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Modified Brayton Refrigeration Cycles
for Liquid Hydrogen in Spallation
Neutron Source Moderator
H.-M. Chang1,2, S.G. Kim1, J.G. Weisend II2, H. Quack3
1
Hong Ik University, Seoul, 121-791, Korea
European Spallation Source, SE-221 00 Lund, Sweden
3
TU Dresden, D-01062 Dresden, Germany
2
ABSTRACT
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to cool liquid hydrogen in spallation neutron facilities. The target moderators under development
at ESS require a refrigeration capacity of 30 kW at 20 K to remove the dissipated energy from
VXEFRROHGOLTXLGK\GURJHQ$VWDQGDUG%UD\WRQUHIULJHUDWLRQF\FOHWRSHUIRUPWKLVUHIULJHUDWLRQLV
GHVLJQHGZLWKKHOLXPDVUHIULJHUDQW$YDULHW\RIPRGL¿HGSURFHVVHVDUHexamined for improved
HI¿FLHQF\DQGVXLWDELOLW\7KHPRGL¿FDWLRQLQFOXGHVWKHFRPSDULVRQRI/3ORZSUHVVXUHDQG+3
KLJKSUHVVXUHFRROLQJGHSHQGLQJRQWKHORFDWLRQRIFU\RJHQLFH[SDQGHULQWKHF\FOHDQGWZR
VWDJHDQGGXDOWXUELQHF\FOHVGHSHQGLQJRQWKHPDQQHURIFRPELQLQJWKHWZRH[SDQGHUV%DVHG
on existing and proposed designs, eight different cycles are selected and analyzed fully with the
DVVXPHGPRGHOVRIWKHFRPSRQHQWV7KHUHVXOWVDUHSUHVHQWHGLQWHUPVRIWKH¿JXUHRIPHULWFOM
as an index of the thermodynamic performance, and the detailed exergy expenditure is also investiJDWHG$VDUHVXOWRIWKLVDQDO\VLVDPRGL¿HGGXDOWXUELQHF\FOHLVUHFRPPHQGHGIRUODUJHFDSDFLW\
refrigeration at 20 K.
INTRODUCTION
Cryogenic
ryogenic refrigeration at 20 K is required for liquid-hydrogen moderators in spallation neutron source facilities1-5. As shown in Figure 1, the dissipated energy of neutrons is removed at the
PRGHUDWRUVE\DFLUFXODWLQJÀRZRIVXEFRROHGOLTXLGK\GURJHQDWWHPSHUDWXUHVEHORZ.DQG
WKHQGHOLYHUHGWRDUHIULJHUDWRUYLDDKHOLXPK\GURJHQ+H+2KHDWH[FKDQJHU+;7KHFORVHG
loop of liquid hydrogen can be plotted as a counterclockwise triangular cycle on the phase diagram,
DVVKRZQLQ)LJXUH7KHFRROLQJÀRZWKURXJKWKHPRGHUDWRUVLVUHSUHVHQWHGE\DGHVFHQGLQJOLQH
according to the magnitude of the pressure drop and the temperature rise, which are restored by
a pump and by the refrigerator, respectively. In order to avoid any vaporization, liquid hydrogen
LVPDLQWDLQHGDWDVXEFRROHGWHPSHUDWXUHDWa.DQGDWWKHDSSUR[LPDWHFULWLFDOSUHVVXUH
03D7KHUHIULJHUDWLRQORDGLVaN:IRUWKHH[LVWLQJV\VWHPVXQGHURSHUDWLRQRUQHDULQJ
completion1-3. A much larger cryogenic moderator system has been recently designed and will be
FRPSOHWHGE\IRUWKH(XURSHDQ6SDOODWLRQ6RXUFH(664,5, where the maximum heat load is
estimated to be over 30 kW during the operation with a full level of beam power.
Cryocoolers 19, edited by S.D. Miller and R.G. Ross, Jr.
©¶International Cryocooler Conference, Inc., Boulder, CO, 2016
463
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BRAYTON CRYOCOOLER DEVELOPMENTS
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Figure 1. Cryogenic refrigeration system and liquid-hydrogen cycle on phase diagram.
