Resfriamento de Joule Tomson a elevadas pressões.pdf

8/12/2019 Resfriamento de Joule Tomson a elevadas presses.pdf

1/13


2/13

The potential for mixed coolants to enhance Joule

Thomson cryocooling has allowed a dramatic reductionin the operating pressure as compared with the pressurerequired by traditional pure coolants in a JouleThomsoncycle. Mixed refrigerants allow efficient operation using asingle stage compression process, which provides operatingpressures that are below 2.5 MPa. Furthermore, to enablelubrication of the compressor, the candidate mixtures areexpected to dissolve some lubricant contamination in theirliquid phase at the cryogenic temperature. Viable and gen-eral-purpose JouleThomson closed cycle cryocoolers withhigh COPs and prolonged reliable run times, driven by sin-gle stage lubricated compressors. are currently available[1216] both with and without phase separators [17,18].

Much less attention has been devoted to the potential of mixed coolants in the context of OC cryocoolers. Note thatthe low-pressure mixtures that have been developed for CCoperation are not applicable, in general, for high-pressureoperation as operation at elevated pressure will preventthem from reaching the cryogenic temperatures. On theother hand, harnessing these mixtures in an OC cryocoolerat low pressure will exhibit an unacceptably lower coolingcapacity and increase the size of the required gas reservoir.

There are several reported studies on OC cryocoolingwith mixtures at elevated pressure. At the moderate pres-sure range of 10 MPa, Brodianski et al. [19] demonstratedexperimentally the potential of mixtures to gain accelerated

cooldown. Brodianski demonstrated cooldown times withmixtures that were eight times faster than could beachieved using pure nitrogen at a similar volumetric owrate and pressure. Boiarski et al. [20] describes an experi-ment with an open cycle regulated cryocooler fed throughtwo pressure vessels, each at 6.2 MPa to utilize the mixingenthalpy. Chorowski [21] discussed open cycle operationwith mixtures of nitrogen with methane and nitrogen withR-13 at pressures up to 14 MPa. Gong et al. [22] discussedthe use of nitrogen and hydrocarbon mixtures for acceler-ating cooldown of open cycle JouleThomson cryocoolers.Only a single analysis at higher pressures (up to 30 MPa)has been reported: Maytal et al. [23] show how the coolingcapacity of a three component mixture can be optimized.Little [24] used a 30 MPa mixed precoolant to acceleratethe cooldown of a nal nitrogen stage.

1

2 3

45

recuperator

evaporator

throttle

heatload

gasreservoir

orcompressor

high, operatingpressure

0.1 MPa

n Q

P

Fig. 1. Layout and notation of the simulated JouleThomson cryocoolingsystem.

Nomenclature

A heat transfer area (m 2)COP coefficient of performanceCOP C coefficient of performance of the reversible cycle

of Carnoth specic enthalpy (J/kmol)D hT integral isothermal JouleThomson effect, (J/

kmol)D hT,PP value of D hT at T PP (J/kmol)_n molar ow rate (kmol/s)NTU number of thermal units, U A=_n c P P pressure (Pa)P OP pressure at which a mixture was optimized (Pa)s specic entropy (J/kmol K)T temperature (K)T AMB ambient temperature, gas inlet temperature (K)T B normal boiling point (K)T M melting/solidication temperature (K)T OP ambient temperature at which a mixture was

optimized (K)D T PP minimum temperature difference along the recu-

perator (K)Q total amount of rejected heat at the cryocooling

temperature (J)_Q cooling capacity, heat load (W)_QREC recuperated enthalpy (W)

V volume of a gas reservoir (m 3)U overall heat transfer coefficient (W/m 2 K)_W minimum compressing power (W)

yi molar fraction of component i Subscripts1 to 5 states along the thermodynamic cycle, Fig. 1i index of any component in mixture j index of the sections along the recuperator in the

numerical modelI number of components in mixtureH high (pressure or temperature) streamL low (pressure or temperature) streamOP state at which a mixture was optimized

Greek q density (kmol/m 3)

Abbreviationsmin y(x) minimum value of ( x) while changing parameter

yOC open cycleCC closed cycleOM optimal mixture

56 B.-Z. Maytal et al. / Cryogenics 46 (2006) 5567


3/13

Longsworth [25] employed binary mixtures of nitrogenand argon at 40 MPa for open cycle fast cooldown. How-ever, these two components have similar boiling pointsand therefore no thermodynamic advantage is expected.Indeed the operating temperatures and rates of coolingwere intermediate between the values that could be

attained using either of the two pure components.The intended contribution of the present study is aninvestigation of the potential of mixed coolants to improvethe performance of high-pressure OC cryocooler applica-tions at 80, 90 and 95 K as alternatives for nitrogen andargon.

2. The model, optimization procedure and tools

The layout and notation associated with the modeledJouleThomson cryocooler are indicated in Fig. 1. Thecryocooler includes a recuperative heat exchanger, throttle

(constant enthalpy expansion), and the evaporator (or loadheat exchanger). A numerical model using the EngineeringEquation Solver software [26] was developed to simulatethe steady state operation of this cycle. The details of thenumerical model are described elsewhere [27] in the contextof optimization of a low-pressure mixture composition.The thermophysical properties of the components and theirmixtures were obtained using the NIST4 numerical code,also known as SUPERTRAPP [28]. Up to 9 componentmixtures can be considered with constituents that includevarious hydrocarbons, halo-carbonated refrigerants, andinert gases.

The total recuperated enthalpy,

_QREC_n

h1 h2 h5 h4 1

is carried in N equal parts by each section, j , along therecuperator.

