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Optimization of Solid Rocket Grain Geometries Deutsches Zentrum Kungliga Tekniska für Luft- und Högskolan Raumfahrt e.V. XR-EE-SPP 2012:002 M. Johannsson Optimization of Solid Rocket Grain Geometries This report contains: 58 pages including 32 Figures 12 Tables 36 References Deutsches Zentrum für Luft- und Raumfahrt e.V. Institut für Raumfahrtsysteme Systemanalyse Raumtransport (SART) 28359 Bremen Master Thesis Report Submitted to Royal Institute of Technology (KTH) in partial fulfilment of the requirements for the degree: Master of Science in Aerospace Engineering Supervised by: Etienne Dumont Nickolay Ivchenko Abstract Solid Rocket Motors (SRMs) are employed in many space launch applications from the booster rockets on the now retired Space Shuttle to the new European launch vehicle Vega. Preliminary design of these complex three dimensional SRMs, given certain requirements and limitations can be considered as an optimization process where a best geometrical solution is sought resulting in a desirable thrust profile. In this project, a derivate free direct search package titled NOMAD is employed together with the internally developed numerical burnback analysis tool SRP-GEO and ballistic solver SRP. An analytical model for the burnback analysis tool is also developed to take advantage of the support for surrogate functions within NOMAD. Due to the local nature of the optimizer, the results for complex geometries are shown to converge toward configurations different from the globally optimal geometries. Yet in most instances, the resulting calculated thrust profiles are shown to correlate well with the desired counterpart. This highlights the importance of carefully chosen initial values and boundaries while also emphasize the many possible solutions to a single problem. Keywords: SRP, Solid rocket motor, grain geometry, derivative free optimization, internal ballistics, NOMAD, solid rocket propellant, numerical burnback analysis, analytical burnback analysis, thrust history Acknowledgement This is a master thesis project performed in DLR Bremen within the SART division during 2011-2012. During the course, I have acquired much knowledge in the field of preliminary design of Solid Rocket Motors and gained a firm understanding in many other related topics in rocket design. I have also acquired skills in software design and general optimization theory which are of use in all areas of engineering. Even though the project required slightly more time than expected, it can be considered a success. Following, I would like to show my appreciation to a few colleagues and friends. I would like to express my deepest gratitude and respect to my DLR supervisor, Etienne Dumont for supporting me during the course of seven months while performing this thesis. Without his guidance and clever insights in all areas of the work, this thesis would not have been possible. I would also like to express my sincere appreciation to my supervisor in KTH Sweden, Nickolay Ivchenko for the insights and comments given of the final report. I would further like to thank Aaron Koch for the help in solving pesky integration issues between Fortran and C++ during late evenings. I would likewise like to thank the whole SART group and Martin Sippel for providing me support and the uplifting spirit necessary for me to finish this thesis. Lastly, I would like to give a special nod to the Awesome Study Group (ASG) of October 2011 - Mars 2012 for being awesome. SART TN-002/2012 i Table of Contents List of Figures iii List of Tables iv Nomenclature v Abbreviations vii 1 INTRODUCTION 1 1.1 Methodology 1 1.2 Scope 3 1.3 Contents 4 2 SOLID ROCKET MOTOR FUNDAMENTALS 5 2.1 Motor Components 5 2.1.1 Casing 5 2.1.2 Nozzle 5 2.1.3 Igniter 6 2.1.4 Insulation 6 2.1.5 Grain 7 2.2 Internal Ballistics 7 2.2.1 Specific Impulse and Losses 8 2.2.2 Burning Rate 9 2.2.3 Area Ratios 9 2.2.4 Thrust and Chamber Pressure 10 3 DIRECT SEARCH OPTIMIZATION ALGORITHM 11 3.1 NOMAD Overview 11 3.2 NOMAD Operation and Features 11 3.2.1 MADS Algorithm 11 3.2.2 Constraint Handling 12 3.2.3 Surrogate Functions 12 3.2.4 Variable Neighborhood and Speculative Search 13 3.2.5 Parallelis m 13 3.2.6 Additional Functionalities 14 4 GEOMETRY OPTIMIZATION PROGRAM 15 4.1 Pre-Processing 15 4.1.1 Input File and Propulsion Database 15 4.1.2 Initial Geometry Selection and Database 17 4.1.3 Geometry Modification 18 4.1.3.1 Dome Structures 18 4.1.3.2 Ignition System and Submerged Nozzle Assembly 20 4.1.3.3 Dome Grain Geometries 21 4.1.4 Constraint, Boundary and Initial Values 22 4.1.5 Miscellaneous 23 4.2 Optimization 24 SART TN-002/2012 ii 4.2.1 NOMAD Implementation 24 4.3 Blackbox 25 4.3.1 Burnback Analyses 25 4.3.1.1 Analytical Radial Burn Analysis 25 4.3.1.2 Analytical Axial Burn Analysis 28 4.3.1.3 Volume Calculations and