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Analysis of room temperature magnetic regenerative refrigeration Farhad Shir Catherine Mavriplis Lawrence H Bennett Edward Della Torre Institute for Magnetics Research George Washington University Washington DC 20052 USA Received 1 May 2004 received in revised form 17 August 2004 accepted 30 August 2004 Available online 10 December 2004 Abstract Results of a room temperature magnetic refrigeration test bed and an analysis using a computational model are presented A detailed demonstration of the four sequential processes in the transient magnetocaloric regeneration process of a magnetic material is presented The temperature profi le during the transient approach to steady state operation was measured in detail A 5 8C evolution of the difference of temperature between the hot end and the cold end of the magnetocaloric bed due to regeneration is reported A model is developed for the heat transfer and fl uid mechanics of the four sequential processes in each cycle of thermal wave propagation in the regenerative bed combined with the magnetocaloric effect The basic equations that can be used in simulation of magnetic refrigeration systems are derived and the design parameters are discussed q 2004 Elsevier Ltd and IIR All rights reserved Keywords Magnetic refrigeration Regeneration Cycle Modelling Heat transfer Froid magne tique a re ge ne ration a tempe rature ambiante analyse Mots cle s Froid magne tique Re ge ne ration Cycle Mode lisation Transfert de chaleur 1 Introduction Compared to conventional vapor compression systems magnetic refrigeration reviewed recently 1 can be an effi cient and environmentally friendly technology 2 Imposing and removing magnetic fi elds creates temperature changes in the magnetic material that acts as a solid refrigerant in a heat pump cycle Magnetic refrigeration has been used in gas liquefaction systems 3 cryogenic applications 4 and is a candidate for room temperature commercial and industrial refrigeration and air conditioning processes 5 Magnetic materials research for room temperature magnetic refrigeration has been conducted 6 7 and application projects of magnetic refrigeration have been demonstrated 8 11 at various institutions The objective of this paper is to describe a setup for a magnetic regenerative refrigeration test bed as well as a model to analytically determine the performance of a magnetic refrigeration system based on materials properties operating conditions and losses An analysis of the experimental results using a computational fl uid dynamics model as well as magneto thermodynamic considerations is performed Although the temperature profi le of the magnetic refrigeration in its steady state operation has been investigated 12 15 no non proprietary model was found available for assessing the system performance based on the transient response of the processes The phenomenon of International Journal of Refrigeration 28 2005 616 627 0140 7007 35 00 q 2004 Elsevier Ltd and IIR All rights reserved doi 10 1016 j ijrefrig 2004 08 015 Corresponding author Tel C1 703 777 8195 fax C1 703 726 8251 E mail address shir gwu edu F Shir regeneration in the magnetic regenerative refrigeration system is complicated because of the transient nature of the heating or cooling of the gas and refrigerant material Conversely the transient process is the most important part of this refrigeration system It determines the time that is required to obtain a certain amount of temperature divergence at both ends of the refrigerant bed and the magnitude of the temperature span Also the effect of change in the design parameters such as ambient tempera ture on the performance of the refrigeration system is addressed in the transient process In order to analyze and design an optimum magnetic regenerative refrigeration system the effects of each parameter on the transient stage need to be considered The transient process also determines the magnitude ofthe divergence of temperature on both ends of the test bed The results of this research can provide information on practical effi ciency attainable by a magnetic regenerative refrigeration system and indicate technical areas where research is needed for overcoming technical barriers limiting the development and application of the system These include selection of heat transfer fl uids magnetic material secondary heat transfer loop design selection and design of magnets for relevant temperature profi le and source and sink materials In Section 2 we will discuss magnetocaloric regener ation Section 3 describes the apparatus designed to experimentally make the measurements Development of a numerical model describing the temperature profi le of the magnetic regenerative bed is discussed in Section 4 The model is developed in two parts fi rst for the magnetization or demagnetization process and second for the regenerative aspects of the magnetic bed Analytical and numerical solutions to model are derived Section 5 outlines the experimental results and the results of the model calcu lations Finally Section 6 summarizes accomplishments of this research 2 Magnetocaloric regeneration Magnetic refrigeration is based on the magnetocaloric effect MCE which in the case of ferromagnetic materials is a warming as the magnetic moments of the atom are aligned by the application of a magnetic fi eld and the corresponding cooling upon removal of the magnetic fi eld 16 Two major diffi culties arise in the design of a magnetic refrigeration system First the magnetocaloric effect is fairly small in room temperature magnetocaloric materials e g in gadolinium Gd the application of a 5 T magnetic fi eld produces a maximum adiabatic temperature change of 11 K 17 Second the refrigerant is solid and thus is not easily pumped through heat exchangers as in the case of gas and vapor cycle refrigerants The problem of heat transfer and temperature span can be overcome with the introduction of a heat transfer fl uid and use