as can be seen in figure 2.1. These processes can also be present simultaneously, and it is the job of the thermal engineer to analyse to what extent each are present in any given scenario. This section describes these mechanisms in detail, and highlights their contribution to the thermal space environment.
Figure 2.1: Conduction, convection, and radiation heat transfer methods [13].
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2.1 Convection
By definition, convection is the transfer of heat due to the bulk movement of molecules within gases and liquids. In space, as there is an almost perfect vacuum, convection is for the most part negligible. For this reason convection is assumed to be zero for the duration of this thesis.
2.2 Thermal Conduction
Thermal conduction is the second largest heat transfer mechanism in space, and is defined as the transfer of heat by collisions of microscopic particles and movement of electrons within a body. Although thermal conduction takes place in all forms of matter, conduction between gases and liquids is considered negligible. Therefore throughout the duration of this thesis it is assumed that there will only be thermal conduction in solids. Thermal conduction can be mathematically described throughFourier’s Law as
q “ ´k∇T rW
m2s (2.1)
where q is the local heat flux [W
m2], ∇T represents the different temperatures [K] one would be measuring between and k is the thermal conductivity rm KW s of the material.
2.2.1 Thermal Conductance
The thermal conductance is another highly relevant factor, also referred to as GL, which defines the conductance between two bodies. This value is applied directly within most thermal simulation tools so it is important to estimate to a high level of accuracy. The equation needed for this is either:
GL “ KA dx rW
Ks (2.2)
or
GL “ hcA rW
Ks (2.3)
where A is the surface area rm2s, k is the thermal conductivity rm KW s, dx is the distance between the two bodies, and hcis the thermal contact conduction coefficient. The hcvalue changes drastically depending on many factors, such as the contact pressure, the interstitial materials, surface deformations, surface roughness, surface cleanliness and surface flatness.
The value of contact conductance is complex to estimate accurately and requires careful consideration when performing the preliminary thermal calculations.
2.3 Thermal Radiation
Thermal radiation is the heat transfer mechanism defined by the thermal motion of charged particles in matter. If a body has a temperature greater than absolute zero (0 rKs /
´273.15 r˝Cs), it will emit thermal radiation. The greater the temperature, the higher the kinetic energy, which means the particles inside the material will vibrate. This means that there will inevitably be inter-atomic collisions, the result being either charge-acceleration and/or dipole oscillation which produces electromagnetic radiation in a given wide spectrum.
Even at a single temperature there will be a wide spectrum of electromagnetic frequencies radiated away. An example of this could be a light bulb, which when switched on radiates in a spectrum which includes visible light.
The radiation emitted from a surface, in a specific wavelength, can more simply be described as the amount of energy emitted by the surface as a function of the temperature. The amount of energy per unit time area, integrated over all wavelengths is given by
Eb “ σT4 (2.4)
which is known as the Total Black Body Emissive Power, Eb, where σ is the Stefan- Boltzmann constant, (5.67 ˆ 10´8rmW2K4s), and T rKs is temperature. In reality, no perfect black body exists, so the relevant surface emissivity is included in the equation, giving
Eb“ εσT4 (2.5)
where ε is the surface emissivity. It is important to highlight other important properties of a surface, relevant to thermal radiation. The three properties that compose of all incident light on a surface are the absoptivity, α, the reflectivity, ρ, and the transmissivity, τ . In the case of a surface, all three of these are related by
α ` ρ ` τ “ 1. (2.6)
In the thermal design of a spacecraft, transparent surfaces are extremely rare, therefore it can be assumed that τ can be 0. Thermal radiation is extremely important to analyse in space as it is one the biggest contributions of heat in a spacecraft and is one of the primary reasons a TCS is required.
The Thermal Environment
In any extensive thermal analysis, a deep understanding of the thermal environment in space is crucial. It is through this understanding that an appropriate thermal design process can be accurately made. This chapter identifies the important aspects of the thermal environment, and explains how each of them are directly important in the thermal design of a spacecraft.
3.1 Spacecraft Orbital Parameters
A full understanding of the orbit of the spacecraft is essential in order to study the thermal environment around it. There are six primary parameters that need to be studied in order to define an arbitrary and unperturbed Keplerian orbit. All of the following parameters can be visualised with the aid of figure 3.1 and table 3.1.
Figure 3.1: Diagram showing the orbital parameters relevant for the TCS [35].
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Table 3.1: List of Orbital Parameters.
Orbital
Parameter Definition Unit
a Semi-major Axis [km]
e Eccentricity [-]
i Inclination [°]
Ω Right Ascension of the
Ascending Node (RAAN) [°]
ν True Anomaly [°]
ω Argument of Perigee [°]
3.1.1 a Semi Major-Axis
The semi-major axis is half of the major axis of an elliptical orbit, the major axis being the longest diameter of the ellipse. It can easily be calculated by knowing the Apogee and Perigee of orbit, as well as using the average radius of the earth, RE “ 6371 rkms. The equation can be seen as
a “ 2RE ` hapogee` hperigee
2 r4s. (3.1)
It is very important to know the value of the semi-major axis, as it is one of the three primary orbital parameters. It is also useful to know that a “ RE ` h for a circular orbit. In general, changing the semi major-axis of an orbit has large, but very predictable implications on the thermal design. The main factors to consider would be the change in time in eclipse and time spent in the sun.
