THE USE OF SAGE SIMULATION SOFTWARE IN THE DESIGN AND TESTING OF SUNPOWER’S PULSE TUBE CRYOCOOLER A thesis presented to the faculty of the Fritz J. and Dolores H. Russ College of Engineering and Technology of Ohio University In partial fulfillment of the requirements for the degree Master of Science Kyle B. Wilson June 2005 This thesis entitled THE USE OF SAGE SIMULATION SOFTWARE IN THE DESIGN AND TESTING OF SUNPOWER’S PULSE TUBE CRYOCOOLER BY KYLE B. WILSON has been approved for the School of Mechanical Engineering and the Russ College of Engineering and Technology by Khairul Alam Moss Professor of Mechanical Engineering Dennis Irwin Dean, Fritz J. and Dolores H. Russ College of Engineering and Technology WILSON, KYLE B. MS. June 2005. Mechanical Engineering The Use of Sage Simulation Software in the Design and Testing of Sunpower’s Pulse Tube Cryocooler (130 pp.) Director of Thesis: Khairul Alam ABSTRACT This thesis discusses the development of a pulse tube cryocooler and the use of a software simulation tool called Sage in this effort. A pulse tube cryocooler is a type of refrigerator that operates in the cryogenic temperature range below 120 K (-153° C). The goal of this thesis spans from a basic understanding of the ideal thermodynamics of the pulse tube cryocooler (PTC) to a grasp of one commercial software package’s ability to model an actual, non-ideal PTC. The history and theory are discussed leading to the state-of-the-art technology. The focus then turns to the specific development efforts of the author at his place of employment, Sunpower, Inc. The specific elements that led to the design of the Sunpower PTC are examined and the use of Sage simulation software is demonstrated. Finally, comparisons between experimental data and Sage predictions show the success of Sage as a simulation tool. Approved: Khairul Alam Moss Professor of Mechanical Engineering ACKNOWLEDGEMENTS I would first like to thank my wife Wendy and my sons Cody and Brendan for their support in my pursuit of this goal. Without their patience and understanding throughout the last five years I never would have been able to complete this work. Thanks to Sunpower, Inc., both the company and the employees, for giving me the opportunity to have a career with a company that makes me look forward to work every day (well, maybe not every day). Neill Lane and Gary Wood were the driving forces behind me starting on my MSME and the continual nudging and support of my co- workers has made the long road bearable. This work would have been impossible without the previous accomplishments of two leaders in the cryocooler industry, David Gedeon and Ray Radebaugh. I have been extremely fortunate to work directly with David Gedeon for the last several years and attempt to absorb just a small amount of his inherent feeling for the underlying physics behind the topic. Ray Radebaugh has shared so much of his experience and knowledge through tireless publications and presentations that allow someone like me to readily find thorough and clear information on the history and theory of pulse tube cryocoolers. Finally I owe thanks to Dr. Khairul Alam and my thesis committee, Dr. Izzi Urieli, Dr. John Deno and Gary Wood for not giving up on me in getting this completed and helping to guide me through the process. 5 TABLE OF CONTENTS ABSTRACT........................................................................................................................3 ACKNOWLEDGEMENTS ..............................................................................................4 LIST OF FIGURES ...........................................................................................................7 LIST OF TABLES ...........................................................................................................10 NOMENCLATURE.........................................................................................................11 Chapter 1. Introduction...................................................................................................14 1.1 Overview................................................................................................................14 1.2 Background............................................................................................................15 Chapter 2. Pulse Tube History .......................................................................................19 2.1 Recent Advances....................................................................................................21 2.1.1 Double Inlet Pulse Tube................................................................................21 2.1.2 Acoustic Streaming.......................................................................................23 2.1.3 Inertance........................................................................................................23 Chapter 3. Theory............................................................................................................24 3.1 Carnot Performance ...............................................................................................24 3.2 Stirling Cycle .........................................................................................................27 3.3 Gifford-McMahon (GM) Cycle .............................................................................30 3.4 Basic Pulse Tube....................................................................................................31 3.5 Orifice Pulse Tube .................................................................................................34 Chapter 4. Orifice Pulse Tube Cryocooler (OPTC) Analysis......................................36 4.1 Enthalpy and Entropy Flow Model........................................................................36 4.2 Ideal Efficiency......................................................................................................38 4.3 Pulse Tube Losses..................................................................................................39 4.4 Phase Shift .............................................................................................................40 Chapter 5. Inertance Tube..............................................................................................42 5.1 Electrical Analogy .................................................................................................42 Chapter 6. Project Motivation and Initial Design Methodology .................................45 6.1 Sunpower Linear Compressor................................................................................47 6.2 Gedeon Associates Sage Software.........................................................................48 6.3 Final Sunpower Pulse Tube Cryocooler Configurations .......................................50 Chapter 7. Modeling the Pulse Tube Cryocooler using Sage.......................................52 7.1 Linear Compressor.................................................................................................53 7.1.1 Piston/Cylinder and Compression space ......................................................53 6 TABLE OF CONTENTS (continued) 7.2 Cold Head ..............................................................................................................58 7.2.1 Main Rejector, Acceptor, Secondary Rejector (Heat Exchanges) ..............59 7.2.2 Main Rejector, Acceptor, Secondary Rejector.............................................60 7.2.3 Parasitic Warm Source and Cold Sink ........................................................61 7.2.4 Regnerator ...................................................................................................62 7.2.5 Pulse Tube ...................................................................................................63 7.3 Inertance Assembly................................................................................................64 7.4 Pulse Tube Cryocooler Assembly..........................................................................65 Chapter 8. Design and Fabrication of Hardware .........................................................67 8.1 Linear Compressor.................................................................................................67 8.2 Cold Head ..............................................................................................................73 8.3 Inertance Assembly................................................................................................77 8.4 Pulse Tube Cryocooler Assembly..........................................................................80 Chapter 9. Sensitivity Analysis .......................................................................................81 9.1 Compressor Swept Volume ...................................................................................81 9.2 Connecting Duct Length........................................................................................83 9.3 Regenerator Porosity..............................................................................................84 9.4 Pulse Tube Volume................................................................................................85 9.5 Inertance Tube Length ...........................................................................................87 9.6 Reservoir Volume ..................................................................................................92 Chapter 10. Subassembly Characterization..................................................................94