Thermal Modelling of the PICSAT Nanosatellite Platform and Synergetic Prestudies of the CIRCUS Nanosatellite

Thermal modelling of the PICSAT nanosatellite platform and synergetic prestudies of the CIRCUS nanosatellite

Tobias Flecht

Space Engineering, masters level 2016

Luleå University of Technology Department of Computer Science, Electrical and Space Engineering Thermal modelling of the PICSAT nanosatellite platform and synergetic prestudies of the CIRCUS nanosatellite

Tobias Flecht

Luleå University of Technology Department of Computer Science, Electrical and Space Engineering

Supervisor: Didier Tiphène Laboratoire d’Etudes Spatiales et d’Instrumentation en Astrophysique Observatoire de Paris

September 2016

Abstract

In the present master thesis, which was written in collaboration with the Observatory of Paris, thermal models of two cubesat missions are created. The goal of this work is to create a simulation to verify the sur- vivability of the systems within the extreme space environment. In a second step suitable countermeasures are suggested, if parts of the satellite exceed a critical temperature limit. Two new cubesat missions are currently developed at the Observatory of Paris. The goal of the PICSAT mission is to observe the transit of the exoplanet Beta Pictoris B in front of his star using a photometer. The mission called Characterization of the Ionosphere using a Radio receiver on a CUbeSat (CIRCUS) aims to conduct measurements in the ionosphere and to space qualify a new instrument. The satellites are currently in different development stages. While PICSAT is in its phase B, early prestudies of phase A are conducted for CIRCUS. A vital part of these studies is the thermal design, which is done in this work. Every part of a satellite can only be operated in a certain temperature range. Exceeding those temperatures means to risk a critical failure of a subsystem or even the loss the complete system. The task of the thermal design is to keep the temperatures of the satellite’s components within those limits. The space environment and its interaction with a spacecraft is the main driver of the temperatures on board of a satellite. The three external heat sources that can be identified to act significantly on a spacecraft in a low Earth orbit are the solar radiation, the planetary radiation and the Earth albedo. An additional heat source is the dissipation on board of the vehicle. The only heat sink in the system is the thermal radiation emitted from the surfaces of the spacecraft into space. The temperatures on board are the result of the balance between emitted thermal radiation and absorbed radiation as well as dissipated heat. To estimate the temperatures, which have to be expected during a mission, simulations and tests are performed. A model of a satellite is created, in which the relevant components with their thermal properties (heat capacity, conductivity and optical surface properties) are represented by nodes. The nodes are conductive and radiative linked to each other and to the space environment. The models are created and the simulations are performed using SYSTEMA/THERMICA. In order to cover all possible temperature ranges, a hot case and a cold case is determined for PICSAT. The hot and cold cases are defined to maximize (respectively minimize) the heat absorbed by the satellite and depend on the satellite’s attitude, orbit, heat dissipation and the distance between the Earth and the Sun. Additionally, relevant failure modes of the satellite are investigated. The considered cases cover malfunctions of the attitude control system and the deployable solar panels. The reliability of the thermal model of PICSAT is verified in thermal tests with the engineering model. For that purpose the thermal model is adjusted to represent the engineering model. The results of the

iii simulations are compared with the measurements. Ultimately, the thermal interfaces in the thermal model are adjusted based on the outcome of the studies. Due to its early development stage only little information is available regarding CIRCUS. In order to make first estimations regarding the thermal behaviour of the CIRCUS satellite, the thermal model of PICSAT is adjusted to represent CIRCUS. Different configurations of CIRCUS were considered. The configurations are distinguished by the arrangement of the deployable solar panels. The results of the simulations conducted in this work will contribute to the further development of both satellites. The simulations show which aspects of the thermal design of PICSAT have to be improved. In the cold case three components (the charging batteries, one of the solar cells and one component of the structure) of PICSAT exceed the temperature limits. Based on the simulations, the utilization of heaters and the change of certain surface properties are recommended. These measures are taken to improve the thermal state of the satellite. Only one of the considered failure modes is critical. This mode might occur, when the attitude control fails and a certain surface of the satellite points to the Sun. Different methods to compensate the impact of this failure are suggested. The results of the conducted simulations will serve as an input for a more detailed analysis of the satellite’s payload and will influence the further development of the project in the aspects of attitude control, surface finishes and the electrical power system. Out of the configurations considered fore CIRCUS in this work, two are recommended for further studies based on the preformed simulations. The first one is a simple three unit cubesat. The second one is a three unit cubesat with deployable solar panels, which are in parallel to the satellites main axis. This configuration is similar to PICSAT. This recommendation is based on the compliance of the simulated temperatures with the temperature limits defined earlier for PICSAT. This work also gives recommendations which aspects of the thermal design have to be considered for the different configurations in the further development of the CIRCUS mission to guarantee a successful operations.

iv Acknowledgements

I would like to thank my advisor Didier Tiphène, for all his help and guidance that he has given me during the preparation of this thesis. I am also grateful for the useful suggestions and comments of Jérôme Parisot, Cyrille Blanchard and especially Napoléon Nguyen Tuong. I would like to thank the Observatory of Paris and the teams of CIRCUS as well as PICSAT for accepting and supporting me as a visiting student researcher. I would like to thank the Laboratory of Excellence ESEP for its support. Also I would like to thank Teresa Mendaza de Cal, Devon Suns and Duong Tran for their interest, patience and helpfulness. I would like to thank Rose Nerriere and Timothée Soriano from the company Airbus Defence and Space for providing a licence of SYSTEMA/THERMICA. I would like to thank the support of the Education, Audiovisual and Culture Executive Agency of the Commission of the European Communities under the Erasmus Mundus Framework. Finally, I would like to thank my family for their support during my studies.

Disclaimer

This project has been funded with support from the European Commission. This publication [communication] reﬂects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein. http://ec.europa.eu/dgs/education_culture/publ/graphics/beneficiaries_all.pdf

vii

Contents

List of Figures xiii

List of Tables xv

List of Acronyms xvii

1 Introduction 1

2 Basics of heat transfer and the thermal space environment 3 2.1 Methods of heat transfer ...... 3 2.1.1 Radiative Heat Transfer ...... 3 2.1.2 Conductive Heat Transfer ...... 6 2.1.3 Convective Heat Transfer ...... 6 2.2 The Thermal Space Environment ...... 7 2.2.1 Solar radiation ...... 7 2.2.2 Planetary albedo ...... 8 2.2.3 Planetary radiation ...... 9 2.2.4 Radiation emitted from the spacecraft ...... 9

3 Basics of thermal simulation 11 3.1 Thermal equilibrium simulation ...... 11 3.2 Thermal mathematical model ...... 12

4 Thermal modelling of the PICSAT nanosatellite platform 15 4.1 Deﬁnition of relevant thermal environments and mission modes ...... 15 4.1.1 Thermal Ground Environment ...... 16 4.1.2 Thermal Launch Environment ...... 16 4.1.3 Beginning of life time environment ...... 16 4.1.4 End of Lifetime ...... 18 4.1.5 Failure Cases ...... 18 4.2 Thermal Properties and requirements of the satellite subsystems ...... 19 4.2.1 Structure ...... 21 4.2.2 Electrical power system ...... 21 4.2.3 Onboard Computer ...... 23 4.2.4 Communication System ...... 23 4.2.5 Attitude Determination and Control System ...... 24 4.2.6 The Payload ...... 24

ix 4.2.7 Overview ...... 25 4.3 Thermal Modeling of the satellite ...... 25 4.3.1 Nodal breakdown and geometrical modeling ...... 26 4.3.2 Definition of nodal properties ...... 26 4.3.3 Definition of conductive links ...... 29 4.4 Thermal tests with the engineering model ...... 31 4.4.1 The Engineering Model and its TMM ...... 31 4.4.2 Test configurations ...... 32 4.4.3 Test results ...... 34 4.4.4 Comparison of the simulation and the measurement ...... 34 4.5 Simulation results of PICSAT ...... 40 4.5.1 Hot Case ...... 40 4.5.2 Cold Case ...... 41 4.5.3 Failure Case 1 ...... 42 4.5.4 Failure Case 2 ...... 43 4.5.5 Failure Case 3 Hot ...... 44 4.5.6 Failure Case 3 Cold ...... 45 4.6 Discussion of the thermal design of PICSAT ...... 46 4.6.1 Compliance of the hot and cold case with the operational temperature ranges ...... 46 4.6.2 Consequences of the considered failure cases ...... 48 4.6.3 Error ...... 50

5 Thermal prestudies of the CIRCUS nanosatellite 51 5.1 Adjustment of the PICSAT model to accomplish the thermal pre-sudies of CIRCUS ...... 51 5.2 The projected orbit and its hot and cold case ...... 52 5.3 Satellite Configurations and their hot and cold cases ...... 53 5.4 Simulation results of CIRCUS ...... 55 5.4.1 Results of Configuration 1: Cold case ...... 55 5.4.2 Results of Configuration 1: Hot case ...... 56 5.4.3 Results of Configuration 2: Cold case ...... 57 5.4.4 Results of Configuration 2: Hot case ...... 58 5.4.5 Results of Configuration 3: Cold case ...... 59 5.4.6 Results of Configuration 3: Hot case ...... 60 5.4.7 Results of Configuration 4: Cold case ...... 61 5.4.8 Results of Configuration 4: Hot case ...... 62 5.5 Discussion of the thermal prestudies of CIRCUS ...... 62 5.5.1 Configuration 1: Non spinning 3U satellite ...... 62 5.5.2 Configuration 2: Spinning 3U satellite ...... 63 5.5.3 Configuration 3: Satellite with two DSPs parallel to the main axis ...... 63 5.5.4 Configuration 4: Satellite with four DSPs perpendicular to the main axis ...... 64

6 Conclusion and Outlook 65 6.1 PICSAT: Compliance with operational temperature requirements and further testing ...... 65 6.2 CIRCUS: First temperature estimations and further studies ...... 66

A Calculation of the properties of a PCB 69

B Conductive Links 71 x C Convection horizontal plate 73

D Convection vertical plate 75

E Voltage demand of an electrical heater 77

Bibliography 79

List of Figures

2.1 Spectral emissive power of a blackbody...... 4 2.2 Deﬁnition of the view factor...... 5 2.3 View factor of two crossing perpendicular plates...... 5 2.4 The thermal space environment ...... 8 2.5 The visibility factor of the albedo ...... 9 2.6 Earth’s planetary radiation spectral distribution ...... 10

4.1 PICSAT hot and cold case ...... 17 4.2 PICSAT Failure Cases ...... 19 4.3 Order of the internal parts of PICSAT ...... 20 4.4 Structure of PICSAT ...... 21 4.5 Location of the solar cells of PICSAT ...... 22 4.6 The payload cube of PICSAT ...... 25 4.7 Example a conductive link between the attached ribs and the corner node...... 30 4.8 FEM simulation of the attached ribs...... 30 4.9 Engineering model of PICSAT and its GMM ...... 32 4.10 Sensor and heater positions of the heating experiments ...... 34 4.11 Results of the heating experiments ...... 35 4.12 Comparison of the measured values with the simulated values without convection ...... 37 4.13 Comparison of the measured values with the simulated values with convection ...... 38 4.14 Comparison of the measured values with the results of the adjusted simulation ...... 39 4.15 Simulated hotcase temperatures for the top and middle cube of PICSAT ...... 40 4.16 Simulated hot case temperatures of the solar cells ...... 40 4.17 Simulated cold case temperatures for the top and middle cube of PICSAT ...... 41 4.18 Simulated cold case temperatures of the solar cells ...... 41 4.19 Simulated failure case 1 temperatures for the top and middle cube of PICSAT ...... 42 4.20 Simulated failure case 1 hot temperatures of the solar cells ...... 42 4.21 Simulated failure case 2 temperatures for the top and middle cube of PICSAT ...... 43 4.22 Simulated failure case 2 temperatures of the solar cells ...... 43 4.23 Simulated failure case 3 hot temperatures for the top and middle cube of PICSAT ...... 44 4.24 Simulated failure case 3 hot temperatures of the solar cells ...... 44 4.25 Simulated failure case 3 cold temperatures for the top and middle cube of PICSAT ...... 45 4.26 Simulated failure case 3 cold temperatures of the solar cells ...... 45 4.27 Predicted and operational temperature ranges of PICSAT...... 47 4.28 Comparison of the temperatures of the batteries and a Sun pointing solar cells ...... 48

xiii 4.29 MLI effect in the second and third failure case ...... 49 4.30 Predicted and operational temperature ranges of PICSAT in failure case 3 ...... 50

5.1 Configuration of the internal parts of CIRCUS ...... 52 5.2 Hot and cold case orbits of CIRCUS ...... 53 5.3 Configuration studies 1 and 2 of CIRCUS ...... 54 5.4 Configuration studies 3 and 4 of CIRCUS ...... 54 5.5 Cold case results of the first CIRCUS configuration ...... 55 5.6 Hot case results of the first CIRCUS configuration ...... 56 5.7 Cold case results of the second CIRCUS configuration ...... 57 5.8 Hot case results of the second CIRCUS configuration ...... 58 5.9 Cold case results of the third CIRCUS configuration ...... 59 5.10 Hot case results of the third CIRCUS configuration ...... 60 5.11 Cold case results of the second CIRCUS configuration ...... 61 5.12 Hot case results of the fourth CIRCUS configuration ...... 62

xiv List of Tables

2.1 Albedo values of different planets ...... 8

3.1 Possible software packages ...... 14

4.1 Data of different launch systems ...... 16 4.2 Simulated orbits of PICSAT ...... 17 4.3 Simulated pointing cases of PICSAT ...... 18 4.4 Materials of the PICSAT structure ...... 22 4.5 Materials of the PICSAT EPS ...... 23 4.6 Materials of the ODHS ...... 23 4.7 Materials of the PICSAT communication subsystem ...... 24 4.8 Materials of the ADCS of PICSAT ...... 24 4.9 Materials of the simplified PICSAT payload ...... 25 4.10 Operational Temperature ranges of the PICSAT subsystems and components ...... 25 4.11 Dissipation of PICSAT components ...... 26 4.12 Nodes of the PICSAT GMM ...... 27 4.13 Heat capacities of the PICSAT GMM ...... 28 4.14 Dissipation in the PICSAT GMM ...... 29 4.15 Approximated convective links for the first test configuration ...... 32 4.16 Approximated convective links for the second test configuration ...... 33 4.17 Characteristics of heaters used for heating tests ...... 33 4.18 Overview of executed heating tests ...... 33 4.19 Overview of the test results ...... 34 4.20 Adjusted conductive links based on the test results ...... 36

B.1 Conductive links in the PICSAT TMM ...... 71 B.2 Continued: Conductive links in the PICSAT TMM ...... 72

List of Acronyms

1D one dimensional 2D two dimensional 3D three dimensional 3U three unit ADCS Attitude Determination and Control System CDS CubeSat Design Speciﬁcation CIRCUS Characterization of the Ionosphere using a Radio receiver on a CUbeSat DSP deployable solar panels EOL end of lifetime ESP end shear panels EPS Electrical Power System FEM ﬁnite element method FMH free molecular heating GMM Geometrical Mathematical Model IR Infrared MLI multilayer insulation ODHS On board data handling system PCB printed circuit boards SSP side shear panels STAR STacked Adc Receiver TMM Thermal Mathematical Model TRL technology readiness level TVC Thermal Vacuum Chamber UHF Ultra High Frequency UV ultraviolet VHF Very High Frequency

xvii

Chapter 1

Introduction

Thermal control is one of the most vital tasks during the development of a new space mission. Every part of the satellite has to be operated in a certain temperature range in order to avoid malfunction or destruction. The temperatures within the satellite depend on several aspects, which have to be taken into account during the simulations. Besides the satellite’s altitude and attitude, its geometrical configuration and the material properties of every single part are elementary. Another aspect that must be considered is the thermal space environment interacting with the spacecraft. During its operation in space every satellite experiences various extreme environmental conditions. Those conditions are mainly characterized by the absence of a surrounding atmosphere, the solar wind and the radiation emitted by the Sun as well as the planets [1, p.11ff.]. The ratio between radiation absorbed and emitted by the surfaces of the satellite is the main driver of the temperature of the spacecraft. The tasks of thermal control are divided into three steps which are conducted in the framework of this thesis: thermal analysis, thermal design, and thermal testing [1, p.357ff.]. The first step contains the simulation of the satellite and its environment in order to obtain the resulting temperature. The second step consists of recommendations for the further development based on the results of the first step. Since simulations alone are not reliable and have to be verified, thermal testing is accomplished with the engineering model of one of the satellites. In the framework of this work the thermal aspect of two satellite missions will be analysed. The first one is a three unit (3U) cubesat PICSAT. The mission of PICSAT is to measure the transit of the exoplanet Beta Pictoris b in front of the star Beta Pictoris [2]. The planet was imaged for the first time in 2007 [3]. Further observations determined the orbit parameters of the planet and predict that the next transit will occur between July 2017 and March 2018 [4]. The primary mission objective is to perform a nearly continuously photometric monitoring of Beta Pictoris in order to observe the next transit [2]. The secondary objective is to characterise the dust cloud surrounding the star, which is typical for young star systems [2]. Observing the star from space avoids atmospheric disturbances and the day/night shift. The orbit parameters of PICSAT are chosen to have an orbit period of 96 min, which allows an observation time of 1 h per orbit. The duration of the transit phenomenon is in the order of a few hours [2]. The state of the PICSAT mission is advanced and currently in phase B. The second mission studied is the satellite called CIRCUS. The mission has two main goals. The first aims to realize a nanosatellite for measurements of the properties of ionospheric plasma [5]. The second is to space qualify a new digital receiver called STacked Adc Receiver (STAR) and thereby to increase its technology readiness level (TRL) [6]. The CIRCUS project is currently in an early stage of development, which corresponds to phase A studies. The thermal analysis of PICSAT is conducted based on its current development state. For CIRCUS early prestudies are performed based on the experience from the analysis of PICSAT. This work is divided into five parts. The basics of heat transfer and the thermal space environment are defined in chapter 2. The simulation method is introduced in chapter 3. In chapter 4 the analysis of the PICSAT satellite is conducted. Based on the thermal model of PICSAT, an early study of CIRCUS is performed in chapter 5. Chapter 6 reviews the obtained results and provides recommendations for further steps.

