Optimal cool-down time of a 4K superconducting magnet cooled by a two-stage cryocooler
Yeon Suk Choi ⇑,Dong Lak Kim,Dong Won Shin
Korea Basic Science Institute,Daejeon 305-333,Republic of Korea
a r t i c l e i n f o Article history:
Received 13April 2010
Received in revid form 6October 2011Accepted 7October 2011
Available online 12October 2011Keywords:
C.Heat transfer
E.Gifford–McMahon
tenderlyF.Cryostats
F.Superconducting magnets
a b s t r a c t
A cool-down time is one of the major factors in many cryocooler applications,especially for the design of conduction-cooled superconducting devices.Cool-down time means a time cooling a thermal mass from a room-temperature to cryogenic-temperature within a stipulated amount of time.The estimation of cool-down time eks the elapd time to cool the thermal object by a cryocooler during initial cool-down process.This procedure includes the dimension and properties of thermal object,heat transfer analysis for cryogenic load,thermal interface between cold mass and cryocooler,and available refriger-ation capacity of cryocooler.The propod method is applied to the specific cooling system for 3T super-conducting magnet cooled by a two-stage GM cryocooler.The r
esult is compared with that of experiment,showing that propod method has a good agreement with experiment.In addition,the initial cool-down time can be shortened by employing thermal link between the cold mass and first-stage of cryocooler.Through a rigorous modeling and analysis taking into account the effect of thermal link size,it is con-cluded that there exists an optimal cool-down time during initial cooling in conduction-cooled supercon-ducting magnet system.
Ó2011Elvier Ltd.All rights rerved.
1.Introduction
One of the most critical factors for successful development of any superconducting device is cryogenic cooling technology.Since the discovery of the phenomenon of superconductivity in the early 1900s [1],a variety of practical cooling systems for superconducting devices have been developed.For the most part,the systems have utilized the niobium titanium (NbTi)and niobium tin (Nb3Sn),so called low temperature superconductors (LTS),requiring a helium temperature environment to achieve their specific properties.In the standard cooling of LTS systems,liquid helium is effectively ud to maintain the systems at around 4K.
In recent years,conduction-cooled superconducting magnet systems have been enabled by the deve
lopment of cryocooler.In a conduction-cooled LTS magnet system,a two-stage cryocooler is basically employed as a heat sink to cool superconducting mag-net down to operating temperature,as shown in Fig.1.The LTS magnets cooled by cryocooler are ud in veral rearch areas,such as biology,chemistry,high energy physics and material sci-ence,and the magnetic fields achieved are comparable to tho of magnets cooled by liquid helium [2].The size of magnets
increas with the magnetic fields,resulting in the longer initial cool-down time in conduction-cooled superconducting magnet systems.Cool-down time means a time cooling a thermal mass from a room-temperature to cryogenic-temperature within a stip-ulated amount of time.
There have been a number of previous works on the develop-ment of conduction-cooled superconducting magnet without any cryogen [3–10].Most of them have mainly reported the magnitude of magnetic field they acquired and associated magnet technolo-gies including cooling results using commercial cryocoolers.In spite of its significance no specific attention,however,has been paid to the initial cool-down time in conduction-cooled supercon-ducting magnet system as far as the authors aware.
In this paper,the method to estimate initial cool-down time in conduction-cooled superconducting ma
gnet system is introduced.The procedure includes the dimension and properties of cooling component,heat transfer analysis for cryogenic loads,thermal interface between magnet and cryocooler,and available refrigera-tion capacity of cryocooler.The method is applied to the conduc-tion-cooled 3T superconducting magnet system developed by ourlves and the results are compared with the experiments.In addition,the optimal cool-down times of LTS magnet are quantita-tively discusd in terms of the size of thermal link.This propod method should contribute to understanding the initial cool-down by a cryocooler as well as designing the conduction cooling system for high field superconducting magnet.
0011-2275/$-e front matter Ó2011Elvier Ltd.All rights rerved.doi:10.nics.2011.10.002
Corresponding author.Tel.:+82428653913;fax:+82428653610.
E-mail address:kr (Y.S.Choi).
2.Numerical analysis of initial cool-down
2.1.Modeling and energy balance
In conduction-cooled superconducting magnet system as schematically shown in Fig.1,a low temperature superconduc-ting magnet is thermally connected to the cond-stage of cryo-cooler through conduction link.A room-temperature bore is located in the center of superconducting magnet suspended by gravitational supports.A pair of binary current lead,a ries
Since the cold head area of a Gifford–McMahon(GM)cryocooler is very limited and additional surface is needed to connect cooling medium in actual engineering fabrication,the extended plate,made of oxygen-free high conductivity copper,is attached to the cold head of GM cryocooler.We define this extended plate as thermal anchor as indicated in Fig.1.A radiation shield and LTS magnet,therefore, are actually connected to thefirst and cond thermal anchor, respectively.
