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RWTH Aachen University Institute of Jet Propulsion and Turbomachinery RWTH Aachen University Institute of Jet Propulsion and Turbomachinery DLR - German Aerospace Center Institute of Space Propulsion Optimization of a Reusable Launch Vehicle using Genetic Algorithms A thesis submitted for the degree of M.Sc. Aerospace Engineering by Simon Jentzsch June 20, 2020 Advisor: Felix Wrede, M.Sc. External Advisors: Kai Dresia, M.Sc. Dr. Günther Waxenegger-Wilfing Examiner: Prof. Dr. Michael Oschwald Statutory Declaration in Lieu of an Oath I hereby declare in lieu of an oath that I have completed the present Master the- sis entitled ‘Optimization of a Reusable Launch Vehicle using Genetic Algorithms’ independently and without illegitimate assistance from third parties. I have used no other than the specified sources and aids. In case that the thesis is additionally submitted in an electronic format, I declare that the written and electronic versions are fully identical. The thesis has not been submitted to any examination body in this, or similar, form. City, Date, Signature Abstract SpaceX has demonstrated that reusing the first stage of a rocket implies a significant cost reduction potential. In order to maximize cost savings, the identification of optimum rocket configurations is of paramount importance. Yet, the complexity of launch systems, which is further increased by the requirement of a vertical landing reusable first stage, impedes the prediction of launch vehicle characteristics. Therefore, in this thesis, a multidisciplinary system design optimization approach is applied to develop an optimization platform which is able to model a reusable launch vehicle with a large variety of variables and to optimize it according to a predefined launch mission and optimization objective. An integration of NASA’s CEA program, detailed mass estimations as well as reverse engineering of Falcon 9’s retropropulsive landing first stage are used to virtually build launch vehicles for a given set of rocket parameters, payload mass and target orbit. Due to the enormous amount of possible parameter combinations, a genetic algorithm is applied to identify optimized launch vehicle configurations fast and accurately. Validating the model with Falcon 9 as reference vehicle demonstrated the ability of the optimizer to predict the gross lift-off weight of a rocket with a maximum deviation of 3.6%. Extensive testing of the optimization program showcased its vast potential in rocket design and indicated that methane is a viable rocket fuel alternative for future launch vehicles. Contents List of Figures i List of Tables v List of Acronyms vii 1 Introduction 1 1.1 Motivation . .1 1.2 Structure of this Thesis . .3 2 Theoretical Background 5 2.1 Basic Rocket Equations and Definitions . .5 2.1.1 Tsiolkovsky Rocket Equation . .5 2.1.2 Thrust and Specific Impulse . .6 2.1.3 Orbits . .7 2.1.4 Delta-v Budget Calculation . .9 2.2 Rocket Propulsion Systems . 12 2.2.1 Liquid Propellant Rocket Engines . 15 2.2.2 Engine Cycles . 16 2.2.3 Liquid Propellant Combinations . 20 2.2.4 Engine Parameter Calculation . 24 2.3 Rocket Staging . 28 2.3.1 Staging Configurations . 28 2.3.2 Stage Optimization . 30 2.4 Mass Estimations . 35 2.4.1 Propulsion System . 36 2.4.2 Structure . 37 2.4.3 Payload Bay Subsystems . 40 2.5 Genetic Algorithms . 42 2.5.1 Procedure . 43 2.5.2 Population Initialization . 44 2.5.3 Evaluation . 44 2.5.4 Selection . 45 2.5.5 Variation . 46 2.5.6 Termination . 47 3 Implementation 49 3.1 Software . 49 3.2 Genetic Algorithm Setup . 50 3.3 Workflow . 51 3.3.1 Input Parameters . 51 3.3.2 Evaluation Procedure . 52 4 Validation 55 5 Hyperparameter Tuning 61 6 Results and Discussion 65 6.1 Comparison of Optimized Launch Vehicle Configurations . 65 6.1.1 GTO Mission . 66 6.1.2 LEO Mission . 73 6.2 Comparison with Current Launch Vehicle Research Studies . 77 6.2.1 XTRAS / AKIRA (DLR) . 77 6.2.2 ENTRAIN (DLR) . 83 6.2.3 RETALT . 85 6.3 Sensitivity Analyses . 88 6.3.1 Delta-v Budget . 88 6.3.2 Specific Impulse . 89 6.3.3 Structural Coefficient . 90 6.4 Alternative Optimization Objectives . 91 6.4.1 Total Structure Mass . 91 6.4.2 Expendable Structure Mass . 93 7 Conclusion 97 7.1 Summary . 97 7.2 Outlook . 