International Journal of Hydrogen Energy 25 (2000) 133±141

Thermal design analysis of a liquid hydrogen vessel

Seo Young Kim, Byung Ha Kang*
Thermal/Flow Control Research Center, Korea Institute of Science and Technology, P.O. Box 131, Cheongryang, Seoul, 130-650,
South Korea

Abstract

Thermal analysis has been performed to design a high-performance liquid hydrogen (LH2) vessel. Analysis
includes the combined insulation of multi-layer insulation (MLI) and vapor-cooled radiation shield (VCS) under
high vacuum. Three types of combined insulation schemes are considered in this study; fully-®lled MLI and serial-
type double vapor-cooled radiation shield (DVCS); fully-®lled MLI and parallel-type DVCS; partially-®lled MLI
and single vapor-cooled radiation shield (SVCS). Thermal analysis for a vapor-cooled heat station to reduce solid
conduction heat in-leak through a ®lling tube is also made. The results indicate that the serial-type DVCS vessel
shows better performance than parallel-type DVCS vessel. The combined insulation of SVCS and partially-®lled
MLI shows a similar performance compared to that of DVCS and fully-®lled MLI. The vapor-cooled heat stations
can enhance substantially the performance of the vessel for cryogenic ¯uids with high Cp/hfg, where Cp the speci®c
heat and hfg the latent heat of vaporization, such as LH2 and liquid helium (LHe). # 1999 International
Association for Hydrogen Energy. Published by Elsevier Science Ltd. All rights reserved.

1. Introduction has been reported by many researchers that the liquid

state of hydrogen is the most promising way of storage
Since the oil shock in the 1970s, much attention has [1±5]. It is light and has less potential risk in terms of
been given to hydrogen as a fuel for the next gener- storage pressure compared with the compressed gas.
ation. First of all, hydrogen is available in vast However, the storage of LH2 at a cryogenic tempera-
amounts on earth and it is the least polluting fuel that ture requires a sophisticated insulation techniques com-
can be used in any modern combustion engine. The pared to the other storage methods.
combustion of hydrogen produces only water vapor For this reason, the development of an ecient insu-
and limited NOx content and is free from CO2 emis- lation scheme for LH2 is of major concern. The vapor-
sion. ization of LH2 is generally minimized by means of a
One of the most important technologies necessary vacuum insulation between the inner and the outer
for the utilization of hydrogen is how to store hydro- vessels that was introduced by James Dewar [6]. With
gen fuel eciently. To date, there have been three the advances in insulation techniques, the evaporation
di€erent storage methods: compressed hydrogen gas loss of LH2 has been substantially reduced in recent
(GH2), metal hydride and liqui®ed hydrogen (LH2). It years. The state-of-the-art insulation techniques are
adopting the combined insulation of vacuum, MLI
and VCS. Such combined insulation can reduce e€ec-
* Corresponding author. Tel.: +82 2 958 5673; fax: +82 2 tively, heat in-leak by gaseous conduction, convection
958 5689. and radiation. Furthermore, the vapor-cooled heat
E-mail address: bhkang@kistmail.kist.re.kr (B.H. Kang). stations are employed to reduce solid-body conduction

0360-3199/00/$20.00 # 1999 International Association for Hydrogen Energy. Published by Elsevier Science Ltd. All rights reserved.
PII: S 0 3 6 0 - 3 1 9 9 ( 9 9 ) 0 0 0 2 0 - 8
134 S.Y. Kim, B.H. Kang / International Journal of Hydrogen Energy 25 (2000) 133±141

Nomenclature

A cross-sectional area of ®lling tube kt apparent thermal conductivity of MLI

a, b, c radius ratios, r2/r1, r3/r1, r4/r1 L length of ®lling tube
.
Cp speci®c heat at constant pressure m mass ¯ow rate of boilo€ hydrogen gas
e1, e2, e3, e4 emissivity
Fe1, Fe3 emissivity factors Greek symbols
hfg latent heat of vaporization DL spacing between heat stations
ks thermal conductivity of ®lling tube ma- s Stefan±Boltzmann constant
terial