The heat load supported by the evaporator,

_Q_n h4 h3 2

matches the cooling capacity of the cycle which is the min-imum departure between the low- and high-pressure iso-

bars in the T h plane at the temperature range, ( T B , T AMB ),_Q_n min

T h P L ; T h P H ; T min

T D hT D hT;PP 3

The allowable minimum temperature difference (the pinch-point temperature difference), D T PP , is an input parameterto the model which reects the nite real nature of the lim-ited area recuperative heat exchanger,D T PP minT H T C 4

The required heat transfer area or thermal conductance(U A) j of the j th section may be determined using the effec-tivenessNTU relationship for a counter ow heat exchan-ger. Other input parameters to the model include: the inlet

pressure and temperature of the mixture at state 1, ( P 1, T 1),the molar ow rate, _n, the temperature of cryocooling, T 4,the species and their fractions, yi , and the outlet pressure,P 5, which was assumed to be 0.1 MPa for all of the resultspresented here.

The minimum compressing power (corresponding to a

reversible and isothermal compression process) is,_W min

_n T 1 s5 s1 h5 h1 5

which enables one to obtain the maximum possible coeffi-cient of performance,

COP _Q

_W min6

The solution for the temperature proles along the recu-perator is obtained iteratively by adjusting the hot temper-ature difference, T 1 T 5 until the specied pinch-pointtemperature difference is achieved. For pure coolants, thepinch-point occurs at the hot end and therefore the hottemperature difference coincides with D T PP .

The numerical model is integrated with a genetic opti-mizing algorithm [29] implemented in Engineering Equa-tion Solver that is characterized by a high capability fornding the global optima of a target function even if thefunction and/or its derivatives and constraints are non-continuous. The genetic optimization algorithm is notconfused by local optima and converges to the globalone.

The scope of optimization is to maximize one of three

target functions: the cooling capacity, the coefficient of per-formance, or the compactness of the recuperator,_Q=U A. Computations are repeated after adjusting thecomposition by the genetic optimizer for further improve-ment of the objective function. Results are generated fordifferent values of: (a) high pressure, (b) number of species,(c) ambient temperatures, and (c) cryocooling temperatures(either 80 or 90 K).

The domain of the optimized-mixture compositions isrestricted by considerations of solidliquid equilibrium inorder to avoid clog formation at the throttle. A conserva-tive approach was adapted in this regard; the freezing tem-perature of the mixture, T M , was estimated according to

T M 6 X I

i1 y i T M ;i 7

and the choice of components for 80 K cryocooling wasrestricted so that,

T M 6 T B nitrogen 8

On the one hand, some rise of the boiling point of the mix-ture may be expected, even if it is relatively small and re-mains in the 80 K cryocooling range. On the other hand,even a small presence of nitrogen, like a few percent, is ade-quate for the mixture to reach the boiling point of nitrogen

B.-Z. Maytal et al. / Cryogenics 46 (2006) 5567 57


4/13

[30]. The condition guaranteeing a non-clogging operationthen is

T 3 P T M 9

The optimized mixtures for 90 K cryocooling still employ asubstantial fraction of nitrogen as the lowest boiling point

specie. Therefore, their throttle exit remains at the sametemperature and the restriction (8) remains valid.Optimizing the composition for maximum _Q= _n may be

accomplished entirely in the T h plane. However, the inte-gration along the recuperator serves to determine its sizeand therefore allows optimization of the composition forthe most compact heat exchanger.

3. Specic cooling capacity

3.1. General scope

Two types of mixtures were examined for cryocooling at80 K. The components of the rst type of mixtures aremainly hydrocarbons and are selected from group I aslisted in Table 1 . The second type of mixture containsmostly halogenated derivatives of hydrocarbons whichare selected from group II listed in Table 1 . Mixtures of the rst type (group I components) are ammable whereasmixtures of the second type (group II components) are not.The composition of each mixture was optimized at a spe-cic pressure, P OP , for maximum specic cooling capacity,_Q= _n.

The lowest boiling point component for either of thetwo groups is nitrogen. The components have to be chosen

so that their normal boiling points will be uniformly dis-tributed over the entire temperature range from 80 to300 K so that the occurrence of a pinch-point at someintermediate temperature might be avoided; the pinch-point constitutes the bottleneck (literarily, in the T h plan)that xes the value of _Q= _n that can be obtained. Thisdiscussion is consistent with Littles [31] formulation of the optimal mixture, namely, equidistant high and low-pressure isobars in the T h plan.

The contribution of each additional componentbecomes more signicant as its involvement bisects andnarrows a larger gap between the boiling points of other

components. Therefore, CF 4, a non-ammable component,is included in group I to narrow the wide gap (73 K)between methane and ethane. Mostitski et al. [32] com-mented in 1981 on the possibility of improving the effi-ciency of hydrocarbon mixtures by employing thecomponent CF 4. Luo et al. [33,34] discussed the benet

of including CF 4 in comparison to mixtures of hydrocar-bons only. Sometimes acetylene, C 2H 4, is also included inorder to bridge the gap between methane and propane[35,36]. A different reason motivates the presence of argonin the mixture. Argon has a signicantly larger integralJouleThomson effect, D hT , than nitrogen, in spite of hav-ing a similar boiling point.

3.2. Hydrocarbon mixtures

Mixtures were optimized in which all 9 components ingroup I were allowed. In addition, 3, 6, 7 and 8 componentmixtures were considered in which only some of the con-stituents listed in group I were considered. The heat rejec-tion temperature used for the optimization, T OP , was 290 Kfor cryocooling at 80 K. The optimized _Q= _n as a functionof the corresponding P OP are displayed in Fig. 2. Eachcurve belongs to a specic group of components. Thesecurves do not describe a single mixture since each of thepoints on a given curve represents a different compositionthat is optimal for the specic pressure. Therefore, eachcurve may be regarded as corresponding to a virtual cool-ant that is referred to as the Optimized Mixture (OM) givena set of components and operating condition. This view-point is analogous to the pure coolants pressure dependentD hT (at ambient or inlet temperature) which reects thehighest attainable _Q= _n. Note that Fig. 2 illustrates the cool-

Table 1Two groups of candidate components to comprise optimized mixtures: thehydrocarbons (I) and the halogenated hydrocarbons (II)

Group I T B [K] Group II T B [K]

