University of Mississippi eGrove Electronic Theses and Dissertations Graduate School 2014 Parametric Scramjet Analysis Jongseong Choi University of Mississippi Follow this and additional works at: https://egrove.olemiss.edu/etd Part of the Aerospace Engineering Commons Recommended Citation Choi, Jongseong, "Parametric Scramjet Analysis" (2014). Electronic Theses and Dissertations. 535. https://egrove.olemiss.edu/etd/535 This Thesis is brought to you for free and open access by the Graduate School at eGrove. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of eGrove. For more information, please contact [email protected]. PARAMETRIC SCRAMJET ANALYSIS A Thesis presented in partial fulfillment of requirements for the degree of Master of Science in the Department of Mechanical Engineering The University of Mississippi by JONGSEONG CHOI May 2014 Copyright Jongseong Choi 2014 ALL RIGHT RESERVED ABSTRACT The performance of a hypersonic flight vehicle will depend on existing materials and fuels; this work presents the performance of the ideal scramjet engine for three different combustion chamber materials and three different candidate fuels. Engine performance is explored by parametric cycle analysis for the ideal scramjet as a function of material maximum service temperature and the lower heating value of jet engine fuels. The thermodynamic analysis is based on the Brayton cycle as similarly employed in describing the performance of the ramjet, turbojet, and fanjet ideal engines. The objective of this work is to explore material operating temperatures and fuel possibilities for the combustion chamber of a scramjet propulsion system to show how they relate to scramjet performance and the seven scramjet engine parameters: specific thrust, fuel-to-air ratio, thrust-specific fuel consumption, thermal efficiency, propulsive efficiency, overall efficiency, and thrust flux. The information presented in this work has not been done by others in the scientific literature. This work yields simple algebraic equations for scramjet performance which are similar to that of the ideal ramjet, ideal turbojet and ideal turbofan engines. ii LIST OF SYMBOLS ao = freestream speed of sound, m/s 2 A2 = diffuser (engine inlet) exit area (Ae =A2), cm ; combustor entrance area A*/A = area ratio . cp = specific heat at constant pressure, kJ / (kg K) F = thrust, N F m o = specific thrust, N / (kg / s) . 2 gc = Newton’s constant, (kg m) / (N s ) h PR = fuel lower heating value, kJ / kg h o = freestream ambient enthalphy, kJ / kg h 9 = enthalphy at engine nozzle exit, kJ / kg h t2 = total enthalphy at combustor entrance, kJ / kg h t4 = total enthalphy at combustor exit, kJ / kg Mc = combustion Mach number Mo = Mach number at freestream flight conditions * Mo = freestream Mach number for maximum F m o ** Mo = freestream Mach number for minimum S *** M o = freestream Mach number for maximum F / A2 M9 = Mach number at engine nozzle exit (M9’ = M9’’ = M9 = Mo) iii m o = mass flow rate of air, kg / s m f = mass flow rate of fuel, kg / s Po = freestream static pressure, Pa P9 = static pressure at engine nozzle exit (Pe =P9), Pa (also P9’ and P9’’) Pto = freestream total pressure, Pa Pt2 = total pressure at combustor entrance, Pa (also P’’2) Pt4 = total pressure at combustor exit, Pa Pt9 = total pressure at engine nozzle inlet, Pa (also Pt9’ and Pt9’’) R = gas constant for air, kJ / (kg . K) s = entropy, (J / K) S = thrust-specific fuel consumption, mg / (N . s) T = temperature, K Tmax = material temperature limit, K T'max = burner exit total temperature, Mc < Mo, K T''max = burner exit total temperature, Mc ≥ Mo, K To = freestream ambient temperature, K Tto = freestream total temperature, K T2 = temperature at combustor entrance, K (also T’2) Tt2 = total temperature at combustor entrance, K (also T’’2) Tt4 = total temperature at combustor exit, K iv T9 = temperature at engine nozzle exit, K (also T9’ and T9’’) Tt9 = total temperature at engine nozzle inlet, K (also Tt9’ and Tt9’’) Vo = freestream velocity V9 = engine nozzle exit velocity (Ve = V9), m / s (also V9’ and V9’’) Wnetout = amount of work per unit time through the net area from T-s diagram, J / s Qin = heat flow rate by combustion, J / s γ = ratio of specific heats f = fuel-to-air ratio τ = total temperature ratio across burner, T / T , τ /τ b t4 t2 λ r τ d = total temperature ratio across diffuser, Tt2 / Tto τ n = total temperature ratio across nozzle, Tt9 / Tt4 2 τr = inlet temperature ratio, Tto / To = [1 + ( γ - 1) Mo / 2] τ = total temperature to freestream temperature ratio, Tt4 / To Tmax / To b = total pressure ratio across burner, Pt4 / Pt2 d = total pressure ratio across diffuser, Pt2 / Pto n = total pressure ratio across nozzle, Pt9 / Pt4 2 / 1 r = inlet