Performances of the mixed-gases Joule–Thomson refrigeration cycles for cooling fixed-temperature heat loads

Cryogenics 44 (2004) 847–857

www.elsevier.com/locate/cryogenics

Performances of the mixed-gases Joule–Thomson refrigerationcycles for cooling fixed-temperature heat loads

M.Q. Gong *, J.F. Wu, E.G. Luo

Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, P.O. Box 2711, 100080 Beijing, China

Received 24 September 2003; received in revised form 12 April 2004; accepted 7 May 2004

Abstract

Numerous mixed-gases refrigeration cycle configurations based on Joule–Thomson effects were developed in the past several

decades. In this paper, comprehensive thermodynamic analyses were made on two typical cycle configurations to learn their per-

formance for cooling fixed-temperature heat loads. One is the single-stage cycle without phase separators; the other is the auto-

cascade refrigeration cycle which has at least one phase separator. An exergy model was developed to analyze the thermodynamic

performance of those refrigeration cycles. Comprehensive comparisons were made on the performance of the recuperative throttling

cycles using multicomponent mixture as refrigerant, including extensive simulations and optimizations of mixtures and cycle

configurations. The results show that the auto-cascade cycle can improve thermodynamic performance in the case of using mixtures

with increased fraction of high-boiling components, however, degrade the performance when using mixtures with increased fraction

of low-boiling components. The results also show that the mixed refrigerant is the most important designing parameter in the design

of such mixed-gases refrigeration system. Different cycle configuration has different optimal mixture composition. When using

optimal mixtures, both cycles (separation and non-separation) can provide approximately equal performance.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: Mixed refrigerant; Throttling refrigeration cycle; Single-stage; Auto-cascade; Fixed-temperature heat loads

1. Introduction

The last two to three decades has seen a remarkable

development of the mixed-gases Joule–Thomson refrig-

erator (MJTR). Driven by an oil-lubricated commercialcompressor makes the MJTR more competitive with

other type coolers. This new revival refrigeration

method with multicomponent mixture has demonstrated

high performance in the cooling temperature range from

80 to 230 K in many applications, such as cooling

infrared sensors, gas chiller or liquefaction, cryo-

surgery, cryo-preservation, water vapor cryo-trapping,

etc. The merits of mixed-gases refrigeration is obvioussuch as low cost, high reliability, high efficiency, and

easily to be produced in industry scale, etc.

Numerous mixed-gases refrigeration cycle configura-

tions based on Joule–Thomson effects were proposed in

* Corresponding author. Tel.: +86-10-62578910; fax: +86-10-

62564049.

E-mail address: [email protected] (M.Q. Gong).

0011-2275/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.cryogenics.2004.05.004

the past several decades in different applications. There

are two typical configurations among those presented

cycles, one is the famous auto-cascade cycle with phase

separators, and the other is simplest single-stage cycle

without phase separators. A schematic diagram of asingle-stage cycle (without phase separators), one stage

auto-cascade cycle (with one phase separator), and two-

stage auto-cascade cycle (with two-phase separators) is

shown in Fig. 1.

The concept of the auto-cascade cycle using mixed-

gases as refrigerant was proposed by Podbielniak [1], and

was first successful developed in the liquefaction of nat-

ural gas by Klemenko [2]. Missimer [3] further improvedthis cycle and used it for other applications above 130 K.

Luo et al. [4] were able to achieve a low temperature of 51

K with a modified auto-cascade cycle configuration. The

mixed-refrigerant auto-cascade cycle driven by a single

compressor is derived from the idea of the traditional

cascade refrigeration cycle, which provides different

refrigeration at different temperature level. In a typical

cascade refrigeration cycle, at least two pure refrigerantloops are assembled in sequence to produce refrigeration

mail to: [email protected]

Nomenclature

E exergy, kJ, J

e specific exergy, kJ/mol

DE exergy difference

F flow rate of the fluid stream, mol/s

i component numberj equipment number

k adiabatic compressing index

p pressure, MPa

Qc cooling capacity, kW, W

Q0 heat rejected, kW, W

QHX recuperative heat load, kJ/mol

S entropy, kJ/molK

T temperature, KTAC outlet temperature of compressor, K

Td temperature difference, K

W , Winput input power, kW, W

Z composition

Greeks

P exergy loss

g exergy efficiency

Subscripts

0 ambient end

1, 2 stream number before mixing

C cold end

CEF Carnot efficiency

CP compressor

H hot sideHX heat exchanger

L cold side

Sep separation

Fig. 1. Different configurations for mixed-refrigerant J–T cycle.