In two-stage cooling system,the heat leakage to the supercon-ducting magnet can be partly removed atfirst-stage temperature,
Nomenclature
A surface area or cross-ctional area(m2)
环保材料服装a accommodation coefficient
c p specific heat at constant pressure(J kgÀ1KÀ1)
E energy(J)
k thermal conductivity(W mÀ1KÀ1)
L length of mechanical support or current lead(m) M molecular weight(kg)
N number of support or MLI
P pressure(Pa)
Q heat transfer rate(W)
R gas constant(J molÀ1KÀ1)
T temperature(K)
t time(c)
V volume(m3)
Greek letters
c ratio of specific heat of gas
e emissivity q density(kg mÀ3)
r Stefan–Boltzmann constant(W mÀ2KÀ4)
Subscripts
1first stage
2cond stage
A thermal anchor
C cryocooler
g gas
H warm(room-temperature)side
k conduction
L cold(low-temperature)side
M superconducting magnet
l current lead
P pressure
r radiation
S radiation shield
TL thermal link
14Y.S.Choi et al./Cryogenics52(2012)13–18
where q,V,T and c p are the density,volume,temperature and spe-cific heat at constant pressure of each component,respectively.The subscripts S,A1,M and A2denote the radiation shield,first thermal anchor,superconducting magnet and cond thermal anchor, respectively.Heat transfer terms,Q’s,in Eqs.(1)–(4)will be de-scribed in detail in the following ctions.
2.2.Cryogenic loads
In most cryogenic temperature applications,effective heat transfer occurs by thermal conduction thro
ugh mechanical sup-port,thermal radiation and conduction through the residual gas.In addition,Joule heating in electrical leads,eddy current heating,mechanical vibration,adsorption or desorption of gas may contribute to the heat transfer[11].In energy balance Eqs.(1)–(4),Q H and Q L denote cryogenic load from room-temper-ature,T H,tofirst-stage temperature or
and T S to superconducting magnet
Major heat transfer process in
ting magnet system consist of support
radiation,Q r,heat through current lead,Q l,
Q g.
Q H¼Q k1þQ r1þQ l1þQ g1
Q L¼Q k2þQ r2þQ l2þQ g2
where subscripts1and2of Q’s indicate the
T S and from T S to T M,respectively.
The magnitude of cryogenic load is
temperature,dimension and properties of
heatflow through mechanical support
tional area,A,is given by
Q k¼N A南宁翻译公司
L
可爱妆容
Z T H
尊敬T L
kðTÞdT
where N and L are the number and length, ical support.In Eq.(7)k(T)is the conductivity of mechanical support.
The heat transfer by thermal radiation to T L from the enclod surface at
mately estimated by
Q r%
rðT4
H
产品说明翻译ÀT4
L
Þ
1Àe H
e H A H
þ1
A L
1
e L
þ2N e
N
ÀN
where A is surface area,r is the
are the emissivity of the surfaces.N is the between two surfaces.
Heat leakage through current lead occurs well as Ohmic heat generation.During initial current is supplied,therefore only heat and Eq.(9)is ud for this application.
Q l¼2A
Z T H
T L
kðTÞdT
where A and L denote cross-ctional area lead,respectively.
The magnitude of gas conduction between the gas pressure level and
be made arbitrarily small by reduction of the is not always possible.Considering an ideal two surfaces at different temperatures with a two surfaces,heat transfer by gas
given by[11].
Q g¼
a0PA cþ1
c
ffiffiffiffiffiffiffiffi
2R
p
r
T HÀT L
ffiffiffi
T
pð10Þ
where M is the molecular weight and c is the ratio of specific heats
of gas,R is the universal gas constant and A is the area of surface.
The averaged accommodation coefficient,a0,depends on the indi-
vidual accommodation coefficient and surface areas[12].The
appropriate value for T is the average temperature of T H and T L.
2.3.Cooling interface and refrigeration capacity
Since no cryogen is ud in the system,conduction is the only way to remove heat from the superconducting magnet or radiation
shield.Flexible copper plate is usually employed as a cooling inter-
face between thermal anchor and radiation shield forfirst stage,
and thermal anchor and superconducting magnet for cond stage.
Fig.4.Specific heat of materials with respect to temperature.
Y.S.Choi et al./Cryogenics52(2012)13–1815
ity of a two-stage GM cryocooler(Sumitomo,
for this numerical analysis.
2.4.Temperature-dependent properties
Thermal conductivity and specific heat
the system depend strongly on
of copper,aluminum,stainless steel and glass
tics(GFRP)are collected from a number of
special effort ensuring consistent values of
ity and specific heat.Figs.3and4show the
ties of material ud in the analysis with
3.Results and discussion
Temperatures of major components in
conducting magnet system are calculated
Eqs.(1)–(4)simultaneously.Cryogenic loads,
refrigeration capacity are linked,taking into
perature dependency of materials.While the modeling and analysis
procedure prented in previous ctions could be applicable to any cryocooled LTS magnet system,a specific ca is considered here for the purpo of quantitative discussion.Table1shows the specifica-tion of conduction-cooled3T superconducting magnet system developed by ourlves[7].