7KHFU\RJHQLFUHIULJHUDWRUVWRFRYHUaN:DW.KDYHEHHQGHVLJQHGDVDVWDQGDUGUHYHUVH
%UD\WRQF\FOH1-3. Helium is the only possible gas refrigerant for this application, as a cryogenic
WXUELQHVKRXOGEHXVHGDWWHPSHUDWXUHVEHORZ.7KHVWDQGDUG%UD\WRQF\FOHFRXOGEHPRGL¿HG
LQYDULRXVZD\VWRLQFUHDVHWKHWKHUPRG\QDPLFHI¿FLHQF\DQGUHIULJHUDWLRQFDSDFLW\RUWRVDWLVI\
other design requirements. The thermodynamic design of the 30 kW refrigerator for ESS is a new
and exciting challenge at 20 K, since it requires not only the largest capacity ever, but also a set of
thermo-hydraulic and geometric constraints5. This study investigates the structures of standard or
PRGL¿HGF\FOHVLQDV\VWHPDWLFZD\DQGSURYLGHVDWKHUPRG\QDPLFEDVLVIRUWKHGHYHORSPHQWRI
large-scale refrigerators at 20 K.
STANDARD AND MODIFIED CYCLES
(LJKWGLIIHUHQWUHIULJHUDWLRQF\FOHVDUHVHOHFWHGDQGVKRZQLQ)LJXUH&\FOH,LVWKHVWDQGDUG
%UD\WRQF\FOHWKDWKDVRQHUHFXSHUDWLYHKHDWH[FKDQJHU+;DQGRQHH[SDQGHU(RUWXUELQH
7KLVF\FOHLVFDOOHG³6WDQGDUGF\FOHZLWK/3ORZSUHVVXUHFRROLQJ´VLQFHWKHFROGKHOLXPVWDWH
HQWHUV+;DIWHUH[SDQVLRQIRUWKHWKHUPDOFRQWDFWZLWK/+2&\FOH,,LVDQRWKHUVLPSOHF\FOHZLWK
RQH+H+H+;DQGRQHH[SDQGHUEXWLVFDOOHG³6WDQGDUGF\FOHZLWK+3KLJKSUHVVXUHFRROLQJ´
VLQFHWKHFROGKHOLXPVWDWHHQWHUV+;EHIRUHWKHH[SDQVLRQ7KHHI¿FLHQF\RIWKHVHVWDQGDUG
F\FOHVKDVDFHUWDLQOLPLWQRPDWWHUKRZKLJKO\HIIHFWLYH+;PD\EHEHFDXVHWKHUHLVDPLVPDWFK
LQWKHVSHFL¿FKHDWRI+HEHWZHHQWKH+3DQGWKH/3VWUHDPV
The limit of standard cycles can be overcome by employing two expanders67KH¿UVWZD\LV
WRDUUDQJHWZRH[SDQGHUVLQVHULHVVXFKWKDWWKH¿UVWZDUPH[SDQGHULVXVHGWRFRPSHQVDWHWKH
PLVPDWFKRIVSHFL¿FKHDWDQGWKHVHFRQGFROGH[SDQGHUSOD\VWKHPDLQUROHRIFU\RJHQLFUHIULJHUDWLRQ&\FOHV,,,DQG,9DUHVXFKH[DPSOHVZKLFKDUHFDOOHG³7ZRVWDJHF\FOHZLWK/3FRROLQJ´
DQG³7ZRVWDJHF\FOHZLWK+3FRROLQJ´UHVSHFWLYHO\,QWKHVHWZRVWDJHF\FOHVWKHÀRZUDWHLVWKH
same for the two expanders, but the operating pressure is different.
Another way is to arrange two expanders in parallel so that they work at the same pressure level.
