||Re-entry Analysis of a Simple Shaped Satellite Using Python and Parallel Computing
||Department of Aeronautics & Astronautics
A ballistic reentry vehicle RV (reentry vehicle) mission consists of three parts: launch, vac-uum, and reentry. During the launch phase the dominant load on the RV is the thrust and not the aerodynamic drag, causing shocks and vibration on the structure. With higher flight velocities, the energy content of the flow increases causing the spacecraft to heat up. While this is neglectable for deep space flight in vacuum, the effect becomes severe during the entry, even though the density and pressure in high altitudes are low. Due to the heating, aerodynamics must be extended to take thermodynamics into account.
In this thesis the reader will understand the problematic of an re-entry flight and how to calculate for a simple object such like a CubeSat its drag coefficient and therefore how to pre-dict the orbit lifetime. This includes the environment, starting from the atmosphere through which the RV is flying from space to ground, it includes the mathematical derivation and physical description to calculate certain properties and finally the code, written in Python, will be explained with which the values were obtained. The innovation lies not within the case-study but within its application with Python. This thesis emphasizes on using free and open source software for a simple but meaningful analysis rather than proprietary software in realizing a highly complex simulation.
Re-entry, satellite, Python, parallel computing, drag coefficient
I Introduction 1
1 Thesis Organization and Structure 2
2 Introduction 4
2.1 Definitions 5
3 History of re-entry research 6
4 Significance 9
II Space Environment 12
5 Atmospheric Stratification 15
5.1 Thermosphere 17
5.2 Exosphere 18
5.3 Ionosphere 18
6 Sun and Solar Radiation 22
6.1 Solar Wind 22
6.2 Interplanetary Coronal Mass Ejections 22
6.3 Sunspots 23
6.4 Solar Radio Flux 23
7 Geomagnetic Field 24
8 Atmosphere Model 26
8.1 U.S. Standard Atmosphere 26
8.2 Jacchia Reference Atmosphere 26
8.3 NRLMSISE-00 27
9 Geopotential Model 28
9.1 Spherical Harmonics Representation 28
10 Main Parameters and Hypothesizes 30
III Mathematical Derivation and Physical Description 31
11 Classical Mechanics 33
11.1 Fundamental Principle and Definitions 33
11.2 Simplified General Perturbations 36
11.2.1 The Propagation Models 36
12 Aerothermodynamics 37
12.1 Modes of Flow 37
12.1.1 Free Mean Path and Knudsen Number 38
12.1.2 Rarefied Mode 45
12.1.3 Continuous Mode 60
IV Implementation into Python and Graphical Representation 62
13 About Python 64
14 Computational Science 67
14.1 Parallel Computing 68
15 Code 70
V Discussion 71
16 Result and Evaluation 72
16.1 Drag Coefficient According to Sentman 72
16.2 Drag Coefficient According to Schaaf 74
16.3 Drag Coefficient According to Cook 80
16.4 Parallel Computing 83
17 Summary 84
18 Future Work 86
VI Appendix 87
A Python Code 88
A.1 Constants 88
A.2 NRLMSISE-00 88
A.3 Drag Coefficient - Sentman 91
A.4 Drag Coefficient - Schaaf 93
A.5 Drag Coefficient - Cook 95
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