Chapter 2

Basics of heat transfer and the thermal space environment

The temperature on a spacecraft is driven by the conditions of the thermal space environment. This environment does not only vary significantly depending on the orbited object, but alters also with the chosen orbit itself. This environment not only varies significantly depending on the orbited object, but also alters with the chosen orbit itself. The properties of the thermal space environment are distinguished by the type, source and magnitude of heat transfer mechanisms influencing the spacecraft’s temperature. Section 2.1 gives a short overview of the three types of heat transfer. The different heat sources acting on an Earth orbit are introduced in section 2.2.

2.1 Methods of heat transfer

Before discussing the thermal space environment it is necessary to understand the physical basics of heat transfer. Three concepts describe how thermal energy is transported [7, p.355ff.]. All three transfer types have in common that energy is always transported in the direction of lower temperatures [7, p.355ff.]. 1. Radiative Heat Transfer is based on radiation without the need of a carrier medium. 2. Conductive Heat Transfer occurs within solid materials. 3. Convective transferred heat moves with a fluid. However, other literature distinguishes only two types of heat transfer and defines convection as a special case of conduction to a fluid [8, p.3].

2.1.1 Radiative Heat Transfer

All materials with a temperature higher than zero kelvin emit electromagnetic radiation [9, p.73ff.]. This radiation is settled in the frequency domain between 0.1µm and 100µm, which covers the ultraviolet (UV) and Infrared (IR) frequency range [9, p.73]. In contrast to the other two transfer methods the radiative heat transfer does not require a propagation medium [9, p.74]. In the simplest case, the radiative behaviour of a body can be described as a black body [9, p.77]. In this case, radiation is absorbed and emitted by the body independent of the frequency and the direction [9, p.77]. The spectral emissive power of a blackbody Eb,λ is given by equation 2.1 with the wavelength Λ, the temperature of the blackbody Tb, the planck constant h, the speed of light c and the Boltzmann constant k [9, p.78].

2π h c2 Eb,λ (λ, Tb) = · · (2.1) 5 h·c λ exp · · 1 · λ k Tb − 3 Figure 2.1 plots the spectral emissive power of a blackbody over the wavelength. For seven different temperatures. The striped area marks the visible frequency range [9, p.78]. The dotted line represents the Wien’s displacement law, which states at which frequency a body emits the most energy depending on its temperature [9, p.78]. Integrating

Figure 2.1: Spectral emissive power of a blackbody. Taken from [9, p.78]. equation 2.1 over the wavelength from 0 to derives the Stefan-Boltzmann law, which is given in equation 2.2. σ ∞ is the Stefan-Boltzmann constant and Eb the energy ﬂuence emitted by the blackbody.

E (T ) = σ T 4 (2.2) b · This equation is only valid for bodies, which can be assumed to be black bodies, e.g. the Sun at a temperature of 5800 K [1, p.359]. For real bodies more properties of the emitting and absorbing surface materials have to be taken into account in order to describe the radiative heat transfer mechanism.

The heat Qrad,ij transferred by radiation from a surface i to a surface j is described by equation 2.3, where Ai is the area of the surface i, Fij the viewfactor of surface j as seen from surface i, ǫij the effective emittance, σ the

Boltzmann constant and Ti as well as Tj the temperatures of the surfaces. In this formula the assumption is made that the view factor remains constant for the whole surface i. [1, p.367ff.]

Q = A F ǫ σ (T 4 T 4) (2.3) rad,ij i · ij · ij · · i − j The quantity of transferred heat is signiﬁcantly inﬂuenced by the geometry of the surfaces and their alignment.

This aspect is considered by introducing the radiative view factor Fij, which is defined as the fraction of radiation leaving the surface Ai that reaches the surface Aj[1, p.367f.]. For two diffuse surfaces the view factor is determined by equation 2.4 [1, p.367], where s is the distance between two elements on the surfaces. The angle Φi is the angle between the surface normal and the direction of the radiated point on the second surface. Conversely Φj is the angle between the surface normal of the second surface and the line between the two observed points. The dependencies of the view factor are illustrated in figure 2.2. 1 cosΦ cosΦ F = i · j dA dA (2.4) ij A · π s2 i j i ZAi ZAj · 4 An important property of equation 2.4 is its symmetry, which allows to deduce a reciprocity relationship for the two surfaces as given in equation 2.5 [1]. A F = A F (2.5) i · ij j · ji In practice, literature offers a wide range of documented view factors for standard configurations [10][11], which

Figure 2.2: Dependencies of the view factor. Taken from [1, p.368]. are sufficient for this thesis, due to the simple CubeSat geometry used. One of these simple cases will be introduced here. It describes two finite rectangles of the same length, which have one common edge and an angle of 90o to each other. The configuration is illustrated in figure 2.3. In that case the view factor is determined by equation 2.6 [12].

1 −1 1 −1 1 −1 1 F1−2 = W tan + H tan √C tan W π · W · H − · rC ! · (2.6) 2 2 2 2 1 1 + W 1 + H W 2 (1 + C) W H2 (1 + C) H + ln · · · 4 · 1 + C · (1 + W 2) (C) · (1 + H2) C · · !

Figure 2.3: Conﬁguration of two crossing perpendicular plates with the relevant data to determine the view factor. Taken from [11].

w W = (2.7) l h H = (2.8) l C = W 2 + H2 (2.9)

5 Besides the geometry, the optical surfaces properties of the two surfaces also influence the magnitude of transferred heat. This impact is considered in equation 2.3 in form of the effective emittance ǫij. For the case of two diffuse surfaces in parallel the effective emittance is described by equation 2.10, if the distance between the surfaces is small compared to the surface area [1, p.369]. This case might also be used as assumption for non-parallel configurations, if ǫi and ǫj are high [1, p.369]. The emittance ǫi and ǫj of the surfaces describe the fraction of the fluence emitted by a real body compared to a blackbody in a certain frequency range. This value is approximately the same as the amount of incoming fluence absorbed by a real body when compared to a blackbody. In literature, the emittance in the IR-frequency range is called emissivity ǫ and in the emittance in the UV-frequency range absorptivity α [1][13]. ǫ ǫ ǫ = i · j (2.10) ij ǫ + ǫ ǫ ǫ i j − i · j This property is also documented in the literature [13].

2.1.2 Conductive Heat Transfer

The second mechanism of heat transfer relevant in space is conduction. This mechanism occurs with and between the solid parts of the spacecraft. The effect is vital for space systems, because it is the major mechanism to transport thermal energy from the inside of the spacecraft to the outer panels and vice versa.

The heat Qc,ij transfer by conduction between two points i and j in an one dimensional case is described by equation 2.11, where hij is the thermal conductance and Ti as well as Tj are the temperatures of the points [1, p.366ff.]. The equation is based on the Fourier law for conduction.

Q = h (T T ) (2.11) c,ij ij · i − j

The thermal conductance hij describes the capability of the material to transfer heat. It depends on the cross- sectional area A, the conductive path length l and the thermal conductivity λ as described in equation 2.12 [1, p.366ff.]. λ A h = · (2.12) ij l The inverse of the conductance is the thermal resistance R between the two points as deﬁned in equation 2.13. 1 Rij = (2.13) hij Thermal resistance is calculated in a comparable way to electrical resistance for both series and parallel conﬁgura- tions. The total resistance Rtot for a series of k resistances is described by equation 2.14. [1, p.366ff.].

Rtot = Rn (2.14) n=0 X The total resistance Rtot for k resistances in parallel is described by equation 2.14 [1, p.366ff.].

1 k 1 = (2.15) R R tot n=0 n X 2.1.3 Convective Heat Transfer

Convective heat transfer occurs during the interaction with a fluid [7, p.363ff.]. Since space can be assumed to be a vacuum, this mechanism of heat transfer is irrelevant for most space missions. Only in very low altitude orbits is the fraction of heat transferred by convection relevant. The altitude of the studied spacecrafts is higher than 600 km. −14 kg The density of the atmosphere at that height, according to the MSIS-E-90 atmospheric model, is 1.03 10 m3 W· [14]. The resulting heat transfer is significantly lower than the solar fluence at Earth distance of 1371 m2 [1, p.359]. Convection will therefore not contribute to the heat exchange of the studied spacecrafts.

6 However, under certain laboratory conditions convection is an important error factor. The heat transfered by convection between an object with temperature Tw and a ﬂuid with temperature Tf is determined using equation 2.16 [7, p.363ff.]. Q˙ = h A (T T ) (2.16) · · f − w h is the h-value, which describes the convective heat transfer per area, while A is the surface area. The calculation of this quantity is rather complex and is therefore determined experimentally [7, p.363ff.]. Using similitude the experimentally obtained data is applied to other cases. This procedure is shown for the cases of a vertical plate in appendix D and for a horizontal plane in appendix C.

2.2 The Thermal Space Environment

A spacecraft operating in an orbit or interplanetary space is exposed to different external heat sources. Possible heat sources are:

Solar UV radiation • Planetary IR radiation • Reflected UV radiation called albedo • Convection with atmosphere • Radiation coming from nearby minor objects, e.g. moons and asteroids • The cosmic mircowave background • A satellite operating in a sufficiently high orbit around Earth is only significantly influenced by the solar radiation, the albedo and the planetary IR radiation [1, p.358ff.]. Other heat sources have to only be taken into account for payloads with a high dependency on temperature. This is not the case for the missions considered. The three relevant types of radiation and their impact on the spacecraft will be explained more in detail in the following sections. Other effects to be discussed include the temperature changes by the radiation emitted from the spacecraft itself and the heat generated within the spacecraft. Also those effects will be discussed. Figure 2.4 shows the thermal space environment with the main external drivers of the spacecrafts temperature.

2.2.1 Solar radiation

The Solar radiation is directly emitted from the star in the center of the solar system. The Sun can be modeled as a black body at a temperature of 5800 K . The energy is mostly (99%) emitted in the wavelength range between 150 nm and 10 µm with an spectral intensity maximum in the visible light range at 450 nm [1, p.359]. The spectral distribution of a 5800 K blackbody is visualised in image 2.1. The intensity FSun of the radiation at a certain distance dSun from the Sun is estimated with equation 2.17. The equation represents the propagation of the power

PSun emitted by the Sun as a spherical surface.

P F = Sun (2.17) Sun 4 π d2 · · Sun 26 From the average power output of the Sun PSun = 3.857 10 W the intensity in Earth distance dEarth = 1AU is W · calculated to F = 1371.5 5 2 [1, p.359]. This value is referred to as the solar constant [1, p.359]. At a Earth ± m distance of 1 AU from the Sun the solar rays can be assumed to be parallel [1, p.360]. This assumption is not valid for spacecrafts close to the Sun [1, p.360].

7 Figure 2.4: The thermal space environment.

2.2.2 Planetary albedo

The albedo is the fraction of the solar radiation which is reflected by the surface and the atmosphere of a planet. The rate depends on the reflective properties of the surface and atmosphere [1, p.360]. The value is neither spatially nor temporally constant. Instead it may vary due to weather conditions and seasonal changes. In the case of planet Earth, the value varies between 0.05 over the surface and 0.8 over the cloud layers [1, p.360]. In practice, a constant average albedo value a is used for the thermal design of spacecrafts. This procedure is reasonable, because the changes occur rapidly [1, p.360]. The average albedo of the Earth is settled at 0.35 [1, p.360]. The values for the other planets of the inner solar system are given in table 2.1. Due to the absorption by the planet’s surface and atmosphere, the spectral distribution of the albedo is changed and does not exactly resemble the spectral distribution of the direct solar radiation. However, the changes are small enough to be ignored during a thermal analysis pocess [1, p.360]. The intensity of the albedo Falbedo depends on the planets size, reflectivity characteristics, SC altitude and an angle β. The beta describes the angle between the local vertical and the Sun rays [1, p.360]. Those dependencies are represented by the visibility factor V . Figure 2.5 shows the influence of the altitude and the beta angle on the visibility factor (in the figure denoted with F ). The calculation of the albedo intensity Falbedo is given in equation 2.18

F = F a V (2.18) albedo solar · ·

Table 2.1: Planetary albedo values of the planets in the inner solarsystem [1, p.360] Planet Mercury Venus Earth Mars Albedo [ ] 0.06 0.10 0.60 0.76 0.31 0.39 0.15 − − −

8 Figure 2.5: The visibility factor of the albedo depends on the altitude and the beta angle. Taken from [1, p.361].

2.2.3 Planetary radiation

In addition to the reﬂected solar radiation, the spacecraft also receives radiation from the planet itself. As stated before every body with a non-zero temperature emits heat in the form of electromagnetic radiation. This is also valid for the planets in the solar system. The Earth radiates heat in the IR range between 2 µm and 50 µm with an maximum at 10 µm [1, p.361]. Most of the planetary radiation absorbed by the spacecraft is emitted by the atmosphere, which resembles a Plank curve with an effective temperature at 218 K [1, p.361]. However, there is a transparent windows through which the radiation emitted by the surface becomes visible. It ranges from 8 µm to 13 µm. The surface might be assumed to be a blackbody at 288 K [1, p.361]. The resulting spectral intensity distribution is shown in ﬁgure 2.6. The intensity of Earth’s thermal radiation has a temporal and spatial dependency. However, for practical purposes a mean value is used [1, p.361]. Similar to the solar radiation, the planetary radiation spreads radially as stated in equation 2.19, where Fplanetary is the intensity of the planetary radiation, REarth the W Earth radius and Rorbit the altitude of the spacecraft. The value of 237 m2 represents the intensity at the top of the atmosphere. 2 W REarth Fplanetary = 237 2 (2.19) m · Rorbit

2.2.4 Radiation emitted from the spacecraft

Up to this point only heat sources have been discussed. Without the possibility to dispose thermal energy, the temperature of the spacecraft would increase until a critical failure occurs. In ground environment conditions, objects are cooled by the surrounding atmosphere via convection. Due to the lack of a surrounding medium this mechanism is not possible in space conditions. Instead the energy has to be radiated into space. It is recommended to operate spacecrafts in a temperature range similar to Earth conditions around 20oC. Hence, the radiation will be in the infrared spectrum. The IR radiation will be emitted into space from the outer surfaces of the spacecraft and possible additionally attached radiators. This radiation is the only possibility to remove thermal energy from the spacecraft system.

9 Figure 2.6: Spectral emissive power for Earth’s planetary radiation.. Taken from [1, p.362].

10 Chapter 3

Basics of thermal simulation

In this chapter two different approaches to simulate the thermal behaviour of a spacecraft are described. The approaches make different assumptions and have an increasing complexity. In both approaches a hot case and a cold case is simulated, which represent the thermal extreme conditions of the satellite. This means the case with highest ﬂux of absorbed heat and the case with the highest heat dissipation onboard the spacecraft and vice versa. First, a static satellite in thermal equilibrium is obtained. This thermal equilibrium simulation neglects the conduction and heat capacity within the satellite. The values obtained from this simulation represent the thermal worst case scenarios which might appear during the lifetime of the satellite. Afterwards the more complex multi node simulation is introduced. For this simulation, a thermal model of the satellite is designed, which includes heat capacity and internal heat ﬂuxes. Also, the simulation is no longer processed in a steady state but now in a transient state.