3.1.2 e Eccentricity
Another very important orbital element is the eccentricity, e, defined as how much an orbit deviates from a perfect circle. This simple table show what difference values of e represent:
Table 3.2: Different Orbital Eccentricities.
Value of e Type of Orbit e = 0 Circular 0 < e < 1 Elliptical
e = 1 Parabola e > 1 Hyperbola
When dealing with most spacecrafts and satellite in orbit, only circular and elliptical orbits are used, so 0 ď e ă 1. The impact the orbital eccentricity can have to the thermal environment is noticeable; generally the higher the eccentricity, the lower the eclipse time, which directly impacts the Solar Flux on the spacecraft.
3.1.3 i Inclination
The inclination, i, of an orbit is the tilt of the object around a celestial body, defined as the angle between the reference plane (the equatorial plane for Earth) and the orbital plane of the object. A change in the inclination of an orbit can have one of the largest impacts on the TCS of the spacecraft. Its impact can be visualised by comparing the eclipse time and time in the sun of a satellite in an equatorial orbit, and a polar orbit. The SSO is partly defined by its highly inclined orbit, and can be positioned in a way in which the satellite is in constant daylight, 24 rhs a day. It is for this reason that the thermal design of a satellite in a SSO is exceptionally different to the other orbital choices.
3.1.4 ω Longitude of the Ascending Node
The longitude of the ascending node shows the orientation of the ascending node of the ellipse, where the orbit passesupwards through the reference plane, in the case of an Earth orbiting satellite; the Equator. It is important to remember when planning the thermal design as, much like the other orbital elements above, can directly change the amount of time the spacecraft spends in eclipse.
3.1.5 β Beta Angle
The β angle is defined as the angle between the Sun and the plane of the orbit. This angle naturally varies as the Earth travels around the sun. Figure 3.2 shows the change in β angle over a general 400 [km] circular 70° inclination orbit.
Figure 3.2: Beta angle over a year for a 400 rkms, 70° inclination orbit [17].
There are two main consequences in the variation of the β angle that the thermal design engineer must consider:
• The orbital time the spacecraft spends in eclipse
• The change in the intensity and direction of the Solar Flux on the spacecraft When performing the thermal analysis, it is important to factor in to both the Hot and Cold Case calculations. For the preliminary calculations the β angle can be assumed at maximum in order to account for all situations, values of which can be seen in section 3.3.
3.1.6 Reentry Environment
One of the biggest challenges in space flight takes place in the Earth’s atmosphere. If a spacecraft wants to de-orbit then it must first travel through the atmosphere, which becomes exponentially more difficult the closer to the surface it gets. This is due to the density of the atmosphere increasing the closer to the surface, where the atmospheric pressure is roughly 1 ratms or 100 rkPas, and reaches close to 0 at around 100 rkms altitude [29]. A spacecraft in LEO has a typical orbital velocity of 7.8 rkms s which must be reduced to 0 while reaching the surface: a challenge that creates a huge build up of heat and will burn up anything that is not specifically designed for reentry.
One of the positive side effects of having such a harsh reentry environment is that it can be used to burn up satellites after they have completed there mission in order to not fill the popular orbital altitudes with orbital debris. In most satellite design cases, there must be enough fuel at the end of the mission to either perform this deorbit burn and break up during reentry, or increase the apogee and perigee of orbit until the spacecraft is in the graveyard orbit, an altitude reserved for unused and waste spacecrafts.
3.2 Perturbations
Once the above orbital parameters have been assessed, then the Keplerian orbit has been defined. Although in a lot of cases it is advisable to use the Keplerian orbit to get more simple calculations, in the real world there exist certain phenomena that cannot be negated.
These are know as perturbations and they exist in all orbits. Perturbations are caused by other forces acting on the orbiting body, such as other gravitational bodies, resistive forces from the atmosphere, and the fact that Earth is not a perfect sphere but anoblate spheroid causing an off centre attraction. A summary of known perturbations is given in table 3.3.
If observed over a short period of time it is difficult to see the effects of the perturbations, but as nominal satellite missions are planned with an operational lifetime spanning several years, it is crucial to analyse every aspect of the various relevant perturbations.
Table 3.3: Summary of Forces Acting on a Spacecraft in Earth Orbit [17].
