High-power cryocooling Citation for published version (APA): Willems, D. W. J. (2007). High-power cryocooling. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR629372 DOI: 10.6100/IR629372 Document status and date: Published: 01/01/2007 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. 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If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected] providing details and we will investigate your claim. Download date: 27. Sep. 2021 High-Power Cryocooling PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op donderdag 20 september 2007 om 16.00 uur door Daniel Willem Jan Willems geboren te Roermond Dit proefschrift is goedgekeurd door de promotoren: prof.dr. A.T.A.M. de Waele en prof.dr. R.M.M. Mattheij drukwerk: Printservice TU/e omslag: Jasper Joppe Geers CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN Willems, Daniel W.J. High-power cryocooling / by Daniel Willem Jan Willems. - Eindhoven : Technische Universiteit Eindhoven, 2007. Proefschrift. - ISBN 978-90-386-1604-9 NUR 924 Trefw.: cryogene techniek / pulsbuiskoelers / thermodynamica / stromingsleer. Subject headings: cryogenics / pulse-tube refrigerators / thermodynamics / fluid dynamics. Contents 1 Introduction 1 1.1 Cryogeniccooling................................ 1 1.2 Stirling and pulse-tube refrigerators . ........... 2 1.3 Requirements for ’new-generation’ cryocoolers . .............. 4 1.4 Scopeofthisthesis............................... 5 2 Introduction to Pulse-Tube and Stirling Refrigerators 9 2.1 Thermodynamics and gas dynamics . 9 2.1.1 First and second law of thermodynamics . 9 2.1.2 Gasproperties ................................. 11 2.2 StirlingCryocoolers ............................. 13 2.2.1 Generalprinciple .............................. 13 2.2.2 Piston-displacer cryocoolers . 17 2.3 Pulse-Tube Refrigerators . 17 2.3.1 GeneralPrinciple.............................. 17 2.4 Regenerators .................................... 24 2.4.1 Introduction .................................. 24 2.4.2 Governing equations . 25 2.5 Lossesinthepulsetube ............................ 33 2.5.1 Introduction .................................. 33 2.5.2 Turbulence ................................... 34 2.5.3 Surfaceheatpumping . .. .. .. .. .. .. .. .. .. .. .. 34 2.5.4 Streaming.................................... 37 2.5.5 Conclusions................................... 39 3 Modeling and Simulation 45 3.1 Introduction.................................... 45 3.2 StirlingModeling................................ 45 3.2.1 TheStirlingModel.............................. 45 3.3 Pulse-tubemodeling .............................. 50 3.3.1 Introduction .................................. 50 3.3.2 Harmonicmodel ................................ 51 3.3.3 The Stirling pulse-tube model . 56 3.3.4 CommercialCFDCode ............................ 63 3.3.5 Dedicated numerical model . 71 3.3.6 Conclusions................................... 79 i ii CONTENTS 4 Inertance tubes and other phase shifters 83 4.1 Introduction.................................... 83 4.2 Inertancetubes .................................. 85 4.2.1 Generalprinciples ............................. 85 4.2.2 Inertance-tube models . 85 4.2.3 Modelresults .................................. 88 4.2.4 Discussion and conclusions . 91 5 Pulse-tube experiments - Setup 1 95 5.1 Introduction.................................... 95 5.2 Experimentalsetup............................... 95 5.2.1 Data acquisition and instrumentation . 100 5.3 Experimentalresults . .. .. .. .. .. .. .. .. .. .. .. .. 102 5.3.1 Introduction .................................. 102 5.3.2 Instabilities ................................. 102 5.3.3 Measurements at different pressures and frequencies . ........... 105 5.3.4 Inertancetube ................................. 105 5.4 Discussion and conclusions . 109 6 Pulse-tube experiments - Setup 2 113 6.1 Introduction.................................... 113 6.2 Experimentalsetup............................... 113 6.3 Experimentalresults . .. .. .. .. .. .. .. .. .. .. .. .. 117 6.3.1 OrificePulsetube ............................... 117 6.3.2 Inertance-tube experiments . 124 6.3.3 Conclusions and discussion . 129 6.4 Stirling Pulse-Tube Model Validation . .......... 130 6.4.1 Discussion and conclusions . 136 6.5 Discussion and conclusions . 136 7 Design of industrial cryocoolers 141 7.1 Introduction.................................... 141 7.2 Generalrequirements. 141 7.3 Compressorintegration . 143 7.4 Pulse-tube cryocoolers with linear drive . ........... 146 7.4.1 Compressor integration . 146 7.4.2 Scaling and further optimization . 146 7.5 StirlingCryocoolers ............................. 148 7.5.1 Designcalculations. 148 7.5.2 The Cryosphere, a free-displacer Stirling cryocooler............. 153 7.6 Discussion and conclusions . 159 8 Conclusions and future work 165 8.1 Conclusions ..................................... 165 8.2 Futurework...................................... 166 Nomenclature 167 Summary 171 CONTENTS iii Samenvatting 173 Nawoord 175 Curriculum Vitae 177 iv CONTENTS Chapter 1 Introduction 1.1 Cryogenic cooling Cryogenics can be described as the branch of physics dealing with the production and effects of very low temperatures [1]. There is no specific definition of ’very low temperatures’. People use the boiling points of nitrogen (77 K), air (79 K), or natural gas (111 K) as the limit. Also the limit of 100 K and lower is often used. Domestic refrigeration techniques used in household or industrial applications such as condensation-evaporation systems are not considered cryogenic. One could say cryogenic cooling is cooling that requires more advanced techniques to reach and maintain those temperatures. Cryogenic cooling can be realized by using so-called cryocoolers. Cryocoolers are machines that supply refrigeration with a working gas that goes through a specific thermodynamic cycle. All these cycles use compression and expansion of gasses to transport energy from one state to the other. Compression of a working gas causes it to heat up. This heat is removed. Expansion of the gas causes it to cool down. This reduction of temperature is used for refrigeration. Compression can be realized by a piston, scroll/screw or even nonmechanical. Expansion can also be done several ways. First of all over a flow restriction, in a so-called Joule-Thomson cooler, where the working fluid is throttled over a flow restriction. This expansion is isenthalpic. In Claude and reverse-Brayton coolers a turbine is used instead of the flow resistance. This way, the efficiency of the cooling cycle is increased because useful work can be extracted from the gas. This class of cryocoolers is called ’recuperative’, since the downstream fluid is recuperated (or precooled) by the upstream fluid. The other class of cycles is called ’regenerative’. In a regenerative cycle, the working fluid is transferred from compression to expansion in a periodical manner. The gas is moving back and forth through the machine. Between compression and expansion, heat is regenerated in a so-called regenerator. The Stirling coolers, pulse-tube refrigerators, and Gifford-McMahon (GM) coolers use a regenerative cycle. The application of cryogenic cooling is quite wide-spread. One can find applications for basically any sector. The biggest cryogenic installations are used for the separation of air. The main components of air are nitrogen (N2) and oxygen (O2). This separation of air on such a large scale is done by cryogenic distillation, in which the cold source is a cryocooler. On such large scales Linde or Claude cycles are used. Primary product of these large-scale air separation 1 CHAPTER 1. INTRODUCTION plants is oxygen. Oxygen is being used in the (petro-)chemical and steel producing industry, for instance for fueling