$PRQJDYDULHW\RISRVVLEOHVWUXFWXUHV&\FOHV9DQG9,DUHVHOHFWHGDVFDOOHG³'XDOWXUELQH
F\FOHZLWK/3FRROLQJ´DQG³'XDOWXUELQHF\FOHZLWK+3FRROLQJ´UHVSHFWLYHO\$WDORFDWLRQRIWKH
+3VWUHDPVWDWHDVPDOOIUDFWLRQRIJDVLVGLYHUWHGH[SDQGHGWKURXJKWKH¿UVWZDUPH[SDQGHU
DQGUHXQLWHGZLWKWKH/3VWUHDPEHORZ+;7KHPDLQ+3VWUHDPFRQWLQXHVWKURXJK+;DQG
+;DQGLV¿QDOO\H[SDQGHGWKURXJKWKHVHFRQGFROGH[SDQGHUWRWKHFROGHVWWHPSHUDWXUH7KH
structure of these cycles is similar to the Claude cycle, except that the JT valve is replaced by a cold
H[SDQGHU,Q+;WKH/3VWUHDPKDVDKLJKHUÀRZUDWHWKDQWKH+3VWUHDPLQRUGHUWRFRPSHQVDWH
IRUWKHPLVPDWFKLQVSHFL¿FKHDW
7KHFROGHQGRIWKHGXDOWXUELQHF\FOHVFRXOGEHIXUWKHUPRGL¿HGE\DGGLQJDZDUPXSÀRZ
WRWKH+3VWUHDPEHIRUHHQWHULQJWKHFROGWXUELQHDVVKRZQLQ&\FOHV9,,DQG9,,,DQGFDOOHG
³0RGL¿HGGXDOWXUELQHF\FOHZLWK/3FRROLQJ´DQG³0RGL¿HGGXDOWXUELQHF\FOHZLWK+3FRROLQJ´
UHVSHFWLYHO\,QWKHVHF\FOHVWKHQXPEHURI+H+H+;¶VLV¿YHDQG+;LVDWULSOHVWUHDP+;
KDYLQJWZRFROGVWUHDPVDQGRQHZDUPVWUHDP7KHZDUPXSÀRZFRXOGEHHIIHFWLYHLQUHGXFLQJ
the temperature difference at the cold end as described later.
MODIFIED BRAYTON REFRIGERATION CYCLES FOR LIQUID H2
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Figure 2. Standard or modified Brayton cycles for sub-cooled liquid hydrogen. (AC: after-cooler, C:
compressor, HX: heat exchanger, E: expander)
CYCLE ANALYSIS
The following assumptions are made to analyze and compare the selected cycles.
Ɣ 7KHDPELHQWWHPSHUDWXUHT0LV.
Ɣ 7KHUHIULJHUDWLRQORDGE\OLTXLGK\GURJHQLVN:
Ɣ $WWKH+H+2+;Whe inlet and exit temperatures of He are 15 K and 20 K, respectively, and
WKHSUHVVXUHGURSRI+HÀRZLV03D7KHPLQLPXPWHPSHUDWXUHGLIIHUHQFHEHWZHHQ+2
and He is 0.5 K.
Ɣ The KLJKSUHVVXUHRIDOOF\FOHVLV03D
Ɣ 7KHSUHVVXUHGURSLQDOO+H+H+;¶VLV]HUR
Ɣ The minimum temperature difference between hot and cold streams is.RU.IRU
+;DQGRURIWKHDEVROXWHWHPSHUDWXUHDW+3VWUHDPIRURWKHU+;¶V.
Ɣ 7KHDGLDEDWLFHI¿FLHQF\RIDOO compressors andWXUELQHVLV
7KHVHFRQGDQGWKLUGDVVXPSWLRQVDUHVSHFL¿HGE\WKHGHVLJQUHTXLUHPHQWVRIWKHWDUJHWPRGerator system at ESS77KHVL[WKDVVXPSWLRQLVPDGHWRLQYHVWLJDWHWKHVL]HHIIHFWRI+;¶VRQHDFK
F\FOHZLWKWZRGLIIHUHQWFDVHV'Tmin .DQG.ZKLFKUHSUHVHQWVUHODWLYHO\KLJKDQGORZ
HIIHFWLYHQHVVUHVSHFWLYHO\7KHWHPSHUDWXUHGLIIHUHQFHJLYHQDVRURIDEVROXWHWHPSHUDture means, for example, that 'Tmin .RU.DWTHP = 100 K and 'Tmin .RU.DW
THP .6LQFHWKHWHPSHUDWXUHRIWKH+3VWUHDPLVGHWHUPLQHGDVDUHVXOWRIWKHF\FOHDQDO\VLV
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BRAYTON CRYOCOOLER DEVELOPMENTS
this assumption will be imposed by a few iterative calculations. In calculating the input power to
the compressors, a single-stage compression is assumed, because the pressure ratio is between 3
DQGDQGVFUHZFRPSUHVVRUVFRXOGEHXVHGLQSUDFWLFH7KHRQO\H[FHSWLRQLV&\FOH,,ZKHUHD
two-stage compression with inter-cooling is assumed for the pressure ratios exceeding 10.