heat in-leak through piping for ®lling and withdrawal two independent paths of VCSs, absorbing heat in-
as well as supports [7]. leak, and eventually exhausts to the ambient air.
The present study is directed at the optimization of As seen in Fig. 1, Q1 denotes the heat transfer rate
combined insulation schemes by one-dimensional ther- from the inner VCS at r=r2 to the inner vessel at
mal analysis for future design purposes. Three types of r=r1. The heat Q1 absorbed by the inner vessel makes
combined insulation schemes are considered: (a) a LH2 evaporate:
vessel fully-®lled with MLI and serial-type DVCS; (b)
a vessel fully-®lled with MLI and parallel-type DVCS; 2pkt …T2 ÿ T1 †
_ fg ˆ
Q1 ˆ mh , …1†
(c) a vessel partially-®lled with MLI and SVCS. The ln…r2 =r1 †
e€ect of a vapor-cooled heat station on solid conduc- .
tion heat in-leak is also investigated in detail. Three where m is the total mass ¯ow rate of the boilo€
equally-spaced heat stations mounted on a ®lling tube hydrogen vapor in the inner vessel and hfg the latent
are selected for the thermal analysis. heat of para-hydrogen (hfg=443 kJ/kg) at 1 atm. kt is
the apparent thermal conductivity of MLI, and it is
assumed kt=0.04 mW/mK for the layer density of 30
layers/cm.
The heat transfer rate from the outer VCS at r=r3
2. Thermal analysis to the inner VCS at r=r2, Q2, can be expressed as a
sum of the heat given directly to the inner vessel, Q1,
The heat transfer to an LH2 vessel includes the radi- and the sensible heat absorbed by the vapor shielding
. .
ation heat in-leak through vacuum insulation between gas, m1Dh1, by energy balance. Here m1 denotes the
the inner and the outer vessels as well as the conduc- fraction of the mass ¯ow rate of the boilo€ vapor pas-
tion heat in-leak through pipings and supports. In the sing through the inner VCS at r=r2 and
present study, we consider three combined insulation Dh1=Cp1(T2ÿT1).
schemes to reduce the radiation heat in-leak by adopt-
2pkt …T3 ÿ T2 †
ing vacuum insulation, MLI, and VCS. The tempera- Q2 ˆ Q1 ‡ m_ 1 ˆ Dh1 ˆ : …2†
ln…r3 =r2 †
tures of the inner and the outer vessels are,
respectively, set at T1=20 K and T2=300 K for one- Furthermore, the heat transfer rate, Q3, from the
dimensional thermal analysis in thermal equilibrium. It ambient temperature to the outer VCS at r=r3 is a
is also assumed that the inner vessel is ®lled with sum of the heat transferred to the inner VCS at r=r2,
99.8% para-hydrogen at the initial stage. Q2, and the sensible heat absorbed by the vapor shield-
. .
ing gas, m2Dh2, where m2 is the fraction of the mass
2.1. Combined insulation for reducing radiation heat in- ¯ow rate of the boilo€ vapor passing through the
leak outer VCS and Dh2=Cp2(T3ÿT1). Therefore, the total
mass ¯ow rate of the boilo€ vapor is expressed as
2.1.1. LH2 vessel with fully-®lled MLI and parallel-type . . .
m=m1+m2. It is assumed that the boilo€ vapor of
DVCS under high vacuum hydrogen passes through two VCSs in equal amounts
Fig. 1 shows the schematic con®guration of an LH2 . . .
(m1=m2=m/2).
vessel with parallel-type DVCS. Two vapor-cooled
radiations shields are mounted at r=r2 and r=r3, re- 2pkt …T4 ÿ T3 †
spectively, and MLI is fully packed between the inner Q3 ˆ Q2 ‡ m_ 2 Dh2 ˆ : …3†
ln…r4 =r3 †
and the outer vessels. Cryogenic hydrogen gas evapor-
.
ated by heat in-leak to the inner vessel passes through Eliminating m after dividing Eq. (1) by Eq. (2), we
 S.Y. Kim, B.H. Kang / International Journal of Hydrogen Energy 25 (2000) 133±141 135

Fig. 1. Combined insulation of fully-®lled MLI and parallel-type DVCS.

obtain 2.1.2. LH2 vessel with fully-®lled MLI and serial-type

DVCS under high vacuum
ln…r3 =r2 † …T2 ÿ T1 † hfg The schematic con®guration of combined insulation
ˆ : …4†
ln…r2 =r1 † …T3 ÿ T2 † Cp with fully-®lled MLI and serial-type DVCS is displayed
hfg ‡ …T2 ÿ T1 †
2 in Fig. 3. Two vapor-cooled radiation shields are
mounted at r=r2 and r=r3, respectively, and MLI is
Here, the speci®c heat of para-hydrogen Cp1, Cp2 are
fully packed between the inner and the outer vessels.
assumed to be constant (Cp1=Cp2=Cp=12.14 kJ/kg
The boilo€ vapor by heat in-leak to the inner vessel
K).
Similarly, dividing Eq. (1) by Eq. (3), we obtain passes through the inner VCS at r=r2, and then the

