Stirling Cycle Engines

Some 200 years after the original invention, the internal design of a Stirling engine has come to be considered a specialist task, calling for extensive experience and for access to sophisticated computer modelling. The low parts-count of the type is negated by the complexity of the gas processes by which heat is converted to work. The design is perceived as problematic largely because those interactions are neither intuitively evident, nor capable of being made visible by laboratory experiment. There can be little doubt that the situation stands in the way of wider application of this elegant concept.
Stirling Cycle Engines re-visits the design challenge, doing so in three stages. Firstly, unrealistic expectations are dispelled: chasing the Carnot efficiency is a guarantee of disappointment, since the Stirling engine has no such pretentions. Secondly, no matter how complex the gas processes, they embody a degree of intrinsic similarity from engine to engine. Suitably exploited, this means that a single computation serves for an infinite number of design conditions. Thirdly, guidelines resulting from the new approach are condensed to high-resolution design charts - nomograms.
Appropriately designed, the Stirling engine promises high thermal efficiency, quiet operation and the ability to operate from a wide range of heat sources. Stirling Cycle Engines offers tools for expediting feasibility studies and for easing the task of designing for a novel application.
Key features:

• Expectations are re-set to realistic goals.
• The formulation throughout highlights what the thermodynamic processes of different engines have in common rather than what distinguishes them.
• Design by scaling is extended, corroborated, reduced to the use of charts and fully Illustrated.
• Results of extensive computer modelling are condensed down to high-resolution Nomograms.
• Worked examples feature throughout.

Prime movers (and coolers) operating on the Stirling cycle are of increasing interest to industry, the military (stealth submarines) and space agencies. Stirling Cycle Engines fills a gap in the technical literature and is a comprehensive manual for researchers and practitioners. In particular, it will support effort world-wide to exploit the potential for such applications as small-scale CHP (combined heat and power), solar energy conversion and the utilization of low-grade heat.