Nitrogen N 2 77.2 N2 77.2Argon Ar 87.3 Ar 87.3Methane CH 4 111.7 CH4 111.7R14 CF 4 145.1 CF4 145.Acetylene C 2H 4 169.1 R23 190.0Ethane C 2H 6 184.5 R116 194.7Propane C 3H 8 231.2 R32 221.2Isobutane C 4H 10 263 R125 224.7

Isopentane C 5H 12 300.6 R134a 246.8

0 10 20 30 40 500

500

1000

1500

2000

2500

3000

methane

7

6

3A

3B

8

argon

nitrogen

3C

9

Q n

J mol

290 K= AMBT 80 K

cryocooling

methane

7

6

3A

3B

8

argon

nitrogen

3C

9

[ ]

OP P [MPa]

Fig. 2. Optimized specic cooling capacity of various hydrocarbonmixtures (OM curves) as a function of the pressure of optimization. Eachcurve indication represents the mixture by the number of its components.Nitrogen, argon, and methane are shown for reference. ( 9) N2 , A, CH 4 ,CF 4, C2H4 , C2H 6 , C3H 8, C4H 10 , C 5H 12 ; (8) like 9 without C 2H 4; (7) like 8without CF 4; (6) like 7 without C 5H 12 ; (3A) N2, C2H6 , C3H8; (3B) N2 ,C3H 8, C4H 10 ; (3C ) N2 , CH4 , C2H 6 .



5/13

ing capacity, _Q= _n , as a function of a mixtures optimiza-tion pressure, P OP , but not the operating pressure, P .Therefore it does not describe the cooling capacityachieved during a discharge process of a gas reservoir.

Fig. 2 includes for reference the _Q= _n (which is equivalentto the D hT (P )) for nitrogen, argon and methane. The com-

position of these pure refrigerants does not change withpressure and therefore these are the corresponding dis-charge curves. The use of nitrogen, argon, and methaneare appropriate for cryocooling at about 78 K, 88 K and112 K, respectively. Note that the optimized mixtures havehigher _Q= _n than argon at any pressure and even higherthan methane below 20 MPa.

Any optimized mixture that is obtained from a largergroup of components that contains as its basis a smallergroup of components must perform better than the originalmixture obtained from the smaller group. In other words,the 9 component OM in Fig. 2 must perform better thanthe 8 component OM which, in turn, must perform betterthan the 7 component OM and so on. The reason is thatat any pressure, the domain of optimization of the originalOM is entirely included in the domain of the mixtures of more components. Put another way, the optimization pro-cedure always has the option to abandon the additionalcomponents of the larger group, by reducing their molarconcentration, if necessary in order to obtain a larger_Q= _n. Indeed, Fig. 2 shows that the various OM curves donot intersect and the one with most components will exhi-bit the highest _Q= _n.

Synthesizing mixtures of 8 components with boilingpoints distributed quite evenly along the entire range of

temperatures from 80 to 300 K provides the condencethat the optimization procedure does not require anyadditional and intermediate components for furtherenhancement of _Q= _n. Therefore, _Q= _n of this OM isexpected to be the envelope that encompasses any possiblehydrocarbon mixture or at least a very good approxima-tion of this envelope. Indeed, Fig. 2 shows that the inclu-sion of a 9th component, which in this case is C 2H 4 , doesnot elevate the performance noticeably at any optimizationpressure even though its boiling point bisects the 40 K gapthat otherwise exists between CF 4 and C 2H 6.

As observed in Fig. 2, the _Q= _n curves of the OM exhibita peaking behavior with pressure that is similar to the D hTof pure gases. However, the peak occurs at lower pressuresand is not related to the inversion of the JouleThomsoneffect. The peaking pressure associated with the 8 compo-nent OM clearly designates the highest attainable cooling

capacity, _Q= _n, that can be achieved by any mixture atany pressure. The highest value of _Q= _n observed in this

study is 3180 J/mol for a heat rejection temperature of 290 K. The corresponding peak pressure is about 20 MPaand its composition is listed in Table 2 (together with opti-mized compositions at 10 and 40 MPa). However, noticethat the peak is relatively shallow and a cooling capacityof nearly 93% of this optimal value may be reached at7 MPa; albeit using a mixture with a different composition.For nitrogen at a similar cryocooling temperature, thecooling capacity _Q= _n is 1200 J/mol at about 40 MPa andfor argon it is 1800 J/mol at 55 MPa.

The three component mixtures N 2 C2H 6 C3H 8 andN 2 C3H 8 C4H 10 develop maximum _Q= _n of about 2620J/mol and 2430 correspondingly, which is more than twicethat of pure nitrogen; these results are consistent with theoptimized peaking values obtained by Maytal et al. [23].The mixture N 2 CH 4 C2H 6 reaches 2520 J/mol at about45 MPa. Six components bring _Q= _n closer to the enveloperepresented by the 8 component OM and achieves a peakcooling capacity of 2960 J/mol. There is essentially no dif-ference in performance exhibited by the 7 and 8 componentOM in the high-pressure region, however the addition of the 8th component (which is CF 4) does improve _Q= _n atlower pressures.

The 7 and 8 component OMs are partially condensed atthe elevated pressures and the discussed temperature of 290 K which means at the inlet to the recuperator. How-ever, the gas phase mass fraction is at least 90%. The pos-sibility of enjoying higher _Q= _n and COP by allowing acoolant to stay in two-phase outside the recuperator waspreviously mentioned in the literature in the context of low-pressure mixtures for CC cryocoolers. Alexeev et al.[15,37] and Boyarski et al. [38,39] compared the perfor-mance of the two classes of Gas Refrigerant Supply(GRS) and Liquid Refrigerant Supply (LRS). On the other

Table 2Composition of mixtures (percent mole fractions) of 8 hydrocarbon components optimized at three values of P OP = 10, 20 and 40 MPa at 290 K formaximum _Q= _n

P [MPa] _Q= _n [J/mol] N2 A CH4 CF 4 C2H6 C3H 8 C4H10 C5H12

1.5 1464 54.1 3.4 10.5 12.1 5.2 5.2 0.0 9.53 2171 55.2 0.2 7.6 13.7 13.3 0.7 0.0 9.35 2751 60.4 0.1 5.0 11.1 11.6 0.8 3.0 8.07 2947 61.2 4.3 5.0 5.5 11.4 2.1 3.8 6.710 3080 64.6 2.0 9.8 1.7 9.0 5.0 0.6 7.320 3180 70.2 2.3 8.6 1.3 7.2 2.2 1.2 7.030 3070 74.6 0.0 7.4 2.5 6.2 2.0 1.0 6.340 2930 75.5 2.3 6.0 2.6 4.7 2.1 1.7 5.1

The highest attainable _Q= _n value occurs at 20 MPa.