3.1 Thermal equilibrium simulation

In the early phase of the thermal modeling of the spacecraft a ﬁrst estimated temperature is needed. The thermal equilibrium temperature is used as such a reference temperature. This temperature results from the balance between incoming Q˙ in (compare chapters 2.2.1, 2.2.2 and 2.2.3) and outgoing Q˙ out (compare chapter 2.2.4) heat from the surfaces of a spacecraft as well as the internal heat sources Pint. The simulation also assumes that all parts of the satellite are in a thermal equilibrium.

Q˙ in + Pint = Q˙ out (3.1)

For a satellite in an Earth orbit the incoming heat is composed of the solar radiation directly from the Sun Q˙ SR, the planetary radiation Q˙ PR and the solar radiation reﬂected by the Earth Q˙ Albedo. An,i represents the effective surface area directed towards the heat source i, where the heat sources are solar radiation, albedo and planetary radiation.

Q˙ in = Q˙ SR + Q˙ Albedo + Q˙ PR (3.2)

The heat coming from these sources and reaching the N outer surfaces of the spacecraft is described as follows according to chapter 2.2. N 3.856 1026 W Q˙ = A α · (3.3) SR n,SR · n · 4π d2 n=1 Sun X · N 3.856 1026 W Q˙ = A a α · V (3.4) Albedo n,Albedo · · n · 4π d2 · n=1 Sun X · 2 N W R Q˙ = A ǫ 237 Earth (3.5) PR n,P R · n · m2 · R n=1 altitude X 11 Putting the equations 3.3, 3.4 and 3.5 into equation 3.2.

N 26 N 26 ˙ 3.856 10 W 3.856 10 W Qin = An,SR αn · 2 + An,Albedo a αn · 2 V =1 · · 4π dSun =1 · · · 4π dSun · n · n · (3.6) X X 2 N W R + A ǫ 237 Earth n,P R · n · m2 · R n=1 altitude X The heat leaving the spacecraft consists only of emitted thermal radiation from the spacecraft surfaces. The outgoing heat Q˙ out is given in equation 3.7 as deﬁned in chapter 2.

N Q˙ = A ǫ σ T 4 (3.7) out n · n · · eq n=1 X Putting the equations 3.6 and 3.7 into 3.1 leads to equation 3.8.

N 3.856 1026 W N 3.856 1026 W An,SR αn · 2 + An,Albedo a αn · 2 V =1 · · 4π dSun =1 · · · 4π dSun · n · n · (3.8) X X 2 N W R N + A ǫ 237 Earth + P = A ǫ σ T 4 n,P R · n · m2 · R int n · n · · eq n=1 altitude n=1 X X Rearranging equation 3.8 for the equilibrium temperature Teq leads to equation 3.9.

N 3.856 1026 W N 3.856 1026 W Teq = (( An,SR αn · 2 + An,Albedo a αn · 2 V =1 · · 4π dSun =1 · · · 4π dSun · n · n · (3.9) X X 2 N W R 1 + A ǫ 237 Earth + P ) )1/4 n,P R · n · m2 · R int · N n=1 altitude n=1 An ǫn σ X · · This equation gives a simple way to make a ﬁrst estimation of the temperature limitsP the satellite might reach. Due to the assumptions made this model has some major limitations. This approach does not consider the thermal capacity of the satellite and is hence not suitable to make predictions about the temporal progression. Another limitation is the reduction of the satellite to a single node. The model gives no statements of local trends. The temperatures calculated might be exceeded locally.

3.2 Thermal mathematical model

For further analysis of a spacecraft, a more detailed model is required. The temperature of the satellite is not homogeneous but varies depending on the time and location. To solve this complex function, a simpliﬁed model of the satellite is created. This model is called the Thermal Mathematical Model (TMM)[1, p.366]. The creation of the TMM is divided into two steps:

Creation of the Geometrical Mathematical Model (GMM) • Creation of the TMM • The GMM represents the geometrical aspects of the mission like the shape of the spacecraft, the orbit and the attitude. The satellite components relevant for thermal simulation are represented by a mathematical node. For the GMM the nodes have no properties except their geometry, their attitude and their location in space at a given time. In order to reduce calculation time, the geometry of the nodes is simpliﬁed to basic shapes such as cuboids, spheres, cylinders and rectangular plates. For the simulation the nodes are assumed to be spatially isothermal. Hence, the temperature calculated is the mean temperature of the node and might be locally higher or lower. The satellite’s orbit is deﬁned by its orbit parameters [1, p.79ff.]:

12 The eccentricity e describes the elongation of the orbit compared to a circle. • The semimajor axis a deﬁnes the size of the orbit ellipse. • The inclination i gives the tilt of the orbit plane with respect to a reference plane. • The longitude of the ascending node Ω rotates the orbit plane within the reference plane with respect to a • reference direction.

The argument of the periapsis ω deﬁnes the orientation of the orbit within the orbit plane. • The satellites attitude dynamics are deﬁned using pointing constraints. Possible pointings are

Sun pointing: A certain surface of the satellite is always directed to the Sun. • Earth pointing: A certain surface of the satellite is always directed to the Earth. • Planet north pointing: A certain surface of the satellite is always pointing in perpendicular direction with • respect to the planets rotational plane.

The attitude movement of a spacecraft is deﬁned by its angular momentum Hc which is given in equation 3.10 [1, p.61]. Where Ixx, Iyy, Izz, Ixy, Iyz and Izx are the moments of inertia and ωx, ωy and ωz the angular velocities around the main axises. I ω I ω I ω xx x − xy y − zx z Hc = I ω I ω I ω (3.10)  yy y − yz z − xy x  I ω I ω I ω  zz z − zx x − yz y  The TMM is an extension of the GMM. In the TMM thermal aspects are added to the model. Those added properties are:

The properties of the nodes. • The radiative and conductive links of the nodes. • The external received heat. • Three properties are allocated to the nodes which are relevant for the thermal analysis:

The heat capacity • The surface properties • The internal heat dissipation. •

The heat capacity Cp describes how much energy has to be transferred to the node to achieve a certain temperature change. This value depends on the material the node is made of. In practice, the heat capacities of minor satellite components, which are not represented by their own nodes, are also added to the heat capacity of a reasonable node. The absorptivity and emissivity depend on the surface ﬁnish of the part. As stated earlier, those values describe the fraction of emitted and absorbed heat when compared to a black body. For the TMM it is assumed that the whole surface of the node has homogeneous surface properties. The internal dissipation is the heat generated within a part. Dissipation occurs mainly within electronics. The nodes are linked with each other via conductive and radiative links. The corresponding equations were introduced in chapter 2.1. Additionally, the heat ﬂux coming from external sources has to be estimated. This is done using approximations as introduced in chapter 2.2 or by mathematically more advanced approaches, e.g. ray tracing [15][16][17]. The considered effects lead to equation 3.11, where N is the number of nodes. This equation has to be solved for every node [1, p.369].

N N dT 4 4 4 C i = Q + Q σǫ A T h j(T T ) σ A F ǫ (T T ) (3.11) p,i dt external,i i − i space,i i − i i − j − i ij ij i − j j=1 j=1 X X 13 For transient calculations a similar approach is used to analyse non-steady conditions. In this case the time time dependencies in equation 3.11 have to be changed. The temperatures and heat inputs are replaced by their mean values over a time interval δt. This leads to equation 3.12 [1, p.369]. The index 0 indicates the values of the time step before, respectively for the initial conditions in case of the ﬁrst time step.

4 T T 0 Q 0 + Q Q 0 + Q T i, 0 + T C i − i, = external,i, external,i + i, i σǫ A i p,i δt 2 2 − i space,i 2 N N 4 4 (3.12) T i, 0 + T T j, 0 + T T i, 0 + T T j, 0 + T h j( i j ) σ A F ǫ i j − i 2 − 2 − i ij ij 2 − 2 j=1 j=1 ! X X The simulations in this work are conducted using SYSTEMA/THERMICA, because of its economical viability, the immediate availability and its successful ﬂight heritage. Another considered option was the software package ESATAN or the creation of an own software. Table 3.1 shows the criteria which led to the decision to utilize SYSTEMA/THERMICA.

Table 3.1: Decision matrix of the software packages for the thermal simulations. +:Positive, o:Neutral, -:Negative Software Price Development time TRL Full code access SYSTEMA/THERMICA + o + - ESATAN - o + - Own code + - - +

14 Chapter 4

Thermal modelling of the PICSAT nanosatellite platform

The first satellite analyzed in this work is the PICSAT nanosatellite. PICSAT is a 3U-CubeSat, which limits the volume of the satellite to 0.03 m3 and mass to 4 kg according to the international CubeSat standard [18]. The mission of the spacecraft is the observation of the transit of an exoplanet at the star Beta Pictoris [2]. To fulfil this task the satellite carries a photometer as payload and has strong constrains regarding the pointing accuracy [2]. The star must stay inside the field of view of the photometer to count the photons accurately in order to record the decay of the light curve when the planet will be in the line of sight of the photometer [2]. The resulting high power demands of this mission made the utilization of additional deployable solar panels necessary [2]. In this chapter the process of the thermal modeling of the PICSAT nanosastellite platform is described. In the framework of this work, the payload is only implemented as a strongly simplified model, because it is the subject of further research. In order to determine the temperature ranges of the satellite, the relevant thermal environments are identified in section 4.1. In a second step, the thermal properties and requirements of the satellites subsystems are investigated in section 4.2. In section 4.3, the acquired data is implemented in a TMM. Subsequent tests are carried out to optimize the conductive links of the model. This process is described in section 4.4. The results of the simulation are presented in section 4.5 and followed by a short discussion in section 4.6.

4.1 Deﬁnition of relevant thermal environments and mission modes

During its lifetime PICSAT will experience different environmental conditions, which are distinguished in terms of their atmosphere and the level of IR- and UV-radiation. As described in chapter 2.2 those conditions will affect the temperature of all parts of the satellite. The thermal design of the satellite has to be robust enough to stand the different environmental conditions. The following environments are considered relevant to the thermal design process and are discussed in detail in this section:

The ground environment • The launch environment • The hot case orbit • The cold case orbit • 15 4.1.1 Thermal Ground Environment

Before a satellite is launched into space it has to be assembled and pass multiple tests on Earth. This procedure might last years. During this time the spacecraft will experience in clean rooms, during transportation and in laboratories an environment which is contrary to space conditions. To avoid excessive costs during the handling of the satellite on the ground, the satellite also has to be able to bear the ground environment conditions. The corresponding thermal conditions are characterized by convection with a surrounding atmosphere and IR radiation. During the handling of the spacecraft on ground, a careful environmental control is essential to avoid degradation of subsystems. The thermal design of the spacecraft also has to take the environment of this period into account even if it is short compared to the whole lifetime of the satellite. The environment is characterized by convection with the surrounding atmosphere and radiative heat transfer with nearby hot objects. Most laboratories are operated at standard conditions with a temperature of approximately 25 oC. During transportation this temperature may vary between 0 oC and 45 oC depending on the selected launch system [19][20][21]. Table 4.1 gives an overview of the minimal temperature TGround,min and maximal temperatures TGround,max a spacecraft might experience when being prepared for the launch with different space launch systems.

Table 4.1: Minimum and maximum Pre-Launch temperatures, Free molecular Heating (FMH) and Fairing Radiation for different launch systems o o W W Launcher TGround,min [ C] TGround,max [ C] FMH m2 Fairing Radiation m2 Ariane 5 [19] 11 27 1135 1000 Euro Soyuz [20] 8 27 1135 800 Vega [21] 9 27 1135 1300 Atlas V [22] 4 30 N/A N/A Falcon 9 [23] 18 24 N/A N/A H-II A [24] 15 27 1135 N/A DNEPR [25] 0 45 1000 N/A

4.1.2 Thermal Launch Environment

The second thermal environment experienced by a satellite is the launch environment. The environmental conditions during this phase depend on the space launch system being used. The operator of those systems provides the users with the relevant data [19][20][21]. From a thermal aspect the launch has two relevant phases. The ﬁrst phase is from take-off until the jettisoning of the fairing and the second phase after that until the satellite is ejected into its orbit [19][20][21]. The altitude at which the fairing is dropped depends on the launcher system, but usually takes place close to an altitude of 115 km [9]. The ﬁrst phase of the launch environment is dominated by the thermal radiation emitted by the fairing. The fairing is heated due to atmospheric drag during the launch and emits the heat to the outside and inside of the rocket. For W the observed rockets the highest value is reached by the Vega launch system with 1300 m2 [21]. After the jettisoning of the fairing the thermal environment is changed instantaneously. The launchpod of the satellite is exposed to the Earth atmosphere as well as solar and planetary radiation. The maximum Free Molecular W W Heating experienced by the satellite is between 1000 m2 and 1135 m2 . More detailed values for the different launch systems as provided by the system operators are given in table 4.1.

4.1.3 Beginning of life time environment

At the beginning of its lifetime the satellite is proposed to operate in a 620 km polar orbit with an inclination of 98o [2]. Those orbit parameters are not ﬁnal and might be subject to change depending on the chosen launch system. The thermal environment acting on the satellite at those altitudes is as described in chapter 2.2 driven by three main factors:

16 1. Solar radiation 2. Earth albedo 3. Earth IR radiation Additionally, the satellite is heated by the dissipation of the electronic devices on board the spacecraft. For further analysis of the spacecraft’s thermal design a hot case and a cold case are defined. They represent the combination of orbit parameters and attitude, which lead to the highest or respectively lowest incoming heat to the satellite. All other possible orbits will receive a heatflux with a magnitude between those two extrema. Hence the temperatures of those two cases represent the maximal and minimal possible temperatures of the satellite. The hot case is characterized by the highest possible incoming flux of solar radiation and Earth IR radiation at the same time. This state is reached when the satellite is orbiting approximately parallel to the terminator, while Earth is at its perihelion. This event occurs on approximately in the mid of January. During this period the solar flux at Earth W distance has approximately a magnitude of 1420 m2 . Additionally, the internal heat production is assumed to be at its maximum. All instruments and electronics are dissipating as much energy as possible. This orbit configuration is illustrated in the middle of figure 4.1. To maximise the heat flux reaching the satellite, the side with the deployable solar panels is always pointing to the Sun, while one of the sides with 3 units is always pointing to the Earth surface. For the cold case the satellite’s orbit is perpendicular to the terminator, while the Earth is at its aphelion. The date for this event is approximately the mid of July. During this period the solar flux at Earth distance has approximately W a magnitude of 1320 m2 . In this orbit configuration the satellite has the longest possible transit through the eclipse. Additionally, it is assumed that during the cold case the internal heat dissipation is minimised. To minimise the heat flux reaching the satellite, one of the sides with 3 units is always pointing to the Sun, while the side of the satellite with the smallest surface is pointing to the Earth surface. Figure 4.1 shows this orbit configuration in the middle. Table 4.1.3 gives an overview of the simulated orbits and table 4.1.3 of the attitude strategy of the satellite.

Figure 4.1: Hot case (left) and cold case (right) of the PICSAT orbit (top) and attitude (bottom.

Table 4.2: Simulated orbits of PICSAT. Case Altitude Inclination Ascending node Date Hotcase 620 km 98o 30o 15.01. Coldcase 620 km 98o 30o 15.07.