848 M.Q. Gong et al. / Cryogenics 44 (2004) 847–857

at different temperature level, in which the high tem-

perature loop precools the low temperature loop. The

mixed-refrigerant auto-cascade driven by a single com-

pressor is a further development of the cascade cycle. In

the mixed-refrigerant auto-cascade cycle, the liquid

fraction mainly composed of high-boiling component

and lubricant separated at a high level temperature range

passes through a throttling device to provide refrigera-tion for precooling the separated vapor fraction. The

separated vapor refraction goes down to provide refrig-

eration at lower temperature level.

The single-stage mixed-refrigerant refrigeration cycle,

in which all refrigerants pass through total parts of the

cycle, was first proposed by Fuderer [5]. A low refrig-

eration temperature of 100 K was achieved with a

pressure ratio of 40 in their first study. Anotherimportant advance of the mixed-refrigerant single-stage

refrigeration was made by Brodianski [6]. A lower

cooling temperature of liquid nitrogen was obtained

with this single-stage mixed-gases Joule–Thomson cycle.

There are several articles published recently to discuss

the performances of these different cycles with or with-

out phase separators for cooling fixed-temperature heat

loads [7–12]. Important contributions were made in

these articles. However, the conclusions in those articles

are incomplete and somewhat conflicting to each other.In this paper, much effort was put on to study this

problem further by systematic and comprehensive

analysis of mixed-gases refrigeration cycles.

2. Thermodynamic cycles

Generally, the efficiency of a mixture refrigeration

system is determined by the irreversibility of the separate

processes in the cycle. For typical mixed-refrigerant

Table 1

Typical thermodynamic processes in close mixed-refrigerant cycles

Thermodynamic process Unit equipment Section specifications

Adiabatic compressing process Compressor Compressing section

Isobaric cooling by air or water After cooler or condenser

Continuing cooling by return stream Recuperative process––counter-flow

heat exchanger

Recuperative section

Continuing evaporation and retraction of the

refrigeration

Phase separation

Separator

Adiabatic mixing Mixer

Isenthalpic throttling expansion Throttle valve Throttle section

Partial evaporation to provide Evaporator Evaporation section

refrigeration

M.Q. Gong et al. / Cryogenics 44 (2004) 847–857 849

throttle cycles, illustrated in Fig. 1, there are about fiveor seven basic thermodynamic processes to complete the

total circuit, which are also listed in Table 1. The effi-

ciency of the whole refrigeration system is determined by

those processes described above. Furthermore, different

process takes different roles on the performance of the

whole system. There will be at least one device for

each thermodynamic process in a real system to com-

plete the circuit. For the auto-cascade cycle, there is atleast one throttle device in the recuperative section

(dashed rectangle in Fig. 1); however, there is only one

main throttle device in the throttle section to generate

refrigeration.

2.1. The single-stage cycle configuration

The single-stage mixed refrigeration cycle is the sim-

plest among those presented cycle configurations. For an

ideal situation, there are five basic thermodynamic pro-

cesses such as adiabatic compressing, isobaric cooling,

recuperative process, isenthalpic throttling process, and

evaporation process. The simplest single-stage system

incorporates only one counter-flow heat exchanger. Allof the refrigerant mixture with overall composition flows

through the complete circuit. The system, illustrated in

Fig. 1 Cycle-A, consists of a compressor, an after-cooler,

a counter-current flow heat exchanger, a throttle device

that is usually a capillary or an orifice, and an evapora-

tor. This arrangement is better suited to smaller and

simpler systems. Any compressor lubricant entrained in

the circulating refrigerant mixture requires proper man-agement, e.g. the employment of an oil separator in the

cycle, to avoid plugging problem in the coldest section.

2.2. The auto-cascade refrigeration cycle

In the auto-cascade refrigeration cycle, at leastone phase separator is installed. The separator divides a

high pressure stream into two fractions: a liquid frac-

tion enriched with the high-boiling components and

lubricant, and a vapor fraction which has an increasedcontent of the low-boiling components. The vapor

fraction is directed to the lower temperature section of

the system. Meanwhile the separated liquid fraction

throttles to the return low-pressure stream to provide

refrigeration at a relative higher temperature range. The

auto-cascade cycle can avoid cold-end clogging essen-

tially with proper cycle configuration.

