CRYOGENIC MICROCOOLING A MICROMACHINED COLD STAGE OPERATING WITH A SORPTION COMPRESSOR IN A VAPOR COMPRESSION CYCLE Johannes Burger The research described in this thesis was carried out at the MESA+ Research Institute of the University of Twente. It was a cooperative project between the Low Temperature Group and the Micromechanical Transducers Group in the Faculty of Applied Physics. The research was financed by the Dutch Technology Foundation (STW). De promotiecommissie: Voorzitter en secretaris: Prof. dr. ir. J.H.A. de Smit Universiteit Twente Promotoren: Prof. dr. H. Rogalla Universiteit Twente Prof. dr. M. Elwenspoek Universiteit Twente Assistent promotor: Dr. ir. H.J.M. ter Brake Universiteit Twente Leden: Prof. dr. Y. Bäcklund Mälardalen University, Sweden Prof. dr. A.T.A.M. de Waele Technische Universiteit Eindhoven Prof. dr. ir. J. van Amerongen Universiteit Twente Prof. dr. ir. T.H. van der Meer Universiteit Twente Deskundige: L.A. Wade Jet Propulsion Laboratory, USA Cover: A cold stage consisting of three micromachined silicon components that are interfaced by two coaxial glass-tube counterflow heat exchangers. The glass-tube heat exchangers are visible as the two thick tubes and consist of two tubes that are placed concentrically around each other; the orange color is caused by a coating. The two thin glass tubes that are visible are included to add mechanical stability to the system. Thin-film heaters with a gold layer on top of it are located on the three silicon parts. The left part combines the high and low pressure gas lines in the first counterflow heat exchanger, the middle part is a condenser where a vapor- liquid transition occurs, and the right part contains a flow restriction and an evaporator. This is the actual cold part. The interior of these three components is visible on the background photo, which shows part of a processed silicon wafer. Cryogenic microcooling – A micromachined cold stage operating with a sorption compressor in a vapor compression cycle / Johannes F. Burger Ph.D. Thesis, University of Twente, Enschede, The Netherlands ISBN 90-365-1536-X Copyright © 2001 by Johannes Burger, Enschede, The Netherlands CRYOGENIC MICROCOOLING A MICROMACHINED COLD STAGE OPERATING WITH A SORPTION COMPRESSOR IN A VAPOR COMPRESSION CYCLE PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Universiteit Twente, op gezag van de rector magnificus, prof. dr. F.A. van Vught, volgens besluit van het College voor Promoties in het openbaar te verdedigen op vrijdag 12 januari 2001 te 16.45 uur. door Johannes Faas Burger geboren op 20 oktober 1969 te Doornspijk Dit proefschrift is goedgekeurd door: Prof. dr. H Rogalla (promotor) Prof. dr. M. Elwenspoek (promotor) Dr. ir. H.J.M. ter Brake (assistent promotor) Contents NOMENCLATURE..................................................................................................................................... V 1 INTRODUCTION................................................................................................................................ 1 1.1 GENERAL INTRODUCTION ...............................................................................................................1 1.2 CRYOGENICS .................................................................................................................................2 1.3 RESEARCH GOALS ..........................................................................................................................3 1.4 OUTLINE OF THESIS ........................................................................................................................4 1.5 REFERENCES..................................................................................................................................4 2 CRYOCOOLER THEORY................................................................................................................. 7 2.1 INTRODUCTION..............................................................................................................................7 2.2 ELEMENTARY REFRIGERATOR THERMODYNAMICS ...........................................................................8 2.3 REGENERATIVE COOLING CYCLES .................................................................................................13 2.3.1 Classification and common aspects of regenerative cooling cycles ..........................................13 2.3.2 The regenerator ......................................................................................................................15 2.3.3 Stirling cycle..........................................................................................................................16 2.3.4 Gifford-McMahon and Solvay cycles......................................................................................25 2.3.5 Vuillemier cycle.....................................................................................................................27 2.3.6 Pulse tube cycle......................................................................................................................29 2.3.7 Regenerative cooling losses ....................................................................................................30 2.3.8 Twente-Stirling cycle .............................................................................................................31 2.4 RECUPERATIVE COOLING CYCLES..................................................................................................37 2.4.1 Classification and common aspects of recuperative cooling cycles ..........................................37 2.4.2 Vapor compression cycle........................................................................................................39 2.4.3 Linde-Hampson cycle.............................................................................................................41 2.4.4 Joule-Brayton cycle ................................................................................................................43 2.5 OTHER COOLING PRINCIPLES.........................................................................................................44 2.5.1 Thermoelectric coolers ...........................................................................................................44 2.5.2 Magnetocaloric cooling ..........................................................................................................47 2.5.3 Optical cooling.......................................................................................................................47 2.6 CONCLUSIONS..............................................................................................................................48 2.7 REFERENCES................................................................................................................................48 3 MINIATURIZATION OF CRYOCOOLERS .................................................................................. 51 3.1 INTRODUCTION............................................................................................................................51 3.2 MICROFABRICATION ....................................................................................................................53 3.2.1 Materials................................................................................................................................53 3.2.2 Micromechanical fabrication techniques.................................................................................55 3.3 THEORY AND SCALING .................................................................................................................58 3.3.1 Mechanics..............................................................................................................................62 3.3.2 Actuators................................................................................................................................63 3.3.3 Fluid mechanics .....................................................................................................................71 3.3.4 Heat transfer...........................................................................................................................73 3.3.4.1 Steady-state conduction ..............................................................................................................73 3.3.4.2 Transient Conduction .................................................................................................................76 3.3.4.3 Radiation....................................................................................................................................78 3.3.4.4 Convective heat transfer .............................................................................................................81 3.3.4.5 Boiling and condensation ...........................................................................................................84 3.3.4.6 Thermal regenerative heat losses ................................................................................................85 3.3.5 Fluid mechanics and heat transfer in microchannels...............................................................85 3.3.6 Scaling conclusions................................................................................................................87 3.4 MINIATURIZATION OF REGENERATIVE COOLING CYCLES.................................................................88 i 3.5 MINIATURIZATION OF RECUPERATIVE