6/13

hand, the ow of the two-phase might be heterogeneousand therefore the performance will be affected by thedetails in this ow regime.

The liqueed part of the 7 component OM includes asubstantial portion of the higher boiling point component,which is isopentane. This component was removed for the

6 component OM and therefore the 6 component OM ismore likely to be in a single phase at the elevated pressure.Notice that the performance of the 6 component OM isonly slightly worse than the 7, 8, or 9 component OM.For instance, the 7 components OM at 20 MPa and30 MPa, both at 290 K, are of two phases. Their gas phasemass fractions are 90% and 97.5% correspondingly. On theother hand, the 6 components OM at 25 MPa and 290 K isof single phase. This mixture is mentioned in Section 10.1for comparison and its composition is displayed in Table5, optimized for 80 K cryocooling.

The composition of the OMs at elevated pressures, nom-inally above 5 MPa, are not affected by the melting pointrestriction and thus strongly fulll the inequality repre-sented by Eq. (8). However, at lower pressures, this meltingpoint restriction becomes constraining and the optimizedcompositions are on the boundary of this restriction andEq. (8) is fullled as an equality. The melting point restric-tion therefore limits the share of higher boiling point com-ponents in the mixture which in general also have highervalues of T M and D hT [40]. Therefore, it might be thatthe optimized _Q= _n is underestimated at low pressures andthe actual values may be higher if the suppression of thesolidication point of the blend were accurately accountedfor. However, this issue was already discussed for low-pres-

sure mixtures for CC cryocoolers [23,41] and is not thefocus of the present study. Even though Table 2 displayssome compositions of OM at the lower pressure range gen-erated by this study.

3.3. Halogenated hydrocarbon mixtures

The results of optimizing _Q= _n for mixtures based on thehalogenated hydrocarbon refrigerants summarized asgroup II in Table 1 are displayed in Fig. 3. The values of _Q= _n for these OMs are smaller than can be achieved usinghydrocarbon components from group I (the 8 componenthydrocarbon envelope previously shown in Fig. 2 is alsoshown in Fig. 3). The shortfall in performance is particu-larly true in the low and intermediate pressure range; how-ever, the performance of the halogenated hydrocarbonsapproaches that of the hydrocarbons at pressures above35 MPa.

The boiling points of the halogenated hydrocarboncomponents are distributed less uniformly than those of the hydrocarbons. Therefore, the inclusion of the 9th com-ponent which is (the ammable) methane in order to nar-row the 57 K boiling points gap between argon and R14does somewhat enhance _Q= _n at elevated pressures. At50 MPa, the value of about 2500 J/mol for halogenatedhydrocarbon only becomes 2600 J/mol when including

methane. Another obstacle is the higher T M value that istypical of the components in group II which causes theseOMs to be on the border of the solidication constraintrepresented by Eq. (8) for most of the optimization pres-sures. Consequently, it is not possible to include higherboiling point components as much as would otherwise beoptimal from the standpoint of enhancing _Q= _n. Refriger-ants that are currently banned, such as R12, R13 and

R21, or an alternative substitute that has a similarly lowerT M value would close the gap between the OM based onhydrocarbons and the synthetic refrigerants. The syntheticrefrigerant OM also exhibits a peaking behavior; the larg-est _Q= _n occurs at 35 MPa and the associated compositionis listed in Table 3 together with two other syntheticOMs that are optimized at 20 and 45 MPa.

4. Coefficient of performance of optimized mixtures

The COP at elevated pressure is another reection of theimproved cooling capacity of the OM. The COP as a func-tion of optimization pressure is shown in Fig. 4 for mix-tures optimized from the same groups of componentsthat are employed from the hydrocarbon category (groupI in Table 1 ) and discussed in the previous section in thecontext of Fig. 2. The OMs with more components andhigher _Q= _n also exhibit higher COP and the COP showsthe same peaking behavior with respect to pressure. How-ever, the pressure associated with the highest COP is some-what lower than the peak pressure associated with; thisbehavior is similar to pure gases as discussed by Mannet al. [42]. The curve associated with the 8 componentOM again represents an envelope that encompasses theperformance associated with other, partial groups of com-

ponents. This envelope has the signicance of representing

0 10 20 30 40 500

500

1000

1500

2000

2500

3000

Q n

[ ]J mol

290 K= AMBT 80 K

cryocooling

OP P [MPa]

argon

nitrogen

8-HC

3-HC

8-HH

Fig. 3. Optimized specic cooling capacity of halogenated hydrocarbonmixtures (OM curves) as a function of the pressure of optimization. Forreference are shown hydrocarbon mixtures, nitrogen and argon. Eachcurve indication represents the mixture by the number of its components.(8-HH ) N2 , A, R14, R23, R32, R134a, R116 and R125; ( 8-HC ) N2 , A,CH 4 , CF 4, C2H6 , C3H 8, C4H10 , C5H 12 ; (3-HC ) N2 , C2H 6, C3H 8 .



7/13

the highest achievable COP with a JT cycle with any mix-ture at any pressure; Fig. 4 shows that for a heat rejectiontemperature of 290 K, the maximum COP is 0.19 which is50% of the COP that can be achieved by a reversibleCarnot cycle, COP C . The maximum COP is achieved atan optimization pressure of only 5 MPa by a mixture of a composition that is listed in Table 4 and includes about60% nitrogen. One may compare it with the compositionof the mixture that optimizes _Q= _n (which peaks at

20 MPa) that includes 70% nitrogen ( Table 2 ). The peakCOP associated with pure nitrogen is about 0.07 and thispeak is reached at about 30 MPa. For argon 0.11 is thepeak COP which is achieved at about 40 MPa. Therefore,not only is the COP of the OM doubled in comparison witha pure substance but it is also achieved at one eighth of thepressure. The halogenated hydrocarbon mixtures reach a

maximum COP of about 0.14 at a pressure of 32 MPafor the same 290 K heat rejection temperature and 80 Kcryocooling temperature.