The number of the heat exchangers and phase sepa-rators in the auto-cascade cycle varies flexibly based on

the required cooling temperature. There are different

arrangement types of the mixed-refrigerant auto-cascade

refrigeration cycle for different cooling temperature or

different applications. In Fig. 1, Cycle-B shows a basic

flow pattern and heat exchanger arrangements of a

single-stage auto-cascade cycle (with one separator);

Cycle-C is a typical configuration of a two-stage auto-cascade cycle (with two separators). The single-stage

auto-cascade system, illustrated in Fig. 1 Cycle-B, em-

ploys two counter-current flow heat exchangers and one

vapor–liquid phase separator. In this system, after the

first cooling step in the counter-current flow heat ex-

changer, the phase separator removes the condensate

from the vapor stream. A throttling device controls

the exiting liquid flow. The liquid passing through thethrottling device usually becomes two-phase blend. The

two-phase blend mixed with the low-pressure return

stream cools the coming high-pressure stream. The

separated vapor fraction is directed to the next stage

heat exchanger, and finally passes through the end

throttling device to produce cooling capacity at the

lowest refrigeration temperature. This procedure is same

for other auto-cascade refrigeration cycle with differentseparator numbers.

In Cycle-B, Cycle-C, illustrated in Fig. 1, those units

enclosed in a dashed rectangle accomplish recuperative

heat exchange just as the counter-flow heat exchanger in

Cycle-A. On the other hand, the single-stage cycle can

also be considered as an auto-cascade cycle with zero

separators.


3. Exergy model of the thermodynamic cycles

3.1. Exergy model

Among all known refrigeration cycle, the Carnot

refrigeration cycle has the maximum value of the ther-

modynamic efficiency. In Carnot cycle, all thermody-

namic processes are assumed to be reversible. However,

this cycle may never be reached in practice; nevertheless,it represents an ideal cycle. In fact, the thermodynamic

efficiency of Carnot cycle is usually used as a reference

index in the evaluation of other refrigeration system.

The coefficient of performance (COP) of Carnot cycle

can be easily given in Eq. (1) [13]:

COPCarnot ¼Qc

Q0 � Qc

¼ TcT0 � Tc

ð1Þ

gCEF ¼ COPreal

COPCarnot

¼ COPreal �T0 � Tc

Tcð2Þ

Eq. (2) shows the COP ratio at same temperature range

of a real refrigeration cycle of the Carnot cycle, which is

also called the exergy efficiency of a real refrigeration

system. In fact, Eq. (2) shows the thermodynamic per-

fect degree of a real refrigeration cycle. With Eq. (2), the

comparison can be made for all real refrigeration sys-tems, no matter what kind refrigeration cycle it is.

Gong et al. [8] proposed an exergy model described

the mixed-refrigerant refrigeration cycle. It is described

in above section that the refrigeration cycle is completed

with different thermodynamic processes. Therefore,

from Ref. [8], the cycle efficiency can be obtained with

the following equations:

W ¼ EQcþX

Pj ¼Z

TTc

�� 1

�dQc þ

XPj ð3Þ

gCEF ¼Exergygained

Exergyinput¼ EQc

W¼ 1�

PPj

Wð4Þ

where EQcis the exergy of the cooling capacity at a fixed

cooling temperature of Tc, Pj is the exergy loss of each

element in the cycle, g is the exergy efficiency of the

refrigeration cycle.

The following task is to find out Pj, the exergy loss of

the each element of the mixed-gases refrigeration cycle.

No variation of mixture composition in the cycle is as-sumed in the following part of this paper. The exergy

loss of the each unit equipment in the cycle can be de-

scribed as follows:

Pcompressor ¼ T0ðSoutlet � SinletÞ ð5Þ

Pcooler ¼ Qrejected � T0ðSinlet � SoutletÞ ð6Þ

Pheat exchanger ¼ DEcold side � DEhot side

¼ T0ðDScold side � DShot sideÞ ð7Þ

Pseparator ¼ Einlet � ðFliquideliquid þ FvaporevaporÞ ð8Þ

Pthrottle ¼ Einlet � Eoutlet ¼ T0ðSoutlet � SinletÞ ð9Þ

Pmixer ¼ F1e1 þ F2e2 � Fafter mixingeafter mixing ð10Þ

Pevaporator ¼ Einlet � Eoutlet � EQcð11Þ

Ploss ¼ EHX�cold outlet � ECP�inlet ð12ÞPloss is caused by insufficient recuperative process. That

is, the temperature of return stream at the outlet of low-pressure passage is lower than ambient temperature.

