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Heat Transfer Correlations Between a Heated Surface and Liquid & Superfluid Helium

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Heat Transfer Correlations Between a Heated Surface and Liquid & Superfluid Helium Heat Transfer Correlations Between a Heated Surface and Liquid & Superfluid Helium For Better Understanding of the Thermal Stability of the Superconducting Dipole Magnets in the LHC at CERN Jonas Lantz LITH-IEI-TEK-A--07/00225--SE Examensarbete Institutionen för ekonomisk och industriell utveckling Examensarbete LITH-IEI-TEK-A--07/00225--SE Heat Transfer Correlations Between a Heated Surface and Liquid & Superfluid Helium For Better Understanding of the Thermal Stability of the Superconducting Dipole Magnets in the LHC at CERN Jonas Lantz Handledare: Arjan Verweij CERN, Accelerator Technology Department Gerard Willering CERN, Accelerator Technology Department Examinator: Dan Loyd IEI, Linköping University Linköping, 19 October, 2007 Avdelning, Institution Datum Division, Department Date Division of Applied Thermodynamics and Fluid Me- chanics Department of Management and Engineering 2007-10-19 Linköpings universitet SE-581 83 Linköping, Sweden Språk Rapporttyp ISBN Language Report category — Svenska/Swedish Licentiatavhandling ISRN Engelska/English Examensarbete LITH-IEI-TEK-A--07/00225--SE C-uppsats Serietitel och serienummer ISSN D-uppsats Title of series, numbering — Övrig rapport URL för elektronisk version http://www.ikp.liu.se/mvs/ http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-10124 Titel Heat Transfer Correlations Between a Heated Surface and Liquid & Superfluid Title Helium For Better Understanding of the Thermal Stability of the Superconducting Dipole Magnets in the LHC at CERN Författare Jonas Lantz Author Sammanfattning Abstract This thesis is a study of the heat transfer correlations between a wire and liquid helium cooled to either 1.9 or 4.3 K. The wire resembles a part of a supercon- ducting magnet used in the Large Hadron Collider (LHC) particle accelerator currently being built at CERN. The magnets are cooled to 1.9 K and using helium as a coolant is very efficient, especially at extremely low temperatures since it then becomes a superfluid with an apparent infinite thermal conductivity. The cooling of the magnet is very important, since the superconducting wires need to be thermally stable. Thermal stability means that a superconductive magnet can remain super- conducting, even if a part of the magnet becomes normal conductive due to a temperature increase. This means that if heat is generated in a wire, it must be transferred to the helium by some sort of heat transfer mechanism, or along the wire or to the neighbouring wires by conduction. Since the magnets need to be superconductive for the operation of the particle accelerator, it is crucial to keep the wires cold. Therefore, it is necessary to understand the heat transfer mechanisms from the wires to the liquid helium. The scope of this thesis was to describe the heat transfer mechanisms from a heater immersed in liquid and superfluid helium. By performing both experi- ments and simulations, it was possible to determine properties like heat transfer correlations, critical heat flux limits, and the differences between transient and steady-state heat flow. The measured values were in good agreement with values found in literature with a few exceptions. These differences could be due to measurement errors. A numerical program was written in Matlab and it was able to simulate the experimental temperature and heat flux response with good accuracy for a given heat generation. Nyckelord Keywords superfluid, helium, heat transfer correlation, cooling Abstract This thesis is a study of the heat transfer correlations between a wire and liquid he- lium cooled to either 1.9 or 4.3 K. The wire resembles a part of a superconducting magnet used in the Large Hadron Collider (LHC) particle accelerator currently be- ing built at CERN. The magnets are cooled to 1.9 K and using helium as a coolant is very efficient, especially at extremely low temperatures since it then becomes a superfluid with an apparent infinite thermal conductivity. The cooling of the mag- net is very important, since the superconducting wires need to be thermally stable. Thermal stability means that a superconductive magnet can remain superconduct- ing, even if a part of the magnet becomes normal conductive due to a temperature increase. This means that if heat is generated in a wire, it must be transferred to the helium by some sort of heat transfer mechanism, or along the wire or to the neighbouring wires by conduction. Since the magnets need to be superconductive for the