Post Processing 29 4.3.2 Thrust Computation 29 4.3.3 Objective Value Determination 30 4.4 Post Processing 31 5 TESTING AND VALIDATION 32 5.1 Validation of Analytical Burnback Algorithm 32 5.1.1 Simple Cylindrical Tube 32 5.1.2 Simple Star 33 5.1.3 Complex Grain 34 5.1.4 Constraint Violation Analysis 34 5.2 Testing and Validation of Optimization Algorithm 35 5.2.1 Cylindrical Tube 35 5.2.2 Star 37 5.2.3 Three Segment Combination 39 5.2.4 P80 FW Derivative 40 5.3 Convergence Analysis 42 6 CONCLUSION 44 6.1 Future Work 44 REFERENCES 46 APPENDIX A 48 Main Input File 48 Propellant Database 50 SRP Input File 51 APPENDIX B 52 Derivation of Dome Equations 52 Length of Nose Dome 52 Nose Dome Outer Radius 52 Derivation of Modified Analytical Star Equations 53 Phase One 53 Phase Two 55 Phase Three 58 SART TN-002/2012 iii List of Figures Figure 1: Current and desired design process of a typical solid rocket motor in SART ................................. 2 Figure 2: Basic structure of the optimization process ................................................................................. 3 Figure 3: Components of a typical SRM ................................................................................................... 6 Figure 4: Classification of grain according to thrust-time characteristics ...................................................... 7 Figure 5 Thrust/Pressure – time curve definitions ...................................................................................... 8 Figure 6: Mesh configurations in MADS algorithm with ....................................................................12 Figure 7: SRP-GEOPT component structure and interaction chart ............................................................16 Figure 8: SRP-GEOPT geometry parameter definitions with three segment example .................................17 Figure 9: P80 FW first stage solid booster with hemispherical nose dome .................................................18 Figure 10: and variation with meters ..................................................................................19 Figure 11: variation with meters ..............................................................................................20 Figure 12: Ignition system and submerged nozzle assembly .....................................................................21 Figure 13: Various modifications to nose dome grain geometry based on the first main segment. ...............22 Figure 14: Validity range of SRP-ANLYT constraints ................................................................................24 Figure 15: Truncated star geometry and phase definition..........................................................................26 Figure 16: Examples of axial segment burning evolutions based on neighboring inner radii ........................28 Figure 17: Comparision of burnback results for single cylinder grain ..........................................................32 Figure 18: Comparision of burnback results for single star grain ................................................................33 Figure 19: Comparision of burnback results for complex grain ..................................................................34 Figure 20: Comparision of burnback results for constraint violated star grain .............................................35 Figure 21: Desired and optimized thrust for single cylinder grain ...............................................................36 Figure 22: Desired and optimized thrust for single cylinder grain with advanced input configuration .............37 Figure 23: Desired and optimized thrust for single star grain .....................................................................38 Figure 24: Desired and optimized thrust for single star grain with advanced input configuration ...................39 Figure 25: Desired and optimized thrust for three segment grain ...............................................................40 Figure 26: Desired and optimized thrust for an SRM derived from P80 FW ................................................41 Figure 27: Desired and optimized thrust for single cylinder grain with VNS strategy ....................................42 Figure 28: Nose cone geometry parameter definitions ..............................................................................52 Figure 29: Phase One truncated star geometry breakdown .......................................................................54 Figure 30: Phase One to Phase Two switching criteria .............................................................................54 Figure 31: Phase Two truncated star analytical denotations ......................................................................55 Figure 32: Phase Three truncated
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