99 A Visible Landing Gear of Falcon 9 101 B Specific Impulse Comparison of Existing and Calculated Engines 102 C Rocket Parameters 104 C.1 Boundary Values . 104 C.2 Constraints . 105 D Optimized Launch Vehicle Data 106 D.1 5000 kg Payload - 12000 m/s Delta-v . 107 D.2 15600 kg Payload - 9500 m/s Delta-v . 110 D.3 7500 kg Payload - 12000 m/s Delta-v . 113 D.4 7500 kg Payload - 11500 m/s Delta-v . 116 Bibliography 119 List of Figures 2.1 Low Earth Orbit [1] . .7 2.2 Medium Earth Orbit [1] . .7 2.3 Geostationary Orbit [1] . .8 2.4 Geost. Transfer Orbit [1] . .8 2.5 Sun Synchronous Orbit [1] . .8 2.6 First stage cost breakdown (a)) [2] and frequency of cause of failure of launch systems (b)) [3] . 12 2.7 Classification of space propulsion systems [3] . 13 2.8 Schematic of a thrust chamber assembly . 15 2.9 Engine cycles. From left to right: gas generator, staged combustion, expander [4] . 17 2.10 Isp as a function of pc for gas generator and staged combustion cycle 2 (Isp [m=s] = Isp [s] · g [m=s ]) [3] . 18 2.11 Number of accomplished missions of the Space Shuttle Main Engines [3] 20 2.12 Vacuum specific impulse as a function of the mixture ratio (pc=100bar, "=45) [5] . 22 2.13 Isp deviation of CEA engine data from data of real engines for shifting and frozen equilibrium with regression line (a)) as well as compari- son of Isp deviation with and without correction formula for shifting equilibrium (b)) . 26 2.14 Current specific impulse and arithmetic mean specific impulses con- sidering all past time steps (green) as well as only the latest and the first time step (orange) for the duration of the first stage engine burn 27 2.15 Serial vs. parallel staging [6] . 29 2.16 Serial staging configuration (mE = ms) [7] . 30 i 2.17 Falcon 9 trajectory [8] . 32 2.18 Schematic of the launch vehicle composition . 35 2.19 Cryogenic-cryogenic gas generator engine mass estimation [9] . 36 2.20 Cryogenic-storable gas generator engine mass estimation [9] . 36 2.21 Exemplary search space [10] . 43 2.22 Pseudocode and evolutionary cycle . 44 2.23 Tournament selection schematic [11] . 45 2.24 Uniform crossover schematic [12] . 46 2.25 Mutation schematic [12] . 47 5.1 Minimum GLOW evolution over 50 generations for various hyperpa- rameter combinations and population sizes . 62 6.1 GLOW comparison of the optimized GTO mission launch vehicles . 67 6.2 Structure comparison of the optimized launch vehicles . 68 6.3 Propulsion system comparison of the optimized launch vehicles . 70 6.4 Minimum acceleration and propulsion system mass comparison of the optimized launch vehicles . 73 6.5 GLOW comparison of the GTO and LEO mission launch vehicles . 74 6.6 Delta-v capability comparison of GTO and LEO launch vehicles with GTO payload as well as LEO and GTO launch vehicles with LEO payload . 76 6.7 GLOW comparison for a 12000 m/s and a 11500 m/s delta-v budget . 78 6.8 Landing propellant mass comparison and first stage structure + land- ing propellant mass comparison . 82 6.9 Delta-v budget sensitivity . 88 6.10 Specific impulse sensitivity . 89 6.11 Structural coefficient sensitivity . 90 6.12 Total structure mass breakdown and delta-v allocation comparison . 92 6.13 Length and GLOW breakdown comparison . 93 6.14 Expendable structure mass, GLOW and first stage delta-v comparison 94 ii A.1 Visible landing gear of Falcon 9 during landing maneuver [13] . 101 B.1 Comparison of the Isp of existing engines with calculated engines with and without correction formula . 103 D.1 Optimization program output - 5000 kg payload, 12000 m/s delta-v, LOX/LH2 . 107 D.2 Optimization program output - 5000 kg payload, 12000 m/s delta-v, LOX/RP-1 . 108 D.3 Optimization program output - 5000 kg payload, 12000 m/s delta-v, LOX/LCH4 . 109 D.4 Optimization program output - 15600 kg payload, 9500 m/s delta-v, LOX/LH2 . 110 D.5 Optimization program output - 15600 kg payload, 9500 m/s delta-v, LOX/RP-1 . 111 D.6 Optimization program output - 15600 kg payload, 9500 m/s delta-v, LOX/LCH4 . 112 D.7 Optimization program output - 7500 kg payload, 12000 m/s delta-v, LOX/LH2 . 113 D.8 Optimization program output - 7500 kg payload, 12000 m/s delta-v, LOX/RP-1 . 114 D.9 Optimization program output - 7500 kg payload, 12000 m/s delta-v, LOX/LCH4 . 115 D.10 Optimization program output - 7500 kg payload, 11500 m/s delta-v, LOX/LH2 . ..
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