An alternative attempt was made to optimize directlythe COP (instead of the cooling capacity) as an objectivefunction for each pressure and it was found that the samecomposition that maximizes _Q= _n also maximizes the COP.This result may be explained by the extremely weak depen-dence of the compression work on the composition of themixture.

5. Temperature effect on optimized mixtures

The T AMB , of an operating mixture has to be consideredin reference to the temperature for which it was optimized,T OP . There are three aspects associated with the inuenceof temperature on _Q= _n for an OM. In general, the inuenceof ambient temperature becomes more sensitive at lowerpressures.

5.1. _Q= _n dependence on T OP

As the temperature for which the optimization is per-formed, T OP , is raised, _Q= _n degrades quite moderately.Fig. 5 shows the 7 component OM, optimized at 290 andat 333 K; these curves represent different mixtures as theoptimization conditions for each are different. At elevatedpressures, above 10 MPa, the difference between the twocurves remains within 15%. The optimization procedurecompensates for the higher temperature by changing thecomposition so that the concentration of the higher boilingpoint components is increased. Therefore, it is possible tooptimize a mixture for operation at elevated temperaturewith a relatively small sacrice of _Q= _n.

5.2. _Q= _n dependence on T AMB when T AMB > T OP

The most evident situation is when T AMB = T OP (forexample, the curves where T AMB = T OP = 290 K andT AMB = T OP = 333 K) so that the OM operates at the

Table 4Composition (percent mole fractions) of 8 components optimized mixture that exhibits the peaking COP value of 0.19 at 290 K reached at the pressure of 5 MPa

N2 A CH4 CF4 C2H6 C3H8 C4H 10 C5H12

60.4 0.1 5.0 11.1 11.6 0.8 3.0 8.0

0 10 20 30 40 500

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

7

8

nitrogenargon

6

3A

3B

3C

COP

OP P [MPa]

290 K= AMBT 80 K

cryocooling

7

8

nitrogenargon

6

3A

3B

3C

Fig. 4. Coefficients of performance as a function of the pressure of optimization (OM curves). The various hydrocarbon mixtures wereoptimized for highest _Q= _n. Each curve indication represents the mixtureby the number of its components. Nitrogen and argon are shown forreference. (8) N2 , A, CH 4 , CF 4 , C2H 6, C3H8 , C4H 10 , C5H12 ; (7) like 8without CF

4; (6) like 7 without C

5H

12; (3A) N

2, C

2H

6, C

3H

8; (3B) N

2,

C3H8 , C4H 10 ; (3C ) N2, CH 4, C2H6 .

Table 3Composition (percent mole fractions) of mixtures of 8 halogenated hydrocarbon components optimized at 3 values of P OP = 20, 35 and 45 MPa at 290 Kfor maximum _Q= _n

P [MPa] _Q= _n [J/mol] N2 A R14 R23 R116 R32 R125 R134a

20 2260 76.0 0.0 0.0 18.7 0.0 4.2 0.5 0.635 2700 73.5 3.6 7.9 6.6 0.2 3.8 0.5 3.945 2550 81.1 0.2 6.1 2.0 1.5 0.0 2.3 6.8

The highest attainable _Q= _n value occurs at 35 MPa.



8/13


9/13

size of the mixed coolant recuperator thus narrowing thedifference between the physical sizes of the two.

7. Open cycle application

7.1. Discharge process of a reservoir

High-pressure coolants are traditionally applied to OCcryocooler systems where a gas reservoir dischargesthrough the JouleThomson cryocooler. If the dischargeprocess occurs slowly, then the gas reservoir may beregarded as isothermal during this process. As previouslydiscussed, the cooling capacity _Q= _n as a function of pres-sure for the 6 component OM of group I, as is shown inFig. 7, is not a description of a discharge process; eachpoint along this curve represents a different mixture com-position. Fig. 7 shows the discharge process associated with5 of these OMs for which the pressure of optimization,P OP , is 50, 40, 35, 30 and 25 MPa; these curves are gener-ated assuming an isothermal discharge process and theinstantaneous _Q= _n are displayed as a function of pressure.Each of these mixtures may also be examined at a higherpressure than the one for which it was optimized. Note thatthe values of _Q= _n at any pressure different from the optimi-zation pressure must lie below the envelope of OM. Fig. 7shows the pressure dependence above and below P OP forP OP = 25 MPa (only a short portion of the curve at higherpressure is shown in order to avoid unnecessarily compli-cating the gure).

The proper criteria for comparing the performance of amixture for an OC cryocooler would be the total refrigera-tion provided at the payload, Q , per unit volume of the res-ervoir. The ow demand is assumed to be ideal in the sense

of instantaneously matching the specic cooling capacityand heat load (as described elsewhere [44] for pure cool-ants) then,

QV

Z P F

P I

D hT;PP dq 12

from the initial high pressure, P I to the nal one, P F . Toaccomplish this integration, one would need the densitydependence of _Q= _n during the isothermal discharge pro-cess, as shown in Fig. 8 for the same ve optimized mix-

tures that were previously described. Fig. 8 also showsthe P OP = 25 MPa OM at P > P OP . The area below thesecurves represents the Q/V values for the various coolants.The curve of P OP = 50 MPa exhibits some uctuations as

0 10 20 30 40 500

10

20

30

40

50

NTU

OP P [MPa]

290 K= AMBT 80 K cryocooling

argonnitrogen

8-HC

6-HC

3-HC

8-HH

= PPT 3K

290 K= AMBT

8-HC

6-HC

3-HC

8-HH

= PPT 3 K

Fig. 6. The required sizes of recuperators performing with D T PP = 3 K, asa function of the pressure of optimization (OM curves). The mixtures were

optimized for highest _Q= _n. Each curve indication represents the mixture bythe number of its components. Nitrogen and argon are shown for

reference. (8-HC ) N2 , A, CH 4 , CF 4 , C2H6 , C3H 8, C4H 10 , C5H 12 ; (6-HC )like 8-HC without CF 4 and C5H12 (3-HC ) N2 , C2H6 , C3H 8; (HH ) N2 , A,R14, R23, R32, R134a, R116 and R125.