With the above equations the thermodynamic perfor-

mance of the mixed-refrigerant refrigeration cycle can be

simulated. An optimization model of this refrigerator

can also be developed. The objective function with the

constraining conditions is expressed as:

g ¼ EQc

W¼ 1�

PPj

Wð13Þ

Xn

1

zi ¼ 1 zi > 0 ði ¼ 1; 2; . . . ; nÞ ð14Þ

Pj P 0 ð15Þwhere z is the molar fraction, i is component number.

3.2. Exergy losses of elements and their influences on the

total system

Eqs. (3), (4) and (13) give the relationship between

exergy losses of elements in the cycle and the exergy

efficiency of the total system. Generally, the influence of

one element on the total system can be expressed as [14]:

xe;j ¼oXe

oxe;i

� �y¼constant

ð16Þ

where Xe is exergy specification of a system, e.g. exergy

efficiency in this paper; xe;j is exergy specification of jelement; the constant number of y means that the vari-

ation value of xe;j is independent from other elements in

the system. Eq. (16) defines the relationship between asystem and its elements, which is determined by the

system configuration. When xe;j is larger, it means that

the influence of i element on the total system is larger.

When a system is optimized, the most effort should be

put on the element with the maximum xe;j.To get the detailed value of xe;j is difficult in most real

systems because all elements behaviors influence each

other. If there is such a system that all elements areindependent, the total exergy efficiency can be expressed

as a product by multiplying all elements efficiency to-

gether:

g ¼ g1g2 � � � gj � � � gn ¼Yj¼n

j¼1

gj ð17Þ


However, Eq. (17) can only be used in a very simplesystem that all elements are independent. For a mixed-

gases Joule–Thomson refrigeration system, even the

simplest cycle configuration––the single-stage cycle, Eq.

(17) cannot be used.

The current analysis was conducted for single-stage

and auto-cascade mixed-gases refrigeration system

based on a single compressor. All the exergy losses in-

clude two constituents: intrinsic and extrinsic exergylosses. Intrinsic losses depend on the thermodynamic

processes of the cycle and mixed-refrigerant properties,

such as Pthrottle throttle irreversibility, Pheat exchanger,

Pevaporator due to temperature difference in the heat ex-

changer and evaporator. Pheat exchanger is always larger

than zero, even if the minimum temperature difference in

the heat exchanger equals to zero. Temperature glide in

the evaporator because of the non-zeotropic mixturecauses exergy loss for constant temperature refrigeration

applications. The intrinsic losses cannot be changed if

the thermodynamic process does not vary. Extrinsic

losses depend on the equipment design and construction,

such as irreversibility in adiabatic compressing process,

heat intakes through the insulation, limited heat transfer

coefficients and area, hydraulic pressure drops, etc. The

highly idealized cycle has no extrinsic losses but onlyintrinsic losses. Thermodynamic performance of an ideal

cycle only depends on mixed-refrigerant used, operating

pressures and cycle configuration.

For small or middle-scale compressors wildly used in

commercial refrigeration, which is also used in low

temperature mixed-gases refrigeration system, there is

about 30–60% of the input electrical power consumed in

the compressor. That is, the compressor efficiency isonly about 40–70%. For a mixed-gases J–T refrigeration

system, the compressor is the most important element,

which has the maximum xe;j in the total system. How-

ever, for idealized cycles analyzed in this paper, the

extrinsic loss caused by limited compressor efficiency is

not considered. That is, the compressing process is

an adiabatic process without entropy increase. Only

Table 2

Specifications of pure candidate components

No. Candidate components Normal boiling

range/K

1 He, H2, Ne 4.2–27.0

N2, Ar 77.4–87.3

CH4 111.7

2 F3N, R14 144.5–145.2

C2H4, C2H6, R23, R116 169.4–194.9

3 C3H8, C3H6, iC4H10, iC4H8, R218, C4H10 225.4–272.7

iC5H12, iC5H10, 2-C6H14 293.3–331.1

the intrinsic loss in the after cooler is considered. Inthis idealized cycle, it is agreed that the recuperative

process (heat exchanger) has the maximum xe;j in the

cycle without a consideration of the efficiency of com-

pressor.