Source Regime Effect in LEO
Earth (point mass) Dominant force for orbits between Earth and Moon*
Results in Keplerian orbit of satellite about the Earths center of mass
Earth (higher/order geopotential)
Significant perturbing force at GEO and below; declines rapidly with increasing altitude
Depends on specific orbit;
orbit plane rotation of up to 14 deg/day is possible Sun/Moon
(point mass)
Dominant force for interplanetary flight; minor perturbing force in Earth orbit
Low level perturbations; orbit plane rotation of up to 0.007 deg/day
Atmosphere LEO only, decays exponentially with altitude
Reentry occurs rapidly below 120 [km] Atmosphere negligible above 1000 [km]
Solar Radiation Pressure
Minor perturbing force for
normal spacecraft Small eccentricity growth Relativistic Effects Near very massive objects Negligible
Incidental Forces (leaks, RF, explosive bolts)
Very minor perturbing force for normal spacecraft
Negligible in most circumstances
*The Sun’s perturbing force is less than 0.01 times the central force below 370,000 [km]; the Earth perturbing force is less than 0.01 times the central solar force above 2.5 ˆ 106.
In the case of this thesis a more preliminary thermal analysis will take place, but one of the steps to further validate the model over the course of an entire multiple year mission would be to input orbital positioning data from specialised software in order to provided the most accurate flux levels across the spacecraft. This enhances the accuracy of the simulation, and can have a large thermal impact over a long mission duration.
3.3 Radiation Flux Sources
Thermal radiation is the largest heat transfer mechanism in space and the one that must be considered the most throughout the design of the TCS. There are three main sources of radiation that are the most important in space when considering thermal radiation; Solar, Earth-Albedo and Earth-infrared, which can be visualised in figure 3.3.
Figure 3.3: Different Sources of Radiation [8].
This section outlines these in particular and highlights the most important aspects of each.
3.3.1 Solar Flux
The Solar Flux is the largest phenomena to consider during the analyse and design of a spacecraft. This is because the amount of flux coming from the sun is orders of magnitude larger than other sources of flux. The reason why thermal design based around the Solar Flux is possible due to the sun being a more predictable radiation source in comparison to other sources.
The direct solar radiation power density, S, ranges from 1321 rmW2s in early July to 1413 rmW2s in early January, with an annual average at 1367 rmW2s. From a satellite’s viewpoint, S, goes to zero in the Earth’s shadow, although there are orbits (such as GEO and certain SSO) where eclipse transits are virtually non-existent [4].
The total Solar Flux absorbed by a surface on a spacecraft is
QS “ αSAsolar (3.2)
where α is the absorptivity of the surface, and Asolar is the surface area rm2s of the surface being exposed to the Solar Flux. It is also important to implement the beta angle (see section 3.1.5 for definition) into the Solar Flux calculation as it can severely reduce the
amount of flux hitting the surface. In most thermal analyses, for the Hot Case the beta angle is assumed to be at maximum for a given orbit, such that the Solar Flux constant is as high as possible. For the Cold Case it is assumed that the beta angle is at minimum for the given orbit, to enable a calculation of the fluxes in the coldest scenario.
3.3.2 Albedo Flux
Albedo Flux is proportional to the Solar Flux that is reflected from the sun by a celestial body, and in the case of most satellites; the Earth. In the same way as Solar Flux, this is also absent during eclipse. There are many factors that affect the value of the Albedo from a planetary surface namely; snow, water, vegetation and ground composition, example values can be seen in table 3.4. This means that certain orbits, such as polar orbits, are affected more by the Albedo and the Albedo factor is far less constant than an equatorial orbit. The Albedo flux calculation can be seen in 3.3.
Table 3.4: Table showing a range of approximated Albedo values around the Earth [6].
Natural Surface Types Approximated Albedo
Black Body 0
Forest 0.05 - 0.2
Grassland and Cropland 0.1 - 0.25 Dark-Coloured Soil Surfaces 0.1 - 0.2
Dry Sandy Soil 0.25 - 0.45
Dry Clay Soil 0.15 - 0.35
Sand 0.2 - 0.4
Mean Albedo of the Earth 0.36
Granite 0.3 - 0.35
Glacial Ice 0.3 - 0.4
Light-Coloured Soil Surfaces 0.4 - 0.5
Dry Salt Cover 0.5
Fresh, Deep Snow 0.9
Water 0.1 - 1
Absolute White Surface 1
The total Albedo Flux absorbed by a surface on a spacecraft is
QA“ αSAAlbedoAF (3.3)
where α is the reflectivity of the surface receiving Albedo Flux, AAlbedo is the area of the surface exposed to the Albedo Flux, and AF is the Albedo Factor, a ratio between 0 and 1.
3.3.3 IR Flux
IR flux is the flux that is directly emitted from an astronomical body [31]. The IR Earth- shine is relatively constant throughout the day, although it is altitude dependent. The IR
flux is very important to consider in LEO, but is negligible at, for example, GEO. The total IR flux absorbed by a surface on a spacecraft is
QIR“ αεTplanet4 Aplanetary (3.4) where α is the reflectivity, ε is the emissivity, Tplanet is the temperature of the planet assuming black body radiation, and Aplanetary is the area of the surface exposed to the IR flux.