ln…r4 =r3 † …T4 ÿ T1 †

ln…r4 =r1 † …T4 ÿ T3 †
hfg
ˆ : …5†
Cp Cp
hfg ‡ …T2 ÿ T1 † ‡ …T3 ÿ T1 †
2 2

Solving Eqs. (4) and (5) for ®xed locations r=r2, r3

.
and r4, it yields T2 and T3 and then we can evaluate m
by using Eq. (1). By repeating the calculation for the
various locations, the optimal location of r2, r3, and r4
.
for minimum m can be achieved.
Compiling the results of one-dimensional thermal
analysis, the variation of mass ¯ow rate of evaporated
.
gas m as a function of a=r2/r1 and b=r3/r1 is demon-
strated in Fig. 2. It is interesting to note that there
.
exist optimal values a and b for minimal m. For a par-
allel-type DVCS, therefore, the best performance can
be achieved when the inner and the outer VCSs are
mounted at the location of about 35 and 50% from Fig. 2. Variation of the mass ¯ow rate of the boilo€ vapor
the inner vessel to the outer vessel, respectively. for parallel-type DVCS.
136 S.Y. Kim, B.H. Kang / International Journal of Hydrogen Energy 25 (2000) 133±141

Fig. 3. Combined insulation of fully-®lled MLI and serial-type DVCS.

outer VCS at r=r3, absorbing heat in-leak, and even- To solve the above Eqs. (6)±(8), dividing, respect-
tually exhausts to the ambient air. ively, Eqs. (6) and (7) by Eq. (8) gives
As mentioned in the above analysis for a parallel-
type DVCS, Q1 denotes the heat transfer from the
inner VCS at r=r2 to the inner vessel at r=r1. The ln…r3 =r2 † …T2 ÿ T1 † hfg
ˆ , …9†
heat Q1 absorbed by the inner vessel makes LH2 evap- ln…r2 =r1 † …T3 ÿ T2 † hfg ‡ Cp …T2 ÿ T1 †
orate:

2pkt …T2 ÿ T1 †
_ fg ˆ
Q1 ˆ mh : …6†
ln…r2 =r1 † ln…r4 =r3 † …T2 ÿ T1 † hfg
ˆ , …10†
ln…r2 =r1 † …T4 ÿ T3 † hfg ‡ Cp …T3 ÿ T1 †
The hydrogen gas evaporated in the inner vessel passes
through the inner VCS at r=r2 and then the outer
VCS at r=r3. By energy balance, therefore, the heat where the speci®c heat of para-hydrogen Cp is assumed
transfer rates Q2 and Q3 can be expressed as: to be constant (Cp=12.14 kJ/kg K). After solving the
.
temperatures at the VCSs, the mass ¯ow rate m can be
2pkt …T3 ÿ T2 †
_ p …T2 ÿ T1 † ˆ
Q2 ˆ Q1 ‡ mC , …7† evaluated by Eq. (6).
ln…r3 =r2 †
As seen in Fig. 4, there also exist optimal values of
.
a=r2/r1 and b=r3/r1 for minimal ¯ow rate m. For a
2pkt …T4 ÿ T3 † serial-type DVCS, the inner VCS located at about
_ p …T3 ÿ T2 † ˆ
Q3 ˆ Q2 ‡ mC : …8† 30% and the outer VCS at about 60% from the inner
ln…r4 =r3 †
vessel to the outer vessel can yield minimal evapor-
Here, the heat transfer rate Q2 is a sum of the heat ation loss. For optimal values of a and b, comparison
given directly to the inner vessel, Q1, and the sensible of the mass ¯ow rate of the boilo€ vapor for the paral-
heat absorbed by the vapor shielding gas passing lel-type and the serial-type DVCS is made and dis-
.
through the inner VCS, mCp(T2ÿT1). Similarly, the played in Fig. 5. As the radius of the outer vessel,
heat transfer rate Q3 from the ambient temperature to c=r4/r1, increases, the evaporation loss substantially
the outer VCS at r=r3 can be expressed as a sum of decreases for both types. The serial-type DVCS shows
the heat transferred to the inner VCS at r=r2, Q2, and 16% better performance than the parallel-type DVCS.
the sensible heat absorbed by the vapor shielding gas Consequently, the serial-type DVCS is recommended
.
passing through the outer VCS, mCp(T3ÿT2). to apply in an LH2 vessel.
 S.Y. Kim, B.H. Kang / International Journal of Hydrogen Energy 25 (2000) 133±141 137

_ fg ˆ Fe1 sA1 …T 42 ÿ T 41 †,
Q1 ˆ mh …11†

where Fe1 denotes the emissivity factor and s the

Stefan±Boltzmann constant (s=5.67  10ÿ8 W/m2
K4). A1 is the surface area per unit length, A1=2pr1.
Q2 is the heat transfer rate through the MLI layer
from r=r3 to r=r2. It is thermally balanced with the
heat transferred to the inner vessel, Q1, and the sensi-
ble heat absorbed by the evaporated gas in the VCS at
.
r=r2, mDh.

