Louisiana State University LSU Digital Commons LSU Master's Theses Graduate School 2013 Instability analysis and suppression of instability in low-density gas jets Sukanta Bhattacharjee Louisiana State University and Agricultural and Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_theses Part of the Mechanical Engineering Commons Recommended Citation Bhattacharjee, Sukanta, "Instability analysis and suppression of instability in low-density gas jets" (2013). LSU Master's Theses. 906. https://digitalcommons.lsu.edu/gradschool_theses/906 This Thesis is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Master's Theses by an authorized graduate school editor of LSU Digital Commons. For more information, please contact [email protected]. INSTABILITY ANALYSIS AND SUPPRESSION OF INSTABILITY IN LOW- DENSITY GAS JETS A Thesis Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Masters of Science in Mechanical Engineering in The Department of Mechanical Engineering by Sukanta Bhattacharjee B.S., Bangladesh University of Engineering and Technology, 2008 August 2013 This thesis is dedicated to my parents, Manik Chandra Bhattacharjee and Supriti Rani Chakraborty, who are with me along these years and assist in terms of guidance, encouragement, advice, monetary support, mental support, and time. ii ACKNOWLEDGEMENTS I would like to thank my advisor Dr. Sumanta Acharya who provides me support and advices in my research work during these years. I thank all of my friends and colleagues I worked with, Baine, James, Krishnendu, Pranay, Sheng, Srinibas, Susheel and especially Prasad. These people helped me a lot when I was facing difficulties in my works. I am very grateful to my friends whom I got wonderful moments in their company and for helping me in many regard at my research and academic courses. Finally, my acknowledgement is due to my parents back in home, who were always behind me with their prayer, love and blessings, encouraged me and provided tremendous support throughout my life. Without their help, I would not have been here. I am very grateful to all of my family members who always support me in this endeavor. iii TABLE OF CONTENTS ACKNOWLEDGEMENTS ........................................................................................................... iii ABSTRACT ................................................................................................................................... vi CHAPTER 1: INTRODUCTION ................................................................................................... 1 1.1. Background .......................................................................................................................... 1 1.2. Low-Density Jet ................................................................................................................... 3 1.3. Literature Survey .................................................................................................................. 4 1.3.1 Experimental studies ....................................................................................................... 4 1.3.2. Numerical Studies........................................................................................................ 15 CHAPTER 2: DEFINITIONS AND NOTATIONS ..................................................................... 18 2.1. Notations ............................................................................................................................ 18 CHAPTER 3: SIMULATIONS .................................................................................................... 20 3.1. Geometry ............................................................................................................................ 20 3.2. Mesh ................................................................................................................................... 22 3.3. Governing Equations .......................................................................................................... 24 3.4. Boundary conditions .......................................................................................................... 27 3.5. Data Processing .................................................................................................................. 30 3.5.1. Q-criterion ................................................................................................................... 31 3.5.2. Determination of the visualization method ................................................................. 31 3.6. Configuration studied ......................................................................................................... 32 3.7. Turbulent energy dissipation and Kolmogorov length scale .............................................. 33 3.8. Grid independence and validation ...................................................................................... 35 3.8.1. Grid independence study ............................................................................................. 35 3.8.2. Flow field validation .................................................................................................... 39 CHAPTER 4: RESULTS AND DISCUSSION ............................................................................ 41 4.1. Basic Jet.............................................................................................................................. 41 4.1.1 Evolution of mean velocity ........................................................................................... 45 4.1.2. Velocity fluctuations.................................................................................................... 47 4.1.3. Evolution of the species ............................................................................................... 48 4.1.4. Species fluctuation ....................................................................................................... 50 4.1.5. Flow structures ............................................................................................................ 52 4.1.6. Generation of the instability ........................................................................................ 54 4.1.7. Iso-surface of vortex structures ................................................................................... 57 4.1.8. Generation of the instability ........................................................................................ 64 4.1.9. Varicose mode generation ........................................................................................... 64 4.1.10. Iso-surface of density ................................................................................................. 69 4.1.11. Vortex merging & hairpin vortex .............................................................................. 72 4.1.12. Spectral analysis & universal scaling ........................................................................ 74 4.2. Controlled jet ...................................................................................................................... 80 iv 4.2.1. Vortex structures.......................................................................................................... 80 4.2.2. Suppression of instability ............................................................................................ 82 4.3. Conclusion .......................................................................................................................... 88 REFERENCES ............................................................................................................................. 90 APPENDIX A ............................................................................................................................... 94 APPENDIX B ............................................................................................................................... 98 APPENDIX C ............................................................................................................................. 103 APPENDIX D ............................................................................................................................. 108 VITA ........................................................................................................................................... 112 v ABSTRACT A numerical study is conducted to understand the global instability of very low-density jets (as encountered in thermal plasmas). The simulations have been carried out for different parameters of density ratios, S = ρj /ρ∞ ranging from 0.5 to 0.03, different Reynolds numbers ranging from 500 to 4000 and different momentum thickness obtained by different extension tube length ranging from 3 to 6 diameter long. The flow parameters and vortex structures has been visualized to understand the details of the evolution of the flow field. The axisymmetric shear layer rolls up in the near field of the jet forming vortex rings. The rings merged, formed secondary mode of instability in the near field before they interacts with each other to form turbulence. Spectra results show that a global instability exists in the range of density ratios investigated. An envelope of the absolutely globally unstable region has been