Comparison of Thermoelectric and Stirling Type Cryocoolers Using Control Thermodynamic Model

Transcription

1 Cmparisn f Thermeletri and Stirling Type Crylers Using Cntrl Thermdynami Mdel A Razani 1,, C Ddsn 3, and T Rberts 3 1 The University f New Mexi Albuquerque, NM Applied Tehnlgy Assiates Albuquerque, NM Spaeraft Cmpnent Thermal Researh Grup Kirtland AFB, NM ABSTRACT New effrts are underway t develp thermeletri materials fr ling f infrared detetrs at rygeni temperatures Stirling type rylers rutinely prdue ling at rygeni temperatures with gd effiieny, but hallenges remain in their miniaturizatin, reliability and vibratin redutin fr spae appliatins In this study, a thermdynami mparisn f Stirling type and Thermeletri (TE) rylers is made fr a typial send stage rygeni refrigeratr (30 K t 80 K) It is assumed that a reservir at 80 K is available and a ling lad at 40 K is desired It is shwn that under the assumptin f availability f TE materials with a reasnably high figure f merit, a multistage TE ryler is required Fr mparisn f the perfrmane f the rylers, thermdynami mdels f the Stirling type and multistage TE rylers are develped The effet f imprtant system parameters n the perfrmane f the rylers is presented The thermal design hallenges f miniaturizatin f Stirling Type rylers and the develpment f multistage TE rylers with high effiieny are disussed INTRODUCTION Stirling Type Refrigeratrs (STRs) play an imprtant rle in satisfying the need fr rygeni ling f spae-based infrared detetrs as well as eletrnis requiring lers with high effiieny Multistage STRs an be used fr ling at very lw temperatures f abut 3 K if required Challenges exist in miniaturizatin f STRs and their vibratin fr spae appliatins STRs, referred t in this study, are a lass f regenerative refrigeratrs that nsists f Stirling Refrigeratrs (SRs) and Pulse Tube Refrigeratrs (PTRs) 1 Thermeletri refrigeratrs pssess great advantages fr ling f spae-based infrared detetrs beause they are slid state devies having n mving parts and are miniature, highly reliable, and easy t integrate int the system There have been many appliatins f the thermeletri effet in bth ling and pwer generatin,3 The develpment f Thermeletri Refrigeratrs (TERs) fr appliatin at rygeni temperatures is ham- 37

2 38 PULSE TUBE ANALYSIS AND EXPERIMENTAL MEASUREMENTS pered by the fat that thermeletri materials fr appliatin at lw temperatures are nt available, and hallenges exist in imprving their ling apaity and effiieny New effrts are underway t develp thermeletri materials fr appliatin at rygeni temperatures In this study we use ntrl thermdynami mdels f STRs and TERs t mpare their perfrmanes with regard t the n-lad temperature, ling apaity, and effiieny Mre speifially, we wuld like t estimate the figure f merit required fr thermeletri materials at the temperature range typial f the send stage ryler (30 K t 80 K) fr a perfrmane mparable t STRs In additin, the effet f imprtant glbal system parameters n the perfrmane f STRs and TERs is evaluated Thermeletri lers are based n the Peltier phenmenn whih exists when eletri urrent is applied t the juntin f tw different nduting materials (typially semindutrs) One material, p-type, ntains psitive harge arriers (hles) and the ther, n-type, ntains negative harge arriers (eletrns) In general, TE materials an be ategrized as unifrm bulk materials r thin films with peridi variatin in struture and mpsitin,4 Bulk materials an pump heat fluxes n the rder f 10 W/m, while thin films an reah an rder f magnitude higher heat fluxes with diret sensr ling apabilities 5 New effrts are underway t develp TE materials fr ling at rygeni temperatures 6 Assuming TE materials at rygeni temperatures are available, ntrl thermdynami mdels f STRs and TERs fr the temperature range f 30 K t 80 K are develped in this study The perfrmanes f rylers are mpared using regeneratr effetiveness fr STRs and the figure f merit fr TERs as the primary ntrl parameters THERMODYNAMIC MODELS OF STRS The ntrl thermdynami mdels f STRs using exergy analysis have been previusly reprted 7,8 Figure 1 gives the shemati f STRs used in the mdel The thermdynami mdels f STRs inlude the mst imprtant ntrl parameters fr analysis f Stirling type rylers Assuming n external irreversibilities assiated with heat transfer between the system and the reservirs, n ndutin heat transfer in the regeneratr, and n heat leaks t the system, the ling apaity f PTRs and SRs an be written respetively as (1) () where the parameters in the equatins are defined as: Mr = mass flw rati arss the regeneratr

