Planetary and low orbit thermal environment for space thermal design

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Universidad Politécnica de Madrid

Escuela Técnica y Superior de Ingeniería Aeronáutica y del Espacio

Doctoral Dissertation

David González Bárcena

Máster Universitario en Sistemas Espaciales

2022

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Instituto Universitario de Microgravedad "Ignacio da Riva"

Escuela Técnica y Superior de Ingeniería Aeronáutica y del Espacio

Planetary and low orbit thermal environment for space thermal design

Doctoral Dissertation

David González Bárcena

Máster Universitario en Sistemas Espaciales

Tutor: Prof. Dr. Ángel Sanz Andrés

2022

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Tribunal nombrado por el Sr. Magfco. de la Universidad Politécnica de Madrid, el día...de...de 20....

Presidente:...

Vocal:...

Secretario:...

Suplente:...

Realizado el acto de defensa y lectura de la Tesis el día...de...de 20.... en la E.T.S.I./Facultad...

Calificación...

EL PRESIDENTE LOS VOCALES

EL SECRETARIO

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Acknowledgements

A mis padres, Pilar y Francisco, a mi hermano Mario y a mi hermana Sara por inculcarme el valor del trabajo con el ejemplo, por aguantarme y por darme su apoyo siempre.

A mi abuela María por su fe ciega en mi, a mi abuelo Pepe por ser mi primer maestro y a mis abuelos Castor y Victoria por todo lo que pudo ser y no fue.

Al resto de mi familia por creer siempre en mi y a mis amigos por darme lo que necesito para mantener el equilibrio en todo momento.

A Isabel por su apoyo constante y por la confianza desde el primer momento que ha hecho posible esta Tesis. A Ángel por toda su ayuda e interés durante estos años y por la oportunidad de poder darle forma a todo el trabajo dentro del IDR.

A mis compañeros del IDR, por ese día a día en compañía.

En especial a Arturo y a Alejandro por todo el trabajo codo con codo durante estos años.

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Abstract

The thermal environment characterization is one of the main steps to be done when facing the thermal analysis of space systems. They are usually analysed using worst-case values, which define the extreme conditions that can drive the system to its maximum temperatures. If the system is analysed under these conditions, temperatures during its whole life would be between these limits. However, it is important to well define the thermal environment in order to both get an appropriate design and to avoid oversizing the thermal control subsystem.

The criteria developed by NASA for selecting the worst-case parameters has been widely used for years in several space missions. However, these criteria has not evolved since 1994 when first Earth radiation budget data were available.

Nowadays, there are many data sources that can be used instead in order to deal with some limitations of the NASA criteria. In addition, the current computing capabilities allow for more complex analysis that can improve the thermal analysis and design of these systems.

In this work, firstly, NASA criteria has been adapted to the thermal analysis of stratospheric balloon missions. This kind of missions have some differences with regard to the space ones, which makes necessary to perform a particularized analysis.

Once at the floating altitude, convection is negligible in most cases but not during the ascent phase when it should be considered together with other parameters.

In addition, the residence time over a point on the Earth surface is much higher than for a satellite. This makes necessary to focus the analysis on the geographic area where the flight is going to be, and to limit the data to the epoch when they can be performed. A complete thermal environment characterization based on real-observation data has been developed in order to define the worst-case analysis for both the float and ascent phases. This methodology has been applied to real missions such as SUNRISE III and TASEC-Lab.

Secondly, NASA criteria for selecting the worst-case thermal environmental parameters in Low Earth Orbits has been reviewed with the aim of identifying its limitation and proposing a new methodology. It is common to analyse satellites from a thermal point of view by identifying worst-case orbits with constant values for the thermal environmental parameters. This method has been successfully used for years but small satellites or low massive parts need a reconsideration since

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based on a particularized characterization.

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Resumen

La caracterización del ambiente térmico es una de las principales tareas a realizar a la hora de afrontar el análisis térmico de un sistema espacial. Por lo general, éstos se analizan utilizando los valores de los "peores casos", que definen las condiciones extremas que pueden llevar al sistema a sus temperaturas máximas y mínimas. Si se analiza el sistema bajo estas condiciones, es posible garantizar que las temperaturas durante toda su vida útil estarían entre estos límites. Sin embargo, es importante definir bien el ambiente térmico para obtener un diseño adecuado y evitar sobredimensionar el subsistema de control térmico.

Los criterios desarrollados por la NASA para seleccionar los parámetros de los peores casos se han utilizado ampliamente durante años en varias misiones espaciales.

Sin embargo, este criterio prácticamente no ha evolucionado desde 1994, cuando se utilizaron para ello los primeros datos disponibles del balance radiativo de la Tierra. Hoy en día, hay muchas fuentes de datos que pueden usarse en su lugar para lidiar con algunas de sus limitaciones. Además, las capacidades informáticas actuales permiten análisis más complejos que pueden mejorar el análisis térmico y el diseño de estos sistemas.

En este trabajo, en primer lugar, se han adaptado los criterios de la NASA al análisis térmico de las misiones de globos estratosféricos. Este tipo de misiones tienen algunas diferencias con respecto a las espaciales que hacen necesario realizar un análisis particularizado de las mismas. Una vez en la altitud de crucero, la convección puede despreciarse en la mayoría de los casos. Sin embargo, esto no ocurre durante la fase de ascenso cuando ésta debe considerarse junto con otros parámetros. Además, el tiempo de residencia de los globos estratosféricos sobre un punto de la superficie terrestre es mucho mayor que el de un satélite. Esto hace necesario centrar el análisis en el área geográfica donde se va a realizar el vuelo y acotar los datos a la época en que se pueden realizar. En esta tesis se ha desarrollado una caracterización completa del entorno térmico basada en datos de observación real para definir los análisis tanto para la fase de crucero como para la de ascenso.

Esta metodología se ha aplicado a misiones reales como SUNRISE III y TASEC-Lab.

En segundo lugar, se ha llevado a cabo una revisión de los criterios de la NASA para seleccionar los peores casos de los parámetros del entorno térmico en órbitas bajas con el objetivo de identificar sus limitaciones y proponer una nueva

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los parámetros del entorno térmico. Este método ha sido utilizado con éxito durante años, pero los satélites pequeños o partes más ligeras de los mismos necesitan una reconsideración de esta metodología ya que están más acoplados a las variaciones en el entorno térmico. En este trabajo se proponen perfiles orbitales dependientes del tiempo para los parámetros térmicos con el objetivo de obtener análisis más precisos basados en una caracterización particularizada a cada satélite.

