NOVEL DIAPHRAGM FREE-PISTON STIRLING CRYOCOOLER Alan Caughley, BE (Hons), ME A thesis presented for the degree of Doctor of Philosophy in Mechanical Engineering Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand, 2015 i CONTENTS List of Figures ................................................................................................................................................ vii List of Tables .................................................................................................................................................. xv Acknowledgements .................................................................................................................................... xvi Abstract .......................................................................................................................................................... xvii Nomenclature ............................................................................................................................................ xviii 1 Introduction ............................................................................................................................................ 1 1.1 Hypotheses ...................................................................................................................................................... 6 1.2 Methodology .................................................................................................................................................... 8 1.2.1 Proof of concept prototype free-piston expander. ................................................................ 8 1.2.2 Modelling of oscillating radial flows ............................................................................................ 9 1.2.3 Improved Diaphragm Stirling Cryocooler. ............................................................................. 10 1.3 Background Theory ................................................................................................................................... 11 1.3.1 Gas refrigeration cycles .................................................................................................................. 11 1.3.2 Stirling Cycle Description .............................................................................................................. 17 1.3.3 Configurations of Stirling machines .......................................................................................... 19 1.3.4 Free-piston Stirling systems ........................................................................................................ 20 1.4 Description of Modelling tools .............................................................................................................. 23 1.4.1 Sage......................................................................................................................................................... 23 1.4.2 CFD analysis with ANSYS® CFX ................................................................................................. 26 1.5 Novel aspects of the work ....................................................................................................................... 35 2 Literature ................................................................................................................................................ 37 2.1 Stirling cycle ................................................................................................................................................. 37 2.1.1 History ................................................................................................................................................... 37 2.1.2 Philips Stirling .................................................................................................................................... 37 2.1.3 Work of Beale ..................................................................................................................................... 37 2.1.4 Work of Cooke-Yarborough ......................................................................................................... 38 ii 2.1.5 Pulse Tube Cryogenic refrigerators .......................................................................................... 39 2.1.6 The IRL diaphragm pressure wave generators .................................................................... 40 2.2 Radial oscillating flow literature review .......................................................................................... 42 2.2.1 Heat transfer in oscillating flows ............................................................................................... 42 2.2.2 Kornhauser and Smith’s Gas spring experiments ............................................................... 42 2.2.3 Huang’s model of flow in a diaphragm pressure wave generator ................................ 48 2.3 Modelling porous regenerator screens ............................................................................................. 49 3 Diaphragm Free Piston Stirling Cryocooler Concept............................................................. 51 3.1 The Concept .................................................................................................................................................. 51 3.2 Modelling ....................................................................................................................................................... 54 3.2.1 Performance prediction, & characteristics ............................................................................ 58 3.2.2 Frequency and cooling power ..................................................................................................... 59 3.2.3 Model sensitivities ........................................................................................................................... 60 3.2.4 Parasitic losses not included in the Sage model .................................................................. 65 3.2.5 Pressure wave generator efficiency .......................................................................................... 66 3.2.6 Conclusions ......................................................................................................................................... 66 3.3 Proof-of-concept prototype ................................................................................................................... 67 3.3.1 Design .................................................................................................................................................... 67 3.3.2 Material Considerations ................................................................................................................. 68 3.3.3 Revised Sage Model ......................................................................................................................... 68 3.3.4 Initial Testing and modifications ............................................................................................... 69 3.3.5 Temperature transients ................................................................................................................. 71 3.3.6 Characterisation and verification Experiment ..................................................................... 73 3.3.7 Cool-down test ................................................................................................................................... 76 3.3.8 Discussion / Conclusions ............................................................................................................... 77 3.4 Second Prototype ....................................................................................................................................... 79 3.4.1 Introduction ........................................................................................................................................ 79 3.4.2 Prototype description ..................................................................................................................... 80 3.4.3 Sage Model.......................................................................................................................................... 81 iii 3.4.4 Experimental Performance .......................................................................................................... 87 3.4.5 Parameters for subsequent modelling .................................................................................... 91 3.4.6 Cool-down experiments ................................................................................................................. 92 3.4.7 Conclusion ........................................................................................................................................... 97 4 CFD Modelling of Oscillating Radial Flows ................................................................................ 99 4.1 Introduction ................................................................................................................................................. 99 4.2 Key Assumptions ...................................................................................................................................... 103 4.3 Modelling Kornhauser & Smith’s experiment .............................................................................. 111 4.3.1 Model 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