4. Simulations and analysis

In this section, the simulations and optimizations of

the mixed-gases refrigeration cycles both of the single-stage cycle and the auto-cascade cycle are made. The

thermodynamic properties of mixtures were calculated

by using a commercial software of ProII [15].

Some pure candidate components selected from the

interest in low temperature refrigeration are listed in

Table 2. For 120 K refrigeration temperature used in

this paper, the candidate components can be divided

into three groups: low-boiling component, middle-boil-ing component and high-boiling component, which is

divided on the basis of normal boiling point tempera-

ture. Therefore, at least one component should be used

in each group to obtain the mixture used in 120 K

refrigeration.

4.1. Performance simulations of Cycle-A and Cycle-B

In order to know the performances of the refrigera-

tion cycles using different mixtures, six typical mixtures

named as Mix #1 to #6 are selected in this simulation,

which are listed in Table 3. Mix #1 to #6 are mixtureswith same components (nitrogen, methane, ethane,

propane, isobutane) but different compositions. Nitro-

gen and methane are in the low-boiling component

group, ethane is middle-boiling component, while pro-

pane and isobutene are high-boiling components. In

detail, Mix #1 contains a relatively reduced fraction of

high-boiling point components (propane and i-butane);

Mix #2 contains a relatively increased fraction of high-boiling point components; Mix #3 contains a relatively

point temperature Group specifications for 120 K

refrigeration

Low-boiling component

Middle-boiling component

High-boiling component

Table 3

Performances of Cycle-A and Cycle-B with different mixtures

Components and Pj Mix#l Mix #2 Mix #3 Mix #4 Mix #5a Mix #6

N2 (%) 60 10 30 10 X1 X1� 3:28

CH4 (%) 25 15 35 15 X2 X2þ 4:42

C2H6 (%) 10 15 2 55 X3 X3þ 2:02

C3H8 (%) 3 25 5 15 X4 X4� 6:68

iC4H10 (%) 2 35 28 5 X5 X5þ 3:52

k 1.282 1.078 1.157 1.147 1.148 1.148

TAC (K) 443.99 373.39 391.89 391.64 389.98 389.72

Winput (kJ/mol) 5.47 4.64 4.992 4.937 4.951 4.948

Cycle-A Pafter�cooler (%) 19.42 21.8 15.05 15.33 14.87 14.81

Pheat exchanger (%) 20.12 38.55 31.72 69.17 28.9 34.06

Pthrottle (%) 53.95 8.15 26.92 6.08 14.0 10.97

Pevaporator (%) 0.14 0.2 1.12 0.24 3.42 3.01

Ploss (%) 0.03 21.37 0.76 0.24 0 0

QHX (kJ/mol) 9.41 19.6 17.28 22.2 20.37 20.24

g (%) 6.33 9.93 24.43 8.92 38.81 37.05

Cycle-B Pafter�cooler (%) 19.42 21.8 15.05 15.33 14.87 14.81

Pthrottle1 (%) 0.4 8.08 0.78 8.02 1.68 0.65

Pmixer 0.22 3.86 2.33 2.13 1.91 2.35

PHX1 (%) 6.25 10.02 / 40.41 3.19 /

PHX2 (%) 1.55 4.28 16.67 4.89 13.5 0.66

PHX3 (%) 27.75 4.88 12.43 6.33 10.1 28.85

Pheat exchanger (%) b 36.16 31.17 32.01 61.78 30.41 32.51

Pthrottle2 (%) 38.71 5.79 28.01 4.35 14.9 10.61

Pevaporator (%) 0.12 2.02 1.18 1.96 3.02 3.3

Ploss (%) 0.03 20.43 0.83 0.08 0 0

PHX (kJ/mol) 8.67 9.86 15.7 16.38 17.72

Tsep (K) 220 285 300 240 290 300

g (%) 5.56 18.78 22.92 16.5 36.83 38.65aX1: 22.78, X2: 32.38, X3: 6.8, X4: 20.9 X5: 17.2.bPheat exchanger ¼ Pthrottle1 þPmixer þPHX1 þPHX2 þPHX3.


reduced fraction of middle-boiling component; Mix #4

is a mixture with a relatively increased fraction of

middle-boiling component; Mix #5 is a mixture with

optimized composition for Cycle-A; and Mix #6 is a

mixture with optimized composition for Cycle-B. Other

calculation conditions are listed as follows:

The ambient temperature is 300 K; high operating

pressure is 1.8 MPa and 0.3 MPa for low operatingpressure; the minimum temperature difference in the

heat exchanger is assumed as 0.2 K; and the refrigera-

tion temperature is 120 K; no pressure drop in the cir-

cuit is considered.