0 10 20 30 40 500

500

1000

1500

2000

2500

3000

Q n[ ]J mol

Optimized mixtures

discharge

25 30 3540 50 MPa

argon

nitrogen

290 K= AMBT 80 K

cryocooling

curves

OP P50 MPa

P [MPa]

Fig. 7. Cooling capacity pressure dependence during isothermal dischargeprocess. The mixtures were optimized for highest _Q= _n and include the 6components: N 2 , A, CH 4 , C2H 6, C3H 8 , C4H10 : the dashed line for

P OP = 25 MPa is extended for P > P OP .

0 2 4 6 8 10 12 14 16 18

500

1000

1500

2000

2500

3000

Q n[ ]J mol

Optimized mixtures

[ ]J mol

25 3040

50 MPa

20

5

7 10

argon

nitrogen

80 Kcryocooling

10

290 K= AMBT

50

30

50

OP P

dischargecurves

0 2 4 6 8 10 12 14 16 18

500

1000

1500

2000

2500

3000

Q n[ ]J mol

[ ]J mol

50 MPa

10

290 K= AMBT

Fig. 8. Cooling capacity density dependence during isothermal dischargeprocess. The mixtures were optimized for highest _Q= _n and include the 6components: N 2 , A, CH 4 , C2H 6, C3H 8 , C4H10 : the dashed line forP OP = 25 MPa is extended for P > P OP .



10/13

a function of q although the curve is smooth when shownas a function of P ; this seems to reect a difficulty with thenumerical properties correlations rather than any realbehavior.

7.2. Examples

The OM for P OP = 40 MPa remains single phase in thegas reservoir while discharging from P OP to 5 MPa. Theintegral shown in Eq. (12) shows that this mixture providesa gas reservoir volume specic refrigeration capacity of Q /V = 22.1 kJ/L. Pure nitrogen for the same pressure rangedischarge can provide only 10 kJ/L Furthermore, the cutoff pressure for pure nitrogen at a similar heat load wouldbe about 10 MPa (because of the lower specic coolingcapacity) therefore, the Q/V would be reduced to only8.8 kJ/L.

The OM associated with P OP = 35 MPa becomes twophase below about 11 MPa; this pressure may thereforebe considered to be the practical limit to the nal pressureof the discharge process. Even so, the Q /V integral for theOM associated with 35 MPa is 18 kJ/L from 35 MPa to11 MPa, which is more than twice that of nitrogen at40 MPa.

The OM associated with P OP = 50 MPa dischargingfrom a reservoir from 50 MPa to 10 MPa can provide Q/V as high as 25 kJ/L. Nitrogen at the same pressure rangeprovides only 11.3 kJ/L.

Indeed, Q/V increases for higher P OP mixtures in thecase where the reservoir is assumed to be charged initiallyto P OP . However, a gas reservoir may be charged to a

higher pressure than P OP in which case each of the OMsshown in Fig. 8 have similar Q/V integrals. In this case,the OMs with higher P OP are more likely to stay singlephase during the discharge process.

8. Closed cycle application

The _Q= _n of OM of group I ( Fig. 2) increase quite shar-ply up to pressures of about 10 MPa where they haveachieved most of the cooling capacity that is possible,about 3000 J/mol and close to 50% of COP C . This strongpressure dependence at low pressures is characterized bya slope of about 400 J/mol per 1 MPa. (The pressuredependence for pure nitrogen is only 50 J/mol per1 MPa). The strong pressure dependence encouragesdesigners to double or triple the pressure of a CC cryoco-oler to about 2 or 3 MPa. This pressure increase wouldrequire adding a single compression stage while remainingin a moderate pressure range (below 10 MPa) but stillenjoy values of _Q= _n and COP that are nearly equal to themaximum attainable. This remains consistent with pub-lished performance data [45] for CC cryocoolers at 2 and5 MPa achieving _Q= _n of about 5001000 J/mol and COPof 2030% of COPC . The practice of using two stages of compression was reported with pure nitrogen [46], hydro-carbon mixtures [47] and synthetic refrigerants [48].

The COP and _Q= _n of OMs do peak at different pressuresand therefore occur for different compositions. Operationat the highest COP (which occurs at 5 MPa) is associatedwith giving up about 15% of the highest attainable _Q= _n(which occurs at about 20 MPa). One may try to compro-mise between these two working points by choosing an

intermediate pressure and composition.

9. Minimum size recuperator

In some applications, the main concern is to minimizethe size of the recuperator even if this means sacricing_Q= _n. Such an example may be the miniature cryosurgicalprobe [27,49,50] or any other case where the platform of the cold end is very delicate.

9.1. Pure coolants

While maintaining a constant ow rate, one may makethe size of a the recuperator progressively smaller in termsof its thermal conductance, U A so that it becomes morecompact; this reduction in conductance is associated withsome loss effectiveness and thus in _Q= _n. The question asto whether and to what extent this strategy pays off isexamined by the parameter of compactness,which is,_Q=U A, and has units of degrees Kelvin. Since _Q andU A are proportional to _n, their ratio is independent of _n and characterizes the recuperator itself. A larger_Q=U A represents a more compact heat exchanger as agiven cooling rate is produced by a smaller recuperator.

