HEAT TRANSFER AND THERMODYNAMIC MODELING OF A STACKED DISK SPIRAL CHANNEL COUNTERFLOW HEAT EXCHANGER FOR USE IN JOULE-THOMSON CRYOCOOLERS By Jonah Latham Dunham A Thesis Submitted to the Faculty of the AEROSPACE AND MECHANICAL ENGINEERING DEPARTMENT In Partial Fulfillment of the Requirements For the Degree of MASTER OF SCIENCE WITH A MAJOR IN MECHANICAL ENGINEERING In the Graduate College University of Arizona 2005 1 STATEMENT BY AUTHOR This thesis has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this thesis are allowable without special permission, provided that accurate knowledge of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of this material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. Signed: _______________________ APPROVAL BY THESIS DIRECTOR This thesis has been approved on the date shown below: _____________________________ ________________________ Larry D. Sobel Date Adjunct Professor in Aerospace and Mechanical Engineering 2 TABLE OF CONTENTS ACKNOWLEDGEMENTS.............................................................................................5 DEDICATION................................................................................................................6 LIST OF FIGURES.........................................................................................................7 LIST OF TABLES ..........................................................................................................9 NOMENCLATURE......................................................................................................10 ABSTRACT..................................................................................................................11 CHAPTER 1 .................................................................................................................12 Introduction...............................................................................................................12 1.1 Background......................................................................................................12 1.1.1 Joule-Thomson Cryocoolers......................................................................12 1.1.2 Silicon Disk Spiral Channel Heat Exchanger.............................................14 1.1.3 Joule-Thomson Expansion ........................................................................18 1.2 Literature Review ............................................................................................20 1.3 Research Objectives.........................................................................................23 CHAPTER 2 .................................................................................................................25 Mathematical Formulations .......................................................................................25 2.1 Counterflow Heat Exchanger Theory ...............................................................26 2.1.1 Spiral Channel Disk Heat Exchanger Theory.............................................29 2.2 Joule-Thomson Expansion ...............................................................................31 2.3 Refrigeration Capacity .....................................................................................32 2.4 Pressure Drop ..................................................................................................33 CHAPTER 3 .................................................................................................................36 3 Numerical Formulations ............................................................................................36 3.1 Discretization of Heat Exchanger.....................................................................36 3.2 Linear Simultaneous Equation Solver...............................................................37 CHAPTER 4 .................................................................................................................40 Integration of REFPROP and Mathcad ......................................................................40 4.1 REFPROP........................................................................................................40 4.2 Mathcad...........................................................................................................40 4.3 REFPROP and Mathcad...................................................................................41 CHAPTER 5 .................................................................................................................43 Results.......................................................................................................................43 5.1 REFPROP Validation ......................................................................................43 5.2 Numerical Study of Varying Number of Disks.................................................45 5.3 Numerical Study of Varying Volumetric Flow Rate .........................................56 5.4 Discussion .......................................................................................................66 5.4.1 Varying Number of Disks .........................................................................66 5.4.2 Varying Volumetric Flow Rate..................................................................70 CHAPTER 6 .................................................................................................................73 Conclusions and Recommendations...........................................................................73 6.1 Conclusions .....................................................................................................73 6.2 Recommendations............................................................................................74 REFERENCE................................................................................................................76 APENDIX A.................................................................................................................78 Files on Disk .............................................................................................................78 4 ACKNOWLEDGEMENTS I would like to acknowledge the help of Eric W. Lemon and Chris D. Muzny, both of the National Institute of Standards and Technology, and both of whom were instrumental in helping me understand how C++ interfaces with REFPROP (NIST Standard Database 23). 5 DEDICATION I would like to dedicate this work to my family and friends for standing by me when things got tough, for never giving up on me, and for their endless love. I would like to especially dedicate this to my little buddy Chali Scooter, who got me through most of my time here at the University of Arizona. Unfortunately, he passed on before he could see me all the way to the end, but without him I never would have made it beyond my first year. 6 LIST OF FIGURES Figure 1.1 Joule-Thomson cryocooler............................................................................13 Figure 1.2 Temperature-entropy diagram for an ideal Joule-Thomson cryocooler..........14 Figure 1.3 Individual silicon disk spiral channel heat exchanger element.......................16 Figure 1.4 Silicon heat exchanger stack.........................................................................17 Figure 1.5 Counterflow heat exchanger in cryostat housing ...........................................17 Figure 1.6 Inversion curve for Joule-Thomson expansion ..............................................19 Figure 1.7 Hampson type JT cooler ...............................................................................21 Figure 1.8 Spiral coil heat exchanger; (a) schematic sketch of SCHE; (b) sketch of one coild..............................................................................................................................22 Figure 2.1 Schematic diagram of counterflow heat exchanger........................................26 Figure 2.2 Temperature profile across a counterflow heat exchanger from hot to cold fluid ..............................................................................................................................27 Figure 2.3 Archimedes’ spiral........................................................................................30 Figure 3.1 Discretization process of counterflow heat exchanger...................................36 Figure 5.1 Validation of isobaric heat capacity ..............................................................43 Figure 5.2 Validation of dynamic viscosity....................................................................44 Figure 5.3 Validation of thermal conductivity................................................................44 Figure 5.4 High-pressure channel Peclet number, varying number of disks....................48 Figure 5.5 Low-pressure channel Peclet number, varying number of disks ....................49 Figure 5.6 High-pressure channel Reynolds number, varying number of disks...............50 Figure 5.7 Low-pressure channel Reynolds number, varying number of disks ...............50 7 Figure 5.8 Outlet