3.3.4 Radiation into Space
The spacecraft will radiate into space in order to maintain thermal equilibrium. The following formula is applicable to the surface facing deep space that will be radiating away heat:
QR“ εσT4Asurf ace (3.5)
where ε is the emissivity, σ is the Stefan-Boltzmann constant (5.67 ˆ 10´8 rmW2K4s), T is the temperature of the surface and Asurf ace is the area [m2] of the surface which is radiating.
In order to accurately calculate the full extent of the spacecraft radiation, it is important to know a few different values. The first step is to assess which components inside and outside the spacecraft are generating heat; this can be simply read from the data-sheets of most of the components. The next step is to determine the view factors inside the spacecraft to calculate the internal heat transfer due to radiation (see section 3.4), and meanwhile also calculate the internal heat transfer due to conduction through the frame of the spacecraft to the radiators (see section 2.2). Once these values have been determined the radiators power dissipation can be calculated and inserted into the thermal balance equation.
3.3.5 Black & Grey Bodies
A black body is theoretical object used to simplify thermal calculations. It assumes that all incident light is absorbed by a body, and also that all the incident light is emitted [4].
Mathematically, it can be assumed that α “ 1 and ε “ 1.
A grey body is a theoretical object which assumes that the absorbed radiation intensity on a body is proportional to the emitted radiation. Mathematically, it can be assumed that
Qabsorbed “ αQincident
and
Qradiated“ εσT4.
Both black and grey bodies are highly important when simplifying certain conditions surrounding radiation; it makes the simulations far simpler and the can hugely reduce the computation time of the simulation. More details on this can be seen in chapter 5.1.
3.4 Radiative View Factor
Radiation between components is completely dependant on the orientation of the surfaces relative to each other. This is accounted for by the view factor [3]. It is important to have a general understanding of the different view factors that will be applied when performing the thermal design of a spacecraft, a summary of which shall be shown in this section.
Usually, it is common for a thermal engineer to use the different view factor configurations that are available in tables, as calculating each and every view factor is time consuming and difficult. Some of the simple geometry and basic principles behind view factor calculations are shown below, and for further analysis please refer to [30].
The view factor Fij is defined as the fraction of the radiation leaving surface i that is intercepted by surface j [12]. This can be be visualised in figure 3.4.
Figure 3.4: View factor associated with radiation exchange between elemental surfaces of area dAi and dAj [12].
A general solution to solve the view factors exists, and can be seen in equation 3.6 below, which has been derived using the geometry shown in figure 3.4 [12] [13]. Note that the equations below assume that the two arbitrary surfaces are diffuse emitters and have uniform radiosity
Fij “ 1 Ai
ż
Ai
ż
Aj
cosθicosθj
πR2 dAidAj. (3.6)
It can be assumed that the view factor Fji can be expressed using the same equation, but substituting in the area Aj, shown as
Fji“ 1 Aj
ż
Ai
ż
Aj
cosθicosθj
πR2 dAidAj. (3.7)
The next logical step is to equate the above integrals, which gives a very important relation, thereciprocity relation, shown as
AiFij “ AjFji. (3.8)
This is a helpful relation that allows the simple calculation of one view factor using the knowledge of the other view factor. Another very useful relation to apply is the rule of summation, sometimes called the enclosure rule, shown in equation 3.9. This is defined following the conservation requirement that all radiation leaving surface i must be intercepted by all the enclosure surfaces. The equation can be seen as
N
ÿ
j“1
Fij “ 1. (3.9)
There are two main steps to calculate the view factors, highly depending on the complexity of the two surfaces. The first step is to useobservation to apply the following assumptions in order to calculate the view factors, in the case where the geometry is simple enough:
• If surface i is a plane or convex, then Fii“ 0
• If surface i is concave, then Fii‰ 0
If step one proves insufficient, then a more analytical approach is required to calculate the first view factor. This requires using either the relevant two or three dimensional view factor relation (tables 13.1, 13.2 in [12]), or by reading the corresponding view factor value off the relevant graph (figures 13.4, 13.5, 13.6 in [12]). In almost all cases the above two steps will be enough to calculate all the view factors in a given scenario, but in the rare case that a scenario provides geometry that does not fall in the parameters of the tables above, then equation 3.6 must be calculated mathematically.
Thermal Control Techniques
In the design of the TCS, there are several tried and tested techniques that function as a way to vary the temperature of some or all of the components inside a spacecraft. The techniques that are almost always used are various methods of passive control, but in some cases active control is required due to the complexity of the components used for various missions.
This chapter introduces these passive and active techniques and describes the functionality of each of them. Every one of these techniques can provide a large level of thermal control, and may or may not be selected due to certain implementation and cost factors. After these techniques have been introduced, a summary will be provided as to compare them generally in terms of functionality and cost.