3 COMPARISON OF COOLERS USING CONTROL THERMO MODEL 39 Figure 1 Shemati f Stirling type refrigeratrs and the parameters used in the mdel Defining the exergeti effiieny f flw in the regeneratr makes the analytial expressin 8 fr the ling apaity f STRs pssible Fr the ideal ase f a thermally perfet regeneratr ( =0), using Eqs (1) and (), the rati f the Ceffiient f Perfrmane (COP) f PTRs t the COP f SRs an be written as ( COP) PTR T e (1 e(1 r)) T e rt 1 ( COP) T (1 ) T T (1 ) T SR e e e e (3) Fr the ideal ase f e r 1, the rati f COP given in Eq (3) is ( 1 T / T) Thermal ineffetiveness f the regeneratr plays an imprtant rle in the perfrmane f STRs Fr example, it an be shwn that the thermdynami bund fr the n-lad temperature f SRs an 8 be btained frm the fllwing expressin: Pa T 1 1 T ( 1 )( ) Cs( ) p Pr 1 T Mr T 1 e (4) where T is the n-lad temperature Eq (4) shws the imprtane f the thermal ineffetiveness f the regeneratr n the n-lad temperature f SRs The thermdynami mdel f thermeletri refrigeratrs using average thermal and eletrial prperties f the TE uples in terms f eletri urrent has been previusly develped 4,9 The ling apaity and input pwer an be written respetively as [ 05 / ( )] in [ I / GI( T T)] Q N IT I G kg T T W N (6) where the parameters in the equatins are defined as: G = gemetri fatr, the rati f rss setin t the length f TE element I = eletri urrent k = thermal ndutivity f TE uple N = number f TE uples Q = ling apaity f TERs W in = input pwer t TERs = Seebek effiient f TE uple = eletri resistivity f TE uple Eqs (5) and (6) an be mbined t find the ling apaity in terms f the input pwer fr mparisn t Eqs (1) and () fr STRs (5)

4 330 PULSE TUBE ANALYSIS AND EXPERIMENTAL MEASUREMENTS W Q NZkG T T T T NkG T T W in 1/ 05 ( )( )[(1 ) 1] ( )] 05 in NZkG( T T) (7) where Z is the figure f merit f the TE uple defined by Z / k Eq (7) like Eqs (1) and () assumes that there is n irreversibility due t the heat transfer between the refrigeratr and the thermal reservirs and the thermal and eletrial prperties f the TE material are independent f the temperature The maximum f ling apaity f TERs an be btained frm Eq (5) using / Q I 0 r frm Eq (7) using Q / W in 0 The maximum ling apaity an be written as: Q NGk [05 ZT ( T T (8) η )] The input wrk rrespnding t the maximum ling apaity f TERs is given by: in NGkZTT W An imprtant quantity t haraterize the perfrmane f TERs is its n-lad temperature represented by: T, TER ( 1ZT 1)/ Z (10) Eq (10) fr TERs rrespnds t the result btained fr the n-lad temperature f Stirling refrigeratrs given by Eq (4) The figure f merit fr TE materials has signifiant effet n the value f the n-lad temperature f TERs Anther methd fr ptimizing TERs is t evaluate the nditin f the maximum COP Using Eqs (5) and (6), the ptimum urrent an be written as: GT ( T) Ipt, COP (11) 1 ZT ( T)/1 Q ( T / T 1) = ex, TER W in, i i Using the abve equatin the ling apaity and the input pwer an be btained frm Eqs (5) and (6), respetively THERMODYNAMIC MODELS OF MULTISTAGE TERS One f the hallenges f using TERs is the fat that the figure f merit f TE materials is nt very high Therefre, the n-lad temperature f TERs given by Eq (10) wuld nt be lw enugh t reah rygeni temperatures frm the temperature f the envirnment in a single stage One slutin is t use multistage TERs between T and T The thermdynami analysis using an ex-reversible mdel f multistage TERs has been previusly reprted 10 Fr the purpse f this study, tw thermdynami mdels fr multistage TERs are develped One mdel is based n the ptimum ling apaity at eah stage using Eqs (8) and (9) The ther mdel is based n the ptimum COP btained frm Eqs (5), (6) and (11) T simplify the ptimizatin press, the temperatures f the ht and ld sides fr eah stage are btained assuming 1/ T / ( / ) n hi Ti = T T where n is the number f stages In this manner the imprtant quantities an be btained fr eah stage suessively T find the thermdynami bund fr multistage TERs, it is assumed that the ht temperature f eah stage is equal t the ld temperature f next stage Therefre, it is assumed that the irreversibility due t heat transfer between the stages is zer Finally the exergeti effiieny (fratin f Carnt effiieny) is alulated frm the fllwing equatin (1) (9)