2pkt
_
Q2 ˆ Q1 ‡ mDh ˆ …T3 ÿ T2 †, …12†
ln…r3 =r2 †

where Dh=Cp(T2ÿT1). Q3 is the radiation heat trans-

fer rate from the outer vessel at r=r4 to the outer sur-
face of the MLI layer at r=r3. By energy balance, Q3
equals to Q2.

Q3 ˆ Fe3 sA3 …T 44 ÿ T 43 † ˆ Q2 , …13†

Fig. 4. Variation of the mass ¯ow rate of the boilo€ vapor
for serial-type DVCS. where Fe3 denotes the emissivity factor and A3 is the
surface area per unit length at r=r3, A3=2pr3. The
emissivity factors in Eqs. (11) and (13) are de®ned as:
2.1.3. LH2 vessel with partially ®lled MLI and SVCS
under high vacuum e1 e2
Fe1 ˆ r1 , …14†
Fig. 6 shows a combined insulation with SVCS and e2 ‡ …e1 ÿ e1 e2 †
MLI of thickness (r3ÿr2). This insulation model was r2
included in the analysis because it is easy to assemble
the vessel. Similarly, Q1 indicates the radiation heat e3 e4
Fe3 ˆ r3 : …15†
transfer rate from the single VCS at r=r2 to the inner e4 ‡ …e3 ÿ e3 e4 †
vessel and evaporates LH2. r4

Fig. 5. Comparison of the mass ¯ow rate of the boilo€ vapor between the parallel- and serial-type DVCS.
138 S.Y. Kim, B.H. Kang / International Journal of Hydrogen Energy 25 (2000) 133±141

Fig. 6. Combined insulation of partially-®lled MLI and SVCS.

Here, the emissivities of the VCS, e2, the inner, e1, and are little a€ected by the size of the outer vessel for
the outer vessels, e4, are 0.08 and the emissivity of ®xed values of a and b. Therefore, it is necessary to
MLI, e3, is set at 0.04. From Eq. (13), make the outer vessel as small as possible after deter-
mining the thickness of the MLI layer. In summary, it
2pkt is preferable to make the VCS close to the inner vessel
…T3 ÿ T2 † ˆ Fe3 sA3 …T 44 ÿ T 43 †: …16†
ln…r3 =r2 † and to thicken the MLI layer (bÿa ) in the manufac-
ture of an LH2 vessel.
Dividing Eq. (11) by Eq. (12) gives

Fe1 sA1 …T 42 ÿ T 41 † hfg

ˆ : …17† 2.2. Vapor-cooled heat stations for reducing conduction
2pkt …T3 ÿ T2 †= ln…r3 =r2 † hfg ‡ Cp …T2 ÿ T1 †
heat in-leak
Solving Eqs. (14)±(17) according to the location r=r2,
r3 and r4, it yields T2 and T3 and then we can evaluate In an e€ort to reduce conduction heat in-leak
.
m from Eq. (11). through a ®lling tube, the e€ect of vapour-cooled heat
Fig. 7 demonstrates the variation of the mass ¯ow stations will be dealt with hereafter. Fig. 9(b) shows
rate of the boilo€ vapor for various values of a=r2/r1 the schematic con®guration of three-stage vapor-cooled
and b=r3/r1. In contrast with the results for the two heat stations that are equally spaced by DL. Vapor-
combined insulation schemes with DVCS and fully- cooled heat stations absorb conduction heat transfer
®lled MLI described above, there is no optimal con- by increasing sensible heat of evaporated gas. In the
.
dition for minimal m. As the thickness of the MLI thermal analysis, it is assumed that heat is transferred
layer, bÿa, increases, the evaporation loss decreases only by steady-state one-dimensional conduction and
substantially. For a ®xed thickness of MLI thermophysical properties are little changed in the tem-
(bÿa = constant), the mass ¯ow rate decreases as the perature ranges considered.
location of the VCS, a=r2/r1, approaches close to the As seen in Fig. 9(b), Q1 is the conduction heat trans-
inner vessel. This trend is maintained for a larger fer rate from the ambient temperature to the ®rst stage
radius of the outer vessel, as displayed in Fig. 7(b). of the heat station at y = 3DL. It is thermally
The e€ect of the size of the outer vessel, c=r4/r1, on balanced with a sum of the heat transferred to the sec-
the mass ¯ow rate of the boilo€ vapor is also depicted ond stage of the heat station at y = 2DL, Q2, and the
in Fig. 8. Here, the values of a and b are ®xed at 1.1 sensible heat absorbed by the boilo€ vapor passing
and 1.2, respectively. It is seen that the mass ¯ow rates through the ®rst stage of the heat station at y=DL,
 S.Y. Kim, B.H. Kang / International Journal of Hydrogen Energy 25 (2000) 133±141 139