17 Table 4.3: Simulated attitudes of PICSAT. Case Sun pointing Earth pointing Earth north pointing Hotcase Small Side with DSP Long side without DSP N/A Coldcase Long side without DSP N/A Small Side with ESP

4.1.4 End of Lifetime

The planned duration of the PICSAT mission is approximately one year [2]. During this time the space environment and the satellite itself will experience two major variations. Due to aerodynamic drag, the altitude of the satellite’s orbit will decrease and due to the lack of a propulsion system there is no possibility to compensate for this effect. In the lower orbit the satellite experiences a new environment, which includes also the convective heat transfer besides the solar radiation, albedo and IR-Radiation also. The influence of the convective transfer method increases with decreasing altitude due to the denser atmosphere. As a second aspect of the lower attitude the influence of the Earth IR-radiation becomes more significant. For the CIRCUS project, a study was performed which showed that a 3U-CubeSat at an altitude of 600 km will decline by less than 5 km within half a year [5, p.32]. This orbit is still at a sufficient altitude to neglect the influence of convection. The radiation environment will also not change significantly. Considering that the radiation flux is proportional to the altitude, the increase of the IR radiation flux in the orbit after half a year is less than 1.5%. The second major change in the thermal conditions of the satellite at the end of lifetime (EOL) is the degradation of the outer surfaces. The spacecraft is affected by charged particles, ultraviolet radiation, high vacuum and contamination, which settles on the surfaces [13, p.143ff.], and can alter the optical properties of the coatings. In general this processes lead to an increase of solar absorptivity and have a negligible effect on the IR emittance α [13, p.143ff.]. The ratio between absorptivity and emittance ǫ changes and thereby shifts the thermal equilibrium temperature of the spacecraft (compare equation 3.9) in the hot and cold case. Depending on the coating material the solar absorptivity may increase within half a year by less than 0.05 [13, p.143ff.]. This effect may also be neglected since the mission duration of PICSAT is so short, making an analysis of the EOL environment for the currently planned mission duration unnecessary.

4.1.5 Failure Cases

Besides the hot and cold case which represent the thermal extreme conditions of the normal mission operations, unplanned cases have to be considered. As part of this work, three other cases will be considered. They are based on a theoretical emergencies due to the malfunction of a satellite part. A large number of those cases are theoretically possible, which include the overheating of a part due to an electronic failure or unforeseen attitude cases due to a malfunction of the Attitude Determination and Control System (ADCS). However, this work will only consider those which are assumed to be most critical:

1. A failure of the ADCS, which would bring the satellite into an attitude with extreme conditions.

2. A malfunction of the deployment mechanism of one deployable solar panels (DSP)

3. A malfunction of the deployment mechanism of both DSPs.

The ﬁrst failure is simulated with a constant Sun pointing of the side with the smallest surface. This is the coldest case which is possible for this satellite. The same orbit as the normal cold case in section 4.1.3 is used. In this case no solar cell is pointing to the Sun. Necessary actions have to be taken to save the satellite in this case. In the second failure case only one of the two deployable solar panels are released. To continue operation, the functioning solar panel will be pointed to the Sun. In terms of interaction with radiation, this means that the surfaces receiving radiation are the same as those in the hot case except with a reduced radiating area. Hence, only a simulation of the hot case for this scenario is reasonable. The same orbit as the hot case in section 4.1.3 is applied for the simulation.

18 The third failure case assumes a malfunction of both DSP. The satellite is brought into an attitude with one of the uncovered sides pointing to the Sun in order to continue operation with a lower power budget. Since in this case the radiation receiving surfaces and the radiation emitting surfaces are reduced, a simulation of the hot case and the cold case is necessary. The orbits and attitudes of the three failure cases are depicted in ﬁgure 4.2.

Figure 4.2: Orbits (top) and attitudes (bottom) of the failure cases of PICSAT. (1) Malfunction of the ADCS. (2): Malfunction of one deployable solar panel. (3): Malfunction of two deployable solar panels in a hot case. (4): Malfunction of two deployable solar panels in a cold case.

4.2 Thermal Properties and requirements of the satellite subsystems

Besides knowledge about the thermal environment that was introduced in section 4.1, the simulation of the satellites thermal behaviour requires information about the satellite itself and its various subsystems. In order to simulate the processes which were introduced in chapter 2, the following information of every part has to be determined:

1. The heat capacity cp

2. The density ρ of the material

3. The thermal conductivity k

4. The solar absorbtance α

5. The IR emissivity ǫ

6. The geometry

7. The interfaces between the different parts

8. The heat dissipated in the part during the hot and the cold case.

For the further analysis it is also vital to know the temperature ranges in which the satellite part is operational. The data is either provided by the manufacturer or it has to be calculated or assumed. The following sections give an overview of the thermal aspect of every subsystem of the PICSAT nanosatellite. Figure 4.3 gives an overview about the location of the parts within the satellites interior and the used coordinate system.

19 Figure 4.3: Left: Stacking order of the parts in the interior of PICSAT. The black bars represent the ribs of the structure. Some ribs are removed in the third cube to mount the payload. Right: Location of the parts within the satellite structure.

20 4.2.1 Structure

The structure of a satellite has two main tasks. The ﬁrst is to carry the other satellite components. To fulﬁl this task the structure even has to stand the harsh loads during the launch. The second task is to protect the satellite from the rough conditions of the space environment. The satellite structure is not developed within the PICSAT project, but is provided by a manufacturer of standardized satellite parts. The structure consist of two aluminium side frames, which are connected by aluminium ribs. On the outside of the framework, aluminium side shear panels (SSP) and end shear panels (ESP) are attached. The parts are assembled using screws made of stainless steel. Steel rods on the inside of the satellite bear the printed circuit boards (PCB). Hexnuts, washers and spacers are used to keep the PCBs in place. The PCBs are additionally conductively connected with their wiring. Table 4.4 gives an overview of the structural parts and their thermal properties. Figure 4.4 shows the structure of the PICSAT satellite. The manufacturer gives a temperature range for the structure between 50 oC and 90 oC [26]. Structures of other suppliers show comparable temperature ranges [27]. − The usual temperature range of structures and mechanisms is given in the literature to be between 0o C and 50o C [1].

Figure 4.4: Open view of the structure of the PICSAT satellite. Three of the shear panels (X+, Y- and Z-) as well as the rods in the middle cube are not shown.

4.2.2 Electrical power system

The Electrical Power System (EPS) contains all elements which are relevant for the generation, storage and distribution of electrical energy. The components of this subsystem are the most temperature sensitive onboard the spacecraft and because of that they are one of the main drivers of the thermal design of a satellite. The typical operational temperature range of electronics is between 15o C and 50o C while rechargeable batteries are usually − operated between 0o C and 20o C [1]. In the case of the PICSAT satellite the EPS consists of 32 solar cells, the battery pack PCB and a power board, which converts and distributes the power. The battery pack holds 4 batteries. The two PCBs are located in the top

21 Table 4.4: Elements of the used 3U structure and their thermal properties [13, p.791ff.][26].

W kg J Part Material k m K ρ m3 cp kg K α [] ǫ [] Side Frames Black Hard Anodised Aluminium 175 h 2770i h 900i 0.76 0.88 Ribs Blank Alodyned Aluminium 175 2770 900 0.08 0.15 SSP Blank Alodyned Aluminium 175 2770 900 0.08 0.15 ESP Blank Alodyned Aluminium 175 2770 900 0.08 0.15 M3 Rods Stainless Steel 16 8000 500 0.47 0.14 Screws Stainless Steel 16 8000 500 0.47 0.14 Hexnuts Stainless Steel 16 8000 500 0.47 0.14 Washers Stainless Steel 16 8000 500 0.47 0.14 Spacers Blank Alodyned Aluminium 175 2770 900 0.08 0.15

of the ﬁrst cube. Figure 4.3 shows the exact location in the stacking order. The manufacturer gives a temperature range from 40oC to 85oC for the power boards [28][29]. The temperature range of the batteries depends on their − charging mode[30]. While the batteries are charging the temperature range is between 5oC and 45oC and while − discharging it is between 20oC and 60oC [30]. − 24 of the 32 solar cells are located on the outside of the satellites primary structure. Respectively 6 cells are placed on the X+, X-, Y+ and Y- side shear panel. An additional 8 solar cells are provided by two deployable secondary structures, with half pointing in the Y+ direction and the other half pointing in the Y- direction. Figure 4.5 shows the location of the solar cells. Two solar cells are always placed together on a PCB [31]. The solar cells have a temperature range between 40oC and 125oC [31]. The structural parts of the deployable solar panels have the − same thermal properties as the primary structure. According to the manufacturer the heat capacity of batteries can be J approximated with 1350 kg K . The dissipation of the batteries varies between 128 mW and 162 mW , additionally the power board has a dissipation of 115 mW . The thermal material properties of all components of the EPS are stated in table 4.5.

Figure 4.5: Location of the solar cells (blue) on the main and the secondary structure of PICSAT. The cell distribution on the not visible sides is symmetrical to the distribution on the visible sides. The antennas are not shown.

22 Table 4.5: Thermal properties of the EPS [13, p.791ff.]. The properties of the PCBs are calculated according to appendix A. After consultation of the manufacturer, the solar cells are modeled to consist mainly of germanium.

W kg J Part Material k m K ρ m3 cp kg K α [] ǫ [] Solar Cells Germanium 58 h 5323i h 310i 0.91 0.89 Solar Cell PCBs PCB 0.3 1700 1000 0.8 0.6 Batterypack PCB 70.1 3211 495 0.8 0.6 Power Board PCB 25.78 2430 551 0.8 0.6

4.2.3 Onboard Computer

The satellite has to be able to operate independently without any support from the ground. For this purpose an onboard computer is integrated into the satellite. Its task is to control and connect all subsystems as well as processing and storing all data. The onboard computer system of PICSAT consists of two boards: a primary and a secondary one. While the primary board is located in the PCB-stacking, the secondary one is connected only to the primary one as a daughter board. Both boards are provided by an external company. The material properties of the two boards are stated in table 4.6. The boards of the onboard computer systems are located in the ﬁrst cube under the boards of the EPS as shown in ﬁgure 4.3.The operating temperature range is stated with 25oC to 65oC and the power consumption ranges from − 400 mW to 550 mW [32].

Table 4.6: Thermal properties of the ODHS [13, p.791ff.]. The properties of the PCBs are calculated according to appendix A.

W kg J Part Material k m K ρ m3 cp kg K α [] ǫ [] Primary Board PCB 100 h 3720i h 472i 0.8 0.6 Daughter Board PCB 15 2250 569 0.8 0.6

4.2.4 Communication System

To receive telecommands from and send telemetry to the ground station a system of antennas and transceivers is required. Together they are categorized as the communication system of the satellite. The PICSAT satellite is equipped with an Ultra High Frequency (UHF) antenna for downlink and a Very High Frequency (VHF) antenna for uplink. The VHF antenna is located on the top of the first cube and the UHF antenna between the first an the second cube. The antennas are carried by PCBs with a small aluminium deployment structure. All other parts of the communication system are settled on a single board in the bottom of the first cube. The locations of the boards in the PCB stacking are shown in figure 4.3. The material properties of the communication system are stated in table 4.7. The antenna boards have a maximal typical power consumption of 20 mW [33], while the power consumption of the communication board lies between 400 mW and 2000 mW [34]. This value for the power consumption of the antenna is exceeded for a few seconds during the deployment of the antennas [33]. Since the exact material composition is not know, the composition of another tape spring antenna is taken as a reference and the material properties of Aramid with a black coating are assumed [35]. The operating temperature range for the communication board is between 20oC and 60oC [34] and for the antennas between 30oC and 70oC [33]. − −

23 Table 4.7: Thermal properties of the COM system [13, p.791ff.]. The properties of the PCBs are calculated according to appendix A.

W kg J Part Material k m K ρ m3 cp kg K α [] ǫ [] Antenna Boards PCB 42 h 2715i h 527i 0.8 0.6 COM Board PCB 92 2430 551 0.8 0.6 Antennas Aramid 0.04 1440 1420 0.9 0.9

4.2.5 Attitude Determination and Control System

To fulﬁl its scientiﬁc operations an accurate pointing is vital for PICSAT. A commercial ADCS system is integrated into the satellite. This system has two major functions:

1. To determine the current attitude of the satellite using different sensors including a star tracker, gyroscopes and magnetometers.

2. To change the attitude if necessary. To fulﬁl this task the satellite is equipped with three magnetorquers and three reaction wheels.

Nearly all parts of this subsystem are located on a single PCB in the central cube of the satellite. Only the star tracker is placed in the third cube next to the payload. According to the manufacturer the temperature range for the star tracker is between 20oC and 40oC. The temperature range of the ADCS board depends on the operation of − the reaction wheels. If the wheels are operated, the temperature range lies between 40oC and 60oC. In the case − that the wheels are turned off, the temperature range is wider between 45oC and 85oC. The maximum power − consumption of the star tracker is 650 mW [36]. Every reaction wheel has a maximum power consumption of 1000 mW [37] and every magnetorquer a maximum power consumption of 225 mW [38]. The material properties of the ADCS are stated in table 4.8.

Table 4.8: Thermal properties of the materials used in the ADCS system [13, p.791ff.]. The properties of the PCBs are calculated according to appendix A. The composition of the ADCS board is assumed based on the values of the payload board.

W kg J Part Material k m K ρ m3 cp kg K α [] ǫ [] ADCS Board PCB 36 h 2606i h 536i 0.8 0.6 Magnetorquer Copper 400 8920 100 0.32 0.02 Reaction Wheels Steel 16 8000 500 0.47 0.14 Support Structures Black Aluminium 0.04 2700 1420 0.76 0.88

4.2.6 The Payload

The detailed thermal analysis of the payload is not in the scope of these studies. However, it is important to include the payload at least in a simplified form into the model to represent the thermal interfaces and thermal inertia. Neglecting the payload in the simulation would lead to a distortion of the conductive links within the satellite and thereby alter the temperature distribution significantly. The payload of the satellite is placed in the middle and the top cube. The payload is simplified to consist of blank aluminium, since this is the main material component of the payload, and represents the overall thermal characteristics. It is also assumed that the payload has a dissipation of 2 W . Additionally a PCB in the middle cube belongs to the payload. The 2 W are assumed to distribute equally on the PCB and the payload cube. An overview of the materials is given in table 4.9. Figure 4.6 shows a picture of the payload with its components.

24 Table 4.9: Thermal properties of the materials used for the PL [13, p.791ff.]. The properties of the PCBs are calculated according to appendix A. It is assumed that the main parts consist of aluminium.

W kg J Part Material k m K ρ m3 cp kg K α [] ǫ [] PL Board PCB 36 h 2606i h 536i 0.8 0.6 Payload Black Aluminium 0.04 2700 1420 0.08 0.15

Figure 4.6: The six components of the PICSAT payload: top plate, instrument housing, the star tracker ST200, the base plate, the mechanical element called Bati and the housing of the piezoelectric components called Capot.

4.2.7 Overview

Table 4.10 gives a recap of the thermal requirements of all satellite subsystems and parts as described in the sections before, while table 4.11 gives the highest and lowest power dissipation for all parts.

Table 4.10: Thermal requirements of all PICSAT parts. (1) No data is available for the secondary ODH board. The same temperature range as for the primary ODH board was assumed. (2) The temperature range of the payload is the subject of further studies and is currently not known. (3) The wider range applies, if the wheels are not operating. Part Min. Temperature [oC] Max. Temperature [oC] Structure -50 90 EPS: Batteries charging 5 45 − EPS: Batteries discharging 20 60 − EPS: NanoPower P31u 40 85 − EPS: solar panels 40 125 − COM: Antenna 30 70 − COM: TRXVU 20 60 − ODH: Primary Board 25 65 − ODH: Secondary Board (1) 25 65 − P/L: Payload (2) N/A N/A ADCS: iADCS100 (3) 40 ( 45) 60 (85) − − ADCS: Star Tracker 20 40 −

4.3 Thermal Modeling of the satellite

Based on the determined satellite properties from section 4.2 as well as the orbits and the mission modes from section 4.1.3 and section 4.1.5, a TMM of the PICSAT mission is created. SYSTEMA/THERMICA is utilized for this purpose. The modelling of the satellite is realised according to following steps:

1. Dividing the satellite into nodes and geometrical modeling of the nodes.

25 Table 4.11: Dissipation of all PICSAT parts. (1) It is assumed that 75% of the power of the transceiver is dissipated. (2) For the payload no data is available. It is assumed that 50% of the power consumption of 2 W is dissipated. (3) For the magnetorquer and the reaction wheel it is assumed that 30% of the power consumption is dissipated. Part Min. dissipation [mW ] Max. dissipation [mW ] EPS: Batteries 128 162 EPS: NanoPower P31u 115 115 COM: Antenna 20 20 COM: Transceiver (1) 400 1500 ODH 400 550 P/L : Payload (2) 0 1000 ADCS: Magnetorquer (3) 0 70 ADCS: Reaction Wheel (3) 0 300 ADCS: Star Tracker 0 650 Sum 1507 5472

2. Assignment of physical properties to the nodes.

3. Deﬁnition of thermal interfaces between the nodes.

These steps will be discussed in detail in the following subsections.

