Liquid Rocket Analysis (LiRA) Development of a Liquid Bi-Propellant Rocket Engine Design, Analysis and Optimization Tool R.R.L. Ernst supervisor: Ir. B.T.C Zandbergen AE5810 Master of Science Thesis Space Systems Engineering Liquid Rocket Analysis (LiRA) Development of a Liquid Bi-Propellant Rocket Engine Design, Analysis and Optimization Tool Master of Science Thesis AE5810 For the degree of Master of Science in Spaceflight at Delft University of Technology R.R.L. Ernst Student nr. 1539833 supervisor: Ir. B.T.C Zandbergen May 8, 2014 Faculty of Aerospace Engineering (AE) · Delft University of Technology Cover photo: Artist’s Impression of Copyright c R.R.L. Ernst an Ariane 5 ECA c ESA-D. Ducros All rights reserved. http://spaceinimages.esa.int/ Delft University of Technology Department of Space Systems Engineering (SSE) The undersigned hereby certify that they have read and recommend to the Faculty of Aerospace Engineering (AE) for acceptance a thesis entitled Liquid Rocket Analysis (LiRA): Development of a Liquid Bi-Propellant Rocket Engine Design, Analysis and Optimization Tool by R.R.L. Ernst in partial fulfillment of the requirements for the degree of Master of Science Dated: May 8, 2014 Chairman of thesis committee: Prof.dr. E.K.A. Gill Supervisor of thesis: Ir. B.T.C Zandbergen Member of thesis committee: Dr. A. Gangoli Rao Abstract The need to increase specific impulse of rocket launcher engines has lead design engineers to start development of ever more complex engine cycles starting from simple gas pressure fed engines to the very complex staged combustion cycle en- gines. Currently a wide range of different cycles does exist. These cycles not only differ in terms of performance, but also in terms of mass, cost, reliability etc., which in general makes it difficult to quickly determine which cycle is best suited for a certain mission or task. For this a tool that is capable of analysing different cy- cles and the impact of design choices has been developed. The tool, named LiRA, has as goal giving the user better system level understanding of the different pos- sible engine cycles and the functions of the components; it can therefore provide valuable and time saving assistance during design or in analysis and optimisation studies. A modular approach is applied where engine components are sized using a performance, dimension and mass model who make use of corrected ideal rocket theory and empirical relations. This work focuses mainly on the methodology and the construction of the models, and further includes the optimisation of an upper stage and a verification, validation and uncertainty and sensitivity analysis of the tool and the optimisation to assess its accuracy, precision and applicability. The completed program has proved to confirm known trends and known cycle character- istics like the mass savings that can be achieved when using turbo-pump fed engines instead of pressure fed engines for mid- to high-thrust booster applications. Further the superior performance of closed cycles, especially staged combustion cycles has been confirmed, and some cycle specific design choices like the need of bypasses in expander cycles have been explained. The tool however is not complete and should be expanded; the addition of a cost and reliability assessment model is for example strongly recommended. There also remain issues with the accuracy and uncertainty of certain estimates which make that the current version should only be used for comparative studies. Master of Science Thesis R.R.L. Ernst ii R.R.L. Ernst Master of Science Thesis Table of Contents Acknowledgements vii Glossary ix List of Acronyms..................................... ix List of Symbols..................................... x 1 Introduction 1 2 Literature Study and State of the Art Review5 2-1 Liquid Rocket Engine Cycle Theory........................... 5 2-2 Software Development and Existing Models with Similar Purpose........... 11 2-3 Conclusions on User Requirements and Plan of Approach............... 13 3 Performance Model 17 3-1 Substance Property and Combustion Thermodynamic Data Tables.......... 17 3-2 Thrust Chamber..................................... 20 3-2-1 Main Combustion Chamber and Nozzle.................... 21 3-2-2 Injector..................................... 28 3-3 Heat Exchanger..................................... 31 3-3-1 Enthalpy and Determination of State...................... 33 3-3-2 Heat Transfer.................................. 35 3-3-3 Cooling Channel Geometry, Pressure Loss and Wall Material......... 37 3-3-4 Impact of Number of Segments on Cooling Mechanism............ 38 3-4 Gas Generator or Pre-burner.............................. 38 3-5 Pump.......................................... 42 3-6 Turbine.......................................... 