Fig. 9 illustrates the compactness parameter, _Q=U A

for pure nitrogen at 40 MPa and 290 K as a function of the NTU. Note that initially, the cooling capacity _Qdecreases more slowly than U A therefore _Q=U Aincreases. However, if U A becomes too small then _Q

2 3 4 5 6 7 8 9 10 110

1

2

3

4

5

6

7

8

NTU

40

40

35

35

30

30

25

25

20

2015

15

10

10

5

53

3

PPT =

PPT =

Q

optimizedmixtures

nitrogen

290 K= AMBT 80 K

cryocooling

40 MPa

NTU

40

40

35

35

30

30

25

25

20

2015

15

10

10

5

53

3

PPT =

PPT U A

290 K= AMBT

Fig. 9. Optimized compactness parameter, as a function of the size of therecuperator, for 7 component hydrocarbon mixtures including N 2, A,CH 4 , C2H 6, C3H8 , C4H10 , C5H12 in comparison to that of nitrogen. TheD T PP values for each size recuperator are noted along the curves.



11/13


12/13

about 26.5 kJ/L while argon at similar conditions provides21.8 kJ/L. Argon compensates its lower _Q= _n by higherdensity at elevated pressure ( Fig. 8) so that its Q/V inte-gral approaches that of the optimized mixtures to within20%.

10.2. Recuperators compactness

The optimization of mixtures for maximum compact-ness parameter, _Q=U A, for cryocooling at 90 K pointsto pure argon as the best choice. In analogy to the discus-sion for 80 K cryocooling in Section 9, at 40 MPa, and290 K the highest value of _Q=U A for argon is 25.2 K.It is more then three times larger than for the optimizedmixtures for 80 K. However, one should still recall thatargon cools down to 90 K instead of 80 K. The associated_Q= _n is 1050 J/mol which is about 50% of the highest attain-able value by pure argon.

This characteristic might explain the use of high pres-sure, open cycle argon for miniature cryosurgical probes[54,55]. In the view of the compactness analysis, the mixedcoolant probes for similar cryocooling temperature cannotbe as compact as that of argon at elevated pressure. Stillmixed coolants are used for cryosurgical probes [56,57]though at higher cryocooling temperatures and lowerpressures.

Acknowledgement

This work was partially sponsored by the Office of Naval Research under contract N00014-03-1-0175.

References

[1] Geist J, Lashmet P. Miniature JouleThomson refrigeration systems.Adv Cryog Eng 1960;5:33142.

[2] Buller J, Guiler G. Closed cycle cooler including a cryostat, US PatentNo. 3204422, 1965.

[3] Lester J, Benedict B. JouleThomson valves for long term service inspace. In: Proc third cryocooler conf., 1984. NIST Special Publication698, Boulder, Colorado, 1985. p. 25766.

[4] Hedegard K, Walker G. Zylstra S. Non-clogging, temperaturesensitive, closed-cycle Linde-Hampson cryocooler. In: Proc 5th intcryocoolers conf, Naval Postgraduate School, Monterey, California,1980. p. 2530.

[5] Wolfe WL, Zessis GJ. The infrared handbook of electro-optics.Infrared Information and Analysis (IRIA) Center, EnvironmentalResearch Institute of Michigan, 1985.

[6] Stephens SW. Advanced design of JouleThomson coolers for infra-red detectors. Infrared Phys 1968;8(1):2535.

[7] Little WA, Paugh RL. Development of a fast cooldown Joule Thomson microminiature refrigerator and vacuum package forinfrared focal plane array at 70 K. In: Proc sixth int cryocooler conf,Plymouth, MA, 1990. p. 1619.

[8] Maytal B-Z. Fast JouleThomson cryocycling apparatus for cryo-surgical applications. Adv Cryog Eng 1998;43:9117.

[9] Mikus PW. Cryosurgical system, Patent No. WO 99/49798, 1998.[10] Longsworth RC. Cryo-Probe, US Patent No. 5452582, 1995.[11] Hughes W, Herr KC. Mariner Mars 1969 infrared spectrometer gas

delivery system and JouleThomson cryostat. Cryogenics 1973;13:

5139.

[12] Fuderer A. Kompressionsverfahren zur kalterzeugung, DPNo. 1241468, 1967.

[13] Fuderer A. Compression process for refrigeration, US PatentNo. 3203194, 1962.

[14] Alfeev VN, Brodyanski VM, Yagodin VM, Nikolsky VA, IvatsovAV. Refrigerants for cryogenic throttling unit, Patent No. GB1336892, 1973.

[15] Alexeev A et al. Further development of a mixture JouleThomsonrefrigerator. Adv Cryog Eng 1988;43:166774.

[16] Luo EC et al. Mixed-refrigerant JouleThomson cryocooler drivenby R22/R12 compressor. Adv Cryog Eng 1988;43:16758.

[17] Longsworth RC. Cryogenic refrigerator with single-stage compressor,US Patent No. 5337572, 1994.

[18] Missimer DJ. Refrigerant conversion of Auto-Refrigerating Cascade(ARC) systems. Int J Refrig 1997;20(3):2017.

[19] Brodianski VM. Efficient throttling cryogenic refrigerants whichoperate on mixture. Chemical petroleum mechanical engineer-ing. New York: Plenum Press; 1972. p. 105761 [Translated fromKhimicheskoe i Neftyanoe Mashinostroenie, Moscow, Russia, 1971,No. 12, p. 168].

[20] Boiarski MYu et al. In: Brodianski VM, editor. Self-contained low-power refrigerators. Moscow: Energoizdat Press; 1984. p. 15563 [inRussian].

[21] Chorowski M. Comparison analysis of LindeHampson refrigeratorssupplied with substances of different properties. PhD thesis, Polo-technika Wroclawska, Poland, 1999 [Polish].

[22] Gong MQ et al. Fast cool-down mixed-refrigerant JouleThomsoncryocoolers used for cooling infrared detectors. Proc SPIE 2000;4130:41321.

[23] Maytal B-Z, Van Sciver SW, McMahon PD. Thermodynamicanalysis of mixed uid JouleThomson cryocoolers. In: Proc sixthint cryocoolers conf, David Tailor Research Center, Bethesda, MD,vol. 2, 1991. p. 11135.