Fig. 2. Q–T diagram

The diagrams of temperature distribution versus the

recuperative heat loads in the heat exchangers for those

above mixtures both in Cycle-A and Cycle-B are shown

in Figs. 2–7. The distribution of logarithmic mean

temperature difference (Td) is also illustrated in those

figures. In Table 3, the separation temperature (Tsep) inCycle-B is preliminary optimized at given conditions.

QHX is the recuperation heat loads in the cycle. Detailsexergy losses of both single-stage cycle (Cycle-A) and

one-stage auto-cascade cycle (Cycle-B) are listed in

Table 3. The results show that for same mixture, the two

typical cycles indicate different performances.

of Mix #1.

Fig. 3. Q–T diagram of Mix #2.







4.2. Performances of different thermodynamic processes

using different mixtures

It is mentioned above that the total efficiency of a

mixture refrigeration system is determined by the irre-

versibility of the separate processes in the cycle. The

following will discuss the influence of different mixtures

on different thermodynamic processes.

4.2.1. Recuperative process

It is known that the mixture refrigeration cycle is a

recuperative refrigeration cycle. Among those thermo-

dynamic processes, the recuperative process is one of the

most important processes in the cycle. Most exergy

losses occur in the heat transfer process (recuperativeprocess). There are many reasons for the exergy losses in

the heat exchanger. From a thermodynamic point of

view, the most likely reason is that the heat capacities of

the two flows do not match each other because of the

difference of pressures. For pure gases, the specific heat

capacity of the high-pressure flow is always larger than

the low-pressure flow. For non-azeotropic mixtures,

especially in two-phase state, the situation may be dif-ferent. Because the latent heat in two-phase state makes

a very important contribution in the total two-phase

specific heat capacity, which of low-pressure is always

larger than that of high-pressure flow. Therefore, it can

be expected that the effective heat capacity of the low-

pressure flow can be proximate to or even larger than

the high-pressure flow over the whole operating tem-

perature range. That is, the phase change can decreasethe difference of the heat capacity caused by the differ-

ence of pressures. The phase-change range is very sen-

sitive to the mixtures used. Fig. 8 shows the latent heat

distribution as a function of temperature for Mix #1 to

Mix #6. It is clear that the latent heat of low-pressure

stream is always larger than that of high-pressure

stream. Meanwhile, when a mixture has high fraction of

middle- and high-boiling component, its phase-changetemperature span is larger at same pressure conditions.

For example, the temperature span for Mix #2 is about

180 K, while for Mix #1, the temperature span is only

110 K. For optimized Mix #5 and Mix #6, the tem-

perature spans are also near about 170 K.The results illustrated in Figs. 2–7 show that the

temperature profile in the heat exchanger is strongly

influenced by the mixture composition. If the mixture

has a low fraction of a certain component, the pinch

point will occur at the corresponding temperature

(corresponding to its boiling point temperature) range of

this component. However, if it has a large fraction of

this component, the temperature difference will increaseat its corresponding temperature range. For example,

Mix #1 has a large fraction of low-boiling components

(nitrogen and methane), the temperature difference at

low temperature end is very large up to 26 K; however

the temperature difference at high temperature end is

very small, see Fig. 2. Fig. 3 shows a contrary temper-

ature profile of Mix #2, which has a large fraction of

high-boiling components. For optimal compositions ofMix #5 and Mix #6, the temperature differences are

small both at high and low temperature ends. For Mix

#3 which has a reduced fraction of middle-boiling

component, the minimum temperature difference occurs

at the middle-temperature section. On the contrary, the

temperature difference for Mix #4 at the middle-tem-

perature section reaches the maximum value.