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List of Figures

1.1 Exploded view of Sputnik-1. NASA History Division. . . 2 1.2 Spectral Solar Irradiance from 200 nm to 100000 nm. NRLSSI2 Daily

Average 1/1/1882 [6]. . . 3 1.3 Balloon inflation for CREAM mission launch. . . 6 1.4 Spectral distribution of solar irradiance at 1 AU and its approximation

by a blackbody at 5780 K (dashed line) [36]. . . 14 1.5 Wavelength absorption by atmospheric gases compared to normalized

spectral distribution of blackbodies at 6000 K and 250 K [37]. . . . 14 1.6 Fraction of orbit in eclipse as a function of the SBA and the altitude

[38] . . . 16 1.7 Thermal modelling process. . . 21 1.8 Temperature ranges for Thermal Control System. . . 22 1.9 Thermal environment characterization process for obtaining unit-

lever boundary conditions. . . 24 2.1 Orbital-average albedo correction term as a function of the orbital

beta angle and correction at minimum SZA [17]. . . 26 2.2 Extreme hat and cold cases (albedo, OLR and combined) [17]. . . . 28 2.3 Mission critical hot and cold extreme environments at low, medium

and high inclinations, and averaging times from 16 seconds to 24 hours [17]. . . 29 2.4 Non-critical hot and cold extreme environments at low, medium and

high inclinations, and averaging times from 16 seconds to 24 hours [17]. 30 2.5 Sample time series of observed ERBE OLR data with multiple hot

and cold pulses superimposed on base values [17]. . . 31 2.6 Extreme hot case set for maximum OLR (Condition Set A) and

maximum albedo (Condition Set B) [40]. . . 32 2.7 Evolution in time of instantaneous effective albedo and average

effective albedo over various periods for a SSO orbit, 800 km, LTAN 18:00 [16] . . . 34 2.8 Comparison between orbital average effective albedo/Earth tempera-

ture for several LEO orbits [16] . . . 34 xiii

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2.9 Correlation between average orbital effective albedo and average orbital effective Earth temperature (for a same orbit) for a SSO orbit, 800 km altitude, LTAN 20:00 over 5 years (2007-2011) [16] . . . 35 2.10 Worst case profile of the evolution of average effective albedo over

various periods for an SSO orbit, 800 km, LTAN 18:00 [16] . . . 35 3.1 Earth’s global mean energy budget for July 2005-June 2015 [41]. . . 38 3.2 Mean sea level pressure and wind at 200 hPa forecast in Europe for

9^th of March 2022. . . 42 3.3 Wind data of Esrange the day of launch of SUNRISE I, June 8^th,

2009 (provided by Esrange/SSC and IRF [50]). . . 43 4.1 Scheme of the thermal environment at the floating altitude. . . 53 4.2 Trajectories followed by SUNRISE I (red) and SUNRISE II (blue). . 53 4.3 (a) Albedo and (b) OLR maps of the considered region at 10:00 AM

UTC the 1^st June 2010. . . 54 4.4 Evolution of OLR over Greenland (68.5 °N, 42.5 °W) in 2009. . . . 54 4.5 Distribution of albedo and OLR for the considered region and period

of time. . . 55 4.6 Six hours average TSI data measured by SORCE mission from June

26^th 2015 to June 26^th 2018 . . . 55 4.7 Albedo and OLR distributions after grid-density clustering. . . 56 4.8 Potential worst hot and cold case points and regression curves. . . . 57 4.9 Correlation of albedo and OLR data with Solar Zenith Angle. . . . 57 4.10 Albedo to OLR correlation for a SZA of (a) 45.5° and (b) 87.7°. . . 58 4.11 Sketch of the analytical model used to estimate main radiative fluxes. 59 4.12 Temperature of the gondola for every thermal environment defined

by the hot case regression curve (α/ε= 0.26). . . 62 4.13 OLR and albedo coefficient maximizing gondola steady-state tem-

perature as a function of the ratio α/ε. . . 63 4.14 (a) Temperature of the gondola for every thermal environment defined

by the cold case regression curve (α/ε= 0.26). (b) OLR and albedo coefficient minimizing gondola steady-state temperature as a function of the ratio α/ε. . . 64 4.15 Environmental conditions parametric studies for the (a) minimum

and (b) maximum temperatures of the cold and hot operational cases respectively. . . 65 4.16 Scheme showing the parameters that affect the system during the

ascent phase. . . 69

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List of Figures xv

4.17 Andoya minimum, mean and 10 percentile temperature profile compared to ISO seasonal (June-July) at 60^o N 10 percentile temperature. 72 4.18 Andoya mean density profile and deviation profile from ISO standard

density. . . 73 4.19 ISO atmospheric pressure profile. . . 73 4.20 Mean, maximum and 95 percentile dew point temperatures of Andoya

as a function of the altitude. . . 74 4.21 Scheme of the process followed to treat wind data statistically. . . . 75 4.22 Original (a) and resampled (b) representation of the wind velocities

for the 1^st June of 2016 for altitude resolutions of 75 m (upper row), 150 m (middle row) and 600 m (lower row). . . 76 4.23 Data correlation between each pair of radar modes corresponding to

a complete day. . . 77 4.24 (a) Mean combination of every resolution measurement for the 1^st

June of 2016, (b) Map after deletion of values out of the mean ± 2σ. 78 4.25 Final wind velocity map for the 1^st June of 2016 after the implemen-

tation of the KNN algorithm. . . 78 4.26 (a) Original wind velocity map of 13^th June 2016 and (b) map

resulting after the treatment. . . 79 4.27 (a) Mean values and (b) 95 percentile values of the month of June of

years 2016 and 2017. . . 79 4.28 Variation of the SZA during the month of June at Esrange. . . 81 4.29 Box plot representation of (a) albedo, (b) OLR, (c) solar irradiance,

and (d) sky temperature as a function of the SZA and the altitude. 81 4.30 Scheme of the process followed to select the worst cold case of albedo

and OLR. . . 83 4.31 Probability density function of albedo and OLR values for several

altitudes and a SZA = 87.4°. . . 84 4.32 Heatmap of the albedo (left) and OLR (right) for the 3 different

worst cold cases. . . 85 4.33 Mean solar irradiance heatmap. . . 86 4.34 Mean sky temperature heatmap. . . 87 4.35 Sketch of the angles pitch Ω and yaw φ which define the relative

position of the plate. . . 87 4.36 Coordinates x, z of the balloon shape profile during the SUNRISE I

ascent phase. . . 92 4.37 Influence of the balloon film in the albedo (top), OLR (middle) and

solar (bottom) incoming flux to the payload. Incoming flux (a) and ratio with respect to the total flux (b). . . 94

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4.38 Infrared flux from the balloon film to the payload as a function of

the altitude. . . 95

4.39 Altitude, latitude and longitude profiles during the ascent phase of PMC-Turbo, HIWIND, SUNRISE I and SUNRISE II. . . 96

4.40 Forces acting on the balloon-borne system during the ascent phase. 97 4.41 SUNRISE I GPS ascent profile compared to simulation outputs. . . 99

4.42 SUNRISE I GPS (a) latitude and (b) longitude profile compared to simulation outputs. . . 100

4.43 SUNRISE I relative velocity profile obtained from simulation outputs.100 4.44 Scheme of the process followed to carry out the ascent phase analysis with B-TASEC. . . 101

4.45 Definition of the orbit trajectory. It is considered the Sun in a constant position with respect to the Earth and the balloon borne system is going to move along a meridian. . . 104