$JHQHUDOSXUSRVHSURFHVVVLPXODWRU$VSHQ+<6<6®ZLWKWKHWKHUPRG\QDPLFSURSHUWLHVRI
KHOLXPDQGSDUDK\GURJHQLVXVHGIRUWKHF\FOHDQDO\VLV8QGHUWKHVSHFL¿HGFRQGLWLRQV&\FOHV,
DQG,,DUHXQLTXHO\GHWHUPLQHGDVWKHQXPEHURIXQNQRZQVLVWKHVDPHDVWKHQXPEHURIJLYHQ
HTXDWLRQV )RU &\FOHV ,,, WKURXJK 9,,, KRZHYHU WKHQXPEHURIXQNQRZQV LVPRUHWKDQWKH
number of given equations by one. The cycle analysis is repeated over one variable, until the input
power can be minimized under the assumptions.
The thermodynamic performance of a refrigeration cycle is evaluated with a dimensionless
index, FOMWKH¿JXUHRIPHULW, which isGH¿QHGDVWKHUDWLRRIPLQLPXPWRWKHDFWXDOZRUN
The minimum work is the thermodynamic limit for a reversible cycle, which can be expressed
DVWKHLQFUHDVHRIH[HUJ\RUÀRZDYDLODELOLW\RIOLTXLGK\GURJHQ
where h and sDUHVSHFL¿FHQWKDOS\DQGHQWURS\UHVSHFWLYHO\. The subscripts e and i denote the exit
and inlet of He-H2+;UHVSHFWLYHO\, as shown in Figure 1 and 2, and T0 is the ambient temperature
at which heat is rejected by the refrigerator. ,QSUDFWLFHWKHSRZHURXWSXWRIWKHH[SDQGHUVWE
may be used to drive the compressors or may be simply dissipated, but the ³QHW´ input WC - WE
is counted inWKHGHQRPLQDWRURI(T2
For a better understanding of the thermodynamic nature of cycles, DQH[HUJ\RUVHFRQGODZ
analysis is presented as well. Combining the energy and entropy balance equations9, the exergy
balance can be written as:
4
where the left-handed side is the exergy input for refrigeration, and the right-handed side shows
VRFDOOHGWKHH[HUJ\H[SHQGLWXUH$VGH¿QHGLQ(T.WKHIUDFWLRQRIWKH¿UVWWHUPLVWKHFOM,
and the remaining terms are the irreversibility or the entropy generation rate multiplied by ambient
temperature. The total irreversibility can be itemized for the components in the system, including
FRPSUHVVRUV&DIWHUFRROHUV$&H[SDQGHUV(DQGKHDWH[FKDQJHUV+;. In case of Cycles
,9 through 9III, the mixing of two streams is another source of entropy generation, but is not
included here, since the magnitude is negligibly small for an optimized cycle10.
RESULTS AND DISCUSSION
The selected eight cycles are fully analyzed with the assumptions described above, and the
results are plotted as temperature-entropy diagram in Figure 3 and exergy expenditure in Figure
4. The cycles with 'Tmin .DUHSUHVHQWHGKHUHDQGZLOOEHGLVFXVVHGODWHUWRJHWKHUZLWK
'Tmin .$VPHQWLRQHGDERYH&\FOHV,,,WKURXJK9,,,KDYHEHHQRSWLPL]HGIRUWKH
maximum FOM.
,QWKHFDVHRIWKHVWDQGDUGF\FOHV&\FOH,ZLWK/3FRROLQJLVPRUHHI¿FLHQWWKDQ&\FOH,,
ZLWK+3FRROLQJ7KHPDLQUHDVRQLVWKDWWKH+3FRROLQJQHHGVDODUJHUSUHVVXUHUDWLRWRSHUIRUPWKH
UHIULJHUDWLRQ7KHSUHVVXUHUDWLRLVDQGLQ&\FOHV,DQG,,UHVSHFWLYHO\,QDVHQVHWKH
+3FRROLQJLVUHJDUGHGDV³LQGLUHFW´FRROLQJEHFDXVHWKHFROGHVW/3VWUHDPFRROVWKH+3VWUHDP
DQGWKHQWKH+3VWUHDPFRROVWKH/+2ÀRZ,WPD\EHVWDWHGLQVWDQGDUGF\FOHVWKDWWKH/3FRROLQJ
LVHVVHQWLDOO\VXSHULRULQHI¿FLHQF\WRWKH+3FRROLQJ2QWKHRWKHUKDQGWKH+3FRROLQJFRXOGKDYH
PHULWVLQRWKHUDVSHFWVVXFKDVDVPDOOHUGLDPHWHURIWUDQVIHUOLQHVIRUFROGKHOLXP7KH+3FRROLQJ
FRXOGDOVREHVDIHUDJDLQVWWKHIUHH]HRXWRIOLTXLGK\GURJHQEHFDXVHWKHFROGHVWKHOLXPDWWKHH[LW
RIWXUELQHLQGLUHFWO\DIIHFWVWKH/+2ÀRZZKHQWKHWHPSHUDWXUHWHPSRUDULO\GURSVDFFRUGLQJWRD
scheduled or unscheduled decrease of thermal load.
