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Reduced-Order Analysis of Dual Mode Supersonic Combustion

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Reduced-Order Analysis of Dual Mode Supersonic Combustion REDUCED-ORDER ANALYSIS OF DUAL MODE SUPERSONIC COMBUSTION RAMJET PROPULSION SYSTEM by VIJAY GOPAL Presented to the Faculty of the Graduate School of The University of Texas at Arlington in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE IN AEROSPACE ENGINEERING THE UNIVERSITY OF TEXAS AT ARLINGTON DECEMBER 2015 Copyright © by VIJAY GOPAL 2015 All Rights Reserved ii Acknowledgements I would like to thank my parents Mrs. Sheelavathy Gopal and Mr. Gopal Ananthan for their complete financial and moral support during the master’s program. Also, I would like to thank my advisor Dr. Donald R. Wilson for his valuable guidance and thesis committee members Dr. Frank Lu and Dr. Atilla Dogan for their ideas and feedback on the research work. I am thankful to my uncle Mr. Venkatesh Ananthan and aunt Mrs. Rekha Venkatesh for their support during my stay at the US. I extend my thanks to my colleague Nandakumar Vijayakumar for valuable suggestions made in the research work. I would like to thank my friends, Shashank Ramesh, Varun Vishwamithra, Purushotham Balaji, Hatim Rangwala, Esteban Cisneros, Rohit Raju, Warren Freitas, Rahul Kumar, and Umang Dighe for their timely help and support during the course of the master’s program. November 20, 2015 iii Abstract REDUCED-ORDER ANALYSIS OF DUAL MODE SUPERSONIC COMBUSTION RAMJET PROPULSION SYSTEM Vijay Gopal, M.S. The University of Texas at Arlington, 2015 Supervising Professor: Donald R Wilson High speed propulsion systems typically possess relatively simple geometry but the complexity involved in the flow characteristics makes their analysis a challenging task. The current research work introduces a reduced order analytical model for a steady operation of dual mode SCRamjet (Supersonic Combustion Ramjet) propulsion system at design and off-design conditions. The model hopes to reduce analysis time and complexity to carry out parametric sweep studies for preliminary design of SCRamjet engines. The analytical model splits the analysis of SCRamjet engine into five interactive components namely: inlet, isolator, injector, burner and nozzle. Each component is modelled using physics of gas-dynamics and semi-empirical relations. The flow characterization of each component and their interactions are modelled carefully based on observed physical phenomenon reported in the existing literature. The model is developed on MATLAB platform providing flexibility to design a parametrized SCRamjet geometry and to select its free stream and fueling conditions for the analysis. The analytical model proposed in the current work is validated with various experimental and computational data of individual components and its reliability for predicting the flow characteristics inside a SCRamjet propulsion system is discussed in detail. iv Table of Contents Acknowledgements .............................................................................................................iii Abstract .............................................................................................................................. iv List of Illustrations ............................................................................................................. viii List of Tables ......................................................................................................................xii Chapter 1 Introduction......................................................................................................... 1 1.1 Why High Speed Atmospheric Propulsion is Necessary? ........................................ 1 1.2 Where Do We Stand as of 2015? ............................................................................. 2 1.3 Technological Barriers .............................................................................................. 3 1.4 How Does Current Work Contribute? ....................................................................... 5 Chapter 2 SCRamjet Propulsion System ............................................................................ 6 2.1 Inlet ........................................................................................................................... 7 2.2 Isolator ...................................................................................................................... 7 2.3 Burner ....................................................................................................................... 7 2.4 Single Expansion Ramp Nozzle ............................................................................... 8 2.5 Literature Review ...................................................................................................... 8 Chapter 3 Physics of High Speed Gas Flows ................................................................... 10 3.1 Review of Thermodynamics ................................................................................... 10 3.2 Characterization of Gas .......................................................................................... 12 3.2.1 Real and Ideal Gases ...................................................................................... 12 3.2.2 Specific Heat Capacities and Classification of Gases..................................... 13 3.3 Chemically Reacting Gases in Equilibrium ............................................................. 15 3.3.1 Chemical Equilibrium ....................................................................................... 15 3.3.2 Thermochemical Properties of Mixture............................................................ 17 3.4 Boundary Layer and Heat Transfer ........................................................................ 19 v 3.4.1 Estimating Viscosity ........................................................................................ 23 3.5 Governing Equations for Gas flows ........................................................................ 24 3.5.1 Mass Conservation .......................................................................................... 24 3.5.2 Momentum Conservation ................................................................................ 24 3.5.3 Energy Conservation ....................................................................................... 25 Chapter 4 Dual Mode SCRamjet Analytical Model ........................................................... 27 4.1 Parametrized SCRamjet Geometry ........................................................................ 27 4.2 Inlet Model .............................................................................................................. 29 4.2.1 Thermally Perfect Oblique and Normal Shockwaves ...................................... 30 4.2.2 Inlet Shock Reflection Model ........................................................................... 32 4.2.3 Inlet Viscous Correction Model ........................................................................ 39 4.3 Isolator Model ......................................................................................................... 41 4.3.1 Shock Free Isolator Model .............................................................................. 42 4.3.2 Oblique Shock Train Isolator Model ................................................................ 44 4.3.2 Normal Shock Train Isolator Model ................................................................. 46 4.4 Fuel Injector Model ................................................................................................. 50 4.5 Burner Model .......................................................................................................... 53 4.5.1 Supersonic Combustion .................................................................................. 55 4.5.1.1 Mass Conservation and Supersonic Mixing ............................................. 55 5.5.1.2 Momentum Conservation ......................................................................... 58 4.5.1.3 Energy Conservation ............................................................................... 59 4.5.1.4 State Relationship .................................................................................... 59 4.5.1.4 Burner Analysis ........................................................................................ 60 4.5.1.5 Non-Equilibrium Approximation ............................................................... 64 4.5.2 Subsonic Combustion ..................................................................................... 67 vi 4.5.3 Isolator Burner Interaction ............................................................................... 73 4.6 External Nozzle Model ............................................................................................ 75 4.6.1 On-Design SERN Analysis .............................................................................. 76 4.6.2 Off-Design SERN Analysis: Over-Expanded Nozzle ...................................... 77 4.6.2 Off-Design SERN Analysis: Under-Expanded Nozzle .................................... 79 Chapter 5 Validation of Analytical Dual Mode SCRamjet Model ...................................... 82 5.1 SCRamjet Inlet Model Validation ............................................................................ 82 5.2 SCRamjet Isolator Model Validation ....................................................................... 91 5.2.1 Shock Free Mode Validation ........................................................................... 91 5.2.2 Oblique Shock Train Mode
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