MASTER'S THESIS Implementation of a Computational Fluid Dynamics Code for Propellant Sloshing Analysis Tiago Rebelo 2013 Master of Science (120 credits) Space Engineering - Space Master Luleå University of Technology Department of Computer Science, Electrical and Space Engineering CRANFIELD UNIVERSITY TIAGO ALEXANDRE RAMOS REBELO IMPLEMENTATION OF A COMPUTATIONAL FLUID DYNAMICS CODE FOR PROPELLANT SLOSHING ANALYSIS SCHOOL OF ENGINEERING MSc in Astronautics and Space Engineering (SpaceMaster) MSc Thesis Academic Year: 2012 - 2013 CRANFIELD UNIVERSITY SCHOOL OF ENGINEERING MSc in Astronautics and Space Engineering (SpaceMaster) MSc Thesis Academic Year 2012 - 2013 TIAGO ALEXANDRE RAMOS REBELO Implementation of a Computational Fluid Dynamics Code for Propellant Sloshing Analysis Supervisors: Ph.D. Jennifer Kingston M.Sc. Manuel Hahn August 2013 This thesis is submitted in partial fulfilment (45%) of the requirements for the degree of Master of Science in Astronautics and Space Engineering © Cranfield University 2013. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright owner. Implementation of a Computational Fluid Dynamics Code for Propellant Sloshing Analysis MSc Thesis Tiago Rebelo Supported by: Supervisors: M.Sc. Manuel Hahn - EADS Astrium Satellites Ph.D. Jennifer Kingston - Cranfield University Ph.D. Johnny Ejemalm - Lule˚aUniversity of Technology August 2013 i This M.Sc. thesis is dedicated to those whose work, sweat and tears allowed me to reach this point... ...to my beloved Parents ...to my inspiring Grandparents iii \S^etodo em cada coisa. P~oequanto ´es No m´ınimoque fazes." - Fernando Pessoa \Be everything in each thing. Put all of yourself Into the slightest thing you do." - Fernando Pessoa Abstract Liquid propellant sloshing inside spacecraft tanks is of crucial importance to the dynamics of the space vehicle. The interaction of the disturbance forces and torques, caused by the moving fuel, with the solid body and the control system, might lead to an increase in the AOCS actuators commands, which can degrade the vehicle's pointing performances and, in critical cases, generate unstable attitude and orbit control. Thus, it is of major importance to accurately predict the behaviour of liquid propellants sloshing inside spacecraft tanks. This M.Sc. thesis is focused on this topic, being its major objective the implementa- tion of a CFD software in an existing EADS Astrium simulation environment. The integrated simulation environment is used to assess the influence of liquid propellant sloshing for specific satellite missions. From a defined set of requirements an open source CFD software based on FEM is chosen - Elmer. The software is integrated and the final simulation environment is evaluated for sloshing purposes using three different sloshing test cases. The first two test cases deal with rectangular and cylindrical laterally excited tanks where comparators are available - the results of the tests are validated against nu- merical and experimental results. The final test case is defined to reduce the gap between the simple test cases per- formed to validate the software and the real sloshing problems faced in space vehicles. A typical liquid propellant tank is selected and real mission conditions are simulated. The liquid sloshing inside the laterally excited tank is deeply studied, being fully characterized. The simulation environment is validated for the implemented liquid sloshing problems. vi Acknowledgements To start with, I would like to express my deepest gratitude to my supervisor at EADS Astrium, Manuel Hahn. I am heartily thankful for the given opportunity, the guidance, the encouragement and the constant support. This gratitude is extended to the AOCS/GNC & Flight Dynamics department of Astrium Satellites, Friedrichshafen, Germany. Special gratitude goes to my supervisor at Cranfield University, Jennifer Kingston. Her support and help during the development of this work, but also during my stay in Cranfield, are not forgotten. At the Lule˚aUniversity of Technology my gratitude goes to Victoria Barabash, for her support in the many different challenges experienced during these 2 years. Also, for his supervision during the development of this thesis, my gratitude to Johnny Ejemalm. To Prof. Wolfgang A. Wall from the Institute for Computational Mechanics of the Technical University of Munich for allowing me to develop my work at his institute, my gratitude. Special acknowledgement goes to ESA's directorate of Human Spaceflight and Operations, for providing a real liquid propellant sloshing problem that brought challenge and value to this thesis. For his support and very useful inputs in all matters related with Elmer, my gratitude goes to D.Sc. Peter R˚aback from the CSC - IT Center for Science, Finland. My gratitude to all the entities that financially supported my M.Sc. studies, namely: ESA Human Spaceflight and Operations directorate, through a study Scholarship; Erasmus and Erasmus Mundus grants from Lule˚aUniversity of Technology and the SpaceMaster