Thermal design analysis of a liquid hydrogen vessel

Thermal design analysis of a liquid hydrogen vessel

International Journal of Hydrogen Energy 25 (2000) 133±141 Thermal design analysis of a liquid hydrogen vessel Seo Young Kim, Byung Ha Kang* Thermal/...

194KB Sizes 0 Downloads 24 Views

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 serialtype 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 Since the oil shock in the 1970s, much attention has been given to hydrogen as a fuel for the next generation. First of all, hydrogen is available in vast amounts on earth and it is the least polluting fuel that can be used in any modern combustion engine. The combustion of hydrogen produces only water vapor and limited NOx content and is free from CO2 emission. One of the most important technologies necessary for the utilization of hydrogen is how to store hydrogen fuel eciently. To date, there have been three di€erent storage methods: compressed hydrogen gas (GH2), metal hydride and liqui®ed hydrogen (LH2). It

* Corresponding author. Tel.: +82 2 958 5673; fax: +82 2 958 5689. E-mail address: [email protected] (B.H. Kang).

has been reported by many researchers that the liquid state of hydrogen is the most promising way of storage [1±5]. It is light and has less potential risk in terms of storage pressure compared with the compressed gas. However, the storage of LH2 at a cryogenic temperature requires a sophisticated insulation techniques compared to the other storage methods. For this reason, the development of an ecient insulation scheme for LH2 is of major concern. The vaporization of LH2 is generally minimized by means of a vacuum insulation between the inner and the outer vessels that was introduced by James Dewar [6]. With the advances in insulation techniques, the evaporation loss of LH2 has been substantially reduced in recent years. The state-of-the-art insulation techniques are adopting the combined insulation of vacuum, MLI and VCS. Such combined insulation can reduce e€ectively, heat in-leak by gaseous conduction, convection and radiation. Furthermore, the vapor-cooled heat 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 a, b, c Cp e1, e2, e3, e4 Fe1, Fe3 hfg ks

cross-sectional area of ®lling tube radius ratios, r2/r1, r3/r1, r4/r1 speci®c heat at constant pressure emissivity emissivity factors latent heat of vaporization thermal conductivity of ®lling tube material

heat in-leak through piping for ®lling and withdrawal as well as supports [7]. The present study is directed at the optimization of combined insulation schemes by one-dimensional thermal analysis for future design purposes. Three types of combined insulation schemes are considered: (a) a vessel fully-®lled with MLI and serial-type DVCS; (b) a vessel fully-®lled with MLI and parallel-type DVCS; (c) a vessel partially-®lled with MLI and SVCS. The e€ect of a vapor-cooled heat station on solid conduction heat in-leak is also investigated in detail. Three equally-spaced heat stations mounted on a ®lling tube are selected for the thermal analysis.

2. Thermal analysis The heat transfer to an LH2 vessel includes the radiation heat in-leak through vacuum insulation between the inner and the outer vessels as well as the conduction heat in-leak through pipings and supports. In the present study, we consider three combined insulation schemes to reduce the radiation heat in-leak by adopting vacuum insulation, MLI, and VCS. The temperatures of the inner and the outer vessels are, respectively, set at T1=20 K and T2=300 K for onedimensional thermal analysis in thermal equilibrium. It is also assumed that the inner vessel is ®lled with 99.8% para-hydrogen at the initial stage. 2.1. Combined insulation for reducing radiation heat inleak 2.1.1. LH2 vessel with fully-®lled MLI and parallel-type DVCS under high vacuum Fig. 1 shows the schematic con®guration of an LH2 vessel with parallel-type DVCS. Two vapor-cooled radiations shields are mounted at r=r2 and r=r3, respectively, and MLI is fully packed between the inner and the outer vessels. Cryogenic hydrogen gas evaporated by heat in-leak to the inner vessel passes through

kt L . m

apparent thermal conductivity of MLI length of ®lling tube mass ¯ow rate of boilo€ hydrogen gas

Greek symbols DL spacing between heat stations s Stefan±Boltzmann constant

two independent paths of VCSs, absorbing heat inleak, and eventually exhausts to the ambient air. As seen in Fig. 1, Q1 denotes the heat transfer rate from the inner VCS at r=r2 to the inner vessel at r=r1. The heat Q1 absorbed by the inner vessel makes LH2 evaporate: _ fg ˆ Q1 ˆ mh