4.3.1 Nodal breakdown and geometrical modeling

Following the concept of nodal simulation introduced in chapter 3.2, the satellite is subdivided into 607 nodes. When designing the GMM the main drivers for the chosen location of a node are primarily the assumption of a approximated thermal equilibrium within the node and a sufﬁcient representation of its radiative relevant surfaces. The realistic modeling of the conductive links is only secondary at this stage of the design, because the conductive links are added to the simulation in a later step. This prioritisation allows SYSTEMA/THERMICA to solve all computation intensive radiative links. In the GMM all nodes are represented by either two dimensional (2D)- rectangles, three dimensional (3D)-cuboids or 3D-cylinders. An overview of all nodes and their corresponding nodal numbers is given in table 4.12.

4.3.2 Deﬁnition of nodal properties

To every node created in section 4.3.1 the corresponding thermal properties are assigned. The relevant properties are:

The density ρ • The speciﬁc heat capacity c • p The thermal conductivity K • The absorptivity α • The emissivity ǫ • The heat dissipation P • The speciﬁc values of every component are given in section 4.2. However, SYSTEMA/THERMICA is not able to calculate the correct total heat capacity Cp of the nodes directly, because the volume V of the node is included into the calculation (compare equation 4.1). C = c ρ V (4.1) p p · · 26 Table 4.12: Overview of the nodes of the PICSAT GMM. (1) Every segment consists of two cuboids to simulate the L-shape of the part. (2) Cuboids consist of seven nodes. Cylinders consist of 4 nodes. (3) Non-geometrical nodes are used to simulate the radiative heat exchange with space. Name Subsystem Node numbers Abun. Shape Note Payload Board PL 530x 1 Rectangle Submeshed into 9 ADCS Board ADCS 540x 1 Rectangle Submeshed into 9 Reaction wheel ADCS 550x,560x,570x 3 Cuboid (2) Magnetorquer ADCS 580x,590x,600x 3 Cylinder (2) Deployable panel STRC 8110x,8210x 2 Rectangle Submeshed into 2 Solar Cell PCB EPS 8x2x0, 22xxxx 16 Rectangle Solar Cell EPS 8x3x0, 21xxxx 32 Rectangle Sidebars STRC 11xxxx 12 Cuboids (1)(2) Corner STRC 12xxxx 24 Cuboid (2) Fixed ribs STRC 13xxxx 10 Cuboids (1)(2) Attached ribs STRC 14xxxx 8 Cuboids (1)(2) SSP STRC 15xxxx 4 Rectangle Submeshed into 3 ESP STRC 16xxxx 1 Rectangle Submeshed into 9 VHF antenna PCB COM 31210x 1 Rectangle Submeshed into 9 VHF antenna COM 3122x0 2 Rectangle UHF antenna PCB COM 31310x 1 Rectangle Submeshed into 9 UHF antenna COM 3132x0 2 Rectangle Battery Pack EPS 41100x 1 Rectangle Submeshed into 9 Battery EPS 412xxx 4 Cylinder (2) Power Board EPS 41300x 1 Rectangle Submeshed into 9 IGIS EPS 42100x 1 Rectangle Submeshed into 9 Primary ODH board ODH 43100x 1 Rectangle Submeshed into 9 Sec. ODH board ODH 43200x 1 Rectangle Submeshed into 9 Transceiver board COM 44100x 1 Rectangle Submeshed into 9 BATI PL 600100 1 Rectangle CAPOT PL 600200 1 Rectangle Base Plate PL 600300 1 Rectangle ST 200 PL 60040x 1 Cylinder (2) Instrument PL 60050x 1 Cylinder (2) Top plate PL 600600 1 Rectangle Space Node N/A 99999999 1 N/A (3)

Since the volumes in the GMM are simpliﬁed as described in section 4.12, SYSTEMA/THERMICA does not know the real volume of the component. The values for Cp are calculated outside of the software and the internally generated value is overwritten. The relative mismatch between the total heat capacities calculated by SYSTEMA/THERMICA and the externally determined values has a maximum of 150%. Additionally the heat capacities of smaller components which are not represented by a node are added to the heat capacities of reasonable nodes nearby. Those parts are:

Screws • Washers • Spacers • Hexnuts • Rods • 27 Electronic components on the PCBs •

Minor strucutral components •

Furthermore the properties of the PCBs are calculated according to appendix A. Table 4.13 presents the total heat J capacities of every node. The total heat capacity of PICSAT sums up to 2690.51 K . The last relevant nodal property

Table 4.13: Overview of the heat capacities of the PICSAT GMM. J Name Subsystem Total Heat Capacity [ K ] Note Payload Board PL 17.7 Incl. Rods and Electronics ADCS Board ADCS 108.0 Incl. Rods, Housing and Electronics Reaction wheel ADCS 32.9 Incl. Housing and Screws Magnetorquer ADCS 31.7 Incl. Attachment and Screws Deployable panel STRC 70.8 Incl. Attachment Solar Cell PCB EPS 15.1 Different layers Solar Cell EPS 0.8 Including Adhesive Sidebars STRC 5.4 Including Screws Corner STRC 8.0 Fixed ribs STRC 1.8 Attached ribs STRC 9.3 Including Screws SSP STRC 97.3 ESP STRC 21.8 VHF antenna PCB COM 30.6 Incl. aluminium parts VHF antenna COM 3.6 UHF antenna PCB COM 30.6 Incl. aluminium parts UHF antenna COM 1.8 Battery Pack EPS 21.5 Incl. Rods and Electronics Battery EPS 58.1 Power Board EPS 18.1 Incl. Rods and Electronics IGIS EPS 15.4 Incl. Rods and Electronics Primary ODH board ODH 25.2 Incl. Rods and Electronics Sec. ODH board ODH 10.8 Incl. Rods and Electronics Transceiver board COM 17.6 Incl. Rods and Electronics BATI PL 154.5 Incl. Screws CAPOT PL 128.6 Incl. Screws Base Plate PL 113.8 Incl. Screws ST 200 PL 100.9 Incl. Screws Instrument PL 235.7 Incl. Screws Top plate PL 57.7 Incl. Screws Space node N/A N/A Constant Temperature Total satellite 2690.6 is the dissipation during the hot and cold cases. From the power consumptions which are given in section 4.2, values for the dissipation are deﬁned for a hot case and a cold case. An overview of the values is given in table 4.14. During the hot case all parts of ADCS are operating, as well as the payload, the onboard computer, the transceiver and the power board. Additionally, dissipation within the batteries occurs due to the conversion of chemical energy into electrical. The power dissipation of the reaction wheels and the torquers is assumed to be 30% of the consumed power. Due to the lack of other data, the dissipation of the batteries is chosen based on the experience of earlier satellites [39][40].

28 Table 4.14: Overview of heat dissipation in PICSAT during the hot case and cold case. Part Nodes Hot case dissipation [W ] Cold case dissipation [W ] Payload 600100, 600300 0.5 0 ADCS Wheels 5800, 5900, 6000 0.3 0 ADCS Torquer 5500, 5600, 5700 0.07 0 Primary ODH 431004 0.55 0.4 Transceiver 44100 1/3/5/7 0.375 0.1 − Antennas 31x102, 31x106 0.02 0.01 Batteries 412x00 0.162 0.128 Power Board 413004 0.115 0.115 Total satellite 4.86 1.467

4.3.3 Deﬁnition of conductive links

While radiative links are calculated by SYSTEMA/THERMICA autonomously [15][?], the conductive links are determined outside of the software and added to the model as an user input. The reason for this procedure is that the real geometry of the parts is not modeled in the software [15][?]. Additionally, some minor parts are not represented by nodes in the model and would be therefore be neglected in the calculation of the conductive links by SYSTEMA/THERMICA. In order to calculate the conductive link between two nodes, the following steps are performed:

1. Identiﬁcation of the parts which contribute to the direct thermal link between the two nodes.

2. Calculation of the thermal resistance of the parts along the heat path.

3. Determination of the thermal resistance of the interfaces between the conducting parts.

4. Reduction of the network of thermal resistances to a single thermal resistance with the equations introduced in section 2.1.2.

5. Conversion of the thermal resistance into thermal conductivity by creating the inverse.

Figure 4.7 shows, as an example the conductive link between an attached rib node and a corner node. Two possibilities are shown to describe the conductive link between the nodes. The first one uses a finite element method (FEM)-approach and a one dimensional (1D)-approach, while the second possibility is only based on a 1D-approach. The first link consists of the conductivity of the complete bar calculated with FEM (1), the surface contact between the two parts (2) and the conduction within the corner (3). For the alternative solution the bar is split into three areas (4)(5) and (6) with different lengths and cross sections, which are solved with a 1D-approach. Two approaches are applied to calculate the conductive links within the part:

1. The 1D-approach, which assumes that the heat is transferred only in one direction within the part.

2. The calculation of the conductive links using a FEM solver.

The ﬁrst approach is valid for most of the structural components like bars, ribs, rods, spacers and washers, as well as for the antennas. It is also applied to calculate the conductive links between the solar cells and the SSP and respectively the DSP. The fourier law for 1D conduction introduced in section 2.1.2 is directly applied to calculate the conductive links in this case. The FEM-approach is used to determine the conductivity within parts which cannot be assumed to be 1D. Those parts are the approximately 2D PCBs and shear panels, as well as 3D parts like the payload. To resolve the o conductive link between two points with the FEM-approach the temperature of one point is ﬁxed to T1 = 0 C, while a heat of Q˙ = 1 W is applied to the second point of interest. After solving this problem using the FEM approach, the thermal resistance R is directly given by the temperature T2 of the point where the heat is applied. The corresponding calculations are based on fouriers law and shown in the equations 4.2 to 4.4. Figure 4.9 shows

29 Figure 4.7: Example of two methods how a conductive link between the attached ribs and the corner node can be modeled. The upper network uses a FEM and a 1D-approach, while the alternative network is only based on the 1D-approach. The thermal resistance 1 in the FEM approach corresponds to the resistances 4, 5, and 6 in the 1d-approach.

Figure 4.8: FEM simulation of the attached ribs. (1) Connection to the PCB stack set to 0oC. (2) Location of the node heated with 1 W . the FEM-simulation of the attached ribs to ﬁnd the conductive link between the contact point to the PCBs (2) and the center of the part (1). A K 1 Q˙ = · ∆T = (T2 T1) (4.2) l R · − T2 T1 R = − (4.3) Q˙ o T2 0 C 1 R = − = T2 (4.4) 1W 1W For the contact resistances there are two distinct cases:

1. Screwed contacts.

2. Contacts with an adhesive.

The thermal contact resistance of parts which are screwed together depends on the pressure between the parts [41]. The literature gives the correlation of the mechanical load and the thermal contact resistance for aluminium and steel [41, p.73f.]. The pressure is calculated based on the geometry of the screws and the torque applied. The surface area relevant for the thermal contact links is determined based on the area of the screw head and the contact area. If the contact area is smaller than twice the screw head area, the conductive link is calculated with the screw head area. Otherwise twice the screw head area is assumed to be the conducting area. Since the screws are made of steel,

30 W W which has a 90% lower conductivity (ksteel = 16 m K [13, p.791ff.]) compared to aluminium (kalu = 175 m K [13, p.791ff.]), their contribution to the conductive link is neglected. For the adhesive contacts a thermal resistance is calculated based on the 1D-approach with the geometry of the adhesive layer and its conductivity. The 54 conductive contacts used within the model are given in appendix B. Four of the calculated conductive links within the structure are replaced by values which are determined during the tests in section 4.4.

4.4 Thermal tests with the engineering model

Simulation results without verification are not reliable. They have to be validated with measured values from ground or in-flight tests. To improve and to confirm the reliability of the numerical model introduced in chapter 4.3, thermal tests are carried out with the engineering model of PICSAT. During these tests the engineering model is heated with a known power at a certain location. With an infrared camera and temperature sensors the resulting temperatures at different locations on the satellite are obtained. The engineering model is only a reduced model of the real satellite however. In the current state of the engineering model only a limited number of links can be tested. Those links are parts of the structural model and the PCB- stacking. Since the engineering model and the simulated model from chapter 4.3 distinguish significantly, a reduced version of the numerical model of the PICSAT was created. Both the engineering model and its TMM are introduced in chapter 4.4.1. It is also important to mention that the test conditions are not optimal. The test is not carried out in vacuum conditions, but rather at a constant room temperature and pressure. This environmental constrain has to be considered when interpreting the results. The precise test conditions are also introduced in chapter 4.4.1. Six different tests are carried out. Their configurations are described in chapter 4.4.2. The measured results are presented in 4.4.3, followed by a short discussion in chapter 4.4.4.

4.4.1 The Engineering Model and its TMM

For the following tests the engineering model of PICSAT is used, which is an assembly of real parts and parts similar to real parts. Figure 4.9 shows on the right the engineering model in its current state. The model consists of the following parts, which are marked in the ﬁgure:

1. A real PCB, which has the properties of the payload PCB, as described in chapter 4.3.

2. Nine PCB replacements, which have the geometry of the real PCBs, but consist only of FR4 without a copper layer.

3. The satellite structure made of Aluminium and steel screws.

4. The rods and spacers used to attach the PCBs.

To achieve comparable results, all screws are tightend with the torques defined in the user handbook of the satellite structure. Due to a defect in the threads, two screws in the top cube of the engineer model are missing (marked in figure 4.9 with X). But since the experiments are carried out in the middle cube, this change in the satellites linking is neglected. This engineering model does not represent the GMM of PICSAT, which was created in chapter 4.3. Therefore the GMM of the real satellite was altered to represent the available engineering model. To achieve a proper representation, all parts, capacities and thermal interfaces which are missing in the engineering model are removed in the GMM. Additionally, the top cube and the bottom cube are filled with the 9 PCB replacements and one real PCB. The GMM of the engineering model is shown in figure 4.9 on the left. Besides the GMM, the simulated environment in the TMM is also adjusted to match the conditions in the laboratory. All orbit and attitude dynamics are removed from the simulation and the satellite is placed into a fixed position.

31 Figure 4.9: Left: GMM of the engineering model. Right: The engineering model of PICSAT. 1: Real PCB. 2: PCB replacements. 3: satellite structure. 4: Rods and Spacers. X: Location of missing screws.

The laboratory is operated at a constant temperature of 23.8oC and under atmospheric conditions of 1 bar. To model those conditions, the temperature of the space node as well as the initial temperature of all parts is changed to 23.8 0.7oC. Due to the atmospheric conditions, convection also has to be taken into account. In a simpliﬁed ± approach to describe the convective heat transfer, the PCBs and structural parts of the GMM are assumed to be either horizontal or vertical plates. The calculations for both cases are stated in appendix C and appendix D. Table 4.15 and 4.16 give the input temperatures for the calculations and the convective links for the nodes of the GMM. The input temperatures are based on a simulation run without convection and are assumed to be constantly the highest temperatures of the node. The test conﬁgurations are explained in the next section.

Table 4.15: Approximated convective links for the ﬁrst test conﬁguration (Test 2: when heated with 5W) Part Input temperature [Co] h-value [W/(m2K)] GL [W/K] SB horizontal 29.5 7.14 0.00689 FB horizontal 38.1 8.45 0.00415 AB vertical 38.1 13.21 0.00660 FB vertical 33 12.34 0.00031 SB vertical 29 8.54 0.01451 Real PCB vertical 78.4 6.64 0.13276 PCB replacement vertical 48.3 5.32 0.10645 PCB replacement vertical 25.3 2.59 0.05174

4.4.2 Test conﬁgurations

The executed tests are based on a local heating of the engineering model and the measurement of the heat within the satellite structure at different locations. The warming is achieved with an electrical heater, while the temperatures are measured with four PT100 thermal sensors. The sensors are placed at locations, where nodes are in the GMM. Kapton tape is used to attach the elements to the engineering model. Depending on the available space at the heated location, two different heaters are utilized. Their contact area and the necessary voltage to achieve different heat levels are stated in table 4.17. The calculation method to determine the voltage is described in appendix E. In total, six thermal tests are preformed. They are distinguished by the amount of heat applied (either 1W or 5W ), the use of an device to reduce convective effect, and the locations of the heater and sensors. The device to reduce convective effects is a closed box made of transparent plastic, which allows no heat exchange with the surroundings. It is three

32 Table 4.16: Approximated convective links for the second test conﬁguration (Test 5: when heated with 5W) Part Input temperature [Co] h-value [W/(m2K)] GL [W/K] SB horizontal 60 11.32 0.02184 SB horizontal 30 7.28 0.01405 FB horizontal 42 10.85 0.00881 FB horizontal 31 8.6 0.00699 AB vertical 42 4.91 0.00491 AB vertical 34 4.21 0.00421 FB vertical 42 13.73 0.00069 FB vertical 30 11.64 0.00058 SB vertical 60 12.08 0.02054 SB vertical 36 9.88 0.01680 Real PCB vertical 29 3.53 0.07068 PCB replacement vertical 26 2.84 0.05686

Table 4.17: Utilized heaters and their contact surface, resistance and voltage demands. Heater Contact area [mm2] Resistance [Ω] Voltage for 1W [V ] Voltage for 5W [V ] 1 645 19 4.36 9.75 2 100 330 18.17 40.62 times the size of the satellite, so the satellite fits inside without touching the sides or the top of the box. Table 4.18 gives an overview of the six tests. Two different configurations of heater and sensor locations are tested. In the first test configuration the real PCB is heated with the 18Ω-heater. In this case the temperatures are measured on the following locations: Sensor 1: The attached bar on the top side of the satellite next to the real PCB. • Sensor 2: In the center of the real PCB. • Sensor 3: At the intersection of the attached bar with a sidebar. • Sensor 4: In a corner of the first PCB replacement. • Table 4.18: Overview of the executed tests. Test Number Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test configuration 1 1 1 2 2 2 Heat applied [W ] 1 5 5 1 5 5 Convection supression No No Yes No No Yes

The heater and sensor locations and the corresponding node numbers are shown in figure 4.10 on the left. In the second test configuration one of the sidebars of the middle cube is heated with the 330 Ω-heater. The sensors are located at following parts: Sensor 1: At one of the sidebars of the central cube. • Sensor 2: At the intersection point of the fixed bar next to the real PCB. • Sensor 3: In the middle of the fixed bar. • Sensor 4: At the attached bar, which is in contact with the same intersection point. • The heater and sensor locations of the second configuration and the corresponding node numbers are shown in figure 4.10 on the right.