7ZRVWDJHF\FOHV&\FOHV,,,DQG,9KDYHFRQVLGHUDEO\KLJKHUFOM’s than the standard
F\FOHV,Q)LJXUHWKHLUUHYHUVLELOLW\LQ+;¶VRI&\FOHV,,,DQG,9LVVPDOOHUWKDQWKDWRI&\FOHV
4
MODIFIED BRAYTON REFRIGERATION CYCLES FOR LIQUID H2
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Figure 3. Temperature-entropy diagram of eight cycles at optimized condition with 'Tmin = 3 K (1%).
Figure 4. Exergy expenditure of eight cycles at optimized condition with 'Tmin = 3 K (1%). (FOM:
figure of merit, AC: after-cooler, C: compressor, E: expander, HX: heat exchanger)
,DQG,,DVWKHWHPSHUDWXUHGLIIHUHQFHLQ+;¶VLVUHGXFHGE\WKHDGGLWLRQRIZDUPH[SDQGHU$
NH\SRLQWKHUHLVWKDWWKH/3FRROLQJLVVWLOOPRUHHI¿FLHQWWKDQWKH+3FRROLQJEXWWKHLUGLIIHUHQFH
in FOMLVQRWVRODUJH,WLVLQWHUHVWLQJWRQRWLFHLQ)LJXUHWKDW&\FOH,9KDVDODUJHULUUHYHUVLELOLW\LQ+;+;WKDQ&\FOH,,,EXWDVPDOOHULUUHYHUVLELOLW\LQ+;7KLVPHDQVWKDWWKH+3
FRROLQJVWLOOUHTXLUHVDODUJHUSUHVVXUHUDWLRIRUDODUJHUWHPSHUDWXUHGLIIHUHQFHEXWWKHSHQDOW\RI
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BRAYTON CRYOCOOLER DEVELOPMENTS
SUHVVXUHGURS03DLQ+;LVOHVVVHYHUHLQ+3FRROLQJ7KHSUHVVXUHUDWLRLVDQGIRU
&\FOHV,,,DQG,9UHVSHFWLYHO\
7KHGXDOWXUELQHF\FOHV&\FOHV9DQG9,KDYHDQHYHQKLJKHUFOM’s than the two-stage
F\FOHV7KHEUDQFKLQJÀRZWKURXJKWKHZDUPWXUELQHLVHIIHFWLYHLQUHGXFLQJWKHWHPSHUDWXUHGLIIHUHQFHLQUHFXSHUDWLYH+;¶VDQGWKHSUHVVXUHUDWLRLVVPDOOIRUERWKF\FOHV/LNHW\SLFDO&ODXGH
F\FOHVWKHPDLQGHVLJQSDUDPHWHULVWKHUDWLRRIWKHÀRZUDWHWKURXJKWKHZDUPWXUELQHWRWKHWRWDO
ÀRZUDWHWKURXJKWKHFRPSUHVVRU. The optimal condition is determined such that the exit temperaWXUHRIWKHZDUPWXUELQHVWDWHPDWFKHVFORVHO\ZLWKWKH/3WHPSHUDWXUHDWWKHSRLQWRIPL[LQJ
7KHÀRZUDWLRLVDQGIRU&\FOHV9DQG9,UHVSHFWLYHO\DQGWKHSUHVVXUHUDWLRLV
DQGIRU&\FOHV9DQG9,UHVSHFWLYHO\
7KHPRGL¿FDWLRQRIGXDOWXUELQHF\FOHZLWKDZDUPXSÀRZLVQRWDVHIIHFWLYHLQLPSURYLQJ
the FOMIRU/3FRROLQJEXWLVYHU\HIIHFWLYHIRU+3FRROLQJ&\FOHV9,,KDVQHDUO\WKHVDPH