consortium; and last but not least the very important support of EADS Astrium during my internships. A special thanks goes to Anna Guerman, for giving me the opportunity to learn from her. Without her I would never have found the beauties of space nor integrated this Master's programme. For those who joined me in this incredible SpaceMaster journey, my deepest gratitude - it would not have been the same without them. Without any disregard to all the amazing people I met during these years abroad, my special gratitude goes to Mauro Aja Prado, Ishan Basyal and Dries Agten, for their true friendship. To my family, for their unconditional love and support throughout my life, my deepest love and gratitude. Special thanks to my parents, Jo~aoand Maria, for providing the conditions that allowed me to develop and aim higher; and to my sister Mara, for her support and belief at all moments. Finally, I want to thank Rita for her love throughout our common life. She gave me the courage and support to take this programme to its end. Without her I would never have made it, my unconditional love and gratitude goes to her. viii Contents Abstract ...................................... v Acknowledgements ............................... vii Contents ...................................... ix List of Figures .................................. xii List of Tables ................................... xviii List of Abbreviations .............................. xix 1 Introduction .................................. 1 1.1 Aim . .2 1.2 Objectives . .3 1.3 Outline . .3 2 Literature Review .............................. 5 2.1 Sloshing . .5 2.1.1 Lateral Sloshing . .6 2.1.2 Introduction to Damping . 11 2.1.3 Introduction to Non-linear Effects in Slosh . 12 2.1.4 Introduction to Micro-gravity Effects - Surface Tension . 13 2.1.5 Other Types of Sloshing . 14 2.2 Computational Fluid Dynamics . 14 2.2.1 Fluid Governing Equations . 15 2.2.2 Boundary Conditions . 17 2.2.3 Meshing . 17 2.2.4 Numerical Methods . 19 2.2.5 Numerical Analysis . 22 2.2.6 Solution Analysis . 24 2.3 Summary . 26 ix Contents 3 Requirements ................................. 28 3.1 Functional Requirements . 28 3.2 System Requirements . 29 4 CFD Software Selection .......................... 30 4.1 Selection Process . 30 4.1.1 Available Codes . 31 4.1.2 Satisfactory Codes . 31 4.1.3 Top 3 Codes . 31 4.1.4 Final Selection . 32 4.2 Results . 32 4.2.1 Available Codes . 32 4.2.2 Satisfactory Codes . 33 4.2.3 Top 3 Codes . 35 4.2.4 Final Selection . 35 5 Elmer - Open Source Finite Element Software ............ 38 5.1 Overview . 38 5.2 Models / Solvers . 41 5.3 Interfaces . 44 5.3.1 Graphical User Interface . 44 5.3.2 Command Line . 45 5.4 Pre- and Post- Processing . 47 5.4.1 Pre-Processing . 47 5.4.2 Post-Processing . 48 6 Simulation Environment Setup ...................... 49 6.1 Simulation Flow . 49 6.2 Pre-Processing Methods . 51 6.3 Post-Processing Methods . 51 7 Test case 1: Rectangular Tank ...................... 53 7.1 Test A . 54 7.1.1 Test Definition . 54 7.1.2 Implementation . 55 7.1.3 Results & Evaluation . 55 7.2 Test B . 60 7.2.1 Test Definition . 60 7.2.2 Implementation . 61 7.2.3 Results & Evaluation . 62 x Contents 7.3 Test C . 69 7.3.1 Test Definition . 69 7.3.2 Implementation . 70 7.3.3 Results & Evaluation . 73 8 Test case 2: Cylindrical Tank ....................... 78 8.1 Test Definition . 78 8.2 Implementation . 79 8.3 Results & Evaluation . 80 9 Test case 3: ESA Tank ........................... 84 9.1 Test A . 85 9.1.1 Test Definition . 85 9.1.2 Implementation . 86 9.1.3 Results & Evaluation . 88 9.2 Test B . 94 9.2.1 Test Definition . 94 9.2.2 Implementation . 95 9.2.3 Results & Evaluation . 95 9.3 Test C . 98 9.3.1 Test Definition . 98 9.3.2 Implementation . 99 9.3.3 Results & Evaluation . 99 10 Conclusions .................................. 106 11 Future Work ................................. 109 References ..................................... 110 A Test case 1 - Results: Test A ....................... 115 B Test case 1 - Results: Test C ....................... 122 C Test case 2 - Results ............................ 131 D Test case 3 - Results: Test A ....................... 135 E Test case 3 - Results: Test B ....................... 157 F Test case 3 - Results: Test C ....................... 160 xi List of Figures 2.1 Slosh wave shapes - first 2 antisymmetric x-modes for a rectangular tank . .8 2.2 Slosh wave shapes - first 2 symmetric x-modes for a rectangular tank8 2.3 Computational solution procedure process . 20 5.1 ElmerGUI main window . 44 5.2 ElmerPost main window & graphics window . 48 6.1 Software installation diagram . 50 6.2 Simulation flow . 50 6.3 Complete software installation diagram . 52 7.1 Rectangular tank - test A a): pressure at t = 0s ............ 56 7.2 Rectangular sloshing tank - test A a): free surface shape evolution . 57 7.3 Rectangular tank - test A a): CoG plots . 58 7.4 Rectangular tank - test A a): sloshing amplitude plot . 59 7.5 Rectangular tank - test B a): pressure at t = 0s ...........