4.46 Schematic process developed by Execution tool. . . 105

4.47 Visualization of the results in ESATAN-TMS. . . 106

4.48 SUNRISE I launch in Esrange (Kiruna, Sweden). . . 107

4.49 SUNRISE III at MPS (Göttingen, Germany). . . 108

4.50 Scheme showing the different instruments in the PFI. . . 109

4.51 Hierarchy of the SUNRISE III thermal model. . . 110

4.52 SUNRISE III ESATAN thermal model. . . 111

4.53 Boundary conditions for the scientific instrumentation in the PFI. . 112

4.54 Boundary conditions for the electronic boxes in the racks. . . 112

4.55 Temperature result for a launch time at (a) 21 h and (b) 10 h. . . . 116

4.56 TASEC-Lab structural configuration . . . 120

4.57 ESATAN-TMS ascent phase temperature profiles (hot, cold and flight day conditions) and flight temperature data of the heated plate. . . 121

4.58 CAD model of the HERCCULES experiment on board BEXUS gondola.124 4.59 Pyranometer and pyrgeometer measuring wavelength (dashed lines). 125 5.1 CERES global map of albedo (upper blue), OLR (upper red) and SZA (lower) corresponding to the 12:00 h UTC of 1^st Jan 2018. . . 133

5.2 Evolution of NASA established criteria for selecting the worst-case environmental conditions. . . 134

5.3 Scheme of the one-node proposed system. . . 139

5.4 Equivalent control system for representing the system temperature response. . . 141

5.5 (a) One year temperature evolution, (b) zoom of the maximum temperature point, (c) SBA evolution for a whole year and (d) SZA evolution for the zoom range in (b). . . 144

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List of Figures xvii

5.6 Scheme of the proposed satellite-Earth model. . . 146

5.7 Heatmap of the average values of (a) albedo and (b) OLR for a whole year. . . 147

5.8 Boxplot of the distribution of (a) albedo and (b) OLR as a function of the orbit inclination. . . 148

5.9 Boxplot of (a) albedo and (b) OLR along the year. . . 149

5.10 Temperature response of different systems for a Sun-Synchronous orbit with constant SBA. . . 150

5.11 Distribution of viewed albedo and OLR values considering their dependence to SZA (color coded as shown on the left). . . 150

5.12 SZA evolution for a LEO satellite during a whole year. . . 151

5.13 Detailed time evolution of Albedo and OLR during five orbits. . . . 153

5.14 Fourier Transform of albedo and OLR five orbit series. . . 154

5.15 Autocorrelation function of albedo and OLR five orbit series. . . 155

5.16 Albedo coefficient decomposition. . . 156

5.17 OLR decomposition. . . 156

5.18 Approximation of the seasonal albedo and OLR variations by curve fitting methods. . . 157

5.19 Location of the maximum temperature point for a satellite with a characteristic time of 112 s together with its heat loads. . . 159

5.20 Location of the maximum temperature point for a satellite with a characteristic time of 896 s together with its heat loads. . . 160

5.21 Temperature response of the systems with (a) t_c = 87 s and (b)t_c = 1733 s, to the resid heat load of albedo and OLR where SZA is lower than 60^◦. . . 160

5.22 Variation of temperature with time of the step function response defined to obtain an equivalent ∆T for the Hot Case. . . 161

5.23 Albedo and OLR trend components value distribution. . . 162

5.24 Albedo and OLR worst hot case profiles. . . 162

5.25 Comparison between the real response, the hot extreme case, and NASA proposed worst-cases for a)t_c = 87 s and b) t_c = 1733 s. . . 164

5.26 Variation of temperature with time of the step function response defined to obtain an equivalent ∆T for the Cold Case. Red dots: time needed to reach the peak temperature. . . 165

5.27 Albedo and OLR worst cold case profiles. . . 166

5.28 Comparison between the real response, the cold extreme case, and NASA proposed cold worst-cases for (a) t_c = 87 s and (b) t_c = 1733 s.166 5.29 Miniaturization process in the space system designs. . . 170

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5.30 Albedo and OLR profiles for the (a) hottest and (b) coldest worst- cases of the tc = 300 s and (c) hottest and (d) coldest worst-cases of the tc = 1100 s. . . 174 5.31 Scheme of the thermal model used in ESATAN-TMS. . . 175 5.32 Case 1 (decoupled nodes) thermal model temperature response for

the (a) coldest and (b) hottest worst-cases using NASA and time- dependent proposed criteria. . . 177 5.33 Case 2 (coupled nodes) thermal model temperature response for

the (a) coldest and (b) hottest worst-cases using NASA and time- dependent criteria. . . 178 A.1 One-dimensional, steady-state conduction in a plane wall. . . 186 A.2 Resistance implementation in a gemetric discretization. . . 187 A.3 Thermal contact resistance between two planar walls. . . 188 A.4 Electromagnetic radiation spectrum where thermal radiation covers

infrared, visible and partially ultraviolet ranges. . . 190 A.5 Blackbody spectral distribution for different temperatures. . . 191 A.6 Distribution of incident radiation on a surface. . . 192 A.7 TOA solar and 300 K body spectral distribution (left) and their

normalized emissive power distributions (right). . . 193

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List of Tables

4.1 Input variables required to compute relative velocity. . . 99 4.2 Input variables required to compute relative velocity. . . 102 4.3 Input variables required to compute relative velocity. . . 103 4.4 ESATAN-TMS files automatically created in Pre-Process tool. . . . 105 4.5 Worst extreme cases vales for SUNRISE III thermal analysis. . . 114 5.1 Orbit and satellite characteristics for the temperature analysis. . . . 142 5.2 Sun-synchronous orbit and satellite characteristics for the worst-case

analysis. . . 152 5.3 Adjusted coefficients for the curve fitting of seasonal albedo and OLR

profiles. . . 157 5.4 Albedo and OLR peak step function characteristics for the Hot Case. 161 5.5 NASA provided extreme worst hot cases. . . 163 5.6 Albedo and OLR peak step function characteristics for the Cold Case.165 5.7 NASA provided extreme worst cold cases. . . 166 5.8 NASA albedo and OLR worst-case values for the considered orbit

and satellite characteristics. . . 172

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List of Symbols

α . . . . Solar absorptance.

β . . . . Solar Beta Angle.

γ . . . . Angle between a normal vector and the Sun direction.

ϵ . . . . Earth obliquity of the ecliptic.

ε . . . . Infrared emissivity.

η . . . . Solar panel efficiency.

θ . . . . Solar Zenith Angle.

µ . . . . Dynamic viscosity.

ν . . . . Knematic viscosity.

ρ . . . . Reflectivity.

ρ_gas . . . . Gas density.

σ . . . . Stefan-Boltzmann constant.

τ . . . . Transmitance.

φ . . . . Yaw angle.

Ω . . . . Pitch angle.

a . . . . Albedo coefficient.

A . . . . Area.

b . . . . Specific buoyancy.

Bi−j . . . . Gebhart factor from element i toj.

c_p . . . . Specific thermal capacity.

C_d . . . . Drag coefficient.

C_i . . . . Thermal capacity of element i.