Fig. 7. Variation of the mass ¯ow rate of the boilo€ vapor as a function of a and b for ®xed c=r4/r1.

. .
mCp(TaÿTb), where m is the mass ¯ow rate of the boil- where ks denotes the thermal conductivity of a ®lling
o€ vapor by conduction heat in-leak. tube. A is the cross-sectional area of the ®lling tube,
A=pt(Doÿt ), where Do is the outer diameter and t is
…T2 ÿ Ta † the thickness of a ®lling tube.
_ p …Ta ÿ Tb † ˆ ks A
Q1 ˆ Q2 ‡ mC , …18†
…L ÿ 3DL† Furthermore, Q2 is a sum of the heat transfer rate
140 S.Y. Kim, B.H. Kang / International Journal of Hydrogen Energy 25 (2000) 133±141

Fig. 8. Variation of the mass ¯ow rate of the boilo€ vapor for the change of radius of the outer vessel at a = 1.1 and b = 1.2.

to the third stage of the heat station, Q3, and the sensi- Here, Q4 evaporates cryogenic ¯uids.
ble heat absorbed by the vapor passing through the
. …Tc ÿ T1 †
second stage of the heat station, mCp(TbÿTc). _ fg ˆ ks A
Q4 ˆ mh , …21†
DL
…Ta ÿ Tb †
_ p …Tb ÿ Tc † ˆ ks A
Q2 ˆ Q3 ‡ mC : …19† where hfg is the latent heat of vaporization.
DL .
Eliminating m after dividing Eqs. (18)±(20) by Eq.
Similarly, (21), we obtain
…Tb ÿ Tc † Q1 Cp …Ta ÿ T2 †
_ p …Tc ÿ T2 † ˆ ks A
Q3 ˆ Q4 ‡ mC : …20† ˆ1‡ , …22†
DL Q4 hfg

Q2 Cp …Tb ÿ T2 †
ˆ1‡ , …23†
Q4 hfg

Q3 Cp …Tc ÿ T2 †
ˆ1‡ : …24†
Q4 hfg

The temperatures at the vapor-cooled heat stations,

i.e., Ta, Tb and Tc, for three di€erent cryogenic ¯uids
are obtained solving Eqs. (22)±(24) and the results are
displayed in Fig. 10. In Fig. 10, the vapor-cooled heat
stations can substantially reduce temperature gradient
at the bottom of a ®lling tube for high Cp/hfg ¯uids
such as liquid hydrogen (LH2) and liquid helium
(LHe). The e€ect of vapor-cooled heat stations com-
pared with a ®lling tube without heat stations is also
demonstrated in Fig. 11. For liquid nitrogen (LN2),
the vapor-cooled heat stations can reduce about 20%
evaporation loss, while it is 55% for LH2 and 85% for
Fig. 9. Three-stage vapor-cooled heat stations. LHe. Consequently, the vapor-cooled heat stations are
 S.Y. Kim, B.H. Kang / International Journal of Hydrogen Energy 25 (2000) 133±141 141

ance than the parallel-type DVCS. The combined insu-

lation with an SVCS covered with MLI also displays a
similar performance to the serial-type DVCS fully
packed with MLI. For SVCS, the evaporation loss
decreases as the location of the SVCS approaches close
to the inner vessel as well as the thickness of the MLI
layer increasing.
Also, the impact of the vapor-cooled heat station on
the conduction heat in-leak has been investigated in
detail by one-dimensional thermal analysis in thermal
equilibrium. A three-stage vapor-cooled heat station
was considered in this study. The vapor-cooled heat
station shows a substantial reduction of the conduction
heat in-leak when it is applied to a cryogenic vessel for
high Cp/hfg ¯uids such as liquid hydrogen (LH2) and
Fig. 10. Temperature pro®les along the ®lling tube for various liquid helium (LHe).
cryogenic ¯uids.

Acknowledgements

This work was ®nancially supported by the

Alternative Energy Program at RaCER (R&D
Management Center for Energy and Resources) of
Korea.

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