Design and Thermal Analysis of a Solar Thermal Thruster
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Design and Thermal Analysis of a Solar Thermal Thruster Krishti Das Technische Universiteit Delft Design and Thermal Analysis of a Solar Thermal Thruster by Krishti Das in partial fulfillment of the requirements for the degree of Master of Science in Aerospace Engineering at the Delft University of Technology, to be defended publicly on Wednesday 28th of November, 2018 at 9:00 AM Student number: 4624408 Supervisor: Dr. Angelo Cervone Daily Supervisor : Fiona Leverone Thesis committee: Prof. dr. E.K.A Gill, TU Delft Dr. Angelo Cervone, TU Delft Fiona Leverone, TU Delft Dr. M.J Heiligers, TU Delft An electronic version of this thesis is available at http://repository.tudelft.nl/. Acknowledgement I would like to start with expressing my deepest gratitude and regard to Dr. Angelo Cervone for his constant guidance, support and answering my silly doubts throughout. At this point, I am genuinely grateful to have had Fiona Leverone as my daily supervisor. She not only supervised me during my thesis and encouraged me to work better but she has helped me become a better researcher. Though I have a long way to go, I have been really fortunate to study at TU Delft and working with professors and students of great caliber. Last but not least, I would like to thank my mom, dad, and sister who have been my backbone throughout from the other side of the world. I am extremely grateful for the friends I have made during my studies and I would thank Maria, Shreyas, and Amantrita. Their unconditional help and support in my life and studies, in general, has been remarkable. I am also deeply grateful to Stanislaus and Jayraj for their critical and supportive feedback on my work. Finally, I owe it to the boys in the MSc student room, especially Mathijs Van de Poel and Sean Pepper, and to our countless late night conversations about space news and sharing ideas with each other. I would also like to thank Samiksha for her constant encouragement and tea breaks. iii Contents Acknowledgement . vii Nomenclature x Glossary xi List of Figures xiii List of Tables xvii 1 Introduction 1 2 Research Framework 3 2.1 Literature Study . 3 2.2 Existing STP Engine Concepts and Designs . 4 2.3 Preliminary Mission Analysis . 8 2.4 System Requirements . 9 2.5 Research Question, Aims, and Objectives . 10 2.5.1 Research Objective . 10 2.5.2 Research Question . 11 2.6 Design Methodology . 12 3 Conceptual Designs 15 3.1 Design Option Tree . 15 3.1.1 Concentrator - Receiver Interface . 15 3.1.2 Heating Method . 17 3.1.3 Cavity Shape . 18 3.1.4 Nozzle Shape. 19 3.2 Conceptual Designs. 19 3.2.1 Heat Exchanger Concept 1. 20 3.2.2 Heat Exchanger Concept 2. 20 3.2.3 Heat Exchanger Concept 3. 21 3.3 Concept Trade-off . 23 3.3.1 Trade-off Criteria . 23 3.3.2 Preliminary Channel Length. 24 3.3.3 Graphical Trade-off . 26 4 Baseline Design 29 4.1 Micro-nozzle Design . 29 4.1.1 Rocket Propulsion Fundamentals . 30 4.1.2 Actual Performance . 33 4.1.3 Effect of Nozzle Geometry on Nozzle Efficiency . 36 4.1.4 Thruster Performance at High Chamber Temperatures . 38 v vi Contents 4.2 Materials. 39 4.3 Heat Exchanger . 41 4.3.1 Flow Regime in Rectangular Micro-channel . 42 4.3.2 Pressure Loss in Rectangular Micro-channels . 43 4.3.3 Channel Wall Thickness . 45 4.3.4 Cavity Dimensioning. 46 4.4 Optical Fiber Cable . 46 4.5 Transmission Efficiency and Attenuation. 47 4.5.1 Optical Fiber Efficiency . 47 4.5.2 Sources of Attenuation . 48 4.6 Optical Fiber Candidates . 52 4.7 Concentrator Design . 53 4.7.1 Mass Estimation and Material . 55 4.7.2 Concentrator - Optical Fiber Requirement. 57 4.7.3 Bundled and Single Optical Fibers . 58 4.8 Initial Design . 62 5 Thermal Modelling 65 5.1 Geometrical Mathematical Model . 66 5.2 Heat Loss Model . 67 5.2.1 Input Thermal Power . 67 5.2.2 Case I: Without Insulation . 67 5.2.3 Case II: With Insulation. 70 5.2.4 Power Lost to Propellant Flow . 71 5.3 Thermal Study of the Optical System . 71 5.3.1 Heat Loss in Optical Fiber . 72 5.3.2 Optical Fiber Power Transmission . 73 5.4 Time Dependent Model . 74 5.5 Flow and Channel Wall Temperature Model . 75 6 Final Design and Results 81 6.1 Heat Exchanger . 82 6.1.1 Ray Tracing Model . 82 6.1.2 Ray Optics Modelling in COMSOL . 85 6.1.3 Conjugate Heat Transfer Model. 89 6.2 Fibre Optic-Receiver Coupling . 94 6.2.1 Optical Fiber Temperature due to Hot Cavity . 94 6.2.2 Fibre Optic-Receiver Coupling Concepts . 96 6.3 Verification of the Analytical model . 103 6.4 Thrust Performance. 103 6.5 Final Design Render . 104 6.6 System Requirements Verification . 