Thermodynamics and Propulsion
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16.Unified: Thermodynamics and Propulsion
Prof. Z. S. Spakovszky
L
^{A}
T
E
X
editing by D. Quattrochi
Notes by E. M. Greitzer, Z. S. Spakovszky, I. A. Waitz
Origins
Acknowledgement from 16.05 Notes
A note on bracketed references
A note on the version
Contents
List of Figures
List of Tables
I
THE FIRST LAW OF THERMODYNAMICS
1
. Introduction to Thermodynamics
1
.
1
What it's All About
1
.
2
Definitions and Fundamental Ideas of Thermodynamics
1
.
2
.
1
The Continuum Model
1
.
2
.
2
The Concept of a ``System''
1
.
2
.
3
The Concept of a ``State''
1
.
2
.
4
The Concept of ``Equilibrium''
1
.
2
.
5
The Concept of a ``Process''
1
.
2
.
6
QuasiEquilibrium Processes
1
.
2
.
7
Equations of state
1
.
3
Changing the State of a System with Heat and Work
1
.
3
.
1
Heat
1
.
3
.
2
Zeroth Law of Thermodynamics
1
.
3
.
3
Work
1
.
3
.
4
Work vs. Heat  which is which?
1
.
4
Muddiest Points on Chapter 1
2
. The First Law of Thermodynamics
2
.
1
First Law of Thermodynamics
2
.
2
Corollaries of the First Law
2
.
3
Example Applications of the First Law; enthalpy
2
.
3
.
1
Adiabatic, steady, throttling of a gas
2
.
3
.
2
QuasiStatic Expansion of a Gas
2
.
3
.
3
Transient filling of a tank
2
.
3
.
4
The First Law in Terms of Enthalpy
2
.
4
Specific Heats
2
.
4
.
1
Specific Heats of an Ideal Gas
2
.
4
.
2
Reversible adiabatic processes for an ideal gas
2
.
5
Control volume form of the conservation laws
2
.
5
.
1
Conservation of mass
2
.
5
.
2
Conservation of energy
2
.
5
.
3
Stagnation Temperature and Stagnation Enthalpy
2
.
5
.
4
Example Applications of the First Law of Thermodynamics
2
.
6
Muddiest Points on Chapter 2
3
. The First Law Applied to Engineering Cycles
3
.
1
Some Properties of Engineering Cycles; Work and Efficiency
3
.
2
Generalized Representation of Thermodynamic Cycles
3
.
3
The Carnot Cycle
3
.
4
Refrigerators and Heat Pumps
3
.
5
The Internal combustion engine (Otto Cycle)
3
.
5
.
1
Efficiency of an ideal Otto cycle
3
.
5
.
2
Engine work, rate of work per unit enthalpy flux
3
.
6
Diesel Cycle
3
.
7
Brayton Cycle
3
.
7
.
1
Work and Efficiency
3
.
7
.
2
Gas Turbine Technology and Thermodynamics
3
.
7
.
3
Brayton Cycle for Jet Propulsion: the Ideal Ramjet
3
.
7
.
4
MIT Cogenerator
3
.
8
Muddiest points on Chapter 3
II
THE SECOND LAW OF THERMODYNAMICS
4
. Background to the Second Law of Thermodynamics
4
.
1
Reversibility and Irreversibility in Natural Processes
4
.
2
Difference between Free and Isothermal Expansions
4
.
3
Features of reversible processes
4
.
4
Muddiest Points on Chapter 4
5
. The Second Law of Thermodynamics
5
.
1
Concept and Statements of the Second Law
5
.
2
Axiomatic Statements of the Laws of Thermodynamics
5
.
2
.
1
Introduction
5
.
2
.
2
Zeroth Law
5
.
2
.
3
First Law
5
.
2
.
4
Second Law
5
.
2
.
5
Reversible Processes
5
.
3
Combined First and Second Law Expressions
5
.
4
Entropy Changes in an Ideal Gas
5
.
5
Calculation of Entropy Change in Some Basic Processes
5
.
6
Muddiest Points on Chapter 5
6
. Applications of the Second Law
6
.
1
Limitations on the Work that Can be Supplied by a Heat Engine
6
.
2
The Thermodynamic Temperature Scale
6
.
3
Representation of Thermodynamic Processes in
coordinates
6
.
4
Brayton Cycle in

Coordinates
6
.
4
.
1
Net work per unit mass flow in a Brayton cycle
6
.
5
Irreversibility, Entropy Changes, and ``Lost Work''
6
.
6
Entropy and Unavailable Energy
6
.
7
Examples of Lost Work in Engineering Processes
6
.
8
Some Overall Comments on Entropy
6
.
8
.
1
Entropy
6
.
8
.
2
Reversible and Irreversible Processes
6
.
8
.
3
Examples of Reversible and Irreversible Processes
6
.
9
Muddiest Points on Chapter 6
7
. Entropy on the Microscopic Scale
7
.
1
Entropy Change in Mixing of Two Ideal Gases
7
.
2
Microscopic and Macroscopic Descriptions of a System
7
.
3
A Statistical Definition of Entropy
7
.
4
The Statistical Definition of Entropy and Randomness
7
.
5
Numerical Example: the Equilibrium Distribution
7
.
6
Summary and Conclusions
8
. Power Cycles with TwoPhase Media
8
.
1
Behavior of TwoPhase Systems
8
.
2
Work and Heat Transfer with TwoPhase Media
8
.