FOMDV&\FOH9HYHQWKRXJKWKHGHWDLOHGF\FOHVDUHVOLJKWO\GLIIHUHQWIURPHDFKRWKHU2QWKH
RWKHUKDQG&\FOH9,,,KDVDVLJQL¿FDQWO\KLJKHUFOMWKDQ&\FOH9,7ZRDGGLWLRQDO+;¶VDW
WKHFROGHQGDQGWKHZDUPXSÀRZPDNHWKHRSHUDWLQJWHPSHUDWXUHRIWKHZDUPWXUELQHKLJKHUDQG
DFFRUGLQJO\WKHRYHUDOOWHPSHUDWXUHGLIIHUHQFHLQWKH+;VLVVPDOOHU7KHÀRZUDWLRWRWKHZDUP
WXUELQHLVDQGIRU&\FOHV9,,DQG9,,,UHVSHFWLYHO\DQGWKHSUHVVXUHUDWLRLV
DQGIRU&\FOHV9,,DQG9,,,UHVSHFWLYHO\
,QRUGHUWRH[DPLQHWKHVL]HHIIHFWRIWKH+;V)LJXUHFRPSDUHVWKHFOM of eight cycles with
WKHPLQLPXPWHPSHUDWXUHGLIIHUHQFHRI.DQG.7KHVWDQGDUGF\FOHV&\FOHV
,DQG,,DUHQRWRQO\SRRULQHI¿FLHQF\LWVHOIEXWDOVRPRUHVHQVLWLYHWRWKHVL]HRI+;VWKDQWKH
PRGL¿HGF\FOHV$PRQJWKHPRGL¿HGF\FOHVGXDOWXUELQHF\FOHVDUHVXSHULRUWRWZRVWDJHF\FOHV
LIKLJKO\HIIHFWLYH+;VDUHXVHG7KHSHQDOW\RIVPDOO+;VL]HLVOHDVWIRU&\FOH9,,,7KLVPHDQV
WKDWDQHI¿FLHQWUHIULJHUDWLRQZLWK+3FRROLQJcan be achieved E\WKHZDUPXSÀRZZLWKRXWDQ
H[WUHPHO\ODUJHVL]HRI+;V
In summary, two cycles are suggested from a thermodynamic point of view. First, the dualWXUELQHF\FOHZLWK/3FRROLQJRU&\FOH9LVDSUHIHUUHGF\FOHIRUERWKVLPSOLFLW\DQGHI¿FLHQF\
7KLVF\FOHLVHVSHFLDOO\UHFRPPHQGDEOHZKHQKLJKO\HIIHFWLYH+;VFDQEHXVHG$OWHUQDWLYHO\WKH
PRGL¿HGGXDOWXUELQHF\FOHZLWK+3FRROLQJRU&\FOH9,,,KDVDQDGYDQWDJHLQHI¿FLHQF\HYHQ
ZKHQWKH+;VDUHQRWVRKLJKO\HIIHFWLYH2QWKHRWKHUKDQGWKLVF\FOHLVFRPSOH[LQVWUXFWXUHDQG
FRXOG\LHOGPRUHSUHVVXUHGURSVLQWKH+;V7DEOHOLVWVWKHGHWDLOHGWKHUPRG\QDPLFGDWDLQFOXGLQJWHPSHUDWXUHSUHVVXUHDQGÀRZUDWHDWHDFKVWDWHIRU&\FOH9ZLWK'Tmin = .DQG&\FOH
9,,,ZLWK'Tmin = .
In determining a refrigeration cycle, there are a number of practical factors to take into account
DVZHOODVHI¿FLHQF\$OWKRXJKWKHGHWDLOVDUHEH\RQGWKHVFRSHRIWKLVWKHUPRG\QDPLFVWXG\D
few comments are mentioned for discussion. First, the availability and performance of cryogenic
turbines should be considered for the selection between the two-stage cycle and the dual-turbine
Figure 5.)LJXUHRIPHULW)20IRUHLJKWF\FOHVZLWK'Tmin .DQG.