33 Figure 4.10: Left: Sensor and heater locations of the first configuration with the corresponding node numbers. Right: Sensor and heater locations of the second configuration with the corresponding node number.

4.4.3 Test results

The heating with 1 W in tests 1 and 4 does not lead to a sufficient increase of the temperature at the sensors which are not placed near the heater. The attempt to suppress convection in tests 3 and 6 by placing the model in a closed box results in complex environmental conditions. The air in the box heats up and alters the GL-value of the convective heat transfer. Simultaneously an IR-camera observed, that the sides of the box heat up with an inhomogeneous temperature distribution between 23.8oC and 41.4oC. The goal of simplifying the environmental conditions by placing the model in a closed environment in tests 3 and 6 was not fulfilled. Instead an environment was created which cannot be easily reconstructed in the simulations due to the lack of data and is therefore not suitable as a reference. For those reasons, the results of tests 1, 3, 4 and 6 will not be discussed further in this work. Figure 4.11 shows the measurement results for the tests two and five. The measured temperature profiles show an approximately logarithmic increment. Table 4.19 gives an overview of the measured data of test 2 and test 5. In test 5 at 330 s a small temperature peak for the second sensor can be observed. This peak appears, because the sensor was affected by human interaction.

Table 4.19: Result overview of test 2 and test 5: Steady State Temperature / Mean Error / Standard Deviation of Error of the four sensors. Test Sensor 1 [oC] Sensor 2 [oC] Sensor 3 [oC] Sensor 4 [oC] 2 28.6 / 0.40 / 0.13 53.4 / 0.58 / 0.14 26.6 / 0.28 / 0.13 30.1 / 0.24 / 0.07 5 50.5 / 1.13 / 0.56 40.3 / 0.39 / 0.06 32.1 / 0.60 / 0.12 29.2 / 0.48 / 0.28

4.4.4 Comparison of the simulation and the measurement

The measured temperatures from section 4.4.3 are compared to the results of the corresponding simulations. This comparison is based on the following procedure:

1. The measured temperatures are compared to the simulated temperatures without convection.

2. Based on the simulated temperatures without convection the temperatures with convection are calculated and compared to the measured temperatures.

34 Figure 4.11: Temperatures of the second (top) and the ﬁfth (bottom) test over time.

35 3. The conductive links between the nodes are adjusted based on the difference between measured temperature and simulated temperaturer with convection.

In figure 4.12, the results of the simulations of the engineering model are shown. The error bars give the deviation from the measured value. The values deviate significantly with a mean error of 18.1% for the second test and 8.2% for the fifth test. In both cases the temperatures are too hot. A possible explanation for this distinction might be convection with the surrounding atmosphere. Hence the convective model, which was introduced in section 4.4.1, is added to the simulation. Figure 4.13 shows that the measured and simulated values correlate better than in the model without convection. The mean error is reduced to 3.8% for the second test and to 6.9% for the fifth test. The simulated temperatures with convection for the fifth test are lower than the measured temperatures. This is more reasonable than the opposite case, because the simulated value represents the mean temperature in the part and the part becomes hotter the closer it gets to the heater. This effect leads to a mean temperature, which is below the measured temperature near the heater. However, it has to be considered in future tests, that the assumption of a flat plate is not suitable for the structural parts of the satellite. In the best case future tests should be carried out in a thermal vacuum test chamber to suppress convection. As a consequence of the tests four conductive links of the model are altered. If the temperature of a node is higher than the measured values, the conductive link to the heat source is reduced and vice versa if the temperature of a node is lower than the measured value. Table 4.20 gives an overview of the adjusted conductive links. Figure 4.14 shows the simulation with the adjusted values. The error bars represent the measured values. With the new conductive links the mean error is reduced to 2.3% for the second test and to 5.8% for the fifth test.

Table 4.20: Overview of the adjusted links as a consequence of the realised tests. Link Temperature Old Link New Link PCB9 to Real PCB Real PCB too cold 0.00057 0.008 Real PCB to AB AB too hot 0.00858 0.005 ABb to CN CN too hot 0.02255 0.015 ABs to CN CN too hot 0.02255 0.015 SBb to CN CN too hot 0.03370 0.01 SBs to CN CN too hot 0.03370 0.01

36 Figure 4.12: Simulated Temperatures of the second (top) and ﬁfth (bottom) test. The error bars give the difference to the measured temperatures.

37 Figure 4.13: Simulated Temperatures of the second (top) and ﬁfth (bottom) test with added convective heat transfer. The error bars give the difference to the measured temperatures.

38 Figure 4.14: Simulated Temperatures of the second (top) and ﬁfth (bottom) test with added convective heat transfer and adjusted links. The error bars give the difference to the measured temperatures.

39 4.5 Simulation results of PICSAT

After adding the adjusted links from section 4.4.4 to the model, the cases introduced in 4.3 are simulated using SYSTEMA/THERMICA. The results are presented in this section. The results are plotted beginning at a simulation time of 30000 s and for a duration of 5.5 orbital periods. At this time the transient effects resulting from the assumed initial temperature at the beginning of the simulation are no longer observed. Due to the high amount of data the curves for the mechanical nodes are not plotted here.

4.5.1 Hot Case

Figure 4.15 shows the temperatures of the parts in the ﬁrst and second cube. Figure 4.16 shows the temperature of solar panels on every side of the satellite and on the DSP.

Figure 4.15: Simulated Temperatures of the top cube (left) and the middle cube (right) of PICSAT for the hot case.

Figure 4.16: Simulated Temperatures of the solar cells of PICSAT for the hot case.

40 4.5.2 Cold Case

Figure 4.17 shows the temperatures of the parts in the ﬁrst and second cube. Figure 4.18 shows the temperature of solar panels on every side of the satellite and on the DSP.

Figure 4.17: Simulated Temperatures of the top cube (left) and the middle cube (right) of PICSAT for the cold case.

Figure 4.18: Simulated Temperatures of the solar cells of PICSAT for the cold case.

41 4.5.3 Failure Case 1

Figure 4.19 shows the temperatures of the parts in the ﬁrst and second cube. Figure 4.20 shows the temperature of solar panels on every side of the satellite and on the DSP.

Figure 4.19: Simulated Temperatures of the top cube (left) and the middle cube (right) of PICSAT for the failure case 1.

Figure 4.20: Simulated Temperatures of the solar cells of PICSAT for the failure case 1.

42 4.5.4 Failure Case 2

Figure 4.21 shows the temperatures of the parts in the ﬁrst and second cube. Figure 4.22 shows the temperature of solar panels on every side of the satellite and on the DSP.

Figure 4.21: Simulated Temperatures of the top cube (left) and the middle cube (right) of PICSAT for the failure case 2.

Figure 4.22: Simulated Temperatures of the solar cells of PICSAT for the failure case 2.

43 4.5.5 Failure Case 3 Hot

Figure 4.23 shows the temperatures of the parts in the ﬁrst and second cube. Figure 4.24 shows the temperature of solar panels on every side of the satellite and on the DSP.

Figure 4.23: Simulated Temperatures of the top cube (left) and the middle cube (right) of PICSAT for the failure case 3 hot.

Figure 4.24: Simulated Temperatures of the solar cells of PICSAT for the failure case 3 in a hot case orbit.

44 4.5.6 Failure Case 3 Cold

Figure 4.25 shows the temperatures of the parts in the ﬁrst and second cube. Figure 4.26 shows the temperature of solar panels on every side of the satellite and on the DSP.

Figure 4.25: Simulated Temperatures of the top cube (left) and the middle cube (right) of PICSAT for the failure case 3 cold.

Figure 4.26: Simulated Temperatures of the solar cells of PICSAT for the failure case 3 in a cold case orbit.

45 4.6 Discussion of the thermal design of PICSAT

An operation of the PICSAT satellite in space is according to the model presented in this work only possible, if the temperature of every component does not exceed its operational temperature ranges during the hot and cold cases. Those operational temperature ranges are deﬁned in section 4.2.7. The predicted temperatures are presented in chapter 4.5. Also, the impact of the failure cases is judged based on compliance of the resulting temperature ranges with the operational temperatures.

4.6.1 Compliance of the hot and cold case with the operational temperature ranges

During the hot case a temporal nearly constant temperature profile is achieved on the satellite. This results from the uninterrupted illumination with solar radiation. However, the small fluctuations of maximal 3oC are induced by the changing IR radiation environment, which occurs when the satellite passes the terminator. The hottest components of the satellite during the hot case are the solar cells with Sun pointing. They reach a temperature of 73oC and are comparable for the solar cells on DSP and the SSP. However, the temperatures of the solar cells without Sun pointing have a significant difference. The solar cells on the DSP are up to 20oC colder than the solar cells on the SSP. The parts within the satellite are heated to a temperature range between 25oC and 41oC. The VHF antenna reaches 19oC, a lower temperature than the internal components. The lower temperature is a result of the location of the VHF-board on top of the satellite. The impact of passing the eclipse is characteristic for the cold case. During this phase the UV radiation of the Sun is blocked from the satellite and only IR radiation acts as an external heat source. Due to this varying environment the amplitude of the temperature oscillations becomes stronger (up to 60oC temperature difference between the hottest and the coldest state for the Sun pointing solar cells) compared to the hot case. The temperatures of the internal parts lie in a range between 16oC and 4oC, while the temperatures of the solar cells vary between 50oC and − − 50oC depending on their pointing direction. Also in the cold case the solar cells on the DSP are colder than the cells on the SSP. In Figure 4.27 the simulated temperature ranges of the hot and cold case (broad black bars) and the operational temperature ranges as given by the manufacturer (green bars) are compared. Yellow bars indicate an unknown operational temperature range. The thin black bars are the simulated minimum temperatures of the first failure case, which is discussed in the next section. The simulated temperature of most of the components lie within the operational temperature ranges. Except for three cases there is always at least a margin of 5oC between the simulated temperature extremes and the operational temperature limits. The three validations of the given limits occur for the following components at their lower temperature limit:

1. The structure

2. The batteries, when charging

3. The solar cells

The lowest temperature of 48oC of the structure does not exceed the operational boundary of 50oC, but there is − − now nearly no margin left. The low temperature of 48oC is only predicted for one of the DSPs, while the other − DSP falls to a temperature of down to 44oC. The DSP are not a temperature sensitive part and will heat spatially − nearly constantly (the difference between the two DSP-nodes is less than 5oC over a distance of 100 mm), because the heat transferred through the local conductive link at the end of the panels is small compared to the radiative coupling which acts on the whole panel. Due to this reason internal tensions induced by temperature gradients will presumably not occur. Since the DSP are only attached at one side, which is on a spatially constant temperature, tensions with other parts will not occur. For those reasons the lack of margin might be seen as not critical. The next coldest part of the structure reaches a temperature of 34oC and is within the temperature range with a sufﬁcient − margin of more than 15oC.

46 Figure 4.27: Simulated Temperatures (Broad black) and operational temperatures (green) of PICSAT for the hot and cold case orbit as well as the failure case 1 (thin black).

While charging, the operational temperature of the batteries is lower compared to discharging. During the discharge the temperature ranges are not violated and hold a sufficient margin of more than 10oC. However, the lower operational temperature limit of the charging batteries is violated by 1.5oC. To understand, if this violation is critical the meaning of this simulated minimum temperature has to be reconsidered in the context of this specific subsystem. The lowest simulated temperature of the solar cells occurs when the satellite is in its cold case in the eclipse, but during this time period the solar cells will not be illuminated and hence the batteries would not charge. The temperature progression of the two components during one orbit period is shown in figure 4.28. A phase shift between the temperature oscillation of the solar cells and the batteries is observable. This phase shift leads to a correlation between the lowest battery temperatures and the charging period outside of the eclipse. The utilized battery pack is equipped with an internal heating circuit and temperature sensors [28]. The heater is able to operate with a power between Pheater 3.5 W and 7 W [28]. Considering the assumed heat capacity CBP of the whole J battery pack of 256 K and assuming the need to heat the batteries by a temperature difference ∆T of 5 K, a heating period ∆t of 6 min with the lowest heater power is necessary. The corresponding calculations are given in equation 4.5. The used energy for this process is 1281 J. This simple assumption neglects the heat transfered from the battery board to the structure and the power board. Hence, the real power consumption of the heater to keep the temperature of the batteries within the operational range will be higher. In conclusion it is recommended to activate a built-in heater control circuit of the battery pack. C 256 J ∆t = BP ∆T = ∆t = K 5 K = 366 s = 6 min (4.5) Pheater 3.5 W · The most significant violation of the operational temperature limits occurs during the cold case simulation within the solar cells which are constantly pointing to deep space. Those solar cells reach a temperature of 50oC, − 47 Figure 4.28: Comparison of the simulated temperatures of the batteries and a Sun pointing solar cells in the cold case.

which is 10oC below the operational temperature range. However, when those temperatures occur, the solar cells are not operating since they are not illuminated. Hence, for this case the operational temperature range does not apply as the temperature limit, but rather the survival temperature range. This temperature range describes the temperature domain in which the part is not operational, but will not take any damage due to the temperature. The temperature limits of the survival temperature are wider than those of the operation temperature range. A request to the manufacturer to obtain the survival temperature range is currently pending. If this request does not confirm a wider survival temperature range, an improvement of the conductive link between the solar cells and the SSP has to be considered. This can be achieved by filling the gap between the solar cell and the SSP with a material with higher thermal conductivity. For three components the operational temperature range is not available. In particular those components are the payload board, the secondary board of the On board data handling system (ODHS) and the IGIS board (connector board). The three components are PCBs. If their simulated temperatures are compared with the operational temperature ranges of other PCBs ( 20oC to 60oC), a compliance with a margin of at least 5oC is noticed. − However, this approach serves only as a first assumption and testing of the corresponding parts will be required.

4.6.2 Consequences of the considered failure cases

The first considered failure case involved a failure of the ADCS which would lead to a wrong pointing. The extreme case which can occur for this failure is constant Sun pointing of the smallest satellite surface. The simulation shows a significant temperature drop compared to the cold case. The temperatures of the solar cells vary between 45oC − and 66oC. The temperatures of the internal parts vary between 43oC and 59oC. Also the UHF antenna − − − board, which points to the Sun is without its temperature ranges. The low temperature for this part results from its good conductive connection to the DSP. The DSP act in this case as radiators and contribute additionally to the temperature reduction of the satellite. The simulated temperatures compared to the operational temperature ranges are shown in figure 4.27 (thin black bars). In this extreme cold case, no requirement concerning the temperature ranges is fulfilled. The temperature limit is exceeded by up to 30oC. An immediate change of the attitude has to be performed to avoid a critical failure of the satellite and to align the solar cells to the Sun. The use of heaters to overcome this problem is not recommended. All internal parts of the satellite together have a J heat capacity of Cinternal = 600 K . Ignoring the conductive links to the structure, an energy of approximately o Einternal = 18000 J is required to heat the internal parts by ∆T = 30 C. The calculation is shown in equation 4.6. This value exceeds the capacity of the battery pack [28]. The real value will be significantly higher due to

48 conduction to the structure. To compensate for the impact of this failure, the ESPs should receive a surface ﬁnish with high solar absorption. Possible surface ﬁnishes are black anodised aluminium or a black coating. Both have an absorptivity of approximately 0.8 and their utilization would increase the amount of absorbed solar radiation by the order of one magnitude. [13, p.791ff.].