4.2.2. Throttle process

The exergy loss in the throttle device strongly de-

pends on the state of the high-pressure stream before

throttling. If in a liquid state, especially in a sub-cooled

liquid state passing through the throttle device, the ex-ergy loss in the throttle process is much less than that in

two-phase or superheated vapor states. The state of the

high-pressure stream before throttling is determined by

the recuperative process. An obvious specification in the

evaluation of recuperative process is the temperature

difference at the cold end of the recuperative section. If

the temperature difference is large, the exergy loss will

increase, e.g. Mix #1 and Mix #3. However, if thetemperature difference is small, the exergy loss in the

final throttle device will decrease. For Mix #1 the exergy

loss of recuperative process is not large only about 20%

Fig. 8. Latent heat distributions of Mix #1 to Mix #6.


of the total input power in Cycle-A. However, because

the cold section temperature difference is as large as 26

K, the exergy loss of the final throttle device is about

54% of the total input power.

4.2.3. Compressing process

The adiabatic compressing process causes intrinsic

exergy loss in the after cooler compared to the idealized

isothermal compressing process. The adiabatic index of

the mixture is an important specification in compressing

process that is directly related to the outlet temperature

of the compressor. If the adiabatic index is larger, the

outlet temperature will increase, see Table 3.

4.2.4. Evaporation

For non-azeotropic mixture, there is temperature

glide in the evaporator. Generally, for mixed-gases

Joule–Thomson low temperature refrigeration applica-

tions, the temperature glide in the evaporation varies

from several to about 20 K. The temperature glidecauses exergy loss for fixed-temperature refrigeration.

From the results in Table 3, the exergy loss in the

evaporator is not very high.

4.3. Influence of cycle configuration on the performance

It is mentioned above that the difference of the heat

capacity in cycles is caused by the difference of the

pressure. Decreasing the difference by optimizing the

mixture composition can be used to increase the ther-

modynamic performance. Using this clue, the separator

in the auto-cascade cycles can be used to play the role ofadjusting the heat capacity of high-pressure flow. When

a part of high-pressure flow is separated, the heat

capacity of the vapor fraction that is directed to the

lower temperature part of the system is decreased. The

liquid fraction joins in the return flow of the heat ex-

changer after passing through the throttle device.

Therefore, the heat capacity of the low-pressure flow

remains unchanged compared with non-separation cyclein the heat exchanger following the separator. However,

one must realize that the separation ratio is very

important for the fixed-temperature refrigeration. If

the separator used is based on the phase equilibrium, the

separation temperature is very important. When the

temperature is higher than the dew point of the high-

pressure flow, there will be no liquid separated, and if


the temperature is very low, the refrigerant directed tothe next stage will be not enough to provide the cooling

capacity required. On the other hand, if the refrigerant

separated is too large, in the following heat exchanger,

the heat capacity of the two flows will not compatible

again because of the lower flow rate of the high-pressure

stream. This will decrease the performance of the heat

exchanger; and furthermore, decrease the performance

of the system. There is an optimal separation tempera-ture. All the separation temperature used in the calcu-

lation illustrations are preliminary optimized at given

conditions. Fig. 9 shows a diagram of separation tem-

perature versus exergy efficiency (CEF) of Cycle-B using

Mix #6.

From Table 3, one can find that the auto-cascade

Cycle-B can improve the refrigeration performance

using a mixture with a relatively increased fraction ofmiddle- and high-boiling point components, e.g. Mix #2

and Mix #4. In the auto-cascade cycle, the vapor frac-

tion separated from the initial charged mixture circu-

lates to the low temperature part of the cycle, which has

an increased concentration of the low-boiling compo-

nents. In the case of using a mixture with an increased

fraction of high-boiling components, the separated

vapor fraction tends towards the optimal mixture com-positions. This will reduce the exergy loss in the heat

exchanger as well as in the last throttle device. Even with

the additional first-stage throttling process and the

blending process, the total exergy losses of the units

enclosed in the dashed rectangle of Cycle-B are less than

that of the heat exchanger in Cycle-A. Therefore, the

total performance will increase. Then the separation

cycle can improve the performance using a mixture withan increased fraction of high-boiling components.