[24] Little WA, Paugh RL. Development of fast cooldown, Joule Thomson microminiature refrigerator and vacuum package foroperation of infrared focal plane arrays at 70 K. In: Proc 6th intcryocoolers conf, David Tailor Research Center, Bethesda, MD, vol.

2, 1991. p. 16169.[25] Longsworth RC, Steyert WA. J-T Refrigerators for fast cooldown to100 K and 80 K. In: Proc interagency meeting on cryocoolers,Monterey, CA, 1988.

[26] Klein SA, Alvarado FL. EES-Engineering Equation Solver, 2002.[27] Keppler F, Nellis G, Klein SA. Optimization of the composition of a

gas mixture in JouleThomson cycle. HVAC&R Res 2004;10(2).[28] James EF, Huber MI. NIST Thermodynamic Properties of

Hydrocarbon Mixtures Database (SUPERTRAPP). US Departmentof Commerce, National Institute of Standards and Technology,1992.

[29] Charboneau P. Release notes for PIKAIA 1.2. NCAR TechnicalNote 451+STR, National Center for Atmospheric Research, Boulder.

[30] Gresin AK, et al. General principles of formation and optimization of multi component working uids for cryogenic systems. In: Proc 15th

int cong refrig, vol. 1, 1979. p. 16973.[31] Little WA. Method for efficient counter-current heat exchanger usingoptimized mixtures, US Patent No. 5644502, 1997.

[32] Mostitski AV et al. Working composition or use in refrigeratorscontains nitrogen, methane, ethane, propane, isobutane and addi-tional Freon-14 to increase efficiency of cooling cycle, SU PatentNo. 1089099, 1984.

[33] Luo EC et al. Thermodynamic analysis and optimization of 80 Kclosed-cycle JouleThomson with gas mixture. Adv Cryog Eng1988;43:167983.

[34] Luo EC, Zhou Y, Gong MQ. New efficient cryogenic mixed-refriger-ants for JouleThomson cryocoolers in 80 K to 100 K temperaturerange. Cryogenics and refrigeration, proc. of ICCR98. Beijing: Inter-national Academic Publishers; 1998. p. 4214.

[35] Longsworth RC. Cryogenic refrigerator with single-stage compressor.

US Patent No. 5337572, 1994.



13/13

[36] Goloubev D, Alexeev A, Haberstroh Ch, Quack H. Efficient study of a nitrogen-mixed gas cascade for cooling the current leads. Proc 18thint cryog eng conf (ICEC-18), Mumbai, India. New Delhi: NarosaPress; 2000. p. 14750.

[37] Alexeev A et al. Low cost mixture JouleThomson refrigerator. Proc16th int cryog conf, Kitakyushu, Japan. Elsevier Sciences Press;1997. p. 3958.

[38] Boiarski M et al. Modern trends in designing small-capacity JTcoolers operating with mixed refrigerants. Cryocoolers, vol. 11. Klu-wer Academic/Plenum Press; 2001. p. 51321.

[39] Boyarski M et al. Enhanced refrigeration performance of the throttlecycle cooler with mixed refrigerants. Adv Cryogc Eng 2000;45:2917.

[40] Maytal B-Z, Van Sciver SW. Characterization of coolants for Joule Thomson cryocoolers. In: Proc 6th int cryocoolers conf, David TailorResearch Center, Bethesda, MD, vol. 1, 1991. p. 24556.

[41] Robinson LB. Phase equilibria in cryogenic mixtures, Part II. Proc8th int cryocooler conf, Vail, Colorado. Cryocoolers, vol. 8. NewYork: Plenum Press; 1995. p. 55967.

[42] Dean JW, Mann, D.B. The JouleThomson process in cryogenicrefrigeration systems, NIST Technical Note No. 227, Boulder,Colorado, USA, 1965.

[43] Alexeev A et al. Study of behavior in the heat exchanger of a mixedgas JouleThomson cooler. Adv Cryog Eng 2000;45:30714.

[44] Maytal B-Z. Performance of an ideal ow regulated JouleThomsoncryocooler. Cryogenics 1994;34(9):7236.

[45] Brodianski VM et al. Retrospective of mixed-refrigerant technologyand modern status of the cryocoolers based on one-stage, oil-lubricated compressor. Adv Cryog Eng 1998;43:17018.

[46] Levenduski R et al. The development of a JouleThomsoncryocooler for space application. Proc 8th int cryocooler conf.Cryocoolers, vol. 8. New York: Plenum Press; 1995. p. 54358.

[47] Kuo DT. Linear compressors for JT cryocoolers. In: Proc 7th intcryocooler conf, Phillips Laboratory, New Mexico, vol. 4, 1993.p. 92130.

[48] Landa YI et al. The self-regulating effect used in JouleThomsonmicro cryogenic systems. In: Proc 14th int cryog eng conf. Cryo-genics, ICEC-14 (Suppl.) 32, 1992. p. 203.

[49] Dobak JD et al. Mixed gas refrigeration method, US PatentNo. 5787715, 1998.

[50] Dobak JD et al. Precoling system for JouleThomson probe, USPatent No. 5758505, 1988.

[51] Longsworth RC. Heat exchangers for JouleThomson cryo-coolers.In: Proc rst int conf on aerospace heat exchanger technology, 1993.p. 61328.

[52] Radebaugh R. Refrigeration fundamentals: a view toward newrefrigeration systems. In: Applications of closed-cycle cryocoolers tosmall superconducting devices. NIST Publication 508, 1978. p. 7.

[53] Maytal B-Z. Noble gases as favorite coolants for JouleThomsoncryostats. Adv Cryog Eng 1994;39B:193541.

[54] Mikus PW et al. Cryoprobe, US Patent No. 5800487, 1998.[55] Maytal B-Z. Fast JouleThomson cryocycling apparatus for cryo-

surgical apllications. Adv Cryog Eng 1988;43A:9117.[56] Dobak J. Cryosurgical Instrument, US Patent No. 5275595, 1994.[57] Li H et al. Gas mixture for cryogenic applications, US Patent

No. 6074572, 1999.


Documents

Resfriamento de Joule Tomson a elevadas pressões.pdf