J E = C ∆T = 600 30 K = 18000 J (4.6) internal internal · K · The second simulated failure case treats the possibility that one of the DSP is not deployed. The result is an 18% reduced emitting surface, which limits the amount of energy radiated into space. Hence, the temperature of the satellite will increase and only an analysis of the hot case needs to be conducted. The temperatures of the internal components vary between 22oC and 45oC. The highest temperature in this second failure case is 9oC higher than the highest temperature in the normal hot case. The highest temperature is reached by the transceiver board an the lowest temperature by the VHF antenna. The temperatures of the solar cells vary between 18oC and − 74oC. However, all simulated components are exposed to temperatures below the operation temperature limit. The simulation showed that the increased temperatures are not only an effect of the reduced emitting surface, but also of a multilayer insulation (MLI) effect occurring due to the undeployed DSP. Figure 4.22 shows the temperatures of the solar cells on the SSP on the Y- side with the failed DSP and of the solar cells on the failed DSP itself. The temperature on the DSP are up to 18oC colder compared to the temperatures on the SSP. The MLI effect is explained as followed: The radiation emitted from the SSP is nearly completely (90%) absorbed by the DSP, while the other 10% of the radiation are reflected back to the SSP. From the DSP again IR-radiation is emitted on both sides of the panel. 50% of the flux returns to SSP and 50% are emitted into space. As shown in figure 4.29 only 45% of the power emitted by the SSP are emitted into space. The effect is amplified by the multiple layers consisting of DSP, Solar cells and PCBs. During the third failure case a malfunction of both DSPs is simulated. The MLI-effect mentioned before will now

Figure 4.29: Occuring MLI effect, if the DSP are not deployed. occur on two sides of the satellite. In the hot case the temperatures of the solar cells vary between 20oC and − 74oC as illustrated in figure 4.24. Figure 4.26 shows a variation of the solar cell temperature between 35oC and − 55oC during the cold case. The temperatures of the internal components alternate during the cold case between 7oC and 13oC (compare figure 4.26) and during the hot case between 18oC and 41oC. In the mean the maximum − temeperatures of the failure case are 5.6% (Standard deviation of 5.7%-points) lower than the corresponding values of the normal test cases, while the minimum temperatures of the failure cases are 96.5% (Standard deviation of 44.6%-points) higher. The resulting temperature ranges for this case are shown in figure 4.30 and compared to the

49 operational temperature ranges. From a thermal point of view the malfunction of the two DSPs would improve the situation of the satellite. No temperature constraints are violated. Every component has a margin of at least 5oC to its operational temperature limits. In conclusion, the satellite would even be operational, if one or two DSPs fail. However, the changed power budget would have to be reconsidered.

Figure 4.30: Simulated Temperatures (Broad black) and operational temperatures (green) of PICSAT for the hot and cold case if both DSPs fail.

4.6.3 Error

For the results of this work no errors are calculated. The system is too complex and contains too many unknowns to give a realistic error analysis in the framework of this thesis. The following aspects have to be studied in depth to give a reasonable error range: Temporal variation of the emitted solar radiation. • Temporal and spatial variation of Earth’s radiation due to temperature changes and surface changes. • Accuracy of the orbit and the attitude. • Production accuracy and surface treatment accuracy of the components. • Production accuracy of the PCBs. • Reliability of the values given by the manufactureres. • Error of the calculations done by SYSTEMA/THERMICA. • However, to minimise the risk of satellite failure due to thermal reasons, a margin is added to the dissipative heat acting on the satellite. A margin of at least 5oC between the simulated extreme temperatures and the operational temperatures is essential. Additionally, further tests in a Thermal Vacuum Chamber (TVC) have to be performed to conﬁrm the reliability of the modeled conductive links and heat capacities.

50 Chapter 5

Thermal prestudies of the CIRCUS nanosatellite

The CIRCUS project aims to realise a nanosatellite for real-time measurements of the plasma density in the ionosphere [5]. In the current phase of the studies of CIRCUS different configurations of solar panel arrangement and pointing requirements are discussed. The Main drivers for this discussion are the available power with a certain configuration and the impact on the thermal house keeping of the satellite. CIRCUS is currently in the A0-phase of its studies and hence its development is less advanced than PICSAT. Most of the components are not chosen, but in order to make a realistic simulation at such an early stage of the development the model of PICSAT is used as foundation and adjusted to represent the different configurations of CIRCUS. This process is presented in section 5.1. In section 5.2 the intended orbit of CIRCUS is introduced with its hot and cold cases. The considered configurations of CIRCUS are shown in 5.3 together with their hot case and cold case attitudes. The results of the simulation are presented in section 5.4. A discussion of the results follows in section 5.5.1.

5.1 Adjustment of the PICSAT model to accomplish the thermal pre-sudies of CIRCUS

The CIRCUS project is currently in its early studies. Most components which will be used are not decided upon yet. However, an initial estimation of the temperatures, that might occur on different satellite configurations, is demanded. In order to do reasonable simulations, the TMM of the PICSAT satellite is adjusted to model CIRCUS. According to the current studies both satellites will consist of similar parts besides of the payload[5]. The variation of the parts from different suppliers is limited, because of the standardisation by the CubeSat Design Specification (CDS) [18]. Even if other suppliers are chosen for CIRCUS, the TMMs of the parts of PICSAT are suitable to do a first approximation of the temperature range of CIRCUS. This procedure avoids to do a rigorous number of assumptions. It also allows to develop the design of the satellites in a synergistic approach to limit the costs. A second advantage is that successful tests and the mission of PICSAT will also verify the model of CIRCUS in a limited scope. To adjust the PICSAT model to represent CIRCUS, the following changes are conducted:

The TMM of the PICSAT payload is removed. • A representation for the CIRCUS payload is added. • Structural parts which are missing in the PICSAT model are added. • Depending on the configuration (which are introduced in 5.3), additional DSPs are added. • Depending on the configuration structural nodes are removed or changed. • 51 CIRCUS and PICSAT have different missions and therefore use different instruments. While the scientific objective of PICSAT is to observe the transit of an exoplanet, CIRCUS aims to do measurements in the ionosphere. The development of the scientific payload of CIRCUS is, as well as the satellite itself, in the A0-phase. Hence only basic information regarding the instrument is available. The instrument is modelled as three PCBs. In a 3U configuration one PCB of the payload is located in the central cube, while the other two are placed in the third cube. The thermal properties of the instrument PCBs are assumed to be the same as the PCB of the PICSAT payload. Additionally a maximum dissipation of 1 W was placed in the middle of each of the three PCBs. This high value gives a sufficient margin. A third antenna was also added at the bottom of the satellite. The antenna itself and the antenna PCB are assumed to have the same thermal properties as the VHF-antenna. The corresponding values are presented in section 4.2.4. For PICSAT some ribs of the standard structure are removed to create sufficient space for the instrument and are therefore missing in the model. For the simulation of CIRCUS those rib are added to represent the standard configuration of the used structure [26]. In total two fixed ribs and four attached ribs are added. The properties of the corresponding parts are introduced in section 4.2.1. The different configurations of CIRCUS are distinguished by the arrangement the of solar cells. Depending on the configuration, additional DSPs are added. The properties of the DSPs of PICSAT, as introduced in section 4.2.2, are used to model the DSPs of CIRCUS. The changes made to the PICSAT GMM to convert it to CIRCUS are shown in figure 5.1.

Figure 5.1: The internal parts of CIRCUS (left). The major changes compared to the GMM of PICSAT (right) are marked.

5.2 The projected orbit and its hot and cold case

The projected orbit of CIRCUS is at an altitude of 600 km with a planed inclination of 83.6o [5]. The hot and cold case of this orbit are comparable to the ones of PICSAT. For the hot case the orbit trajectory follows the terminator during middle of January. During the cold case the orbit plane is perpendicular to the terminator at middle of July. The hot and cold case orbits of CIRCUS are illustrated in ﬁgure 5.2.

52 Figure 5.2: Hot (top) and cold (bottom) case of the CIRCUS orbit.

5.3 Satellite Conﬁgurations and their hot and cold cases

Four different conﬁgurations of the CIRCUS satellite are discussed, which will be introduced in this section. They are distinguished by the arrangement of the DSPs. The conﬁgurations considered are:

1. Simple 3U CubeSat not spinning

2. Simple 3U CubeSat spinning

3. 3U CubeSat with two DSPs parallel to the satellites main axis

4. 3U CubeSat with four DSPs perpendicular to the satellites main axis

Due to their diverse geometries, different hot and cold cases apply for every satellite. The first configuration (figure 5.3 left) is located in its hot case attitude, with one of the 3U-surfaces pointing to the Sun and another 3U-surface pointing to the Earth. The cold case is reached if the side with the smallest surface points to the Sun and one of the 3U-surfaces points in the north direction of the planet. The extreme cases of the second configuration (figure 5.3 right) are defined by the attitude of the rotational axis. For the hot case the rotational axis is perpendicular to the Sun line. During the cold case the rotational axis points to the Sun. This study is only supposed to show the rev impact of a rotation on the temperature distribution in general. A rotational speed of 5 h is assumed. For deeper studies of this case additional rotational speeds have to be considered. The third configuration (figure 5.4 right) is identical with the one of PICSAT. For the hot case a side with a DSP has constant Sun pointing and one of the 3U surfaces is directed to the Earth surfaces. In the cold case the smallest surface is pointing to the Sun, while one of the 3U surfaces points to the planets north direction. In the fourth configuration (figure 5.4 right), the four DSPs are pointing to the Sun and one of the 3U surfaces to the planet north. The cold case is contrariwise. All cold cases here are the most extreme conditions possible. They do not represent possible mission modes, since the solar cells are not illuminated in these cases.

53 Figure 5.3: Studied conﬁgurations 1 (left) and 2 (right) of CIRCUS in a 3U version.

Figure 5.4: Studied conﬁgurations 3 (left) and 4 (right) of CIRCUS in a 3U version.

54 5.4 Simulation results of CIRCUS

The results of the six conﬁgurations deﬁned in section 5.3 are presented in this section. A detailed discussion of the results follows in section 5.5.1.

5.4.1 Results of Conﬁguration 1: Cold case

The simulation results of the first configuration in the cold case are presented in figure 5.5 . The plots show the temperatures of the ADCS and the PL (top left), the components in the first cube (top right) and the solar cells (bottom).

Figure 5.5: Temperatures for the cold case of CIRCUS conﬁguration 1 over simulation time. Data of the ADCS and the PL (top left), the PCBs in the ﬁrst cube (top right) and the solar cells (bottom).

55 5.4.2 Results of Conﬁguration 1: Hot case

The simulation results of the first configuration in the hot case are presented in figure 5.6 . The plots show the temperatures of the ADCS and the PL (top left), the components in the first cube (top right) and the solar cells (bottom).

Figure 5.6: Temperatures for the hot case of CIRCUS conﬁguration 1 over simulation time. Data of the ADCS and the PL (top left), the PCBs in the ﬁrst cube (top right) and the solar cells (bottom).

56 5.4.3 Results of Conﬁguration 2: Cold case

The simulation results of the second configuration in the cold caseare presented in figure 5.7. The plots show the temperatures of the ADCS and the PL (top left), the components in the first cube (top right) and the solar cells (bottom).

Figure 5.7: Temperatures for the cold case of CIRCUS conﬁguration 2 over simulation time. Data of the ADCS and the PL (top left), the PCBs in the ﬁrst cube (top right) and the solar cells (bottom).

57 5.4.4 Results of Conﬁguration 2: Hot case

The simulation results of the second configuration in the hot case are presented in figure 5.8 . The plots show the temperatures of the ADCS and the PL (top left), the components in the first cube (top right) and the solar cells (bottom).

Figure 5.8: Temperatures for the hot case of CIRCUS conﬁguration 2 over simulation time. Data of the ADCS and the PL (top left), the PCBs in the ﬁrst cube (top right) and the solar cells (bottom).

58 5.4.5 Results of Conﬁguration 3: Cold case

The simulation results of the third configuration in the cold case are presented in figure 5.9. The plots show the temperatures of the ADCS and the PL (top left), the components in the first cube (top right) and the solar cells (bottom).

Figure 5.9: Temperatures for the cold case of CIRCUS conﬁguration 3 over simulation time. Data of the ADCS and the PL (top left), the PCBs in the ﬁrst cube (top right) and the solar cells (bottom).

59 5.4.6 Results of Conﬁguration 3: Hot case

The simulation results of the third configuration in the hot case are presented in figure 5.10 . The plots show the temperatures of the ADCS and the PL (top left), the components in the first cube (top right) and the solar cells (bottom).

Figure 5.10: Temperatures for the hot case of CIRCUS conﬁguration 3 over simulation time. Data of the ADCS and the PL (top left), the PCBs in the ﬁrst cube (top right) and the solar cells (bottom).

60 5.4.7 Results of Conﬁguration 4: Cold case

The simulation results of the fourth configuration in the cold case are presented in figure 5.11 . The plots show the temperatures of the ADCS and the PL (top left), the components in the first cube (top right) and the solar cells (bottom).

Figure 5.11: Temperatures for the cold case of CIRCUS conﬁguration 4 over simulation time. Data of the ADCS and the PL (top left), the PCBs in the ﬁrst cube (top right) and the solar cells (bottom).

61 5.4.8 Results of Conﬁguration 4: Hot case

The simulation results of the fourth configuration in the hot case are presented in figure 5.12. The plots show the temperatures of the ADCS and the PL (top left), the components in the first cube (top right) and the solar cells (bottom).

Figure 5.12: Temperatures for the hot case of CIRCUS conﬁguration 4 over simulation time. Data of the ADCS and the PL (top left), the PCBs in the ﬁrst cube (top right) and the solar cells (bottom).

5.5 Discussion of the thermal prestudies of CIRCUS

Four different satellite conﬁgurations were simulated in their hot and cold case. The results of the simulations are shown in section 5.4 and are to be discussed in this section. The operational temperature ranges introduced in chapter 4.2.7 are used to make a ﬁrst evaluation of the simulated temperatures.

5.5.1 Conﬁguration 1: Non spinning 3U satellite

The simulations show that the configuration of the DSP as well as the spinning of the satellite has a significant impact on the temperature of the satellite components. The highest temperature is determined for the solar cells of the non-spinning normal 3U satellite (configuration 1, compare figure 5.6) . However, considering the operational temperatures of the PICSAT solar cells this temperature is still in the operational range. The temperature of the parts in the satellites interior varies between 26oC and 59oC for the hot case (compare figure 5.6) and between 62oC and 43oC for the cold case (compare figure 5.5). The − − temperature on the outer parts of the satellite oscillates within a temperature range of 20oC, while the internal parts experience temperature changes of up to 6oC. The hot case temperatures fulfill the operational requirements, but

62 without leaving a margin. The cold case temperatures are, for most components, out of the operational temperature range with an excess of up to 20oC. To increase the temperatures of the satellite in the ﬁrst conﬁguration, the following measures are recommended:

The ESPs should be covered with a surface ﬁnish with a high UV absorptivity. Possibilities are black • anodized aluminium instead of blank aluminium or to use a black coating [13, p.792ff.].

The constant Sun pointing of the smallest surfaces should be avoided by the ADCS. A thermal safe mode • should require the satellite to point one of large surfaces to the Sun, if the temperature falls below the operational limits.

The use of a heating device for the batteries is vital. •

5.5.2 Conﬁguration 2: Spinning 3U satellite

The spinning of the second satellite configuration reduces the range of temperature oscillations when compared to configuration number one. The oscillation range for external parts is reduced by 50% to 10oC, while the range for internal parts is still at 6oC (compare figure 5.8 and figure 5.7). However, the smaller amplitude of the thermal fluctuations is achieved in a trade-off for a higher frequency (compare figure 5.8 bottom). This temperature frequency also represents the frequency at which the solar cells are illuminated. In the simulated case of 5 revolutions per 1 hour the frequency of the temperature changes during the hot case is 5 h . Due to a violation of the Nyquist theorem this frequency is not visible in figure 5.8. In this case the temperature of the solar cells ranges between 63oC − and 55oC. The temperatures of the internal parts vary between 50oC and 70oC. Those values exceed every − operational temperature limit which was defined for PICSAT. The temperatures of the internal parts are deteriorated by 3oC for the cold case and by 12oC in the hot case. This is a result of the lower temperatures on the outer surfaces of the satellite. The energy radiated into space from the outer surfaces depends on their temperature to the power of four as stated in section 2.1.1. A reduction of the temperature by 50% implies therefore a reduction of the radiated heat by 93.7%, which leads to a higher temperature on the inside of the satellite. Therefore it can be concluded that rev spinning with 5 h degrades the thermal state of the satellite and is not recommended. However, other rotational frequencies might positively contribute to the thermal state of the satellite.