43 Master of Science Thesis R.R.L. Ernst iv Table of Contents 3-6-1 Turbine Power and Required Mass Flow.................... 44 3-6-2 Turbine Efficiency................................ 45 3-6-3 Turbine Pressure Ratio............................. 45 3-6-4 Turbine Functioning within Cycle........................ 46 3-6-5 Turbine Inlet Temperature........................... 46 3-7 Propellant Tanks.................................... 47 3-8 Pressurant Tank..................................... 48 3-9 Feed Lines........................................ 49 3-10 Additional Performance Parameters Calculated..................... 51 3-11 Validity of Performance Model............................. 52 4 Mass and Size Model 55 4-1 Size Model........................................ 55 4-1-1 Overall Engine Size............................... 55 4-1-2 Propellant and Propellant Tank Volume.................... 56 4-1-3 Pressurant and Pressurant Tank Volume.................... 57 4-1-4 Nozzle...................................... 59 4-1-5 Combustion Chamber.............................. 61 4-1-6 Gas Generator or Pre-burner.......................... 61 4-1-7 Turbo-pump................................... 62 4-2 Mass Model....................................... 62 4-2-1 Overall Engine Mass............................... 64 4-2-2 Propellant Tank and Pressurant Tank Mass.................. 64 4-2-3 Stage Dry Mass................................. 65 4-2-4 Propellant Mass................................. 66 4-2-5 Pressurant Mass................................. 66 4-2-6 Thrust Chamber................................. 66 4-2-7 Gas Generator or Pre-burner.......................... 67 4-2-8 Turbo-Pump................................... 68 4-3 Validity of Mass and Size Model............................ 69 5 Program Set-up 71 5-1 Engine Analysis Calculation Order........................... 71 5-2 Model Parameters.................................... 72 5-3 Overview of Typical, Calculated and Assumed Parameter Values Used in LiRA.... 74 5-4 Overview Components.................................. 74 5-5 Model Output...................................... 77 5-6 Balancing of Propulsion System............................. 78 5-6-1 Thrust Chamber Assembly Calculation Routine................ 78 5-6-2 Balancing of the Feed System in the Presure-fed Cycle............ 78 R.R.L. Ernst Master of Science Thesis Table of Contents v 5-6-3 Balancing of the Feed System in the Gas Generator Cycle........... 80 5-6-4 Balancing of the Feed System in the Staged Combustion Cycle........ 80 5-6-5 Balancing of the Closed Expander Cycle.................... 81 5-6-6 Balancing of the Feed System in the Bleed Expander Cycle.......... 81 5-7 Overview Developed Code................................ 82 5-8 Large Figures and Tables................................ 82 6 Important General Statistical Analysis Theory Used for Verification, Validation and Sensitivity Analysis 95 6-1 Verification and Validation............................... 96 6-2 Sensitivity Analysis................................... 97 6-3 Data Interpretation and Acceptance.......................... 97 6-4 Repeatability or reproducibility............................. 98 6-5 Large Figures and Tables................................ 98 7 Verification and Validation of LiRA 101 7-1 Verification........................................ 102 7-1-1 Checking of Model Code on Errors by Comparison of Results with Hand Calculations................................... 102 7-1-2 Tool Build-up Structure, Operation, Input and Output Comparison with Other Similar Software................................. 103 7-1-3 Comparison of test cases with other models.................. 103 7-2 Validation........................................ 111 7-3 Conclusions on Verification and Validation....................... 111 7-4 Large Figures and Tables................................ 113 8 Optimisation with LiRA 123 8-1 Optimisation Rationale................................. 124 8-2 Optimisation Methods.................................. 124 8-3 Optimisation Routine.................................. 125 8-4 Precision and Reproducibility of Results and Impact of Allowed Tolerance in Require- ments and Number of Samples Used on the Outcome................. 127 8-5 Example Optimisation of an Upper Stage....................... 128 8-5-1 Requirements and Constraints......................... 128 8-5-2 Results for a Stage with a Gas Generator Cycle................ 129 8-5-3 Results for Other Cycles............................. 134 8-5-4 Discussion of Results for All Cycles....................... 134 8-6 Validity of Optimisation................................. 138 8-7 Large Figures and Tables................................ 138 Master of Science