3
The Carnot Cycle as a TwoPhase Power Cycle
8
.
3
.
1
Example: Carnot steam cycle
8
.
4
The ClausiusClapeyron Equation
8
.
5
Rankine Power Cycles
8
.
6
Enhancements of Rankine Cycles
8
.
7
Combined Cycles for Power Production
8
.
8
Some Overall Comments on Thermodynamic Cycles
8
.
9
Muddiest Points on Chapter 8
III
PROPULSION
9
. Introduction to Propulsion
9
.
1
Goal: Create a Force to Propel a Vehicle
9
.
2
Performance parameters
9
.
3
Propulsion is a systems endeavor
10
. Integral Momentum Theorem
10
.
1
An Expression of Newton's 2
^{nd}
Law
10
.
2
Application of the Integral Momentum Equation to Rockets
10
.
3
Application of the Momentum Equation to an Aircraft Engine
11
. Aircraft Engine Performance
11
.
1
Overall Efficiency
11
.
2
Thermal and Propulsive Efficiency
11
.
3
Implications of propulsive efficiency for engine design
11
.
4
Other expressions for efficiency 
and SFC
11
.
5
Trends in thermal and propulsive efficiency
11
.
6
Performance of Jet Engines
11
.
6
.
1
Notation and station numbering
11
.
6
.
2
Ideal Assumptions
11
.
6
.
3
Ideal Ramjet
11
.
6
.
4
Turbojet Engine
11
.
6
.
5
Effect of Departures from Ideal Behavior
11
.
7
Performance of Propellers
11
.
7
.
1
Overview of propeller performance
11
.
7
.
2
Application of the Integral Momentum Theorem to Propellers
11
.
7
.
3
Actuator Disk Theory
11
.
7
.
4
Dimensional Analysis
11
.
8
Muddiest points on Chapter 11
12
. Energy Exchange with Moving Blades
12
.
1
Introduction
12
.
2
Conservation of Angular Momentum
12
.
3
The Euler Turbine Equation
12
.
4
Multistage Axial Compressors
12
.
5
Velocity Triangles for an Axial Compressor Stage
12
.
6
Velocity Triangles for an Axial Flow Turbine Stage
13
. Aircraft Performance
13
.
1
Vehicle Drag
13
.
2
Power Required
13
.
3
Aircraft Range: the Breguet Range Equation
13
.
3
.
1
Relation of overall efficiency,
, and thermal efficiency
13
.
3
.
2
The Propulsion Energy Conversion Chain
13
.
4
Aircraft Endurance
13
.
5
Climbing Flight
14
. Rocket Performance
14
.
1
Thrust and Specific Impulse for Rockets
14
.
2
The Rocket Equation
14
.
3
Rocket Nozzles: Connection of Flow to Geometry
14
.
3
.
1
Quasionedimensional compressible flow in a variable area duct
14
.
3
.
2
Thrust in terms of nozzle geometry
IV
HEAT GENERATION AND TRANSFER
15
. Generating Heat: Thermochemistry
15
.
1
Fuels
15
.
2
FuelAir Ratio
15
.
3
Enthalpy of formation
15
.
4
First Law Analysis of Reacting Systems
15
.
5
Adiabatic Flame Temperature
15
.
5
.
1
Approximate solution using ``average'' values of specific heat
15
.
5
.
2
Solution for adiabatic flame temperature using evolutions of specific heats with temperature
15
.
5
.
3
Solution for adiabatic flame temperature using tabulated values for gas enthalpy
15
.
6
Muddiest points on Chapter 15
Additional References
16
. Conductive Heat Transfer
16
.
1
Heat Transfer Modes
16
.
2
Introduction to Conduction
16
.
3
SteadyState OneDimensional Conduction
16
.
3
.
1
Example: Heat transfer through a plane slab
16
.
4
Thermal Resistance Circuits
16
.
5
QuasiOneDimensional Heat Flow
16
.
5
.
1
Cylindrical Shell
16
.
5
.
2
Spherical Shell
16
.
6
Muddiest Points on Chapter 16
17
. Convective Heat Transfer
17
.
1
The Reynolds Analogy
17
.
2
Combined Conduction and Convection
17
.
3
Dimensionless Numbers and Analysis of Results
17
.
4
Muddiest Points on Chapter 17
18
. Generalized Conduction and Convection
18
.
1
Temperature Distributions in the Presence of Heat Sources
18
.
2
Heat Transfer From a Fin
18
.
3
Transient Heat Transfer (Convective Cooling or Heating)
18
.
4
Modeling Complex Physical Processes
18
.
5
Heat Exchangers
18
.
5
.
1
Simplified Counterflow Heat Exchanger (With Uniform Wall Temperature)
18
.
5
.
2
General Counterflow Heat Exchanger
18
.
5
.
3
Efficiency of a Counterflow Heat Exchanger
18
.
6
Muddiest Points on Chapter 18
19
. Radiation Heat Transfer
19
.
1
Ideal Radiators
19
.
2
Kirchhoff's Law and ``Real Bodies''
19
.
3
Radiation Heat Transfer Between Planar Surfaces
19
.
3
.
1
Example 1: Use of a thermos bottle to reduce heat transfer
19
.
3
.
2
Example 2: Temperature measurement error due to radiation heat transfer
19
.
4
Radiation Heat Transfer Between Arbitrary Surfaces
19
.
4
.
1
Example: Concentric cylinders or concentric spheres
19
.
5
Muddiest Points on Chapter 19
Index
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