operation of the particle accelerator, it is crucial to keep the wires cold. Therefore, it is necessary to understand the heat transfer mechanisms from the wires to the liquid helium. The scope of this thesis was to describe the heat transfer mechanisms from a heater immersed in liquid and superfluid helium. By performing both experi- ments and simulations, it was possible to determine properties like heat transfer correlations, critical heat flux limits, and the differences between transient and steady-state heat flow. The measured values were in good agreement with values found in literature with a few exceptions. These differences could be due to mea- surement errors. A numerical program was written in Matlab and it was able to simulate the experimental temperature and heat flux response with good accuracy for a given heat generation. v Acknowledgments This thesis have been conducted at the AT-MCS-SC group at CERN, and I would like to thank my supervisor Arjan Verweij for his invaluable support, thoughts and guidance during the year I spent at CERN. I would also like to give my warm thanks to my ”unofficial” supervisor and collegue Gerard Willering who supported me throughout my project, took the time to answer my stupid questions and helped me with a lot of other things, no matter if it was work-related or just finding the fastest way up a mountain. Dank u wel! For support in the laboratory and help with the cryogenic systems I would like to give my sincere thanks to Stefano Geminian, Pierre-François Jacquot, Alejandro Bastos Marzal, Jean Louis Servais, and David Richter. Without your help my measurements would not have been done. Un grand merci à tous! A big thanks also goes to my examiner Dan Loyd, who gave valuable feedback and ideas to my project. Tack! Finally, I would like to thank all my friends in Geneva for making my time here unforgettable. I am going to miss the snowboarding, hiking, partying and all the other good times we shared during this year. Thank you, Merci, Tack, Takk, Danke, Grazie, Gracias...! Jonas Lantz Geneva, September 2007 vii Contents 1 Introduction 9 1.1 CERN, a Short Introduction . .9 1.2 The Large Hadron Collider - LHC . .9 1.3 The Proton Beam . 11 1.4 Detectors . 11 1.5 The LHC Dipole Magnets . 11 1.6 Superconducting Cables . 13 1.7 Problem Formulation . 14 2 Theory 15 2.1 Superconductivity . 15 2.2 Superfluidity . 17 2.3 Liquid Helium . 18 2.3.1 Introduction . 18 2.3.2 Thermal Properties of Liquid and Superfluid Helium . 19 2.4 Helium as a Classical Fluid, He I . 21 2.4.1 Transient Heat Flow . 21 2.4.2 Natural Convection . 22 2.4.3 Nucleate Boiling . 23 2.4.4 Film Boiling . 23 2.4.5 Summary of He I Heat Flow . 24 2.5 Helium as a Quantum Fluid, He II . 25 2.5.1 The Two-fluid Model . 25 2.5.2 He II Dissipation Mechanisms . 26 2.5.3 He II Heat Transport . 27 2.5.4 Kapitza Conductance . 30 2.5.5 Transient Heat Flow Mechanisms . 30 2.5.6 Film Boiling . 31 2.5.7 Summary of He II Heat Flow . 32 3 Experimental Setup 33 3.1 Preparation . 34 3.1.1 Constantan Wire . 34 3.1.2 Thermocouples . 34 ix x Contents 3.1.3 Wiring . 37 3.1.4 Heat Generation and Heat Flux . 37 3.1.5 Signal Amplification . 37 3.1.6 Data Acquisition System, DAQ . 38 3.1.7 Cryostat . 38 3.1.8 Cernox Temperature Probes . 38 3.1.9 Assembly . 39 3.2 Measurements . 39 3.2.1 Measured Parameters at 4.3 K, He I . 40 3.2.2 Measured Parameters at 1.9 K, He II . 43 4 Numerical Model 45 4.1 Derivation of Governing Equations . 46 4.1.1 Finite Differences . 46 4.1.2 Boundary Conditions . 47 4.1.3 Material Parameters . 48 4.1.4 Heating . 49 4.1.5 Helium Heat Flow . 49 4.2 Matlab Implementation . 50 5 Results & Discussion 53 5.1 Results for He I . 53 5.1.1 Experimental Results . 53 5.1.2 Numerical Results . 57 5.1.3 Comparison . 59 5.2 Results for He II . 60 5.2.1 Experimental Results . 60 5.2.2 Numerical Results . 64 5.2.3 Comparison . 65 6 Conclusions & Future Work 67 Bibliography 69 A Calculations 71 A.1 Estimation of Heating Power to Heat up the Wire . 71 A.2 Scaling of Power and Current for Numerical Program . 72 A.3 Thermal Radiation Estimation . 73 B Graphs 75 B.1 Scale Factors . 75 B.2 Experimental Results at 4.3 K . 76 B.3 Experimental Results at 1.9 K . 79 C Source Code for Matlab Programs 82 C.1 Batch file . 82 C.2 Numerical program . 83 List of Figures 1.1 Layout of the CERN particle accelerators, not in scale. 10 1.2 The cross-section of the twin-aperture LHC dipole magnet. 12 1.3 The magnetic field produced in the dipole magnet. 12 1.4 Left: Photo of a Rutherford cable. Center: Photo of the cross- section of one wire, showing the copper matrix and bundles con- taining the Nb-Ti filaments. Right: Photo of the filaments in each bundle.
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