4.1 Passive Control
Passive control are control methods that are unpowered and work constantly, and produce predictable, efficient results. Passive control is almost always preferred over active control as it is much simpler to design, test and integrate into the spacecraft. The main forms of passive control are; radiators, MLI, and applying an optical surface coating. This relies on the geometry and architecture of the spacecraft. This section will give a brief overview of these techniques.
4.1.1 Radiators
Almost all spacecrafts integrate and use some form of radiator, for the reason that it is the simplest way to reject any unwanted heat power from the spacecraft. They are simple to design and also fairly simple to integrate into the spacecraft. The radiators on all satellites and spacecraft always face into deep space so the surface area of the radiator does not absorb any unwanted fluxes. In some cases, such as in the International Space Station (ISS) shown in figure 4.1, radiators are actively controlled to extend, much like the Solar
Panels, as a much larger surface area is required to radiate into space.
15
Figure 4.1: Thermal Radiator [33].
4.1.2 Surface Coating
Surface coatings are highly common and important elements to consider in the design of a TCS. By simply changing the coating or ’paint’ on the various surfaces inside and outside of the spacecraft, the temperatures across each of the nodes can be drastically changed in a predictable manner. What makes changing the surface coating desirable is its potential to give large results with relatively small cost. One such example can be seen on the outside of the Space Shuttle shown in figure 4.2.
Usually a coating is chosen from a predefined table such as table A.2 in the Appendix, and simulated to see how the material changes the temperatures inside the satellite.
Figure 4.2: Surface Coating on board the Space Shuttle Discovery [26].
4.1.3 Reflective Mirrors
Reflective Mirrors used on board a spacecraft for thermal applications are used very often.
One form of this is known as Optical Solar Reflector (OSR). OSR’s are a form of mirror that are positioned on the outside of a spacecraft, almost always on the surface of the
radiators. The working principle behind the OSR is that there are two layers, a mirror inner layer and a quartz outer layer. The quartz outer layer allows solar light to pass through and into the reflective mirror, which results in low absorption, whilst also being a good emitter of IR. This means that the mirror reflects the visible light and the quartz layer reflects the IR light resulting in a high emitting, low absorbing material which works well on a radiator. Usually the metal reflector is polished pure beryllium (Be).
Another form of reflecting surface is the First Surface Mirror (FSM), which is a single layer used to reflect light; usually the material is Aluminium (Al) for visible light and gold (Au) for infrared. Eighteen First Surface Mirror’s will be used on the James Webb Space Telescope (JWST) in order to keep the telescope as cool as possible, as can be seen in figure 4.3.
Figure 4.3: The 18 first mirrors on the JWST [22].
4.1.4 Multi-Layer Insulation (MLI)
Multi-Layer Insulation (MLI) is another passive thermal control technique which uses several layers of insulation on top of each other, in order to reduce heat loss through internal radiation, and is used heavily in almost all satellites. MLI can be used all over the spacecraft, from the exterior solar facing panels, to the interior, wrapped around the fuel tank.
In order to save mass, and since that these layers do not require structural rigidity, the layers can be made incredibly thin, between roughly 6 rµms and 12 rµms. They can also be very close together, as long as they are not in contact in such that thermal conductance is zero. In most cases there is a form of spacing element, such as a mesh or grid, as shown in figure 4.4a.
Space hardware companies are constantly trying to develop MLI that uses more layers with lower emissivity in order to increase the insulation provided by the MLI. In order to reduce the emissivity of the layers, various materials can be chosen. The materials used are highly important due to the great variances in mass and size. Common materials used
for this layered insulation are: Mylar, Kapton, Silver (Ag) and Aluminium (Al), where different of the values can be seen in table A.2.
Sometimes the MLI can be used to protect against Micro-Meteoroids & Orbital Debris (MMOD), where the MLI is placed at least a few millimetres from the spacecraft to absorb the impact of the particles. In the spacecraft design calls for such protection, a mechanically strong material such as beta-cloth will be integrating into the layering.
Single-Layer Insulation is a sub-form of MLI, and is simply a more cost effective, less efficient insulation method. SLI is used in applications where a high level of insulation is not required. An example of this can be seen in figure 4.4b. It is cheaper than MLI as it is far simpler to manufacture, and can be used in situations in where the thermal control system demands are not as strict. They can usually be bought in colours of gold or black, depending on which properties are required for the mission.
(a) MLI - showing the different levels and outer layers [1].
(b) SLI [7].
Figure 4.4: Figures showing different forms of external insulation.
4.1.5 Heat Pipes
Heat Pipes are an increasingly useful passive control method due to them working very well with thermal radiators, and also due to their various properties:
• Due to micro-gravity they can transport heat over great distances, relative to on the Earth’s surface
• They do not require any power
• They operate nearly isothermally
Using heat pipes in certain situations, such as to transport heat from hot electronic chips to the radiators, is a relatively cheap and effective method which could be used in place of more complex, active control methods. Heat pipes can use different working fluids depending on their application. For ground applications there are two main working fluids; water and R134a, the former mostly used for electronics and the latter used in many Heating, Ventilation and Air Conditioning (HVAC) systems. For numerical data on common working fluids, please see table A.3.