2pkt …T2 ÿ T1 † , ln…r2 =r1 †

…1†

. where m is the total mass ¯ow rate of the boilo€ hydrogen vapor in the inner vessel and hfg the latent 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 to the inner VCS at r=r2, Q2, can be expressed as a sum of the heat given directly to the inner vessel, Q1, and the sensible heat absorbed by the vapor shielding . . gas, m1Dh1, by energy balance. Here m1 denotes the fraction of the mass ¯ow rate of the boilo€ vapor passing through the inner VCS at r=r2 and Dh1=Cp1(T2ÿT1). Q2 ˆ Q1 ‡ m_ 1 ˆ Dh1 ˆ

2pkt …T3 ÿ T2 † : ln…r3 =r2 †

…2†

Furthermore, the heat transfer rate, Q3, from the ambient temperature to the outer VCS at r=r3 is a sum of the heat transferred to the inner VCS at r=r2, Q2, and the sensible heat absorbed by the vapor shield. . ing gas, m2Dh2, where m2 is the fraction of the mass ¯ow rate of the boilo€ vapor passing through the outer VCS and Dh2=Cp2(T3ÿT1). Therefore, the total mass ¯ow rate of the boilo€ vapor is expressed as . . . m=m1+m2. It is assumed that the boilo€ vapor of hydrogen passes through two VCSs in equal amounts . . . (m1=m2=m/2). Q3 ˆ Q2 ‡ m_ 2 Dh2 ˆ

2pkt …T4 ÿ T3 † : ln…r4 =r3 †

…3†

. 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 ln…r3 =r2 † …T2 ÿ T1 † ˆ ln…r2 =r1 † …T3 ÿ T2 †

hfg : Cp …T2 ÿ T1 † hfg ‡ 2

…4†

Here, the speci®c heat of para-hydrogen Cp1, Cp2 are assumed to be constant (Cp1=Cp2=Cp=12.14 kJ/kg K). Similarly, dividing Eq. (1) by Eq. (3), we obtain

2.1.2. LH2 vessel with fully-®lled MLI and serial-type DVCS under high vacuum The schematic con®guration of combined insulation with fully-®lled MLI and serial-type DVCS is displayed in Fig. 3. Two vapor-cooled radiation shields are mounted at r=r2 and r=r3, respectively, and MLI is fully packed between the inner and the outer vessels. The boilo€ vapor by heat in-leak to the inner vessel passes through the inner VCS at r=r2, and then the

ln…r4 =r3 † …T4 ÿ T1 † ln…r4 =r1 † …T4 ÿ T3 † ˆ

hfg : Cp Cp hfg ‡ …T2 ÿ T1 † ‡ …T3 ÿ T1 † 2 2

…5†

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 demonstrated in Fig. 2. It is interesting to note that there . exist optimal values a and b for minimal m. For a parallel-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 the inner vessel to the outer vessel, respectively.

Fig. 2. Variation of the mass ¯ow rate of the boilo€ vapor 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 eventually exhausts to the ambient air. As mentioned in the above analysis for a paralleltype DVCS, Q1 denotes the heat transfer from the inner VCS at r=r2 to the inner vessel at r=r1. The heat Q1 absorbed by the inner vessel makes LH2 evaporate: _ fg ˆ Q1 ˆ mh

2pkt …T2 ÿ T1 † : ln…r2 =r1 †

…6†

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 transfer rates Q2 and Q3 can be expressed as: _ p …T2 ÿ T1 † ˆ Q2 ˆ Q1 ‡ mC

2pkt …T3 ÿ T2 † , ln…r3 =r2 †

…7†

_ p …T3 ÿ T2 † ˆ Q3 ˆ Q2 ‡ mC

2pkt …T4 ÿ T3 † : ln…r4 =r3 †

…8†

Here, the heat transfer rate Q2 is a sum of the heat given directly to the inner vessel, Q1, and the sensible heat absorbed by the vapor shielding gas passing . through the inner VCS, mCp(T2ÿT1). Similarly, the heat transfer rate Q3 from the ambient temperature to the outer VCS at r=r3 can be expressed as a sum of the heat transferred to the inner VCS at r=r2, Q2, and the sensible heat absorbed by the vapor shielding gas . passing through the outer VCS, mCp(T3ÿT2).

