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Development of a Modeling Framework of the Feeding System for the Characterization of Pogo Oscillations

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Development of a Modeling Framework of the Feeding System for the Characterization of Pogo Oscillations UNIVERSITA’ DEGLI STUDI DI PISA Master Thesis in Space Engineering DEVELOPMENT OF A MODELING FRAMEWORK OF THE FEEDING SYSTEM FOR THE CHARACTERIZATION OF POGO OSCILLATIONS Candidate Mario Amoroso Supervisor Dott. Ing. Angelo Pasini Academic Year 2016-2017 Abstract This thesis has been carried out within the framework of the MIT-UNIPI Project funded by MISTI Global Seed Funds and entitled “Dynamic Characterization of POGO Instabilities in Cavitating Turbopumps”, which provides a collaboration between the Massachusetts Institute of Technology and the University of Pisa, aiming to jointly develop a novel theoretical foundation capable of characterizing the dynamics of POGO oscillations and devising new design guidelines. The first section of this thesis deals with a literature review of the past POGO experiences of NASA human spaceflights and a collection of some procedures used to obtain a prediction of the dynamic performances of space rocket turbopumps. In the second part, a modeling framework defined in the time-domain has been developed to characterize the steady-state and dynamic behaviour of each component of a typical feeding system for liquid rocket engines. A typical water loop for experimental characterization of liquid rocket turbopumps has been modeled according to the modeling framework in order to understand the best way to perform forced experiments for the characterization of the transfer matrix of cavitating turbopumps necessary for understanding the POGO instability phenomena that affect rocket launchers. The best results in terms of capability of generating mass flow rate and pressure oscillations at the inlet of the inducer, have been obtained by means of a device that produces a volume oscillation located downstream of the pump. 1 Contents 1 Detailed Review of the POGO Instability ........................................................................... 7 1.1 Introduction ................................................................................................................................... 7 1.2 POGO Instabilities Episodes in NASA Human Spaceflight Vehicles .......................................... 8 1.2.1 Gemini – Titan II Experience ................................................................................................ 8 1.2.2 Apollo – Saturn V Experience ............................................................................................ 10 1.2.3 1970 POGO State of the Art ............................................................................................... 15 1.2.4 Space Shuttle Experience .................................................................................................... 17 1.2.5 Recent Challenges ............................................................................................................... 18 2 Characterization of the Dynamic Transfer Matrix of Space Rocket Turbopumps ............ 21 2.1 Introduction ................................................................................................................................. 21 2.2 The Dynamic Transfer Matrix of a Cavitating Pump ................................................................. 21 2.3 Analytical and Experimental Turbopump Matrix Characterization ............................................ 22 3 Mathematical Model of the System ................................................................................... 40 3.1 Introduction ................................................................................................................................. 40 3.2 Development of the Dynamic Equations for the Subsystems ..................................................... 41 3.2.1 Incompressible Duct: Straight (ID-S), Elbow (ID-E) and Tapered (ID-T) ......................... 42 3.2.2 Compressible Duct Straight (CD-S).................................................................................... 42 3.2.3 Silent Throttle Valve (STV) – Exciter ................................................................................ 43 3.2.4 Volume Oscillator Valve (VOV) – Exciter ......................................................................... 44 3.2.5 Tank (T) – Exciter ............................................................................................................... 45 3.2.6 Pump (P) ............................................................................................................................. 46 4 System Design Tools ......................................................................................................... 48 4.1 Introduction ................................................................................................................................. 48 4.2 Incompressible VS Compressible Solution ................................................................................. 48 4.2.1 Downstream Mass Flow Rate and Pressure Signal Comparison ........................................ 48 4.2.2 Conclusions and Results ..................................................................................................... 73 4.2.3 Duct Transfer Matrix Comparison ...................................................................................... 73 4.2.4 Conclusions and Results ..................................................................................................... 77 4.3 Hydraulic Loop System Design, Semi-Compressible Approach ................................................ 77 4.3.1 Conclusions and Results ..................................................................................................... 84 5 Conclusions and Future Developments ............................................................................. 85 6 Appendixes ........................................................................................................................ 86 6.1 Appendix A, Mathematical Model Equations ............................................................................. 86 6.1.1 Introduction ......................................................................................................................... 86 2 6.1.2 Subsystems Mathematical Model ....................................................................................... 86 6.1.3 Incompressible Duct (ID) .................................................................................................... 87 6.1.4 Compressible Duct Straight (CD-S).................................................................................... 93 6.1.5 Silent Throttle Valve (STV) .............................................................................................. 100 6.1.6 Volume Oscillator Valve (VOV) – Exciter ....................................................................... 104 6.1.7 Tank (T) – Exciter ............................................................................................................. 105 6.1.8 Pump (P) ........................................................................................................................... 109 6.2 Appendix B, Matlab Code ........................................................................................................ 113 6.2.1 Introduction ....................................................................................................................... 113 6.2.2 Steady-State System Parameters ....................................................................................... 113 6.2.3 Dynamic System Parameters ............................................................................................ 115 6.3 Appendix C, Simulink Modeling of the Hydraulic Loop ......................................................... 118 6.3.1 Introduction ....................................................................................................................... 118 6.3.2 Simulink Environment ...................................................................................................... 118 6.4 Appendix D, Simulink Modeling for the Comparison of the Incompressible Solution with the Compressible Solution .......................................................................................................................... 127 6.4.1 Downstream Mass Flow Rate and Pressure Signal Comparison Circuit .......................... 127 6.4.2 Duct Transfer Matrix Comparison Circuit ........................................................................ 128 6.5 Appendix E, Table of Figures ................................................................................................... 130 6.6 Appendix F, List of Tables ....................................................................................................... 136 3 Introduction The subsequent work aims to: 1. Present a review of the POGO instability episodes occurred in the past and collect the analytical and experimental procedures exploited worldwide to study the behavior of the pump withstanding unsteady conditions and to prevent the occurring of unstable phenomena; 2. Develop a mathematical model able to predict the steady and unsteady-state of the subsystems operating within the hydraulic context of the pump; 3. Develop some tools useful to drive the design of an experimental apparatus, pointing out whether to exploit the simplified incompressible assumption of the working fluid and, in case, provide a solution able to take into account the compressibility effects. 4 Nomenclature A Cross-section area, m2. a , a0 Unperturbed acoustic velocity, m/s. a Unsteady acoustic velocity,
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