D . . . . Drag force.

E . . . . Energy.

Fi−j . . . . View factor from element i toj.

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G_L_i,j . . . . Linear conductor between element i and j.

G_R_i,j . . . . Radiative conductor between element i and j. g . . . . Gravity acceleration.

G_S . . . . Solar constant.

h . . . . Altitude.

hc . . . . Contact conductance.

¯h_i . . . . Convective heat transfer coefficient.

H_s . . . . Transfer function.

i . . . . Inclination.

k . . . . Thermal conductivity.

l_c . . . . Characteristic length.

m . . . . Mass.

M . . . . Molecular mass.

p . . . . Pressure.

Q . . . .˙ Heat flux.

Q˙_a . . . . Albedo heat flux.

Q˙_S . . . . Solar heat flux.

Q˙_E . . . . Earth infrared heat flux.

˙

q_E . . . . Outgoing Longwave Radiation.

R_E . . . . Earth radius.

R_gas . . . . Specific gas constant.

Rth . . . . Thermal resistance.

t . . . . Time.

t_c . . . . Characteristic time.

T . . . . Temperature.

v . . . . Velocity.

V . . . . Volume.

w . . . . Wind speed.

W . . . . Weight.

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List of Abbreviations

APL . . . . Applied Physics Laboratory.

AU . . . . Astronomical Unit.

C3S . . . . Copernicus Climate Change Service.

CAMS . . . . . Copernicus Atmosphere Monitoring Service.

CEMS . . . . . Copernicus Emergency Management Service.

CERES . . . . Clouds and Earth Radiant Energy System.

CFD . . . . Computer Fluid Dynamics.

COTS . . . . . Commercial off-the-shelf.

CSBF . . . . . Columbia Scientific Balloon Facility.

CU . . . . University of Colorado.

CWS . . . . Correlated Wavefront Sensing.

DLR . . . . German Aerospace Cente.

ECMWF . . . European Centre for Medium-range Weather Forecast.

ECSS . . . . . European Cooperation for Space Standardization.

EU . . . . European Union.

EUMET-SAT European Organisation for the Exploitation of Meteorological SATellites.

EPS . . . . Electrical Power Subsystem.

ERB . . . . Earth’s Radiation Budget.

ERBE . . . . . Earth Radiation Budget Experiment.

ERBS . . . . . Earth Radiation Budget Satellite.

ESA . . . . European Space Agency.

ESE . . . . Earth Science Enterprise.

ESRAD . . . . Esrange MST Radar.

FCA . . . . Full Correlation Analysis.

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GEO . . . . Geostationary Earth Orbit.

GMM . . . . . Geometrical Mathematical Model.

GMAT . . . . General Mission Analysis Tool.

GPS . . . . Global Positioning System.

HERCCULES Heat-transfer and Environment Radiative and Convective Char- acterization in a University Laboratory for Experimentation in the Stratosphere.

HTL . . . . Heat Transfer Lab.

IAA . . . . Instituto de Astrofísica de Andalucía.

IAC . . . . Instituto de Astrofísica de Canarias.

ICS . . . . Inertial Coordinate System.

IDR . . . . Instituto Universitario de Microgravedad "Ignacio da Riva".

IMU . . . . Inertial Measurement Unit.

INTA . . . . . Instituto Nacional de Técnica Aeroespacial.

ISLiD . . . . . Image Stabilization and Light Distribution.

ISS . . . . International Space Station.

KIS . . . . Leibniz-Institut fuer Sonnenphysik.

KNN . . . . . k-Nearest Neighbor.

LASP . . . . . Laboratory for Atmospheric and Space Physics.

LDB . . . . Long Duration Balloon.

LEO . . . . Low Earth Orbit.

LHA . . . . Local Hour Angel.

LLDPE . . . . Linear Low-Density Polyethylene.

MCF . . . . Million Cubic Feet.

MCRT . . . . Monte-Carlo Ray Tracing.

MPS . . . . Max-Planck-Institut für Sonnensystemforschung.

MODIS . . . . Moderate Resolution Imaging Spectroradiometer.

MORABA . . Mobile Rocket Base.

MUSE . . . . . Máster Universitario de Sistemas Espaciales.

NAOJ . . . . . National Astronomical Observatory of Japan.

NADU . . . . Navigation and Attitude Determination Unit.

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List of Abbreviations xxv

NASA . . . . . National Aeronautics and Space Administration.

NFOV . . . . . Narrow-Field-Of-View.

NOAA . . . . . National Oceanic and Atmospheric Administration.

OBC . . . . On-Board Computer.

ODE . . . . Ordinary Differential Equation.

OLR . . . . Outgoing Longwave Radiation.

PCB . . . . Printed Circuit Board.

PCU . . . . Power Control Unit.

PFI . . . . Post Focus Instrumentation.

RAAN . . . . Right Ascension of the Ascending Node.

REF . . . . Radiative Exchange Factor.

SBA . . . . Solar Beta Angle.

SCIP . . . . SUNRISE Chromospheric Infrared spectropolarimeter.

SDPU . . . . . Sensors Data Processing Unit.

SIM . . . . Spectral Irradiance Monitor.

SLI . . . . Single Layer Insulation.

SNSB . . . . . Swedish National Space Board.

SOLSTICE . . Solar Stellar Irradiance Comparison Experiment.

SORCE . . . . Solar Radiation and Climate Experiment.

SSC . . . . Swedish Space Corporation.

STEM . . . . . Simple Thermal Environment Model.

SUSI . . . . SUNRISE Ultraviolet Spectropolarimeter and Imager.

SZA . . . . Solar Zenith Angle.

TASEC . . . . Thermal Analysis Support and Environment Characterization.

TCS . . . . Thermal Control Subsystem.

TIM . . . . Total Irradiance Monitor.

TMM . . . . . Thermal Mathematical Model.

TMU . . . . . Temperature Measurement Unit.

TOA . . . . Top of Atmosphere.

TRASYS . . . Thermal Radiation Analysis System.

TRMM . . . . Tropical Rainfall Measuring Mission.

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TSI . . . . Total Solar Irradiance.

TSIS . . . . Total and Spectral Solar Irradiance Sensor.

TSS . . . . Thermal Synthesizer System.

TuMag . . . . Tunable Magnetograph.

UPM . . . . . Universidad Politécnica de Madrid.

USA . . . . United States of America.

USSR . . . . . Union of Soviet Socialist Republics.

UTC . . . . Coordinated Universal Time UV . . . . Ultraviolet.

VIIRS . . . . . Visible Infrared Imaging Radiometer Suite.

VF . . . . View Factor.

VZA . . . . Viewing Zenith Angle.

WFOV . . . . Wide-Field-Of-View.

XPS . . . . XUV Photometer System.

ZARM . . . . Center of Applied Space Technology and Microgravity.