About the Author xi Foreword xiii
Preface xvii
Notation xix
1 Stirling myth - and Stirling reality 1
1. 1 Expectation 1
1. 2 Myth by myth 2
1. 3 . . . and some heresy 7
1. 4 Why this crusade? 7
2 R eflexions sur le cicle de Carnot 9
2. 1 Background 9
2. 2 Carnot re-visited 10
2. 3 Isothermal cylinder 11
2. 4 Specimen solutions 14
2. 5 'Realistic' Carnot cycle 16
2. 6 'Equivalent' polytropic index 16
2. 7 R eflexions 17
3 What Carnot efficiency? 19
3. 1 Epitaph to orthodoxy 19
3. 2 Putting Carnot to work 19
3. 3 Mean cycle temperature difference, Tx = T - Tw 20
3. 4 Net internal loss by inference 21
3. 5 Why no p-V diagram for the 'ideal' Stirling cycle? 23
3. 6 The way forward 23
4 Equivalence conditions for volume variations 25
4. 1 Kinematic configuration 25
4. 2 'Additional' dead space 27
4. 3 Net swept volume 32
5 The optimum versus optimization 33
5. 1 An engine from Turkey rocks the boat 33
5. 2 . . . and an engine from Duxford 34
5. 3 Schmidt on Schmidt 36
5. 4 Crank-slider mechanism again 41
5. 5 Implications for engine design in general 42
6 Steady-flow heat transfer correlations 45
6. 1 Turbulent - or turbulent? 45
6. 2 Eddy dispersion time 47
6. 3 Contribution from 'inverse modelling' 48
6. 4 Contribution from Scaling 50
6. 5 What turbulence level? 52
7 A question of adiabaticity 55
7. 1 Data 55
7. 2 The Archibald test 55
7. 3 A contribution from Newton 56
7. 4 Variable-volume space 57
7. 5 D esax e 59
7. 6 Thermal diffusion - axi-symmetric case 60
7. 7 Convection versus diffusion 61
7. 8 Bridging the gap 61
7. 9 Interim deductions 64
8 More adiabaticity 65
8. 1 'Harmful' dead space 65
8. 2 'Equivalent' steady-flow closed-cycle regenerative engine 66
8. 3 'Equivalence' 68
8. 4 Simulated performance 68
8. 5 Conclusions 70
8. 6 Solution algorithm 71
9 Dynamic Similarity 73
9. 1 Dynamic similarity 73
9. 2 Numerical example 75
9. 3 Corroboration 79
9. 4 Transient response of regenerator matrix 80
9. 5 Second-order effects 82
9. 6 Application to reality 82
10 Intrinsic Similarity 83
10. 1 Scaling and similarity 83
10. 2 Scope 83
10. 3 First steps 88
10. 4 . . . without the computer 90
11 Getting started 97
11. 1 Configuration 97
11. 2 Slots versus tubes 98
11. 3 The 'equivalent' slot 102
11. 4 Thermal bottleneck 104
11. 5 Available work lost - conventional arithmetic 107
12 FastTrack gas path design 109
12. 1 Introduction 109
12. 2 Scope 110
12. 3 Numerical example 110
12. 4 Interim comment 118
12. 5 Rationale behind FastTrack 118
12. 6 Alternative start point - GPU-3 charged with He 121
13 FlexiScale 129
13. 1 FlexiScale? 129
13. 2 Flow path dimensions 130
13. 3 Operating conditions 133
13. 4 Regenerator matrix 137
13. 5 Rationale behind FlexiScale 137
14 ReScale 141
14. 1 Introduction 141
14. 2 Worked example step-by-step 141
14. 3 Regenerator matrix 145
14. 4 Rationale behind ReScale 145
15 Less steam, more traction - Stirling engine design without the hot air 149
15. 1 Optimum heat exchanger 149
15. 2 Algebraic development 150
15. 3 Design sequence 153
15. 4 Note of caution 159
16 Heat transfer correlations - from the horse's mouth 163
16. 1 The time has come 163
16. 2 Application to design 166
16. 3 Rationale behind correlation parameters RE and XQXE 167
17 Wire-mesh regenerator - 'back of envelope' sums 171
17. 1 Status quo 171
17. 2 Temperature swing 171
17. 3 Aspects of flow design 173
17. 4 A thumb-nail sketch of transient response 181
17. 5 Wire diameter 184
17. 6 More on intrinsic similarity 190
18 Son of Schmidt 199
18. 1 Situations vacant 199
18. 2 Analytical opportunities waiting to be explored 200
18. 3 Heat exchange - arbitrary wall temperature gradient 201
18. 4 Defining equations and discretization 205
18. 5 Specimen implementation 206
18. 6 Integration 208
18. 7 Specimen temperature solutions 211
19 H2 versus He versus air 215
19. 1 Conventional wisdom 215
19. 2 Further enquiry 216
19. 3 So, why air? 217
20 The 'hot air' engine 219
20. 1 In praise of arithmetic 219
20. 2 Reynolds number Re in the annular gap 222
20. 3 Contact surface temperature in annular gap 223
20. 4 Design parameter Ld Mg 225
20. 5 Building a specification 226
20. 6 Design step by step 228
20. 7 Gas path dimensions 229
20. 8 Caveat 234
21 Ultimate Lagrange formulation? 235
21. 1 Why a new formulation? 235
21. 2 Context 235
21. 3 Choice of display 236
21. 4 Assumptions 238
21. 5 Outline computational strategy 240
21. 6 Collision mechanics 240
21. 7 Boundary and initial conditions 244
21. 8 Further computational economies 244
21. 9 'Ultimate Lagrange'? 245
Appendix 1 The reciprocating Carnot cycle 247
Appendix 2 Determination of V2 and V4 - polytropic processes 249
Appendix 3 Design charts 251
Appendix 4 Kinematics of lever-crank drive 257
References 261
Name Index 267
Subject Index 269