5 COMPARISON OF COOLERS USING CONTROL THERMO MODEL 331 Figure Shemati f a fur-stage thermeletri refrigeratr and the parameters used in the mdel As an example, the shemati f a fur-stage TER and parameters used in this study are shwn in Fig RESULTS AND DISCUSSION Lad urves are ften used t haraterize the perfrmane f rylers Lad urves ( Q vs T ) are reprted fr different values f the envirnmental temperature and input pwer t the rylers Eqs (1), () and (7) give the thermdynami bund fr ling apaity f PTRs, SRs, and TERs, inluding imprtant ntrl parameters influening the refrigeratrs Figure 3 shws the lad urves fr the input pwer f 50 W and the envirnmental temperature f 300 K The results f Eqs (1) and () are given in the figure fr seleted parameters typial f STRs The lad urves fr TERs an be btained frm Eq (7) fr a given number f TE uples Fr mparisn t STRs, the lad urves are given fr different figures f merit f TE uples alulated frm Eqs (8) and (9) with number f TE uples as a free parameter Therefre, the results fr the ling apaity are the ptimum values and rrespnd t the thermdynami bund f the lad urves f TERs fr the example under nsideratin Sine the number f TE uples is used as a ntrl parameter, the smth urves given in the figure shuld be interpreted as the interplated values rrespnding t an integer number f TE uples The figure merit is the ntrl parameter in this alulatin, and it is assumed that the Seebek effiient an be hanged while ther parameters fr the TE material are nstant Frm the figure it an be seen that the figure f merit f TERs must be high t prdue lad urves mparable t the high perfrmane STRs at rygeni temperatures Suh high Figure 3 Lad urves fr TERs, SRs and PTRs fr seleted parameters

6 33 PULSE TUBE ANALYSIS AND EXPERIMENTAL MEASUREMENTS Figure 4 Cling apaity and effiieny diagram f a thermeletri refrigeratr fr different values f Z and T =60 K Figure 5 Cling apaity and effiieny diagram f a thermeletri refrigeratr fr different values f Z and T=40 K values fr the figure f merit are an rder f magnitude higher than what is ahievable at the present time The n-lad temperature given in Fig 3 rrespnds t the values btained frm Eq (10) Figure 4 gives the pwer effiieny diagram ( Q vs η ex ) fr the lad temperature f 60 K and the envirnmental temperature f 80 K The results are btained using Eqs (5) and (6) with the eletri urrent as a free parameter Other parameters are given in the figure The figure shws that even fr the small temperature differene arss the TER, reasnably high values fr the figure f merit are neessary t btain aeptable values f effiieny Fr example, the exergeti effiieny f typial SRs fr the same temperature range btained frm Eq () is abut 05 It is interesting t nte that the pwer effiieny diagram is a lpedshape urve indiating a mprmise between ling apaity and effiieny f TERs Figure 5 shws the same result as in Figure 4 when the lad temperature is redued t 40 K As expeted, lwering the lad temperature requires higher values fr the figure f merit f the TE uple t prdue reasnable ling apaity and effiieny Fr example, fr values f Z lwer than 001 K -1 the limit f ling apaity f TERs is reahed fr the temperature range under nsideratin T reah a lad temperature f 40 K frm the envirnmental temperature f 300 K, Eq (10) shws that a very large figure f merit f the rder f Z=03 is required