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Introduction 1

Contents

1.1 Motivation . . . . 1 1.2 Objective . . . . 7 1.2.1 Literature production . . . 10 1.3 Basic concepts . . . . 12 1.3.1 Planetary and space thermal environment . . . 12 1.3.2 Spacecraft Thermal Control . . . 18 1.3.3 Thermal modelling . . . 19

1.1 Motivation

One of the biggest steps in the human history took place in 1957. The 4^thof October that year, the Soviet Union (USSR) successfully launched the world’s first artificial satellite. It was called "Sputnik" and it meant the beginning of a long trip around the Earth and beyond for years. It is really intriguing thinking about the design process of these first missions. What did they know about space? How did they performed their simulations? Nowadays, we live in a era in which we depend on the computers and the technology for almost everything. We cannot even imagine not using them for designing or testing new satellites. But more important than technology is our dependence on years and years of studies and knowledge about the space and the experience acquired in thousands of ballooning, rockets and satellite missions. The Sputnik-1 satellite, which is shown in Figure 1.1, was conceived not as a scientific satellite itself but as a the simpliest satellite (prosteishyi sputnik 1) to

1

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become the first orbiting the Earth [1]. However, it provided valuable information about the density of the upper atmosphere and the ionosphere characteristics.

Figure 1.1: Exploded view of Sputnik-1. NASA History Division.

By the time the Sputnik 1 was launched, many studies were carried out with the aim of understanding the upper-atmosphere, its properties and its composition.

In 1804, Gay-Lussac an Biot used a manned balloon for firstly measuring the air composition and the magnetic field at 7000 m [2]. Since the first unmanned balloon flight realized by Hermite and Besangon in 1892, the study of the atmosphere improved by the use of sounding balloons which were capable of reaching altitudes above 30000 m. Based on these researches, scientists hold their attention beyond.

First theoretical studies of the upper-atmosphere showed many fascinating phenomena which made reaching this nearly empty region a challenge from a technological and scientific point of view. By the time sounding rockets made their appearance in the mid-1940’s, a coherent picture of the upper-atmosphere was theoretically set forth by B. Haurwitz in his publication of 1937 about "The Physical State of the Upper Atmosphere" [3]. It provided helpful information for those who began using rockets for the study of this region.

Such were the problems to which the rocket experimenters addressed themselves [4]. Once started, the results of their research flowed in a steady stream into the

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1. Introduction 3

literature, contributing to a growing understanding of upper atmospheric phenomena.

The first questions rockets experimenters addressed themselves were those ground- based scientist considered more significant. Studying the solar spectrum from ground had several limitations due to the atmospheric absorption. It was in 1946 when Richard Tousey and his colleagues firstly measured the solar spectra from above the ozonosphere [5]. This event marked the beginning of many years of intensive research on the structure and energy content of the solar spectrum, which still continues nowadays. From a thermal point of view the interesting wavelength range goes from 0.2 µm to 100 µm, where the solar spectrum can be approximated by a blackbody radiating at a 6000 K temperature. The computed solar irradiance spectrum observations from the Solar Radiation and Climate Experiment (SORCE) in the thermal radiation wavelength range are shown in Figure 1.2.

Figure 1.2: Spectral Solar Irradiance from 200 nm to 100000 nm. NRLSSI2 Daily Average 1/1/1882 [6].

Atmospheric structure, that is, the variation of pressure, temperature, and density with altitude, as well as its chemical composition, also received the early attention of the rocket experimenters. Almost every flight carried gauges to measure these fundamental parameters. As a result of many rocket observations, in the early 1950s the Rocket and Satellite Research Panel was able to issue an improved estimate of upper-atmospheric structure for use by geophysics [7]. By the time Sputnik went into orbit, the groundwork had been laid to give a considerable amount of information about both geographical and temporal variations of these quantities.

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Although satellite missions allowed experimenters for a better study of all these parameters, sounding rockets continued being launched since they provided the best means of obtaining vertical cross sections of atmospheric properties up to satellite altitudes. In addition, they also were cheaper devices for testing new instrumentation or making exploratory measurements of phenomena to be studied in detail later with more expensive spacecraft. Their relatively low cost and the speed with which a sounding rocket experiment could be prepared and carried out also made sounding rockets useful for graduate research where the students needed to complete a project in a reasonable amount of time to support his dissertation.

But not only did students find sounding rockets attractive. Many professional space scientists continued to favor sounding rockets for much of their research, as opposed to the more complicated, more expensive, and more demanding satellites.

One of the biggest problems experimenters had to face when they required long-duration observations is the design of the spacecraft to carry their scientific payload on board up to space. There were some proposals for building a standardized satellite to serve experimenters as a common platform. This would have considerably reduced the development time and cost and it would have improved the reliability of space missions. However, for each satellite a great deal of tailoring was required in terms of orbit, orientation, telemetry, electrical energy supply, thermal control, etc.

Such problems defeated the efforts to produce standardized satellites. Nevertheless, a considerable level of uniformity was achieved. Similar design approaches were adopted by spacecraft based on technology used successfully by previous missions.

In addition, when the design of a new satellite starts, engineers had already in mind a lot of information about the orientation capabilities, the potential thermal issues or the required structural loads, etc. Not only did the technology used by spacecrafts acquire over the years a high level of standardization but also did the design process in terms of procedures, requirements, analyses, test, etc.

All these first missions provided valuable information for the design of the next satellites since the experience acquired and the data obtained were continuously compiled into the literature. Nowadays, the design process of a satellite is completely standardized with the aim of guaranteeing the success of the mission, reducing cost, optimizing work, etc. It seems quite obvious that if there is a lack of information when designing a satellite, an oversizing would be necessary to reduce risks and guarantee the success of the mission. This is why space missions have become more and more complex with time. Information about the satellites performance in space or the knowledge of the environment to deal with is continuously increasing allowing the experimenters to be more focused on the scientific objective of the spacecraft.

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1. Introduction 5

For a successful mission, it is necessary to ensure the good performance of the scientific payload and the support equipment during the whole life of the spacecraft.

To do so, many analyses and tests are performed during the design process. In order to deal with all these tasks, satellites are usually divided into different subsystems for structuring the work into well separated disciplines. The Thermal Control Subsystem (TCS) of a satellite shall guarantee the survival of the equipment to the harsh environment in space. According to Ref [8], the TCS is the responsible of

"maintaining all spacecraft and payload components and subsystems within their required temperature and gradients limits for each mission phase". Once defined the thermal requirements and constraints of the system and the different components, the determination of the thermal environment should be performed in order to select the worst-case analyses to be done in the design process.

As pointed out before, the thermal characterization of the satellites environment is possible thanks to other many space mission that were performed before. The thermal environment criteria used for spacecraft design has evolved as the technology has done over the years. The availability of Earth-observation data has provided a valuable information which has allowed for a better characterization of the thermal environment.

Not only have the analysis capabilities hugely improved, but also has the amount of information about the space environment considerably increased. In the last decade, the growth of the internet capacities together with an increasing interest for big data strategies have led to the main organizations, the National Aeronautics and Space Administration (NASA) and the European Space Agency (ESA), to provide open access to huge satellite-based observations databases. Using this data and carefully analysing it using statistical methods, the characterization of the thermal environment could be particularized to each mission in order to reduce uncertainties and get more complex designs avoiding the over-sizing.

