Preface v
List of symbols viii
1 Introduction 1
1.1 Themes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Length scales . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Overview and examples . . . . . . . . . . . . . . . . . . . . . 8
1.3.1 Standing-wave heat engine . . . . . . . . . . . . . . . 9
1.3.2 Standing-wave refrigerator . . . . . . . . . . . . . . . . 14
1.3.3 Orifice pulse-tube refrigerator . . . . . . . . . . . . . . 17
1.3.4 Thermoacoustic-Stirling heat engine . . . . . . . . . . 22
1.4 Thermoacoustics and conventional technology . . . . . . . . . 25
1.5 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2 Background 30
2.1 Laws of thermodynamics . . . . . . . . . . . . . . . . . . . . . 30
2.1.1 The first la
w . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.2 The second law . . . . . . . . . . . . . . . . . . . . . . 34
2.2 Laws of fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2.1 Continuity (mass) . . . . . . . . . . . . . . . . . . . . 39
2.2.2 Momentum . . . . . . . . . . . . . . . . . . . . . . . . 40
2.2.3 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2.4 Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3 Ideal gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.1 Thermodynamic properties . . . . . . . . . . . . . . . 44
2.3.2 Transport properties . . . . . . . . . . . . . . . . . . . 47
2.3.3 Shortcuts . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.3.4 Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.4 Some consequences of the laws . . . . . . . . . . . . . . . . .
48
2.4.1 Carnot's eficiency . . . . . . . . . . . . . . . . . . . . 48
2.4.2 Maxwell relations . . . . . . . . . . . . . . . . . . . . . 49
2.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3 Simple oscillations 55
3.1 The harmonic oscillator and complex notation . . . . . . . . . 55
3.2 Acoustic approximations to the laws of gases . . . . . . . . . 59
3.3 Some simple oscillations in gases . . . . . . . . . . . . . . . . 64
3.3.1 The gas spring . . . . . . . . . . . . . . . . . . . . . . 64
3.3.2 Simple sound waves . . . . . . . . . . . . . . . . . . . 66
3.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 Waves 72
4.1 Lossless acoustics and ideal resonators . . . . . . . . . . . . . 72
4.2 Viscous and thermal effects in large channels . . . . . . . . . 79
4.2.1 Viscous resistance . . . . . .
. . . . . . . . . . . . . . 80
4.2.2 Thermal-relaxation conductance . . . . . . . . . . . . 85
4.3 Inviscid boundary-layer thermoacoustics . . . . . . . . . . . . 89
4.4 General thermoacoustics . . . . . . . . . . . . . . . . . . . . . 92
4.4.1 The math . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.4.2 The ideas . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5 Power 112
5.1 Acoustic power . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.1.1 Acoustic power dissipation with dTm/dx = 0 . . . . . 116
5.1.2 Acoustic power with zero viscosity . . . . . . . . . . . 119
5.2 Total power . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.2.1 Traveling waves . . . . . . . . . . . . . . . . . . . . . . 131