In both manned and unmanned space applications, most instruments working temperature range is the low temperature range, which is between 200 rK] and 550 rK], and the most
common working fluids in this region are ammonia, acetone, the Freon compounds, and water. Heat pipes are extremely reliable when used in a space application, due to having no moving parts and a high wall thickness in order to stop leaks from occurring.
Figure 4.5: Heat Pipes on board the SAM instrument [28].
4.1.6 Thermal Filler
Thermal Filler describes a material that is positioned between other materials in order to change the conduction between them. The idea of using a filling element is to mas- sively increase or decrease the thermal conductivity between the two different components depending on the application. A Thermal Filler, also known as a gasket, is usually a soft material that is chosen for each specific situation and is usually made of Indium (In), CHO-THERM™ or Sigraflex™. Annealed Pyrolytic Graphite (APG) is also known as Thermally Annealed Pyrolytic Graphite, and is also a popular choice when choosing a Thermal Filler for spacecraft applications. A diagram showing where the Thermal Filler would be applied can be seen in figure 4.6.
Figure 4.6: Thermal Filler in an orbiter tile - the filler can be seen in brown [2].
4.2 Active Control
4.2.1 Heaters
Heaters are small electrically controlled circuits which provide local heat to where they are positioned. In the optimal case, only passive thermal control would be used in a spacecraft, but sometimes it is simply not enough due to the harsh thermal conditions in space. In this case heaters could be used to keep the sensitive components within the correct temperature ranges. Heaters are the most common form of active thermal control due to their relative simplicity when compared against other active methods. The most common type of heater used is the patch heater, which is effectively a heating circuit sandwiched between two layers of electrically insulating material. An example of two patch heaters can be seen in figure 4.7, heating up the Swift’s X-Ray Telescope (XRT) instrument for the SWIFT mission. As the system is active and must be controlled, there is always the chance that the heating circuit will fail, and for this reason redundancy must be taken into account.
There are two ways in which redundancy is used in the case of patch heaters, either by using multiple heating circuits in the same heater, or using multiple heaters in a small surface area.
Figure 4.7: Thermal Heater on the XRT instrument [11].
4.2.2 Cryogenic Coolers
Cryogenic Coolers or Cryocoolers, are special coolers that are designed to cool components down to cryogenic temperatures. This temperature range is not well defined, but is generally considered to be temperatures 122 rKs and below [5]. The main application for using cryogenic coolers is to cool instruments down to their optimal working temperature range; for example IR telescopes must be cooled to as close to absolute zero as possible, as any temperature over induces noise into the IR measurements, reducing the Signal-to-Noise Ratio (SNR). Cryocoolers are also often used for gamma-ray and x-ray telescopes too; so for scientific missions they are very commonly used.
When Cryocoolers are required for the thermal design of the spacecraft, careful consider- ation needs to be taken to their positioning within the spacecraft. Cryocoolers are very power consuming and are often heavy relative to other TCS. Various technologies for several cryogenic ranges can be seen in table 4.1.
Table 4.1: Cryocooler Technology Temperature Ranges [25].
Cooler Typical
Temperature Typical
Heat Lift Advantages Disadvantages
Radiator 80 K 0.5 W Reliable, low vibration,
long lifetime Complicates orbit
Cryogen 4 K 0.05 W Stable, low vibration Short lifetime, out-gassing, massive, complex
Stirling – 1 stage 80 K 0.8 W Efficient, heritage Vibrations
Stirling – 2 stage 20 K 0.06 W Intermediate temp Under development Pulse tube 80 K 0.8 W Lower vibrations Lower efficiency than
Stirling
Peltier 170 K 1 W Lightweight High temp, low efficiency
Joule-Thompson 4 K 0.01 W Low vibrations Requires hybrid design
Sorption 10 K 0.1 W Low vibrations Under development
Rev. Brayton 65 K 8 W High capacity Complex
ADR 0.05 K 0.01 mW Only way to reach
these temps Large magnetic field
Figure 4.8: Cryocooler designed for the MIRI mission [15], which uses three stage pulse-tube cooling [23].
4.2.3 Peltier Element
A Peltier Element, sometimes known as Thermoelectric Heat Pump, is an active pump that transfers heat from one side of the device to the other, while consuming electrical energy. Although with current technology Peltier Heaters are rather electrically inefficient, they are still highly favoured for space application due to having no moving parts, very long life, its relative small size, and its near-invulnerability to leaks.