Nowadays, the access to space has been opened to private investments, research institutes, universities, etc, by the use of small satellites. During the last decade, the standardization has become a reality in form of CubeSat platforms [9]. These small cubic satellites provide suitable platforms for small scientific experiments or technology demonstration. The miniaturization of the electronics has allowed for improving the capabilities of this emerging technology. Nevertheless, there are cheaper alternatives for experimenters than reaching the space. The stratosphere is also a very suitable place for these purposes. Being above 99 % Earth’s atmosphere mass, wave front distortions due to atmospheric turbulence are virtually non- existent [10] providing an advantageous location compared to ground-based solar

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observations. Scientific balloons also provide a platform for the demonstration of promising new instrument and spacecraft technologies [11]. Furthermore, residence time over a determined area is huge when compared to Low Earth Orbits (LEO).

For that reason, stratospheric platforms are being presented as a suitable solution to provide communication coverage to non-accessible areas [12] or just to monitor the Earth environment [13]. The capabilities and utilities of these kind of flights are constantly increasing and as a result, the design process of these systems is becoming more and more relevant.

Figure 1.3: Balloon inflation for CREAM mission launch. NASA Columbia Scientific Balloon Facility (CSBF).

From a thermal point of view, stratospheric missions have many similarities with space missions. Being in the stratosphere, radiation is the main heat transfer mechanism as in most cases, convection could be considered negligible. This is why, stratospheric balloon payloads are usually analysed using the same tools used for the space systems analysis. However, there are two big differences with respect to the satellites thermal analysis. Firstly, the ascent phase of this kind of platforms should be analysed due to the convective effects. The low temperatures in the tropopause as well as the high relative wind speed make freezing a real problem that must be avoided. Secondly, these analyses used to be performed using averaged values for the environmental conditions [14] without taking into account the local characteristics or the seasonal variability. Increasingly complex systems, such as SUNRISE III, a project the Instituto Universitario de Microgravedad "Ignacio da Riva" (IDR) from Universidad Politécnica de Madrid (UPM) is involved in, require deeper studies to ensure survival to both the ascent and float phases. Using real- data based environments, uncertainties could be reduced by defining particularized worst-cases accounting for every influencing parameter.

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1. Introduction 7

1.2 Objective

The work developed in this Doctoral Dissertation is divided in two main parts. Since the early space missions, stratospheric flights and LEO spacecraft have been always related between each other. Not only the similarities in the system performance but also in the thermal environment make that the same analysis methodologies are used in both cases. However, some differences must be considered.

The thermal environment characterization is one of the most important steps for performing the thermal analysis of a experiment on board a stratospheric balloon or a spacecraft. Without a good knowledge of the influencing parameters it is not possible to reach an appropriate design. However, just knowing about it is not enough to face the thermal analysis. It is necessary to obtain the combination of parameters that would lead the system to its maximum and minimum temperatures. These combinations are called worst-cases, what means that if the system temperature requirements are fulfilled for them and the model is accurate enough, the flight temperatures would be between these limits. One may think that if the worst hot case is under study, using the maximum values for the environmental parameters could be the answer to the thermal environment characterization. However, reality is not that simple since they are partially correlated in one way or another. For this reason, statistically studying them may help to understand their relationships and to better select the worst-cases for the thermal analysis [15]. The next section of this chapter will introduce the reader with the heat transfer mechanisms and the main elements involved in the thermal environment. This background would be enough to understand the work developed in this Doctoral Dissertation.

Even the logic may say that this field has been widely studied by years, the truth is that only NASA and few researchers have focused their studies on the selection of the worst case environmental conditions for space thermal design [14, 16].

Regarding the stratospheric flights, even one can think it is an easier application, the great number of variable parameters make of this study a complex one. Sometimes, space characterization methodologies are directly applied without considering the potential limitations. In other cases, the ignorance or the underestimation of the thermal environment influence forces to an over-sizing due to the uncertainties or worse, to a bad design that could affect the system performance. In order to understand how the worst-case selection has evolved during the last decades, the NASA methodology which has been conventionally used will be explained in Chapter 2. In addition, last studies of Peyrou-Lauga et al., who aimed at updating the NASA criteria, will be also exposed.

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NASA criteria is based on real-observation data from ERBE mission, based on measurements of Earth Radiation Budget Satellite (ERBS) and National Oceanic and Atmospheric Administration (NOAA) satellites from 1984 to 1987 [17]. Since then, many other satellites have been observing the Earth and acquiring data from the Earth Radiative Balance in order to study the global warming. The Clouds and Earth Radiant Energy System (CERES) have been collecting data for more than two decades and treating them with the aim of providing a global grid of radiative parameters [18]. This data is of free-access to the scientific community allowing for many other studies as the one developed in this Doctoral Dissertation. However, CERES is not the only available database. During the last years, free-access have been provided for a very wide range of satellite-data. Chapter 3 provides a summary of the data source used in this work for characterizing the albedo, the Outgoing Longwave Radiation (OLR), the solar irradiance, not only at the Top of the Atmosphere but also below, where the sky temperature, the air temperature and the wind speed, are also relevant parameters.

As previously pointed out, stratospheric balloon missions are becoming more and more relevant with time as suitable platforms for solar and exoplanets observation, technology demonstration, CubeSat pre-flight test or even student experimentation.

The IDR/UPM, has participated in SUNRISE mission since its first scientific fight in 2009 [19]. This mission consists on a solar telescope on board a Long Duration Balloon (LDB) with the objective of studying the structure of the magnetic field of the solar atmosphere [20]. In the last flight, SUNRISE III, the IDR was the group responsible for the thermal analysis and design at system level [21]. This is why the author firstly focused on the thermal environment characterization of stratospheric missions. He realized that the literature regarding this field was scarce and the methodology used by other missions could be considerably improved using real-data observations. In addition, regarding the ascent phase of this missions, only analytical studies were preformed without considering the influence of a very variable radiative environment [22, 23].

Therefore, the main objectives of this Doctoral Dissertation regarding the planetary thermal environment characterization for stratospheric balloon thermal analysis are the following:

• Study of the relationship between the system’s characteristics and the worst- cases for the float steady state thermal analysis.

• Development of a new methodology for selecting the worst-case conditions particularized to stratospheric balloon missions.

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1. Introduction 9

• Parametrization of the potential worst-case condition in order to analyse the influence of the thermo-optical properties and the orientation of the considered instrument on board a LDB.

• Characterization of the thermal environment during the ascent phase of stratospheric balloons.

• Evaluation of the thermal influence of the balloon film on the payload.

• Development of a new methodology for the thermal analysis of the ascent phase of stratospheric balloon missions.

All of this has been performed using previous mentioned data, python [24] as the programming language and ESATAN-TMS for the thermal analysis. Chapter 4is focused on the "Planetary Thermal Environment" where firstly the methodology is explained and then, all the work is applied to the SUNRISE III mission. In a lower scale, TASEC-Lab [25, 26], which is a stratospheric experiment developed by UPM students and led by the author, was also analysed following the same approaches. It is also introduced and a comparison between flight data and the thermal analysis is shown.

