LEADING POINTS CONCEPTS IN TURBULENT PREMIXED COMBUSTION MODELING A Dissertation Presented to The Academic Faculty by Alberto Amato In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Mechanical Engineering Georgia Institute of Technology August 2014 Copyright 2014 by Alberto Amato LEADING POINTS CONCEPTS IN TURBULENT PREMIXED COMBUSTION MODELING Approved by: Dr. Tim Lieuwen, Advisor Dr. Yuri Bakhtin School of Aerospace Engineering School of Mathematics Georgia Institute of Technology Georgia Institute of Technology Dr. Jerry Seitzman Dr. P. K. Yeung School of Aerospace Engineering School of Aerospace Engineering Georgia Institute of Technology Georgia Institute of Technology Dr. Caroline Genzale School of Mechanical Engineering Georgia Institute of Technology Date Approved: May 8, 2014 To my parents Carlo and Teresa iii ACKNOWLEDGEMENTS “[The discovery of the Higgs boson] certainly shows to us the value of just imagining… and try to follow the leads that you get from simple ideas… that is worthwhile doing this and see where you come out.” Gerald Guralnik, co-discoverer of the Higgs boson July 4, 2012, www.youtube.com/cerntv This thesis would be incomplete without mentioning several people who assisted, supported and encouraged me during the course of my study. First and foremost, I would like to thank my advisor, Prof. Tim Lieuwen, for his guidance and continuous support during the long and challenging years spent at Georgia Tech. I am neither the first nor I will be the last person to acknowledge Tim’s leadership: he truly has inspired our group to be better thinkers and persons. In a similar vein, I would like to thank Prof. Jerry Seitzman for many insightful comments on my work. His lucid mind and scientific curiosity are infectious and constantly challenge us students to be and do our best. I am also profoundly indebted to Dr. Marcus Day for providing me with many of the data utilized in this thesis and for patiently explaining the many subtleties involved in their analysis. Likewise, I am very appreciative of all the assistance that Prof. Yuri Bakhtin provided to help me understand many mathematical details of this thesis. I would also like to express my gratitude to my committee members, Prof. Caroline Genzale and Prof. P.K. Yeung, for agreeing to serve on my committee in spite of their extremely busy schedules, and for offering constructive and valuable critiques regarding my research work. The Ben T. Zinn Combustion Laboratory provided me with the perferct home during all the years of my doctorate. Andrew Marshall and Prabhakar Venkateswaran, with the late iv addition of Julia Lundrigan, were my companions in this research project. I shared with them many highs and lows, so frequent in turbulent combustion research, and this work would not have been possible without their help. I am very grateful to Vishal Acharya, Dong-Hyuk Shin, Shreekrishna and Jack Crawford for helping me understand many aspects of combustion theory and numerical computations. I will always cherish the memory of the time spend shoulder to shoulder in our office with also Jordan Blimbaum. Our “legacy” is in good hands with Nick Magina and Luke Humprey. The “experimentalists” (in no particular order) Jacqueline O’Connor (“Lab-mom”), Chris Foley, Ben Emerson, Ben Wilde, Bobby Noble, Brandon Sforzo, Ianko Chterev, Mike Aguilar, Michael Malanoski, Ryan Sullivan, Sai Kumar, Yash Kochar, Benjamin Knox and Gina Magnotti, were always kind to me and a true source of inspiration. Here I would also like to acknowledge the many “slivers” of Italy that I befriended in Atlanta and helped me miss less my home. In August 2008 I arrived in the United States with Daniele Bertolotti and Paolo Manenti; for the first few months, before they moved back to Italy, they were my roomates and travelmates, without them I would have not enjoyed as much this experience. Matteo Senesi and Luca Airoldi shared with me the choice of staying longer in the US to pursue a PhD. Our summer trip to Savannah with Alice Sacchetti and Andrea Trimarco will always remain one of my funniest memories. Martina Baroncelli shared with me one year of life at the Combustion Lab. When she arrived at the lab from Florence, I immediately started to appreciate the pleasure of hearing a familiar “buongiorno” in a Tuscan accent first thing in the morning. Finally, I would like to thank my family for its unfailing support during these years. To my parents Carlo and Teresa goes all my affection. My uncle Roberto with his wife Sara v and their children Antonio and Elisagiulia never failed to cheer me up with their Skype phonecall. My cousins Pierluigi and Silvia with my grandmother Elisabetta, my uncle Guido and aunts Manuela and Giovanna were always the first people that I wanted to see when traveling home for Christmas and have been always a source of strength for me. Unfortunately, my uncle Davide passed away at a very young age while I was in the middle of my graduate studies. He had been enthusiastic and encouraging about my studies since day one. To him goes my deepest graditude. vi TABLE OF CONTENTS Acknowledgements .......................................................................................................... iii List of Tables .....................................................................................................................ix List of Figures ..................................................................................................................... x Symbols and Abbreviations ......................................................................................... xxii Summary ......................................................................................................................... xxv CHAPTER 1: Introduction ............................................................................................... 1 1.1 Motivation ............................................................................................................... 1 1.2 Molecular transport effects on turbulent premixed flame propagation and structure: experimental evidence ........................................................................... 4 1.3 Scope and organization of the thesis....................................................................... 9 CHAPTER 2: Background.............................................................................................. 11 2.1 Preferential diffusion and Lewis number effects .................................................. 11 2.1.1 Flame speed definitions ............................................................................... 19 2.1.2 Nonlinear and unsteady effects .................................................................... 27 2.2 Turbulent premixed combustion modeling ........................................................... 35 2.3 Lewis number and preferential diffusion effects: direct numerical simulations of turbulent premixed flames ................................................................................... 41 2.4 Leading points concept ......................................................................................... 54 2.4.1 Leading points burning rates ........................................................................ 55 2.4.2 Dynamical significance of leading points .................................................... 57 CHAPTER 3: Leading IPoints IBurning IRates.............................................................. 63 3.1 Numerical procedures ........................................................................................... 65 3.2 Definitions ............................................................................................................ 69 3.3 One dimensional numerical simulations ............................................................... 73 3.4 Turbulent flame front structure ............................................................................. 77 3.4.1 Local flame front curvatures, shapes and strain rates .................................. 77 3.4.2 Case A31 ...................................................................................................... 82 vii 3.4.3 Case B31, C31 and D31 ............................................................................... 84 3.4.3.1 Cylindrical and spherical flamelets ...................................................... 89 3.4.3.2 Flamelets with low curvature ............................................................... 93 3.5 Flame front structure at the leading edge.............................................................. 96 3.6 Conclusions ......................................................................................................... 102 CHAPTER 4: Leading IPoints IDynamics .................................................................... 105 4.1 G-equation .......................................................................................................... 107 4.2 Problem formulation and mathematical background .......................................... 109 4.2.1 One dimensional problem formulation ...................................................... 109 4.2.2 Hopf-Lax formula and Huygens propagation ............................................ 113 4.2.3 Aubry-Mather theory ................................................................................. 114 4.2.4 Definition of Aubry-Mather Leading Points .............................................. 120 4.3 Example problem ...............................................................................................