6
MODIFIED BRAYTON REFRIGERATION CYCLES FOR LIQUID H2
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Table 1.7HPSHUDWXUHSUHVVXUHDQGÀRZUDWHRIWZRVXJJHVWHGF\FOH
F\FOH,QWZRVWDJHF\FOHVWKHZDUPWXUELQHUHTXLUHVDVPDOOSUHVVXUHUDWLRZLWKDODUJHÀRZUDWH
In dual-turbine cycles, on the contrary, the warm turbine requires a large pressure ratio with a small
ÀRZUDWH
'HWDLOHG+;GHVLJQFRXOGEHLPSRUWDQWIRUDWKRURXJKDQGIDLUFRPSDULVRQRIWKHF\FOHV,WLV
UHFDOOHGWKDWWKHUHVXOWVSUHVHQWHGDUHEDVHGRQDVLPSOL¿HGPRGHORIPLQLPXPWHPSHUDWXUHGLIIHUHQFHDQGDQDVVXPSWLRQRIQRSUHVVXUHGURSLQWKH+;V7KHDFWXDOVL]HDQGWKHUPRK\GUDXOLF
FKDUDFWHULVWLFVRIWKH+;VFRXOGDIIHFWWKHVHOHFWLRQWRDQH[WHQW Finally, an optimization theory is
FLWHGKHUHZLWKUHJDUGVWRWKHHIIHFWRI¿QLWH+;VL]HVHVSHFLDOO\ZKHQDF\FOHLVFRPSRVHGRIPXOWL
VWDJHVRI+;V,WLVDOZD\VWUXHWKDWDVDQ\+;DUHDLQFUHDVHVWKHWHPSHUDWXUHGLIIHUHQFHEHWZHHQ
KRWDQGFROGVWUHDPVLQWKH+;GHFUHDVHV,WLVDQLPSRUWDQWGHVLJQVWUDWHJ\KRZHYHUWRDOORFDWH
WKH+;DUHDWRHDFKVWDJHLIWKHWRWDOVXPRI+;DUHDLV¿[HG7KLVLVDZHOONQRZQRSWLPL]DWLRQ
problem subject to a constraint, which has been solved by the method of Lagrange multiplier. The
results show that the best thermodynamic performance is achieved when the temperature difference
is proportional to the absolute temperature9,11.
5
This condition has been already incorporated as an assumption of the cycle analysis.
CONCLUSIONS
6WDQGDUGDQGPRGL¿HG%UD\WRQUHIULJHUDWLRQF\FOHVDUHLQYHVWLJDWHGZLWKDQDLPDWWKHHI¿FLHQW
UHIULJHUDWLRQRIN:IRUVXEFRROHGOLTXLGK\GURJHQDW.%DVHGRQH[LVWLQJDQGSURSRVHG
V\VWHPVDYDULHW\RIPRGL¿FDWLRQVDUHWULHGLQDV\VWHPDWLFZD\DQGWKHLUHI¿FLHQF\LVFDOFXODWHGLQ
terms of FOM¿JXUHRIPHULWWKURXJKDIXOOWKHUPRG\QDPLFDQDO\VLV7KHPRGL¿FDWLRQVLQFOXGH
WKH/3ORZSUHVVXUHRU+3KLJKSUHVVXUHFRROLQJGHSHQGLQJRQWKHORFDWLRQRIWKHFU\RJHQLF
expander in a cycle, and the two-stage or dual-turbine cycles, depending on the combination of the
two expanders. Among the eight cycles under consideration, two cycles are suggested along with
WKHUHTXLUHGVL]HRI+;VDQGRWKHUFRQVWUDLQWV$GXDOWXUELQHF\FOHZLWK/3FRROLQJRU&\FOH9
LVSUHIHUUHGIRUVLPSOLFLW\DQGHI¿FLHQF\DWWKHVDPHWLPHLIKLJKO\HIIHFWLYH+;VFDQEHXVHG$
PRGL¿HGGXDOWXUELQHF\FOHZLWK+3FRROLQJRU&\FOH9,,,KDVDQDGYDQWDJHLQHI¿FLHQF\HYHQ
LIOHVVHIIHFWLYH+;VDUHXVHG7KHUHVXOWVRIWKLVWKHUPRG\QDPLFVWXG\DUHLPPHGLDWHO\DSSOLFDEOH
to the neutron source moderators at ESS, and should be useful in large-scale refrigeration at 20 K
as well.
ACKNOWLEDGMENT
This work was partially supported by 2016 Hong Ik University Research Fund for sabbatical
leave in a foreign institute.
7
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