Once defined the planetary thermal environment for stratospheric flight applications, the author wanted to focus on the Low Earth Orbit thermal environment with the aim of reviewing the NASA criteria using a next generation of real-data and trying to update the methodology for a closer characterization of the thermal environment [27]. Other space agencies, as ESA through the European Cooperation for Space Standardization (ECSS) [28], recommends the use of these criteria due to its success in several missions since the nineties. However, they provide some warnings saying that "assumptions made are not valid for some cases". The main objective is focused on improving the existing criteria for accounting their limitations and adapting the selection methodology to the capabilities of the current software analysis tools. For this reason, the proposed methodology, based on time-dependent profiles instead of constant values for the thermal environmental parameters is then applied to the thermal analysis of small satellites [29]. Their low thermal inertia makes that their behavior under variable conditions cannot be completely analysed by the convectional criteria because they are considerably coupled to the thermal environmental variations.

Therefore, the main objectives of this Doctoral Dissertation regarding the Low Earth Orbit thermal environment characterization for space thermal analysis are the following:

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• Study of the relationship between the orbital, environmental and system’s parameters.

• Development of a new methodology for the selection of the worst-case conditions based on time-dependent profiles.

• Adaptation of the proposed methodology to be used by current analysis tools.

• Application to the small satellites thermal analysis.

As done before, here, CERES data is analysed using python as the programming language together with ESATAN-TMS for the thermal analysis and General Mission Analysis Tool (GMAT) [30] for the orbit calculations. This methodology is presented in Chapter 5.

Conclusions and some guidelines for future works are drawn in Chapter 6 where the contribution of this Doctoral Dissertation to the current state of the field is discussed.

1.2.1 Literature production

In this dissertation, the content of Chapter 4 and Chapter 5 summarized different studies that have been already published in the literature. During the development of this Doctoral Dissertation, five articles have been published in major journals of aerospace engineering, in collaboration with other PhD. candidate researchers and professors of the Universidad Politécnica de Madrid.

• Arturo González-Llana et al. “Selection of extreme environmental conditions, albedo coefficient and Earth infrared radiation, for polar summer Long Duration Balloon missions”. In: Acta Astronautica 148 (2018), pp. 276–284

• David González-Bárcena et al. “Real data-based thermal environment definition for the ascent phase of Polar-Summer Long Duration Balloon missions from Esrange (Sweden)”. In: Acta Astronautica 170 (2020), pp. 235–250

• David González-Bárcena et al. “Ascent Phase Thermal Analysis of Long Duration Balloons”. In: Acta Astronáutica 195 (2022), pp. 416–429

• David González-Bárcena et al. “TASEC-Lab: A COTS-based CubeSat- like university experiment for characterizing the convective heat transfer in stratospheric balloon missions”. In: Acta Astronautica 196 (2022), pp. 244–258

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1. Introduction 11

• David González-Bárcena et al. “Selection of time-dependent worst-case thermal environmental conditions for Low Earth Orbit spacecrafts.” In: Submitted to Advances in Space Research (2022)

Furthermore, five more articles have been presented in prestigious congresses of the space sector,

• David González-Bárcena et al. “Parametric Worst Case thermal environment conditions selection for Polar Summer Long Duration Balloon missions”. In:

24th ESA Symposium on European Rocket and Balloon Programmes and Related Research. 2019

• David González-Bárcena et al. “Methodology for the thermal analysis of instrumentation in Long Duration Balloon missions”. In: 8th European Conference for Aeronautics and Space Sciences (2019). doi: 10 . 13009 /

EUCASS2019-323

• David González-Bárcena et al. “Challenges in the thermal analyses of the ascent and float phases of SUNRISE III”. in: International Conference on Environmental Systems. 2020

• Alejandro Fernández-Soler et al. “Thermal Analysis of SUNRISE III ascent phase”. In: International Conference on Environmental Systems. 2021

• David González-Bárcena et al. “The worst-case thermal environment parameters of small satellites based on Real-Observation Data”. In: International Conference on Environmental Systems. 2021

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1.3 Basic concepts

In order to completely understand the work developed in this Doctoral Dissertation, the author has considered important to previously explain some basic concepts about the thermal environment properties in the stratosphere and out of the atmosphere.

In addition, some information regarding the basics of spacecraft thermal control and how thermal analysis are usually performed is included on this Chapter. If the reader is not specialized in the field, it could be convenient to refresh some concepts about the heat transfer mechanisms that can be found in common literature. A brief summary has also been included in Appendix A.

1.3.1 Planetary and space thermal environment

Being in a LEO, a spacecraft receives thermal energy from three different sources and radiates it to the outer space at a equivalent temperature of 3 K. These three main sources are the incoming solar radiation, the Earth infrared radiation and the albedo, which is the solar radiation reflected by the Earth. If one could consider the Earth and the atmosphere as a whole, averaging valued during a considerably period of time, the incoming, absorbed and outgoing fluxes are in balance. Nevertheless, there is a high geographically and temporary variability of the thermal parameters because these fluxes are not in balance everywhere. Hence, the spacecraft thermal environment depends on the orbit characteristics.

The thermal environment drives the thermal behaviour of the satellite, which is also in balance between the incoming fluxes and the radiated one to the outer space. However, the temperature response of a satellite depends not only on the environmental parameters but also on its own characteristics. Thermo-optical properties, thermal conductivity, heat capacities, etc are parameters that determine the response to changes in the thermal environment. For that reason, both, the thermal environment characterization and the thermal design should not be considered separately because they are one way or another related.

Being in the stratosphere, the thermal environment is very similar to a LEO.

This makes stratospheric balloons to be analysed as the satellites are. At an altitude of around 30 km, 99 % atmosphere is below so heat transfer is mainly driven by radiation. In contrast to satellites, stratospheric flights can last up to 60 days and they are limited to a specific region so the thermal environment characterization should be also restricted to the epoch and flight area. In addition, the residence time of a balloon payload over a determined area is much higher than the residence time of a LEO satellite. An LDB following a circumpolar trajectory in summer

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flies towards the west at an average speed of about 30 km/h. Considering a typical float altitude of 40 km, this results in the system having an effective view of a local point during about 12 hours.

Here, main parameters that take part in the planetary and space thermal environment are explained as well as some geometric factor that are essential for understanding the following sections. The particularities in each case will be then presented in Chapter 4 and Chapter 5 for the planetary and space characterization, respectively.

1.3.1.1 Solar irradiance

For most spacecraft, direct solar radiation is the greatest heat source. The solar constant or solar irradiance is defined as the solar radiation flux that falls on a unit are of a surface normal to the line of the Sun direction at 1 Astronomical Unit (AU) outside the atmosphere and it has an average value of G_S,1AU= 1361.5 W/m².

However, this solar constant is not really constant since a 11-year cycle make energy emitted by the Sun varies reaching monthly-averaged values from 1360.8 W/m² to 1363.0 W/m². However, larger variations up to ± 5 W/m² are common on time scales of days to weeks.