However, when a mixture with a reduced fraction of

high-boiling point components is used, such as Mix #1

and Mix #3, the performance of the auto-cascade cycle

(Cycle-B) is less than that of the single-stage cycle

(Cycle-A). When the mixture has a reduced fraction of

Fig. 9. Optimal separation temperature for Mix #6.

middle- and high-boiling components, the temperatureof the separator is very low to ensure there is liquid

separated. Then the separated vapor fraction has an

increased fraction of low-boiling components higher

than the initial charged mixture. This increases the

temperature difference in the low temperature part of the

cycle. Therefore, the performance of the recuperative

process is even worse than the heat exchanger in

Cycle-A. The performance of Cycle-B is degraded (Mix#1 and Mix #3).

From the simulation results listed in Table 3, it is also

easy to see that the optimal mixture compositions for

different cycles are different. When a mixture optimized

for single-stage cycle (Cycle-A) is used in an auto-

cascade cycle (Cycle-B), the performance of Cycle-B is

less than that of Cycle-A. Conversely, when a mixture

optimized for Cycle-B is used in Cycle-A, the perfor-mance of Cycle A is worse. However, the decrease of

performance is very little. When using optimal mixtures,

both cycles (separation and non-separation) can provide

approximately equal performance. A careful compari-

son of these mixtures reveals that Mix #5 contains a

little greater fraction of low-boiling components than

Mix #6.

For auto-cascade cycles, the optimal separationtemperature of the first separator is near ambient tem-

perature. At this temperature, the liquid separated from

the high-pressure flow is about 5–10% of the total cir-

culating refrigerant. The fraction of exergy loss caused

by blending process is also very small, less than 5% of

the total losses. The multistage separation cycle cannot

provide better performance than one stage separation

cycle or the single-stage cycle. The calculation results ofdifferent separation stages illustrated in Fig. 10 verify

this conclusion, in which the multistage separation cycle

has the same configuration style as Cycle-C in Fig. 1,

and the calculation conditions are same as that

described in above section. For a fixed-temperature

refrigeration no lower than 80 K, one-stage auto-

Fig. 10. Performances for different cycle configurations.


cascade cycle can achieve a good performance whileremaining a relatively simple configuration.

From the results listed in Table 3, in mixed-gases

refrigeration system, all processes are strongly influ-

enced by each other. The optimization should be carried

out from a consideration of all aspects, not just from

one or two processes. For example, for Mix #1 used in

Cycle-A, the exergy loss in the heat exchanger is only

about 20%, however, for Mix #5 in Cycle-A, the exergyloss reaches up to 28.9%. It cannot say that the first one

has a higher efficiency. Indeed, Mix #5 is more efficient

than Mix #1, no matter what kind cycle is used.

5. Conclusions

In this paper, the thermodynamic performances fordifferent cycle configurations with different multicom-

ponent mixtures were studied. The following conclu-

sions can be made from the results of calculation and

analysis presented above.

1. The components of the mixture are the most impor-

tant parameters in the design of the refrigeration sys-

tem, and are the basis for the consideration of otherparameters. The temperature difference in the heat ex-

changer is caused by the difference of mixture proper-

ties which are dependent on pressures. Because of the

difference of pressures, the heat capacities of the two

sides in the counter-flow heat exchanger do not

match. Adjusting mixture compositions can change

the properties of the circulated refrigerant to change

its effective heat capacity. The separation of thehigh-pressure refrigerant can also be used to change

the flow rate and compositions.

2. Different thermodynamic process has different role in

the influence on the total efficiency of the system. For

idealized cycles, the recuperative process has the most

important role in the cycle. However, the optimiza-

tion of a system should take all aspects in consider-

ations.3. For non-optimal mixtures with a relatively increased

fraction of high-boiling components, the auto-

cascade cycle can improve performance; for mixtures

with a reduced fraction of high-boiling components,

the performance of auto-cascade cycle is degraded.

Different cycles have different optimal mixture com-

position to achieve best performance. When using

optimal mixtures, both cycles (separation and non-separation) can provide approximately equal perfor-

mance.

4. For fixed-temperature refrigeration not lower than 80K, one-stage auto-cascade cycle can provide good

performance while remaining a relatively simple con-

figuration. There is more freedom in selecting the

mixture compared to the single-stage cycle which

may not run properly because of a larger fraction

of components with high-boiling points charged in

the system.

Acknowledgements

This work is financially supported by the National

Natural Sciences Foundation of China under the

contract number of 50206024.

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Documents

Performances of the mixed-gases Joule–Thomson refrigeration cycles for cooling fixed-temperature heat loads