Design of a Two-Dimensional Supersonic Nozzle for use in Wind Tunnels a project presented to The Faculty of the Department of Aerospace Engineering San José State University in partial fulfillment of the requirements for the degree Master of Science in Aerospace Engineering by Yousheng Deng May 2018 approved by Dr. Fabrizio Vergine Faculty Advisor © 2018 Yousheng Deng ALL RIGHTS RESERVED The Designated Project Advisor(s) Approves the Thesis Titled DESIGN OF A TWO-DIMENSIONAL SUPERSONIC NOZZLE FOR USE IN WIND TUNNELS by Yousheng Deng APPROVED FOR THE DEPARTMENT OF AEROSPACE ENGINEERING SAN JOSÉ STATE UNIVERSITY May 2018 Dr. Fabrizio Vergine Department of Aerospace Engineering Advisor ABSTRACT DESIGN OF A TWO-DIMENSIONAL SUPERSONIC NOZZLE FOR USE IN WIND TUNNELS By Yousheng Deng This paper outlines the theory, process, and verification of the design of a two- dimensional nozzle. Fundamental concepts of isentropic and non-isentropic flows are reviewed. Then a gradual-expansion nozzle is designed using the two-dimensional method of characteristics, modified to include a gradual expansion section. Inviscid CFD simulations are then ran to verify the final nozzle is capable of accelerating the flow to the wanted supersonic speed without any shocks. Viscous simulations are then ran to account for boundary layer effects on the walls. ACKNOWLEDGEMENTS I would like to sincerely thank my parents for their endless support and encouragement over the course of this project. I would also like to thank my advisor, Dr. Fabrizio Vergine, for his knowledge and guidance throughout this project. Table of Contents List of Symbols .............................................................................................................................. iv List of Figures ................................................................................................................................. v List of Tables ................................................................................................................................. vi 1 Introduction ............................................................................................................................. 1 1.1 Motivation ........................................................................................................................ 1 1.2 Literature Review ............................................................................................................. 2 Wind Tunnel Components ........................................................................................ 2 de Laval Nozzle ........................................................................................................ 2 1.3 Flow Through a CD Nozzle ............................................................................................. 4 1.4 Project Proposal ................................................................................................................ 5 1.5 Methodology .................................................................................................................... 5 2 Reduced Order Model .............................................................................................................. 6 2.1 Isentropic Flow ................................................................................................................. 6 2.2 Flow With Shocks ............................................................................................................ 8 Normal Shock ........................................................................................................... 9 Oblique Shock ......................................................................................................... 10 3 Finalization of the Nozzle ...................................................................................................... 12 4 Nozzle Contour Design ......................................................................................................... 17 4.1 Method of Characteristics: Derivation ........................................................................... 17 4.2 Method of Characteristics: Application ......................................................................... 19 5 CFD Analysis and Verification ............................................................................................. 24 5.1 Mesh Generation and Problem Setup ............................................................................. 24 5.2 Results and Discussion ................................................................................................... 28 Inviscid Simulation Results .................................................................................... 28 Viscous Simulation Results .................................................................................... 30 6 Conclusion ............................................................................................................................. 33 7 Future Works ......................................................................................................................... 34 References ..................................................................................................................................... 35 Appendix A: Reduced Order Model MATLAB Code .................................................................. 36 Appendix B: Trade Study MATLAB Code .................................................................................. 42 Appendix C: Method of Characteristics ....................................................................................... 45 ii Appendix D: Nozzle Contour Coordinates ................................................................................... 49 Appendix E: SST Variable Definitions and Constants ................................................................. 57 iii List of Symbols Symbol Definition Units (English) 2 A Area in 2 A* Throat Area in 2 2 k Turbulent Kinetic Energy ft /s M Mach Number ------- P Pressure psi Pr Prandtl Number ------- T Temperature Rankine t Time s u Velocity along x-axis ft/s 3 V Volume in v Velocity along y-axis ft/s Greek Symbols β Shock Angle deg or rad γ Specific Heat ------- µ Local Mach Angle deg or rad ν Prandtl-Meyer Function deg or rad θ Mach Angle deg or rad ω Dissipation Rate 1/s Subscripts ( )0 Total ------- Acronyms CFD Computational Fluid Dynamics ------- CAD Computer Aided Design ------- CD Convergent-Divergent ------- iv List of Figures Figure 2.1 The geometry of the nozzle. The throat location is denoted by a red line ................. 7 Figure 2.2 Pressure ratio and Mach number of isentropic nozzle flow at Mach 5. Mach 1 and 8 Figure 2.3 Pressure ratio and Mach number of isentropic supersonic flow and supersonic flow with a normal shock. Mach 1 and the throat location are denoted by red lines. The shock location is denoted by a green line ................................................................................................................ 9 Figure 3.1 Schematic of the wind tunnel with the control volume in red ................................. 12 Figure 3.2 Runtime vs Mach for overexpanded flow at various exit areas ............................... 14 Figure 3.3 Runtimes vs plenum pressure for Mach 3 flow at various exit areas ...................... 15 Figure 3.4 Length of shock-free area vs plenum pressure for Mach 3 at various exit areas ..... 16 Figure 3.5 Length of shock-free area vs runtimes for Mach 3 at various exit areas ................. 16 Figure 4.1 Preliminary Method of Characteristics with Wall Points ........................................ 20 Figure 4.2 Preliminary Method of Characteristics with Labeled Points ................................... 20 Figure 4.3 10-Line Method of Characteristics with Internal Lines ........................................... 23 Figure 4.4 Method of Characteristics Nozzle Contour ............................................................. 23 Figure 5.1 SolidWorks Drawing ............................................................................................... 25 Figure 5.2 CFD-GEOM Boundary Labels ................................................................................ 25 Figure 5.3 CFD-GEOM Mesh .................................................................................................. 25 Figure 5.4 CFD-FASTRAN Model .......................................................................................... 26 Figure 5.5 Pressure Contour of Converged Inviscid Simulation .............................................. 28 Figure 5.6 U Velocity Contour of Converged Inviscid Simulation .......................................... 29 Figure 5.7 V Velocity Contour of Converged Inviscid Simulation .......................................... 29 Figure 5.8 Mach Contour of Converged Inviscid Simulation ................................................... 29 Figure 5.9 Pressure Contour of Converged Viscous Simulation .............................................. 30 Figure 5.10 U Velocity Contour of Converged Viscous Simulation ........................................ 30 Figure 5.11 V Velocity Contour of Converged Viscous Simulation ........................................ 31 Figure 5.12 Mach Contour of Converged Viscous Simulation ................................................. 31 v List of Tables Table 3.1 Final Nozzle Parameters ........................................................................................... 15 Table 4.1 10-Line Method of Characteristics.