7 COMPARISON OF COOLERS USING CONTROL THERMO MODEL 333 Figure 6 Cmparisn f ling apaity and exergeti effiieny fr a fur-stage TER based n tw different riteria f ptimizatin A well-knwn slutin t relax the requirement f a high figure f merit fr TE uples in rder t reah a reasnably lw lad temperature is t use multistage TERs Eah stage in the multistage TERs will require a lwer value f figure f merit mpared t the single stage fr the same ht and ld temperature limits Figure 6 shws the ling apaity and exergeti effiieny fr a fur-stage TER shwn shematially in Figure All thermal and eletrial prperties are assumed t be the same in all stages The results are given fr tw ptimizatin riteria based n the maximum ling apaity and maximum COP The effet f the tw ptimizatin riteria n ling apaity and effiieny f the multistage TER is learly shwn In these alulatins the number f TE uples in eah stage is taken t be the ntrl parameter It shuld be pinted ut that in the alulatin f the thermdynami bund f the multistage TER, it is assumed that there is n heat transfer irreversibility between the stages In many appliatins this irreversibility is signifiant, whih results in a substantial redutin in effiieny and ling apaity f multistage TERs Even thugh the effiieny f STRs is muh higher than the effiieny f TERs, espeially at rygeni temperatures, the latter has great advantage fr spt ling Great hallenges exit in the miniaturizatin f STRs, and thermal and physial limits exist in the design f suh rylers Well designed STR mirlers have a ling apaity per unit vlume f the rder f W/liter ( mw/m 3 ) at rygeni temperatures f abut 100 K 11 In ntrast, a reent three stage thin-film superlattie thermeletri multistage TER an prdue a ling heat flux n the rder f 100 W/m f ling apaity 1 This rrespnds t a ling apaity per unit vlume f several rders f magnitude larger than STRs It shuld be pinted ut that the n-lad temperature f suh a ler is muh larger that STRs High heat flux requirements f TERs fr spt ling reates thermal management issues fr the design f suh heat sink limited mir devies, espeially in the multistage arrangement CONCLUSIONS Using ntrl thermdynami mdels f Stirling type and thermeletri refrigeratrs, their ling perfrmanes and their effiienies were mpared with emphasis n their perfrmane at rygeni temperatures It is shwn that high values f figure f merits fr thermeletri materials are neessary even when they are used at rygeni temperatures typial f send stage rylers (80 K t 30 K) Thermdynami bunds fr a fur-stage thermeletri refrigeratr typial f a send stage ryler under the ptimum ling apaity and ptimum effiient f perfrmane are investigated There are physial and thermal limits t miniaturizatin f Stirling type

8 334 PULSE TUBE ANALYSIS AND EXPERIMENTAL MEASUREMENTS refrigeratrs, and thermeletri refrigeratrs have lear advantages here due t their very small size The resulting high ling heat flux f thermeletri refrigeratrs reates thermal management issues espeially when applied in multistage nfiguratins at rygeni temperatures REFERENCES 1 Radebaugh, R, Pulse tube rylers fr ling infrared sensrs, Preedings f SPIE, Vl 4130 (000), pp Rwe, DM, CRC handbk f thermeletri, CRC, Ba Ratn, FL, (1995) 3 DiSalv, FJ, Thermeletri ling and pwer generatin, Siene, Vl 85 (1999), pp Rwe, DM, CRC handbk f thermeletri: Mar t nan, CRC, Ba Ratn, FL, (006) 5 Venkatasubramanian, R, Siivla, E, Clpitts, T, and O Quinn, B, Thin-film thermeletri devies with high rm-temperature figures f merit, Nature, Vl 413 (001), PP Bentien, A, Jhnsen, S, Madsen, GKH, Iversen, BB, and Stegkih, F, Clssal Seebek effiient in strngly rrelated semindutr FeSb, Eurphysis letters, Vl 80, (007), pp Razani, A, T Rberts and B Flake A Thermdynami Mdel Based n Exergy Flw fr Analysis and Optimizatin f Pulse Tube Refrigeratrs, Crygenis, Vl 47 (007), pp Razani, A, C Ddsn and T Rberts A Mdel fr Exergy analysis and Thermdynami Bunds f Stirling Refrigeratrs, Crygenis, Vl 50 (010), pp Phelan, PE, Chiria, VA, Lee, TT, Current and future miniature refrigeratin ling tehnlgies fr high pwer eletrnis, IEEE Transatins n Cmpnents and Pakaging Tehnlgies, Vl 5 (00), pp Xuan, PE Optimum staging f multistage ex-reversible refrigeratin systems, Crygenis, Vl 43 (003), pp Petah, M, Waterman, M, Pruitt, G and Tward, E, High frequeny axial pulse tube mirlers, Crylers 15, ICC Press, Bulder, CO (009), pp Bulman, GE, Siivla, ED, Wiitala, R, Venkatasubramanian, R Aree, M, and Ritz, N Threestage thin-film superlattie thermeletri multistage mirlers with a ÓTmax f 10 K, Jurnal f Eletrni Materials, Vl 38 (009), pp