108 7 Conclusions and Recommendations 111 Appendices 115 A Optical Fiber Specifications Sheet 117 B Advanced Ceramics Property Sheet 119 C Nusselt Number of Three Side Heated Walls 121 D Verification of Analytical and Comsol Model 123 Contents vii Bibliography 125 Nomenclature 훼 Absorption coefficient of the cavity material Δ푉 Velocity change ̇푚 Mass flow rate 휖 Emissivity of a surface 휂 Receiver efficiency Γ Vandenkerckhove constant 훾 Specific heat ratio 휇 Dynamic viscosity at a propellant temperature 휙 Solar flux at LEO 휌 Reflectivity Factor 퐴/퐴 Cavity opening area to internal area Ratio 퐴 Nozzle exit area 퐴/퐴 Expansion ratio 퐴, 퐴 Throat area of the nozzle 퐵 Gebhart Factor 퐶 Concentration ratio 퐶 Conductive Coupling 퐷 Throat diameter of the nozzle 푒 Cavity internal surface emissivity 푒 Cavity external surface emissivity 퐹 Thrust 퐹 View Factor 푔 Gravitational Acceleration 퐼 Specific Impulse 푘 Thermal Conductivity 푀 Propellant Mass 푀 Satellite Wet Mass ix x Contents 푃 Power collected 푃 Chamber pressure 푃/푃 Pressure ratio 푃 Power collected by Concentrator 푄 Incoming solar energy 푄 Heat flow to the propellant 푄 Hear lost through re-radiation 푄 Heat lost from the cavity external surface 푄 Heat lost by reflection 푄 Solar radiation absorbed by the absorber cavity 푅 Specific gas constant 푅 Radiative Coupling 푅푒 Reynolds number at nozzle throat 푆 Cross-sectional area of the concentrator 푇 Temperature 푇 Internal surface temperature of cavity 푇 Chamber temperature 푇 External surface temperature of cavity Glossary AFRPL Air Force Rocket Propulsion Laboratory. 4 CSF Conduction Shape Factor. 69 LEO Low Earth Orbit. 1 LUMIO Lunar Meteoroid Impact Observer. 9 MEMS Micro-Electro-Mechanical-Systems. 2 OH Hydroxyl Ion. 52 OW Optical Wave. xiii, xvii, 15, 17 STP Solar Thermal Propulsion. 2 STS Space Transportation System. 5 xi List of Figures 2.1 Solar thermal propulsion mechanism ........................... 3 2.2 Performance of solar thermal propulsion systems vs chemical, electric, and nuclear thermal propulsion options ................................ 4 2.3 Conceptual design of a solar thermal propulsion system ................ 5 2.4 Single crystal molybdenum solar thermal thruster sketch ................ 6 2.5 Mk.I thruster design ................................... 7 2.6 Final RAC design with nozzle ............................... 7 2.7 STP engine concept for PocketQubes ........................... 8 2.8 Design methodology .................................... 13 3.2 Left: Schematic of conventional solar thermal propulsion [1]; Right: Optical wave (OW) guide solar thermal propulsion system with integrated optical wave guide ACS [2] 15 3.1 Design option tree ..................................... 16 3.3 Net irradiance distributions on corrugated and flat samples [3] ............. 19 3.4 Concept 1 - trapezoidal cavity and serpentine channels ................. 20 3.5 Concept 2 - rectangular corrugated cavity and rectangular channels .......... 21 3.6 Platelet heat exchanger .................................. 22 3.7 Concept 3 - platelet heat exchanger ........................... 22 3.8 Graphical trade-off between conceptual designs ..................... 27 4.1 Conical nozzle configuration ............................... 30 4.2 Effect of divergence angle on thrust efficiency ...................... 38 4.3 The insulation thickness vs temperature for Pyrogel ................... 40 4.4 Total internal reflection phenomena in an optical fiber ................. 47 4.5 Thermal power flow through the Heat Exchanger Receiver Cavity system without insulation .......................................... 49 4.6 Projection of rays into a rectangular closed cavity through bending in optical fibers . 50 4.7 Attenuation due to microbends [4] ............................ 50 4.8 Power output in optical fibers of different numerical apertures with varying core diameter 55 4.9 Inflatable Concentrator using torus and tripod tube as support structure [5] ..... 56 4.10 Possible configuration of single optical fiber system ................... 59 4.11 Bundled optical fibers ................................... 60 4.12 A possible configuration of bundled optical fiber system ................ 60 4.13 Optical system mass for single and bundled fiber system ................ 61 4.14 Trade-off matrix for optical system concept ....................... 62 4.15 Baseline design ...................................... 63 5.1 Structure of the thermal model for flow and channel wall temperature ........ 65 5.2 Thermal power flow through the Heat Exchanger Receiver Cavity system without insulation .......................................... 66 5.3 Schematic diagram of enclosed cavity and outer geometry with effective gap (thick- ness) for conduction .................................... 69 5.4 Total power output vs. No. of optical fibers plot ..................... 73 xiii xiv List of Figures 5.5 Cavity wall temperature with increasing no. of optical fibers .............. 75 5.6 Effect of channel height on the final flow temperature ................. 76 5.7 Effect of channel aspect ratio on the final flow temperature .............. 77 5.8 Determining the required (minimum) channel length to reach a flow temperature of 1000 K ........................................... 78 5.9 Pressure drop in the channels with respect to aspect ratio for a constant channel length of 4.023 cm .................................... 79 5.10 Baseline design dimensions: front view ........................