5.2.2 Standing waves . . . . . . . . . . . . . .
. . . . . . . . 132
5.3 Some calculation methods . . . . . . . . . . . . . . . . . . . . 133
5.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6 Efficiency . . . 144
6.1 Lost work and entropy generation . . . . . . . . . . . . . . . . 145
6.2 Exergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
6.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
7 Beyond Rott's thermoacoustics 164
7.1 Tortuous porous media . . . . . . . . . . . . . . . . . . . . . . 167
7.2 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
7.2.1 Minor losses . . . . . . . . . . . . . . . . . . . . . . . . 177
7.3 Entrance effects and joining conditions .
. . . . . . . . . . . . 182
7.3.1 Entrance effects . . . . . . . . . . . . . . . . . . . . . . 182
7.3.2 Joining conditions . . . . . . . . . . . . . . . . . . . . 183
7.4 Mass streaming . . . . . . . . . . . . . . . . . . . . . . . . . . 190
7.4.1 Gedeon streaming ("dc flow") . . . . . . . . . . . . . . 193
7.4.2 Rayleigh streaming . . . . . . . . . . . . . . . . . . . . 197
7.4.3 Jet-driven streaming . . . . . . . . . . . . . . . . . . . 202
7.4.4 Streaming within a regenerator or stack . . . . . . . . 204
7.4.5 Deliberate streaming . . . . . . . . . . . . . . . . . . . 205
7.5 Harmonics and shocks . . . . . . . . . . . . . . . . . . . . . . 212
7.6 Dimensionless groups . . . . . . . . . . . . . . . . . . . . . . . 216
7.6.1 Insight . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
7.6.2 Empirical correlation . . . . . . . . . . . . . . . . . . . 218
7.6.3 Scale models . . . . . . . . . . . . . . . . . . . . . . . 219
7.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
8 Hardware . . . . . 223
8.1 Prelude: the gas itself . . . . . . . . . . . . . . . . . . . . . . 223
8.2 Stacks and regenerators . . . . . . . . . . . . . . . . . . . . . 224
8.2.1 Standing wave . . . . . . . . . . . . . . . . . . . . . . 225
8.2.2 Traveling wave . . . . . . . . . . . . . . . . . . . . . . 231
8.3 Heat exchangers . . . . . . . . . . . . . . . . . . . . . . . . . 233
8.3.1 Common arrangements . . . . . . . . . . . . . . . . . 233
8.3.2 Thermoacoustic choices . . . . . . . . . . . . . . . . . 234
8.4 Thermal buffer tubes, pulse tubes, and flow straighteners . . 238
8.5 Resonators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
8.5.1 Dissipation . . . . . . . . . . . . . . . . . . . . . . . . 239
8.5.2 Size, weight, and pressure-vessel safety . . . . . . . . . 241
8.5.3 Harmonic suppression . . . . . . . . . . . . . . . . . . 242
8.6 Electroacoustic power transducers . . . . . . . . . . . . . . . 243
8.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
9 Measurements . . . 252
9.1 Easy measurements . . . . . . . . . . . . . . . . . . . . . . . . 252
9.1.1 Pressures and frequency . . . . . . . . . . . . . . . . . 253
9.1.2 Mean temperature . . . . . . . . . . . . . . . . . . . . 255
9.2 Power measurements . . . . . . . . . . . . . . . . . . . . . . . 256
9.2.1 Acoustic power . . . . . . . . . . . . . . . . . . . . . . 256
9.2.2 Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
9.3 Difficult measurements . . . . . . . . . . . . . . . . . . . . . . 262
9.4 Points of view . . . . . . . . . . . . . . . . . . . . . . .
. . . . 263
9.4.1 Natural dependence . . . . . . . . . . . . . . . . . . . 264
9.4.2 Evidence . . . . . . . . . . . . . . . . . . . . . . . . . 266
9.4.3 Performance . . . . . . . . . . . . . . . . . . . . . . . 268
9.4.4 A thermoacoustic perspective . . . . . . . . . . . . . . 271
9.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
A Common pitfalls 285
B DeltaEC files . . . 287
B.1 Standing-wave engine . . . . . . . . . . . . . . . . . . . . . . 287
B.2 Standing-wave refrigerator . . . . . . . . . . . . . . . . . . . . 290
B.3 Orifice pulse-tube refrigerator . . . . . . . . . . . . . . . . . . 292
B.4 Thermoacoustic-Stirling heat engine . . . . . . . . . . . . . . 295
Bibliography . . . 302
Author index . . . 313
Subject index . . . 316
Greg Swift received his PhD in physics at the University of California at Berkeley in 1980, and has worked in the Condensed Matter and Thermal Physics Group at Los Alamos National Laboratory (LANL) ever since. He is a Fellow of the Acoustical Society of America, of the American Physical Society, and of LANL. He received the Acoustical Society's Silver Medal in Physical Acoustics in 2000, an award that has been given, on average, only every three years. He received the US Department of Energy's E.O. Lawrence Award in 2004, in the category of Environmental Science and Technology. The main focus of Greg's research has been the invention and development of novel energy-conversion technologies. He enjoys the thermodynamics of heat engines and refrigerators, the thermodynamics of non-ideal-gas fluids, physical acoustics, hydrodynamics, and low-temperature physics. He hopes that thermoacoustic engines and refrigerators will play a meaningful role in the energy economy of the 21st century.
At Los Alamos, Greg has mentored two Masters students, three Ph.D. students, and 13 postdocs, and enjoyed significant partnerships with ten corporate collaborators. He is co-author (or, occasionally, sole author) of about 100 articles in refereed journals and conference proceedings. He is responsible for two dozen patents, and the thermoacoustics design and analysis software most commonly used worldwideDeltaEC.