Close to the Earth, from a Low Earth Orbit, solar irradiance is also affected by the distance to the Sun which is not constant throughout the year due to the eccentricity associated to the elliptical orbit of the Earth. This variation (around 1.7 % along the year) makes solar irradiance to vary from a minimum value of 1315 W/m² when the Earth is at is aphelion to a maximum value of 1410 W/m² at its perihelion. This variation can be estimated using the inverse square law as,

GS,r =GS,1AU

1

r², (1.1)

Due to the large distance to the Sun, it can be considered as a source point and its rays as parallel for thermal calculations.

Another important aspect of the solar radiation is the spectral distribution. It can be approximated by a blackbody spectrum at 5780 K reaching a maximum at a wavelength of 0.5 µm (0.45 µm in the real one). The solar spectral distribution, which is mostly contained in a wavelength range from 0.15 to 10 µm (around 99 %) is shown in Figure 1.4.

For some applications where solar irradiance is required below the top of atmosphere (TOA), the absorption of the atmosphere should be considered. As shown in Figure 1.5, gases in the atmosphere have a considerable level of absorption

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Figure 1.4: Spectral distribution of solar irradiance at 1 AU and its approximation by a blackbody at 5780 K (dashed line) [36].

in some ranges of the spectrum. This makes that the solar irradiance decreases when approaching to the Earth surface. This effect will be later analysed when characterizing the thermal environment during the ascent phase of stratospheric balloons.

Figure 1.5: Wavelength absorption by atmospheric gases compared to normalized spectral distribution of blackbodies at 6000 K and 250 K [37].

The direct absorbed solar flux, ˙Q_solar_i for an element i whose surface normal

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vector forms an angle γ_i with the Sun direction can be easily calculated by,

Q˙_S,i =α_iA⊥G_Scosγ_i (1.2) Nevertheless, reflected solar fluxes by nearby elements should be also considered.

1.3.1.2 Solar Zenith Angle

At any location on Earth, the angle of incidence of the solar rays varies. From a thermal point of view, it has several implications. The Solar Zenith Angle (SZA) is defined as the angle between two vectors: (1) the vector from the Earth’s centre to a given location and (2) the vector from the Earth’s centre to the Sun. As the solar rays at a distance of 1 AU can be considered parallel, this angle is the same as the angle between the first vector and the vector between a surface or orbital point and the Sun. This angle varies between 0° (for the Sun at zenith) and 180° (for the Sun at nadir). When the Sun is at the horizon for a surface location, SZA is 90°. As will be studied, it not only does have a direct influence on the angle of incidence over the satellite surfaces but also it indirectly affects the albedo heat load reaching the system.

1.3.1.3 Solar Beta Angle

Solar Beta Angle (SBA) is defined as the minimum angle between the Earth-Sun vector and the orbital plane. This angle can take values between ± 90° and it directly depends on the orbit inclination by β =±(ϵ+|i|) where ϵ is the Earth’s obliquity of the ecliptic which is about 23.4°. Its influence on the thermal behavior of a satellite in space may be divided in,

• It determines the time spent in eclipses as shown in Figure 1.6 [38].

• The intensity and direction of heating incident on spacecraft surfaces changes with β.

• The SZA range for a satellite in space is limited by |β| and 180°.

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Figure 1.6: Fraction of orbit in eclipse as a function of the SBA and the altitude [38]

1.3.1.4 Albedo

Albedo is the fraction of the incident solar radiation that is reflected or scattered by a planet surface or atmosphere. It is usually expressed as a fraction or percentage which is called albedo coefficient, a. As part of the solar radiation it can be assumed that the spectral distribution is the same as the direct solar radiation which approximates a blackbody with a temperature of 5780 K. Due to the roughness of a planet’s surface, the albedo is assumed to be diffuse as a first approximation.

However, the albedo coefficient has a considerable dependence on the SZA increasing its value with it as will be explained. The altitude dependence is important across the atmosphere. This is because part of the solar radiation can be reflected by the clouds instead of the surface. In addition, atmospheric absorption makes the incoming solar radiation to increase for higher altitudes. Albedo, as well as OLR are usually referred to the top of the atmosphere which is a virtual surface located at about 30 km. For quantifying the albedo radiation for any satellite, TOA should be considered as the source of radiation.

Albedo coefficient is highly variable across the globe. It mainly depends on the type of surface below and the presence or not of clouds, their type, etc. Reflectivity increases with the cloud cover where typical values of 0.8 can be reached. Continental areas generally have higher albedo values than ocean areas where the most of incident radiation is absorbed. Here albedo coefficient values range between 0.05 and 0.1. In contrast, ice covered surfaces reflects most of the incoming solar radiation reaching values up to 0.95. This local variability makes albedo has a high dependence of the latitude. Polar regions, where surfaces are mostly covered by snow or ice, the

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cloud presence is higher and the SZA increases, have a higher averaged albedo.

From a spacecraft point of view, albedo coefficient depends on the orbit inclination since the averaged values for polar orbits are around 0.4 versus equatorial orbits, where albedo coefficient is typically around 0.25. The mean value for albedo in the Earth is taken as 0.3 which can be compared with the higher albedo coefficient of Venus (≈ 0.65) and the lower of Mars (≈ 0.15).

When quantifying the heat loads on a spacecraft, it is important to bear in mind that there is only an albedo flux when a portion of the Earth viewed by the satellite is in sunlit. However, its calculation is complex and requires computational implementation. Nevertheless, simplified albedo models which are accurate enough usually assumes that it directly depends on the SZA cosine of the sub-satellite Earth point being the albedo heat load maximum at the sub-solar point. It becomes zero when the SZA is 90° what means Sun is in the horizon. From an element i on board a satellite, albedo heat flux can be calculated assuming the Earth is an sphere with an homogeneous albedo coefficient,

Q_a,i =aG_SA_iFi−Ecosθ, (1.3) where a is the albedo coefficient, G_S the solar irradiance, A_i the surface area of the element i, Fi−E the View Factor from the element i to the Earth, and θ the SZA which is between ±π/2.

1.3.1.5 Outgoing Longwave Radiation

OLR is the emitted radiation by the planet. It is a combination of the radiation emitted in the wavelength band by the atmospheric gases, the Earth surface and the top of the clouds. Although the spectral distribution is complex, from a thermal point of view it can be assumed a greybody spectrum at a temperature between 250 K and 300 K. As is the case with the albedo, OLR is assumed to be diffuse and it is also referred to the TOA in order to eliminate the altitude dependence throughout the atmosphere.

Assuming the Earth is in thermal balance, a relationship between the emitted radiation and the absorbed solar radiation can be assessed. From a thermal point of view, OLR can be quantified in terms of the blackbody equivalent temperature of the planet, T_E. Considering the Earth to be an sphere of radius R_E, it can be estimated by,

T_E = ⁴

sG_S(1−a)

4σ , (1.4)

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It can be deduced that OLR increases as the reflected energy decreases, what means that the emitted radiation depends on the albedo coefficient. Even though Equation (1.4) is