of regeneration Regeneration can be accomplished by blowing fl uid in reciprocating Nomenclature asurface area per unit volume Cheat capacity CH specifi c heat at constant fi eld Dsolid particle diameter H magnetic fi eld strength ilength position In modifi ed Bessel function Kthermal conductivity Llength of the regenerator Mmagnetization mmass ntime position NuNusselt number PrPrandtl number sentropy Ttemperature ttime ReReynolds number trmean transit time T dimensionless temperature V specifi c volume xposition ynormalized distance zdimensionless length Znormalized period Greek letters m0magnetic permeability of free space 3porosity of the packed bed vinterstitial velocity tnon dimensional time ldimensionless number rdensity Subscripts ggas ssolid g0initial gas s0initial solid ininlet F Shir et al International Journal of Refrigeration 28 2005 616 627617 fashion through a porous bed of magnetocaloric material that is alternately magnetized and demagnetized Magnetic materials available for room temperature magnetic refrigeration are mainly Gd GdSiGe 18 alloys MnAs like 19 materials and Perovskite 20 materials We theoretically demonstrated in 21 that based on the refrigerant capacity calculations 22 nanocomposite clus ters could yield large MCE in a wide temperature region and have several advantages compared to the other refrigerants for a room temperature magnetic refrigeration system including the ability to closely follow the desired operating line and enhanced temperature change at high temperature and low fi eld 23 The active magnetic regenerator AMR is a specifi c kind of regenerator for magnetic refrigeration in which the magnetic material matrix works both as a refrigeration medium and as a heat regeneration medium while the fl uid fl ows in the porous matrix working as a heat transfer medium The basic theory of the active magnetic regen erator xv 24 is similar to that of an ordinary regenerator except that the thermophysical properties of the material are varied by the application and removal of a magnetic fi eld An AMR cycle consists of the four following segments bed magnetization warming the magnetic material and the bed fl uid by the MCE cold to hot fl uid fl ow through the bed transferring heat to the hot heat exchanger bed demagne tization cooling the magnetic material and fl uid and hot to cold fl uid fl ow through the bed absorbing heat at the cold heat exchanger Fig 1 shows the start of the transient process in a temperature vs time plot for both ends of the refrigerant bed The fi rst cycle can start with the demagnetization process and cooling down the entire bed to lower temperature During the cold blow process the temperature of the bed increases with a different rate at each end This causes the divergence in temperature profi le at both ends In the following magnetization process both ends of the refriger ant bed warm up Finally in the last process of the cycle in the warm blow the temperature of the bed decreases but again with different rates at each end This amplifi es the divergence phenomenon and at the end of the fi rst cycle the bed has a temperature distribution as a result of the AMR process 3 Experimental apparatus and measurements To study the critical parameters develop a model and evaluate tools for assessing active magnetic regenerative refrigeration atestbedwasdesigned Theschematicofthetest bedisshowninFig 2 ThisAMRtestbedwasusedtoevaluate theeffectoftheMCEinaregenerativeporousbedofGdwhile theexchangefl uidwasfl owinginareciprocatingpatternanda variable fi eld was applied to the refrigerant bed The test bed consists offour major parts 1 A commercial permanent adjustable fi eld magnet magic ring magnet produces a magnetic fi eld with a magnitude varying between 0 and 2 T over a range of frequencies Two nested permanent magnet cylinders generate the magnetic fi eld each of these producing 1 T The outer cylinder isfi xed a stepper motorrotatesthe inner cylinder to vary the magnitude of the resulting rotating fi eld In our set up the measured magnetic fi eld shows sinusoidal time dependence 2 The active regenerative porous bed consists of impure Gd magnetocaloric material in the form of turnings inserted intotheinnertubeofthemagnetthatspansthetemperature differencebetweencoldandhotendsoftherefrigerantbed 3 Between magnetic cycles the displacer moves the heat transferexchangegasthroughthebed absorbingheatatthe cold heat exchanger and rejecting heat to the hot heat exchanger This double acting displacer consists of a pair of reciprocating pistons cylinders operating in parallel 4 Thewarmandcoldheatexchangersystems whichremove the thermal energy produced in the magnetization and demagnetization process Water circulation in the inner tubesoftheheatexchangertransfersenergytothecoldand warm reservoirs This set up enables us to change different parameters and Fig 1 Schematic of temperature vs time for the fi rst sequential processes of an AMR cycle at both ends of the refrigerant bed Fig 2 Schematic of the basic operation of an AMR 1 permanent magnet 2 regenerative bed 3 piston cylinder displacer 4 heat exchanger F Shir et al International Journal of Refrigeration 28 2005 616 627618 investigate their effects on the performance of the cycle These parameters are the nature of the magnetocaloric material the shape and geometry of the refrigerant bed the nature and speed of the exchange fl uid the cycle period and the intensity of the magneticfi eld Inour experiment weused helium as the exchange fl uid to avoid oxidation of Gd in the bed The set up can be modifi ed and the temperature profi le forotherexchangefl uidssuchaswatercanbeinvestigatedfor non reactive refrigerants The temperature transients due to the periodic cycling of the AMR are shown in Fig 3 During the transient the difference inthe mean temperatureat the hot and coldends of the bed increases as does the peak to peak temperature variation of the quasi periodic temperature cycle When steady state is reached the