Fig.5shows the heat leakage contributed by each cryogenic load as a function of temperature forfirst stage.As described above,cryo-genic load consists of support conduction,shield radiation,thermal leak through current lead and gas conduction.As indicated in Fig.5, the sum of cryogenic load is subdivided into the four potions.Even though current lead was optimized for a given operating current, the heat leak through current lead is dominant in the contributions over a wide temperature range.On the other hand,the amount of gas conduction is quite small so can be negligible.Heat leakage in-creas asfirst-stage temperature or shield temperature decreas. As shield temperature decreas,the heat leakage fromfirst-stage to cond-stage decreas,however large capacity of refrigeration atfirst-stage is required to lower the temperature atfirst-stage.
A greater heat transfer due to current lead results in the growth of total cryogenic load at lower temp
erature near30K.When the temperature atfirst stage is40K,the amounts of heat leakage by support conduction,shield radiation,current lead and gas conduc-tion are0.83,1.4,18.3and0.01W,respectively.Asfirst stage tem-perature decreas to below50K,heat leakage through current lead is sharply incread.It is mainly becau the thermal conduc-tivity of current lead material or copper increas below50K steeply as shown in Fig.3.
The temperatures of thermal shield,thermal anchor1,supercon-
Fig.6.Initial cool-down temperature of conduction-cooled magnet system after turning on a cryocooler.
16
analysis had some variation within3%at the beginning of cool-down.As a whole,it is stated with the comparison that the devel-oped numerical analysis had good agreement and estimated exact cool-down times.
There appear to be a growing need for large-scale superconduc-ting magnet to obtain higher magneticfield[2–4,9].The size of superconducting magnet increas with the magneticfields,there-for
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e it takes more time for superconducting magnet to be cooled down initially in conduction cooling system.In Fig.6,it is obrved that the temperature of thermal anchor1is much lower than the others,especially that of superconducting magnet for06t612h. Thus,in order to shorten initial cool-down time it would be a wi method to thermally connect thermal anchor1and superconduc-ting magnet until the temperature of superconducting magnet be-comes lower than that of thermal anchor1.
The thermal link connected to the thermal anchor1is parated from the superconducting magnet when the temperature of the magnet becomes below that of the thermal anchor1.The thermal link has a plug so that it can be inrted into a female socket in-stalled on the former of the superconducting magnet.A female socket has many parallel louvers so thermalflow could be occurred through the contacted area with a pre-determined force in the operating range of the spring characteristics.The plug moves ver-tically by the nonmetallic rod which is enclod by an edge-welded bellows on the topflange,forming vacuum during paration process.
When we utilize thermal link between superconducting magnet and thermal anchor1,the energy balance of the system can be slightly changed such that heatflow between superconducting magnet and thermal anchor1is occurred as indicated by dotted line in Fig.2.Hence,energy balances for therm
al anchor1and superconducting magnet,Eqs.(2)and(3),will be revid as following;
dE A1
¼
d
ðq Vc p TÞA1¼Q A1þQ TLÀQ C1ð11Þ
Temperatures of major components in conduction-cooled
superconducting magnet system are computed again by solving
Eqs.(1),(4),(11),and(12)simultaneously.Shown in Fig.7is the
reprentative temperature history of thermal anchor1and super-
少儿英语歌曲mp3conducting magnet after turning on a cryocooler.When the copper
thermal link is employed,two ts of temperature(indicated by so-
lid lines)have small temperature difference and meet earlier than
tho of previous ca.As predicted earlier,the initial cool-down
time of superconducting magnet becomes short,taking11.7h to
reach4K when the shape ratio,cross-ctional area to length(A/
L),of thermal link is2.
In the calculation,we assume that the mass of thermal link be-
longs to that of thermal anchor1since thermal link is connected to
ownagethermal anchor1directly and disconnected near superconducting
magnet when the temperature of magnet becomes lower than that
of thermal anchor1.Therefore,initial cool-down characteristics
may be affected by the dimension of thermal link becau the
amount of heatflow increas with heat transfer area.The temper-
ature of superconducting magnet cooled by a cryocooler is plotted
in Fig.8with various shape ratio of thermal link.No thermal link is
ud when the shape ratio of thermal link is zero.As shape ratio
increas from0to3,the initial cool-down time of superconduc-
ting magnet decreas from13.1to11.6h.However,as shape ratio
further increas from3to8initial cool-down time increas from
11.6to11.8h.
From thermal point of view,heat transfer rate is obviously great-
er when cross-ctional area is larger for a given length[18].How-
ever,the cooling efficiency of thermal link decreas becau the
incread cross-ctional area,resulting in heavier weight,requires
more cooling capacity.For afixed cooling capacity of cryocooler,image是什么意思
there exists an optimal initial cool-down time when the shape ratio
of thermal link is approximately3in3T conduction-cooled super-
conducting magnet system as shown in Fig.9.In Fig.9,y-axis is
cool-down time difference,determining by subtracting initial
cool-down time without thermal link from that with thermal link.
Initial cool-down time can be optimized and shorten1.5h compar-
Y.S.Choi et al./Cryogenics52(2012)13–1817