pressure ratio, Pto / Po = [1 + (γ - 1) Mo / 2] T = thermal efficiency v P = propulsive efficiency o = overall efficiency vi ACKOWLEDGEMENTS I would like to gratefully acknowledge the enthusiastic supervision of Dr. Jeffrey A. Roux during this research. There has been his great contribution toward this thesis, which has yielded three journal publications in the past two years. I offer my sincerest appreciation for the learning opportunities and support provided by Dr. Arunachalam M. Rajendran. His guidance has provided me a thoughtful and rewarding journey. I would like to thank to Dr. Chung Song for general advice concerning scholastic life besides my research. While data collecting and researching, Kiyun Kim spent countless hours listening to me talk about my thoughts on my research. I am grateful to all my friends from KSA and OKCC. I have received support and encouragement from my friend group named Sekye from Korea. Finally, I am forever indebted to my parents for their understanding, endless patience, and encouragement when it was most required. vii TABLE OF CONTENTS ABSTRACT ........................................................................................................................... ii LIST OF SYMBOLS ............................................................................................................... iii ACKOWLEDGEMENTS ...................................................................................................... vii TABLE OF CONTENTS ...................................................................................................... viii LIST OF TABLES .................................................................................................................. xi LIST OF FIGURES ................................................................................................................ xv INTRODUCTION .....................................................................................................................1 1.1 Hypersonic Propulsion .............................................................................................1 1.2 Parametric Thermodynamic Cycle Analysis for Ideal Engines .................................2 1.3 Definition .................................................................................................................3 1.3.1 Ramjet ...................................................................................................................3 1.3.2 Scramjet ................................................................................................................5 1.4 Scramjet Components ...............................................................................................8 1.5 Historical Development ............................................................................................9 1.6 Materials and Fuels Candidates .............................................................................. 13 1.6.1 Materials ............................................................................................................. 14 viii 1.6.2 Fuels ................................................................................................................... 15 1.7 This Work .............................................................................................................. 17 STATEMENT OF THE PROBLEM...................................................................................... 19 2.1 Definition of the Problem ....................................................................................... 19 2.2 T-s Diagram .......................................................................................................... 20 2.2.1 Situations for Mc < Mo ......................................................................................... 21 2.2.2 Situations for Mc ≥ Mo ......................................................................................... 24 2.3 Materials and Fuels Selection ................................................................................. 25 ANALYSIS .......................................................................................................................... 27 3.1 Fundamental Assumptions for Parametric Analysis ................................................ 27 3.2 Parametric Analysis for Ideal Mass Flow Scramjet ................................................. 28 3.2.1 Summary of Equations – Ideal Mass Flow Scramjet ............................................ 36 3.3 Parametric Analysis for Non-Ideal Mass Flow Scramjet ......................................... 37 3.3.1 Summary of Equations – Non-Ideal Mass Flow Scramjet .................................... 43 * 3.4 Optimum Freestream Mach Number