5.5.3 Conﬁguration 3: Satellite with two DSPs parallel to the main axis

For the third configuration two DSPs are attached to the satellite. This configuration is comparable to the one of PICSAT. In the hot case the internal components reach a temperature of up to 56oC and the solar cells reach a temperature of 80oC (compare figure 5.10). In the cold case the internal parts reach a temperature of 61oC and − the external parts 65oC (compare figure 5.9). The temperatures of the hot case are slightly higher than those of the − hot case of PICSAT, while the temperatures of the cold case are comparable to those of the failure case of PICSAT. This is reasonable, because the definition of the attitudes of PICSAT’s failure case 1 and the cold case of CIRCUS configuration 3 are identical, while the dissipation in the hot case is higher. The temperature oscillations have an amplitude of up to 7oC for the internal parts and 20oC for the external parts (compare figure 5.10). In the hot cases the simulated temperature satisfies the limits of PICSAT, but in the cold case all temperature limits are exceeded by up to 30oC. The following measures are recommended to increase the satellites temperature in the cold case:

For the Sun pointing ESPs a surface ﬁnish with high emissivity should be utilized (e.g. black paint or black • anodized aluminium [13, p.792ff.]).

The ADCS should change the satellites attitude, if the temperature falls to a critical value. The requirement • of this new attitude is to maximise the surface pointing to the Sun.

As for failure case three of PICSAT the utilization of heaters is not recommended due to the high exceedance • of the temperature limits, which would lead to a high power consumption of the heaters.

63 5.5.4 Conﬁguration 4: Satellite with four DSPs perpendicular to the main axis

In the fourth configuration, four DSPs are attached to the satellite. They are arranged perpendicular to the satellite’s main structure. This configuration has the largest surface with constant Sun-pointing (45% larger than the third case) and thereby the highest heat income by solar radiation. However, at the same time the emitting surface is also increased and decreases the satellites temperature. The resulting temperatures settle in a range between 29oC − and 50oC for the internal parts, while the external parts reach a temperature range between 52oC and 80oC − (compare figure 5.11 and 5.12). The solar cells undercut the lower limit by 12oC, while the battery temperatures vary between 18oC and 47oC, thereby exceeding the maximum temperature limit by 2oC and the minimum limit − by 13oC. However, four of the PCBs undercut the minimum temperature limit by up to 4oC. The oscillations of the temperature cover a range of 23oC (compare figure 5.11). Different approaches might be utilized to increase the temperature of the satellite. In the simulated configuration the satellite body is covered by solar cells, which have a rather high emittance. In its normal operation the main body of this satellite configuration will not point in Sun direction. Those solar cells are only used during emergency cases and for this purpose are not required to cover the whole satellite surface. The satellite’s temperature can be increased by removing the solar cell and using a surface finish with low emittance. Another approach is to improve the heat exchange between the DSPs and the main body by adding a high conductive link between the DSP and the structure. Due to its large surface of solar cells, this satellite configuration has an extended power budget. However, the utilization of this power to operate heaters is not reasonable for two reasons. One is that the complexity of the system would increase significantly. The other is that while this configuration would increase the power budget, the only reason to consider this configuration would be to power heaters. If this additional power is utilized to heat the satellite, the advantage is canceled out.

64 Chapter 6

Conclusion and Outlook

The objective of this work was to conduct a thermal analysis of the nanosatellite PICSAT. Based on the thermal model of PICSAT a ﬁrst thermal study of the nanosatellite CIRCUS was conducted. The outcome of the studies as well as the next recommended steps are discussed for PICSAT in section 6.1 and for CIRCUS in section 6.2

6.1 PICSAT: Compliance with operational temperature requirements and further testing

PICSAT is in an advanced development stage and currently in the phase B of its development. In the framework of this work the expected temperatures of the satellite were determined for the hot case of the mission, the cold case of the mission and three failure cases. The thermal model of the satellite was created and simulated using SYSTEMA/THERMICA. The simulations showed for most components a compliance with the operational temperature limits for the mission’s hot and cold case. The temperatures of the batteries exceed their lower limits by 2oC and the solar cells by 10oC in the cold case. The simulated temperatures of the structure complies with the temperature ranges, but has no margin left. It was concluded that the temperature of the structure might not be critical, because of the absence of thermal gradients for thermal tension. The compliance of the battery temperatures with the operational temperature range might be achieved using a heater. The low minimum temperature of the solar cells was seen to be most critical. As a counter measure the utilization of a highly conductive material between the solar cells and the SSPs (respectively the DSPs) was recommended. The simulation of the three failure cases led to contrary results. The first failure case assumed a failure of the ADCS, which leads to constant Sun pointing of the smallest satellite surface. The simulations showed that this failure results in a significant drop in temperatures of the satellite of up to 40oC compared to the normal cold case. Every lower temperature limit is exceeded in this case. As a counter measure, an adjustment of the surface finishes of the ESPs was suggested along with the introduction of a thermal safe mode. This mode should couple the temperature sensors with ADCS and move the satellite to an attitude in which one of the DSPs has Sun-pointing. The other two failure modes studied the cases of a failure of one DSP or both DSPs. The simulations showed, that in those cases the temperature range on the satellite becomes more narrow and is in compliance with the operational temperature limits. A MLI-effect of the DSPs was identified as the reason for the increased satellite temperatures. In a next step, the reliability of the thermal model of PICSAT has to be verified. It is suggested to conduct tests similar to the ones in section 4.4. Based on the experience gathered during this work, the following adjustments to the tests are suggested:

To exclude the inﬂuence of convective heat transfer the tests should be performed in a TVC. • 65 To be able to test all conductive links, the tests should be conducted with either a detailed engineering model, • which has reasonable representations for every component, or on the ﬂight model.

The following links are seen as particularly critical and require a veriﬁcation:

The DSPs collect 40% of the solar radiation which reaches the satellite. They also provide 37% of the • emitting surface. Therefore they have a signiﬁcant inﬂuence on the temperatures of the main structure, depending on the quality of the conductive link between the DSPs and the main strucutre.

The batteries are the most temperature sensitive part of the satellite. Their temperature depends primarily on • the conductive link to the battery pack.

80% of the satellite surface is covered with solar cells. The heat absorbed and emitted by the solar cells is the • main driver of the satellites temperature. The amount of heat transferred from the solar cells to the satellite structure depends on the conductive link between the solar cells and the SSPs.

6.2 CIRCUS: First temperature estimations and further studies

The CIRCUS project is currently in its early phase A0 studies. Most components are not defined yet. However, a first estimation of the temperature ranges of different satellite configuration was demanded. To make realistic estimations regarding the satellite components the thermal model of PICSAT was adjusted to represent the thermal properties of CIRCUS. Four possible configurations of CIRCUS were simulated in their hot and cold case. The configurations are distinguished by the arrangement of their solar cells. The simulation results were compared to the thermal requirements of PICSAT. None of the tested satellites fulfil the temperature limits of the PICSAT satellite. However, some of the configurations are more suitable for the purpose of the CIRCUS mission than others. The first configuration with a simple 3U satellite has a long flight heritage in earlier missions. It is also the least complex configuration. The temperature ranges were partially exceeded by up to 20oC. However the low temperatures, that exceed the temperature limits, might be easily avoided by using an ADCS and pointing the larger satellite surfaces to the Sun. Therefore, the utilization of this configuration is recommended. In the second configuration, the influence of rotation on the satellites temperature was tested. Only one test was rev conducted with a rotational speed of 5 h . The test showed a degradation of the thermal conditions. The temperature on the outer surfaces decreased, but the frequency of the temperature changes increased. On the other hand the temperatures of the internal parts increased. With the tested rotational speed the second configuration can not be recommended. However, further tests with other rotational speeds might lead to differing recommendations. In the third configuration, two DSPs are utilized. This configuration is identical with PICSAT and the simulation showed similar temperature ranges. Besides the first configuration, this configuration is preferred for the CIRCUS mission. The simulations showed a good compliance with the temperature ranges. The CIRCUS project would also benefit from the experience of the PICSAT project. The fourth satellite configuration with four DSPs is not recommended. This configuration exceedes all temperature limits significantly. The utilization of heaters would cancel out the only advantage of this configuration. Additionally this is the most complex configuration. For all satellite configurations counter measures were recommended to improve the satellite’s thermal behaviour. In the further development process, a final configuration of the satellite has to be chosen. The results of this work might serve as an input for this decision, but also studies of other subsystems. The thermal aspects of the chosen configuration have to be studied more in detailed. In order to allow a detailed analysis, this process should start, when most of the satellite components are defined. It is recommended to use the thermal model of CIRCUS that was created in this work as a basis for further simulations. This procedure would cover the following advantages:

The thermal model of CIRCUS is based on PICSAT. A successful PICSAT mission will conﬁrm the robustness • of the model.

66 Some of the tests conducted by PICSAT do not have to be repeated for CIRCUS. • Adjusting an existing model allows faster analysis than creating a new one. •

Appendix A

Calculation of the properties of a PCB

The density ρPCB, the speciﬁc heat cp,P CB and the thermal conductivity kPCB within the plane of a PCB are calculated based on the sum tcu of the thicknesses of all copper layers and the sum tcm of the thicknesses of the carrier material. Since the layer thicknesses are constant over the plate, the sum of the thickness in of the copper is simultaneously its volume fraction xvol,cu within the PCB. The same is valid for the volume fraction of the carrier material xvol,cm. With the density of the copper ρcu and the carrier material ρcm it is possible to calculate the mass fractions xm,cu and xm,cm using equation A.1 and equation A.2.

xvol,cu ρcu xm,cu = (A.1) xvol,cu ρcu + xvol,cm ρcm

x = 1 x (A.2) m,cm − m,cu

The PCB density ρPCB is calculated in equation A.3 based on the volume fractions xvol,cm and xvol,cu as well as the densities ρcu and ρcm.

ρPCB = xvol,cm ρcm + xvol,cu ρcu (A.3)

The speciﬁc heat cp,P CB of the PCB also depends on the volume fractions. It is calculated based on the speciﬁc heats of the two layer materials cp,cu and cp,cm in equation A.4.

cp,P CB = xvol,cm cp,cm + xvol,cu cp,cu (A.4)

The thermal conductivity kPCB of the PCB, on the other hand, is calculated in equation A.5 using the mass fractions and the thermal conductivities of the two layer materials kcu and kcm.

kp,P CB = xm,cm kcm + xm,cu kcu (A.5)

Appendix B

Conductive Links

Table B.1: Overview of the theoretical conductive links in the PICSAT TMM. (1) In the model replaced by a measured value. W Node 1 Node 2 Conductive link GL [ m K ] Note Side bar small Side bar big 3.26507 Side bar small Corner 0.03370 (1) Side bar big Corner 0.03973 (1) Side bar small Side bar small 0.00666 Side bar big Side bar big 0.00786 Fixed rib small Fixed rib big 3.36000 Fixed bar small Corner 0.02470 Fixed bar big Corner 0.02470 Attached rib small Attached rib big 3.87545 (1) Attached rib small Corner 0.02255 (1) Attached rib big Corner 0.02255 SSP Attached rib small 0.06397 SSP Corner 0.06501 Solar cell Solar cell 0.01168 Attached rib big Battery pack board 0.01976 Battery Battery 0.14984 Battery Pack inner PCB Battery 0.04030 Battery Pack outer PCB Battery 0.06461 Battery Pack Power Board 0.00958 Battery Pack connector Power Board connector 0.02710 Power Board IGIS short arm 0.01140 Power Board IGIS long arm 0.01148 Power Board connector IGIS connector 0.06674 IGIS short arm Primary ODH 0.01167 IGIS long arm Primary ODH 0.01175 IGIS connector ODH connector 0.06593 ODH primary ODH secondary 0.00578 ODH primary Transceiver 0.00793 ODH primary connector Transceiver connector 0.03300

71 Table B.2: Continued: Overview of the theoretical conductive links in the PICSAT TMM. (1) In the model replaced by a measured value. W Node 1 Node 2 Conductive link GL [ m K ] Note Transceiver Attached rib big 0.02491 Attached rib big BATI 0.08435 Corner BATI 0.10576 BATI CAPOT 0.45698 CAPOT Baseplate 1.47763 Baseplate Instrument 1.05582 Baseplate St200 0.00221 St200 Top plate 0.00295 Top plate SSP 0.07691 Top plate Corner 0.06128 ESP Antenna PCB Node 1 0.04272 ESP Antenna 0.00035 ESP Antenna PCB Node 2 0.05406 Antenna PCB UHF Attached rib big 0.02944 Antenna PCB VHF Antenna 0.00001 Antenna PCB UHF Antenna 0.00001 Antenna PCB VHF Attached rib big 0.01386 DSP SSP 0.11524 Solar cell Solar cell PCB 0.59873 Solar cell PCB SSP 1.59911

72 Appendix C

Convection horizontal plate

The temperature of the boundray layer Tb is approximated as the mean of the temperature of the ﬂuid Tf and the surface Ts [7]. T + T T = f s (C.1) b 2

∆T is the difference between Ts and Tf . ∆T = T T (C.2) s − f The perimeter P of a rectangle is half the sum of its height H and its width W [7]. H + W P = (C.3) 2 The characteristic length L of the plate is the surface A divided by its perimeter P [7]. A L = (C.4) P

The dimensionless Prandtl Number P r of a fluid is calculated based on its viscosity µ, specific heat capacity Cp and its conductivity k [7]. µC P r = p (C.5) k The dimensionless Grashof Number depends on the characteristic length of the plate L, the gravitational constant g, as well as the density ρ, viscosity µ and conductivity k of the fluid [7].

L3ρ2g∆T β Gr = (C.6) µ2 The Rayleigh number Ra is the product of P r and Gr [7].

Ra = P r Gr (C.7) · The Nusselt number Nu for a wide range of Ra-values is calculated based on Ra [7].

1 Nu = 0.27 Ra 4 (C.8) · The h-value h describes the convective heat transfer per surface area [7]. Nu k h = · (C.9) L To receive the convective link GL, the h-value h is multiplied with the convecting area A.

GL = h A (C.10) ·

Appendix D

Convection vertical plate

The temperature of the boundary layer Tb is approximated as the mean of the temperature of the ﬂuid Tf and the surface Ts [7]. T + T T = f s (D.1) b 2

∆T is the difference between Ts and Tf ∆T = T T (D.2) s − f

The dimensionless Prandtl Number P r of a fluid is calculated based on its viscosity µ, specific heat capacity Cp and its conductivity k [7]. µC P r = p (D.3) k The dimensionless Grashof Number depends on the height of the plate L the gravitational constant g as well as the density ρ, viscosity µ and conductivity k of the fluid [7].

L3ρ2g∆T β Gr = (D.4) µ2 The Rayleigh number Ra is the product of P r and Gr [7].

Ra = P r Gr (D.5) · The Nusselt number Nu for a wide range of Ra-values is calculated based on Ra [7].

2 1 6 0.387 Ra / Nu = 0.825 + · 8 27 (D.6)  9 16 /  1 + (0.492/P r) /     The h-value h describes the convective heat transfer per surface area [7].

Nu k h = · (D.7) L To receive the convective link GL the h-value h is multiplied with the convecting area A [7].

GL = h A (D.8) ·

Appendix E

Voltage demand of an electrical heater

The electrical Power Pelectrical depends on the voltage U and the current I.

P = U I (E.1) electrical · The current I caused by a certain voltage U over a resistance R is deﬁned by Ohms Law.

P = U I (E.2) electrical · Putting equation E.2 into equation E.1 gives the Power in dependency of the voltage and the resistance.

U 2 P = (E.3) electrical R

Rearranging of equation E.3 gives the voltage U required to achieve a certain power Pelectrical at a resistance R. Since the resistor does not fulﬁl any work, all power is dissipated as heat.

P = P = √P R (E.4) heat electrical ·

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