temperature cycle is periodic and the average temperature difference between the bed ends remains constant The effect of regeneration is to change the rate of the temperature change at the two ends of the bed due to the transit time of the exchange gas through the bed Partof the data in Fig 3 inthe transientperiodfor the cold end of the refrigerant bed is expanded in Fig 4 This fi gure shows the four sequential processes of the AMR cycle bed magnetization warming the magnetic material and the bed fl uidby the MCE coldtohot exchange fl uidfl ow through the bed warm blow transferring heat to one end of the bed bed demagnetization cooling the magnetic material and exchange fl uid and hot to cold fl ow through the bed cold blow absorbing heat at the opposite end of the bed 4 Model In order to analyze and design an optimum magnetic refrigeration system it is important to model the magne tothermal behavior of the regenerative refrigerant bed during the four sequential processes of an AMR cycle Based on the theory of a magnetic regenerative refrigeration system that was presented and shown in Fig 1 there are four sequential processes in the AMR system Two of these processes magnetization and demagnetization of the refrigerant bed cause the temperature of the solid material to change as the result of the MCE These two processes share similarities in concept and are modeled together in the next section In between these two processes the exchange fl uid fl ows through the magnetocaloric bed and transfers the energy that is generated in the refrigerant Each of these two processes cold and hot blows provides an effective heat exchange based on the concept of regeneration in a porous solid material bed exposed to a fl uid stream passing through the bed These two regenerative processes associated with thermal wave propagation through the solid bed are modeled in the following section The bridges between these two models are the initial and boundary conditions of each process that connects thermal behavior of the two sequential processes to allow a cyclical operation of the AMR system We will derive the governing equations of the temperature profi le for the refrigerant bed and the exchange gas in transient process of an AMR These equations relate the magneto thermal properties of the refrigerant bed to the thermo fl uid aspect of the regenerative process in a quantitative model for two nonfl ow magnetization and demagnetizations steps and two regenerative hot and cold blows processes 4 1 Modeling of magnetization and demagnetization processes ThebasicthermodynamicsoftheMCEiswellknown 25 Fig 3 Experimental temperature profi le at the two ends of an AMR Gd test bed showing divergence with time Fig 4 Temperature profi le in the cold end of the magnetic regenerative test bed identifying the four sequential steps in each cycle F Shir et al International Journal of Refrigeration 28 2005 616 627619 We have performed 26 an entropy balance for the magnetocaloric solid refrigerant and the entrapped gas in the AMR bed dstotalZms CH T dT Cm0Vms vM vT HdH Cm gdsg 1 where s is the entropy m is the mass V is the specifi c volume of the magnetocaloric material m0is the magnetic permeability offree space CH is the specifi c heat at constant applied fi eld H is the magnetic fi eld strength and M is the magnetization The subscripts s and g refer to the solid and gas phases To study the transient behavior we have developed a time dependent model In our test bed the mass of the entrapped gas mg can be ignored compared to the mass of the refrigerant Gd ms With this assumption the magnetiza tion dependence of the temperature profi le for AMR isentropic system is dT dt ZK T CH m0V vM vT H dH dt 2 Eq 2 shows the change in the temperature of the magnetic refrigerant bed in the presence of a changing fi eld This fi rst order differential equation governing the magneti zation and demagnetization processes was solved as an initial value problem using numerical methods 4 2 Modeling of the regenerative warm and cold blow processes In the present procedure a packed bed made of Lumps of impureGdturningsisusedtosimulatetheregeneratorpacked withsolidparticlesintherefrigerantbed Theconvectiveheat transfer coeffi cient h for packed beds has been evaluated using different correlations 27 In our developed model we use the analysis offered by Whitaker 28 that has been used in heat transfer calculations of the packed beds for broken solids In this approach the Nusselt number Nu is a function of both the Reynoldsnumber Re and the Prandtlnumber Pr for a packed bed given by Nu Z hD k 3 1K3 Z 0 5 Re1 2C0 2 Re2 3 Pr1 3 3 where D is the solid particle diameter k is the thermal conductivity of the exchange fl uid and 3 is the porosity of the packed bed The analysis and equations in the following sections are based on the cold blow process in the refrigerant bed of the magnetocaloric material at constant minimum fi eld which has been cooled as the result of the MCE in the previous demagnetization process The concepts that are applied are exactly the same as the warm blow process that follow the magnetization process The only difference is the direction of the exchange gas and the initial conditions A fi rst step to develop a model to predict the behavior of a regenerative magnetic core during the regenerative gas blow processes in the AMR cycle is to make the following simplifying assumptions 1 The temperature of the exchange gas entering at each end of the refrigerant bed is constant The heat exchangers are expected to be very effi cient such that the fl uid fl owing from the heat exchanger into the refrigerant bed is assumed to maintain a constant temperature equal to the ambient temperature 2 The axial conduction loss in the regenerative magnetic core is negligible 3 The magnetic core is perfectly insulated 4 The physical parameters remain constant with time and temperature throughout the refrigerant bed 5 The velocity of gas is constant during the period of gas blow 6