Peltier Elements can also be used as a Thermoelectric Generator, simply by applying its working principle in a different way. If one side of the element is exposed to a high temperature than the other, through theSeebeck effect there will be a resulting voltage build up. Usually, in order to efficiently use the Peltier Element for this purpose a dedicated design should be used to optimise the efficiency. In the generator format, the Peltier Element has been used in many unmanned spacecraft applications including NASA’s Curiosity Rover.
Figure 4.9 shows an example Peltier Element with its necessary components, such as the heat sink and the temperature sensor, connecting to the temperature controller on the right.
Figure 4.9: Example Peltier Element in a Thermoelectric cooling application [20].
4.2.4 Louvres
Louvres are a mechanical shutter that can be actively opened and closed in order to change how much surface area is radiating into space. In general, in the fully open state, the Louvre will allow up to six times as much heat rejection as it does in the fully closed state. Such a Louvre can be seen in 4.10 which is placed on top of the radiators on board ESA’s Rosetta Mission. Most commonly a Louvre is placed over the highly emmittance, low absorptance external radiators on the spacecraft, and are driven by actuators which effectivelycontrol the emission from the radiators. The main reason why a Louvre would be chosen as a thermal control method is in the scenario that the internal power dissipation varies extensively due to the different equipment’s duty cycles.
Figure 4.10: Thermal Louvres for ESA’s Rosetta Mission [10].
4.3 Thermal Control Techniques Summary
To summarise this chapter, table 4.2 has been created which compares the general prices and performances of the various Thermal Design Techniques mentioned. It is meant to be used as a guideline to enable selecting the desirable technique for a given application, and will be referred to later in this thesis.
Table 4.2: Price/Performance Characteristics of Common Thermal Control Techniques.
Thermal Design
Technique Function Price Range
(€ - €€€€) Performance
(I - IV) Advantages Disadvantages Image
Thermal Radiator Passive / Active, Radiation
€ II
• Easy to implement
• When passively implemented very cheap
• Can be easily adapted by adding surface coating
• Limited by physical size on spacecraft
• Can add a lot of mass
4.1
Surface Coating Passive,
Radiation € III
• Very cheap to implement
• Huge impact in reducing direct radiation
• Can easily be modified in order to tweak thermal system performance
• Can degrade quickly depending
on the environment it is exposed to 4.2
Mirrors Passive,
Radiation €€ I • Passive control method for achieving
near absolute zero temperatures
• Difficult to implement and increases
complexity in AIT phase 4.3
Multi-Layer Insulation
Passive,
Radiation €€ II
• Does not require maintenance
• Can also integrate MMOD shielding in the layers
• Large impact in raditation reduction with relatively small mass impact
• Easily adjustable to specific situations
• Can be very expensive to manufacture custom MLI and integrate it onboard a spacecraft
4.4a
Single-Layer Insulation
Passive,
Radiation € I
• Very cheap to implement
• Much easier to integrate into the thermal design
• Not adjustable
• Limited performance 4.4b
Heat Pipes Passive,
Conduction €€ III
• Extremely high reliability due to no atmosphere and the wall thickness is thick for extremely low chance of leakage
• Added reliability due to no moving parts
• Use of working fluid complicates integration and care must be taken with the chosen fluid
4.5
Heat Straps Passive,
Conduction €€ I • Cheap way to dissipate heat away
from components.
• Limited by the thermal conductivity of the material
Thermal Fillers Passive,
Conduction € - €€ I
• Easy insulation method to implement
• Range from cheap to more expensive depending on the application, but in general it is a cost effective solution to improve the thermal coupling
4.6
Thermal Washer Passive,
Conduction € I • Cost virtually nothing and take
up very little space
• Could potentially decrease the structuralintegrity of the components it attaches to, depending on the washer material
Thermal Heaters
Active, Conduction/
Radiation
€€ - €€€ II
• Can actively change the temperature autonomously so can adapt to eclipse/
sun exposure
• No moving parts which increases reliability
• Simply by needing to be actively controlled, the reliability is decreased:
for example if the link between the OBC and the heater is severed then the heater could malfunction
4.7
Cryogenic Coolers Active,
Conduction €€€€ IV
• Can cool to temperatures unobtainable through other thermal design techniques - an essential need on some missions that require near absolute zero temperatures
• Can be very expensive, and add a lot
of mass to the spacecraft 4.8
Peltier Element Active,
Conduction €€€ III
• No cryogen required
• No moving parts resulting in no vibration or mechanical noise
• Simple to install
• A single element has low power output - several must be connected together in order to achieve large effect thermal cooling
4.9
Louvres Active,
Radiation €€ II
• Can easily be integated with thermal radiators to vary the thermal performance
• Relatively cheap to install
• Requires no power when in its open or closed state
• Can add lots of mass and take up a lot of physical space
• Uses moving parts which always have a lower reliability
4.10
Method
This chapter explains the complete setup and defines everything that is needed to complete a thermal simulation accurately. The first section defines all of the assumptions that should be taken into account for the rest of the thesis. These assumptions are very important to define, in order to validate the final result of the simulations and show where any region of potential error could lie.
