Course Objectives

This course covers the fundamental principles of jet propulsion systems. By the end of the course, you should be able to

1. understand the major elements of a jet engine, and the reasons for their presence

2. calculate the overall performance of a jet engine, given a few critical parameters

3. understand technological limitations on the performance of engines

4. understand the differences in design between engines intended for different applications

We will not attempt to teach you about the detailed parts or workings of any particular engine. Instead we will attempt to ensure that you have the capability to analyze any engine.

FUNDAMENTALS OF PROPULSION AND COMBUSTION

Course Outline

Compressible Flows (F)	Propulsion (P)	Combustion (C)
F1. Introductory concepts	P1. Introduction to Propulsion	C1. Introduction to combustion
F2. Conservation equations: continuity and momentum	P2. Review of thermodynamics	C2. Introductory combustion chemistry
F3. Energy equation	P3. Review of isentropic flow relations	C3. Chemical thermodynamics
F4. Isentropic flow	P4. Thrust of a jet propulsion system	C4. Chemical equilibrium
F5. Velocity-area relations; choking	P5. Brayton cycle: cycle efficiency; choice of parameters	C5. Adiabatic flames
F6. Convergent-divergent nozzles	P6. Ideal ramjet cycle	C6. Chemical kinetics
F7. Normal shocks	P7. Turbojet, turbofan, and turboprop engines	C7. Premixed flames
F8. Oblique shocks	P8. Optimization of propeller work fraction	C8. Hugoniot and Rayleigh Lines
F9. Prandtl-Meyer waves	P9. Gas turbine engine analysis	C9. Flame speed
F10. Wind tunnel starting problem	P10. Engine component design considerations	C10. Stirred reactor
F11. Inlet starting	P11. Inlets	C11. Blowout
F12. Design of a multi-ramp inlet	P12. Nozzles	C12. Spray combustion
F13. Flows with friction	P13. Burners	C13. Diffusion flames
F14. Compressor aerodynamics	P14. Turbomachines	C14. Stabilization
F15. Turbine aerodynamics	P15. Single stage analysis
	P16. Multistaging
	P17. Engine performance prediction using a computer spreadsheet

1: Introduction

In this course, we will learn how jet engines work, and to analyze the performance of any jet engine. We will do this by reducing the complex mechanisms of an engine to a few essential features. Shown above is a cut-away view of a modern turbofan engine. Many of the complex parts have been deleted. Starting from the left, we see a compressor system which does work on the air entering the engine, increasing its pressure. In this engine, the compressor is in two parts, running on two different shafts which can operate at different speeds. Next, we see pipes introducing fuel into the combustion chamber, where the fuel is mixed with air and burned. Thus, heat is added to the air. Next we see a turbine, which takes work out of the air leaving the combustion chamber, and uses it to run the compressor. Finally, the air leaving the turbine blows out at high speed through a nozzle. Upon closer examination, we see that some of the air entering the engine goes through the outer parts of the compressor, called a "fan", and then blow out of the engine directly without going through the combustion chamber or nozzle.

The net effect of the engine is that the momentum of the air leaving the engine is greater than that of the air entering the engine. The reaction to this added momentum is reflected in the thrust of the engine.

In this course, we will consider the features of the overall engine, and then of each of the components in turn. To understand the flow in the compressor, turbines, intakes, and nozzles, we will first learn some concepts in compressible fluid dynamics. To understand the flow in the combustor, we will first learn about combustion and reacting flows. These concepts will then be brought together to develop analysis procedures for complete engines, and to compute their performance over a range of flight conditions.

Thrust and Engine Design

Momentum of incoming air is per unit time.

Momentum of outgoing air is per unit time.

By Newton's 2nd Law of Motion, force is equal to the rate of change of momentum. The thrust is the reaction to this force, acting in the direction opposite to the increase in momentum.

As shown above, the thrust of a jet engine is given approximately by

, the increase in momentum of the propellant,

where is the mass of propellant flowing out of the engine per unit time, and is the increase in velocity of the propellant through the engine. Thus if a jet engine takes in (and expels) 100 kg/s of air, and increases its velocity from 200 m/s to 300 m/s, its thrust is approximately 10,000 Newtons (1020 Kgf, or 2248 lbf). This equation is surprisingly useful for jet engines, where the contribution from "pressure thrust" is small or zero, as we will see later, and the fuel mass flow rate is only about 1 to 2% of the air mass flow rate.

Thus, we can design engines to either

a) accelerate a small amount of air through a large velocity increment (examples: rockets, ramjets, turbojets), or

b) accelerate a large through a small (examples: turbofan, turboprop, propfan )

Approach	Advantages	Disadvantages	Typical Applications
(a) small , large	1. small engine area & weight. 2. better high-speed performance 3. better high-altitude performance	1. less efficient conversion of thermal to kinetic energy 2. noise 3. jet blast	rockets, ramjets, high-altitude flight; turbojets, low-bypass turbofans.
(b) large , small	1.High efficiency 2. Better low-altitude performance 3. Better performance below Mach 1. 4. Low noise	1. Large engine diameter 2. More complex engine 3. Slower acceleration	Commercial aircraft: high-bypass turbofans, propfans, turbojets.

In the following sections, we see the factors which determine the maximum or "ideal" efficiency of a given design: this can be calculated from basic thermodynamics if we know a very few crucial parameters of the design, without worrying about the precise shape or complexity of a particular engine.