Allan J. Organ, formerly of University of Cambridge, UK - now retired.
Before his retirement Allan J. Organ was a lecturer at the University of Cambridge, specializing in thermodynamics and gas dynamics of the Stirling cycle machine and regenerator.He has studied stirling cycle machines throughout his career and is a leading authority in the field. As well as his teaching work, he has acted as a consultant in this area for numerous companies including Hymatic Ltd, Premier Precision Ltd, Lucas Aerospace Ltd, British Aerospace PLC, as well as for the Ministry of Defense.

Foreword xiii

Preface xvii

Notation xix

1 Stirling myth – and Stirling reality 1

1.1 Expectation 1

1.2 Myth by myth 2

1.2.1 That the quarry engine of 1818 developed 2 hp 2

1.2.2 That the limiting efficiency of the stirling engine is that of the Carnot cycle 4

1.2.3 That the 1818 engine operated ‘…on a principle entirely new’ 5

1.2.4 That the invention was catalyzed by Stirling’s concern over steam boiler explosions 5

1.2.5 That younger brother James was the true inventor 6

1.2.6 That 90 degrees and unity respectively are acceptable ‘default’ values for thermodynamic phase angle α and volume ratio κ 6

1.2.7 That dead space (un-swept volume) is a necessary evil 6

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, εTx = 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

5.3.1 Volumetric compression ratio rv 37

5.3.2 Indicator diagram shape 37

5.3.3 More from the re-worked Schmidt analysis 40

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

10.2.1 Independent variables 84

10.2.2 Dependent variables 85

10.2.3 Local, instantaneous Reynolds number Re 87

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

14.2.1 Tubular exchangers 142

14.2.2 Regenerator 143

14.3 Regenerator matrix 145

14.4 Rationale behind ReScale 145

14.4.1 Tubular exchangers 145

14.4.2 Regenerator 146

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 REω and XQXE 167

16.3.1 Corroboration from dimensional analysis 169

17 Wire-mesh regenerator – ‘back of envelope’ sums 171

17.1 Status quo 171

17.2 Temperature swing 171

17.2.1 Thermal capacity ratio 172

17.3 Aspects of flow design 173

17.4 A thumb-nail sketch of transient response 181

17.4.1 Rationalizations 181

17.4.2 Specimen temperature solutions 183

17.5 Wire diameter 184

17.5.1 Thermal penetration depth 187

17.5.2 Specifying the wire mesh 189

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

18.4.1 Ideal gas law 205

18.4.2 Energy equation – variable-volume spaces 205

18.5 Specimen implementation 206

18.5.1 Authentication 206

18.5.2 Function form 207

18.5.3 Reynolds number in the annular gap 207

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

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