The next section’s purpose is to define the thermal design process, the steps that will be followed, when proceeding on with the analysis. Each step is important and provides valuable information which will determine the input for the simulation in the thermal design software. The list below serves as a general introduction to the methodology behind the decided process.
Within the thermal design process, there are two main halves. The first half shows the background information that must be gathered in the lead up to setting up the software, and the second half is concerning with how specific thermal elements are modelled. The goal of this chapter is to provide all the information to simulate the worst case scenarios of the satellite in orbit.
5.1 Assumptions
For any thermal simulation, it is important to first outline all assumptions that are made, and have these assumptions in one place which used in the duration of the thesis. These next sections highlight the assumptions that were made for both the coldest and the hottest scenario, as well as universal constants and, if applicable, software assumptions.
5.1.1 Universal Constants
For any calculations or simulations that will be performed, the universal constants that are used for both Hot and Cold Case must be predefined to trace any errors later in the project. The constants assumed are:
Mean Earth Radius, REART H “ 6378 rkms Stefan-Boltzmann Constant, σ “ 5.67ˆ10´8 r W
m2K4s Standard Gravitational Parameter, µ0 “ 3.9860044189ˆ1014rm3
s2 s
25
5.1.2 Coldest Case Scenario
For the coldest case scenario, certain assumptions and simplifications must be taken in order to perform a reliable calculation. The assumptions will be that:
• The surface coatings on the spacecraft will be assumed to be homogeneous over the entire surface where it is applied
• The simulation performed will be Steady State
• The spacecraft will be in eclipse, so both the Solar and Albedo Flux will be ignored
• The temperature of the Earth will be assumed to be constant, at a Cold Case value of 251.27 rKs [14]
• Surface coatings will assume an Beginning-Of-Life (BOL) scenario. More info in section 5.3.3.2
• Perturbations will be ignored, the orbit will be assumed to be Keplerian
5.1.3 Hottest Case Scenario
The hottest case scenario will be modelled similar to the Cold Case, although with some different values and several different assumptions:
• The surface coatings on the spacecraft will be assumed to be homogeneous over the entire surface where it is applied
• The simulation performed will be Steady State
• The β angle will be assumed to be 90° and the calculation will be made in winter, when the solar constant is 1414 rmW2s [14]
• The temperature of the Earth will be assumed to be constant, at a Hot Case value of 255.6 rKs [14]
• The albedo value will be constant, and will be assumed to equal 0.33 [14]
• Surface coatings will assume an End-Of-Life (EOL) scenario. More info in section 5.3.3.2
• Perturbations will be ignored, the orbit will be assumed to be Keplerian
These Cold and Hot Case scenario assumptions are provided as a reference point for the next section, where the thermal modelling and more accurate simulation using computer software is shown.
5.1.4 Software Boundary Conditions
When using software to simulate different environments, it is very important to form as- sumptions in such a way that they maximise the accuracy of the simulation, but drastically simplify both the entering of parameters and the computer simulation time. Some of the below mentioned assumptions are both generic for the thermal control design, and some are more specific towards the simulation software of choice.
5.1.4.1 Summed Thermal Conductivity in Materials
When entering several conduction elements in contact with each other, the total conductiv- ity can be summed and replaced by a single value. This was done for all of the components inside the spacecraft, the details can be seen later in this report in chapter 5.3.4.
5.1.4.2 Constant Thermo-Optical Material Properties
It is assumed that when using Thermica, that all of the thermo-optical properties set to the different materials will be constant. This means that good care must be taken when assigning the relevant numerical values, and phenomena such as the differences between beginning-of-life and end-of-life absorptivity, the exact values, and optical surface coatings
chosen are highly important and can be seen in Appendix A.2.
5.2 Thermal Design Process
After all of the assumptions and boundary conditions have been defined, the next step is to fully assess the design process that will be followed in this chapter. In this chapter, there will be a total of two main sections. The first will concentrate on defining the background information specific to the case of the satellite, and the second will focus on the actual analysis and simulation. This section adheres mostly to the thermal flowchart A.1 shown in reference [36]. The following list shows the breakdown of each section, where each part will be analysed and defined later in the chapter.
Phase 1: Background Information & Set Up 1. Assess orbital parameters
2. Analyse and document material properties and surface coating properties, and how they will be used within Thermica
3. Analyse components, including internal dissipation and conductive path calculations 4. Analyse the different modes of operation
5. Preliminary cube/sphere model for initial calculations in order to define the maximum and minimum temperature limits for the spacecraft
6. Analyse and display the component temperature requirements Phase 2: Thermica Modelling Phase
1. Assess the Geometric Mathematical Model (GMM) that will be used for the simula- tions
2. Understand and define how many thermal nodes are required and how they are represented in the software
3. Describe and show how MLI will be defined within Thermica
4. Final thermal mass check to verify whether the model accurately represents reality
