CONTENTS Real chemistry e ects Scramjet operating envelope Problems

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1 Contents 1 Propulsion Thermodynamics Introduction Thermodynamic cycles The Carnot cycle The Brayton cycle The standard atmosphere Problems Engine performance parameters The definition of thrust Energy balance Capture area Overall e ciency Breguet aircraft range equation Propulsive e ciency Thermal e ciency Specific impulse, specific fuel consumption Dimensionless forms Engine notation Problems The ramjet cycle Ramjet flow field The role of the nozzle The ideal ramjet cycle Optimization of the ideal ramjet cycle The non-ideal ramjet Ramjet control Example - Ramjet with un-started inlet Very high speed flight - scramjets

2 CONTENTS Real chemistry e ects Scramjet operating envelope Problems The Turbojet cycle Thermal e ciency of the ideal turbojet Thrust of an ideal turbojet engine Maximum thrust ideal turbojet Turbine-nozzle mass flow matching Free-stream-compressor inlet flow matching Compressor-turbine mass flow matching Summary - engine matching conditions Example - turbojet in supersonic flow with an inlet shock How does a turbojet work? The compressor operating line The gas generator Corrected weight flow is related to f (M 2 ) A simple model of compressor blade aerodynamics Turbojet engine control Inlet operation The non-ideal turbojet cycle The polytropic e ciency of compression The polytropic e ciency of expansion The e ect of afterburning Nozzle operation Problems The Turbofan cycle Turbofan thrust The ideal turbofan cycle The fan bypass stream The core stream Turbine-compressor-fan matching The fuel/air ratio Maximum specific impulse ideal turbofan Turbofan thermal e ciency Thermal e ciency of the ideal turbofan The non-ideal turbofan Non-ideal fan stream Non-ideal core stream Maximum specific impulse non-ideal cycle

3 CONTENTS Problems The Turboprop cycle Propellor e ciency Work output coe cient Power balance The ideal turboprop Optimization of the ideal turboprop cycle Compression for maximum thrust of an ideal turboprop Turbine sizing for the non-ideal turboprop Problems Rocket performance Thrust Momentum balance in center-of-mass coordinates E ective exhaust velocity C e ciency Specific impulse Chamber pressure Combustion chamber stagnation pressure drop The Tsiolkovsky rocket equation Reaching orbit The thrust coe cient Problems Multistage Rockets Notation The variational problem Example - exhaust velocity and structural coe cient the same for all stages Problems Thermodynamics of reacting mixtures Introduction Ideal mixtures Criterion for equilibrium The entropy of mixing Entropy of an ideal mixture of condensed species Thermodynamics of incompressible liquids and solids Enthalpy Enthalpy of formation and the reference reaction Condensed phase equilibrium

4 CONTENTS Chemical equilibrium, the method of element potentials Rescaled equations Example - combustion of carbon monoxide CO Combustion at K using Gibbs free energy of formation Adiabatic flame temperature Isentropic expansion Nozzle expansion Fuel-rich combustion, multiple phases Rocket performance using CEA Problems Solid Rockets Introduction Combustion chamber pressure Dynamic analysis Exact solution Chamber pressure history Problems Hybrid Rockets Conventional bi-propellant systems The hybrid rocket idea The fuel regression rate law Specific impulse The problem of low regression rate Historical perspective High regression rate fuels The O/F shift Scale-up tests Regression rate analysis Regression rate with the e ect of fuel mass flow neglected Exact solution of the coupled space-time problem for n = 1/ Similarity solution of the coupled space-time problem for general n and m Numerical solution for the coupled space-time problem, for general n and m and variable oxidizer flow rate Example - Numerical solution of the coupled problem for a long burning, midsize motor as presented in reference [1] Sensitivity of the coupled space-time problem to small changes in a, n, and m Problems

5 CONTENTS 5 A Thermochemistry A-1 A.1 Thermochemical tables A-1 A.2 Standard pressure A-2 A.2.1 What about pressures other than standard? A-4 A.2.2 Equilibrium between phases A-5 A.2.3 Reference temperature A-7 A.3 Reference reaction and reference state for elements A-7 A.4 The heat of formation A-8 A.4.1 Example - heat of formation of monatomic hydrogen at K and at 1000 K A-9 A.4.2 Example - heat of formation of gaseous and liquid water A-10 A.4.3 Example - combustion of hydrogen and oxygen diluted by nitrogen. A-13 A.4.4 Example - combustion of methane A-14 A.4.5 Example - the heating value of JP A-16 A.5 Heat capacity A-17 A.6 Chemical bonds and the heat of formation A-20 A.6.1 Potential energy of two hydrogen atoms A-20 A.6.2 Atomic hydrogen A-22 A.6.3 Diatomic hydrogen A-23 A.7 Heats of formation computed from bond energies A-26 A.8 References A-28 B Selected JANAF data B-1

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