To solve the above Eqs. (6)±(8), dividing, respectively, Eqs. (6) and (7) by Eq. (8) gives hfg ln…r3 =r2 † …T2 ÿ T1 † ˆ , hfg ‡ Cp …T2 ÿ T1 † ln…r2 =r1 † …T3 ÿ T2 †

…9†

hfg ln…r4 =r3 † …T2 ÿ T1 † ˆ , ln…r2 =r1 † …T4 ÿ T3 † hfg ‡ Cp …T3 ÿ T1 †

…10†

where the speci®c heat of para-hydrogen Cp is assumed to be constant (Cp=12.14 kJ/kg K). After solving the . temperatures at the VCSs, the mass ¯ow rate m can be evaluated by Eq. (6). 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 serial-type DVCS, the inner VCS located at about 30% and the outer VCS at about 60% from the inner vessel to the outer vessel can yield minimal evaporation loss. For optimal values of a and b, comparison of the mass ¯ow rate of the boilo€ vapor for the parallel-type and the serial-type DVCS is made and displayed in Fig. 5. As the radius of the outer vessel, c=r4/r1, increases, the evaporation loss substantially decreases for both types. The serial-type DVCS shows 16% better performance than the parallel-type DVCS. Consequently, the serial-type DVCS is recommended to apply in an LH2 vessel.

S.Y. Kim, B.H. Kang / International Journal of Hydrogen Energy 25 (2000) 133±141

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

137

…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 sensible heat absorbed by the evaporated gas in the VCS at . r=r2, mDh. _ Q2 ˆ Q1 ‡ mDh ˆ

2pkt …T3 ÿ T2 †, ln…r3 =r2 †

…12†

where Dh=Cp(T2ÿT1). Q3 is the radiation heat transfer rate from the outer vessel at r=r4 to the outer surface of the MLI layer at r=r3. By energy balance, Q3 equals to Q2. Fig. 4. Variation of the mass ¯ow rate of the boilo€ vapor for serial-type DVCS.

2.1.3. LH2 vessel with partially ®lled MLI and SVCS under high vacuum Fig. 6 shows a combined insulation with SVCS and MLI of thickness (r3ÿr2). This insulation model was included in the analysis because it is easy to assemble the vessel. Similarly, Q1 indicates the radiation heat transfer rate from the single VCS at r=r2 to the inner vessel and evaporates LH2.

Q3 ˆ Fe3 sA3 …T 44 ÿ T 43 † ˆ Q2 ,

…13†

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: Fe1 ˆ

Fe3 ˆ

e2 ‡

e1 e2 , r1 …e1 ÿ e1 e2 † r2

e3 e4 : r3 e4 ‡ …e3 ÿ e3 e4 † r4

Fig. 5. Comparison of the mass ¯ow rate of the boilo€ vapor between the parallel- and serial-type DVCS.

…14†

…15†

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 the outer vessels, e4, are 0.08 and the emissivity of MLI, e3, is set at 0.04. From Eq. (13), 2pkt …T3 ÿ T2 † ˆ Fe3 sA3 …T 44 ÿ T 43 †: ln…r3 =r2 †

…16†

Dividing Eq. (11) by Eq. (12) gives hfg Fe1 sA1 …T 42 ÿ T 41 † ˆ : 2pkt …T3 ÿ T2 †= ln…r3 =r2 † hfg ‡ Cp …T2 ÿ T1 †

…17†

Solving Eqs. (14)±(17) according to the location r=r2, r3 and r4, it yields T2 and T3 and then we can evaluate . m from Eq. (11). Fig. 7 demonstrates the variation of the mass ¯ow rate of the boilo€ vapor for various values of a=r2/r1 and b=r3/r1. In contrast with the results for the two combined insulation schemes with DVCS and fully®lled MLI described above, there is no optimal con. dition for minimal m. As the thickness of the MLI layer, bÿa, increases, the evaporation loss decreases substantially. For a ®xed thickness of MLI (bÿa = constant), the mass ¯ow rate decreases as the location of the VCS, a=r2/r1, approaches close to the inner vessel. This trend is maintained for a larger radius of the outer vessel, as displayed in Fig. 7(b). The e€ect of the size of the outer vessel, c=r4/r1, on the mass ¯ow rate of the boilo€ vapor is also depicted in Fig. 8. Here, the values of a and b are ®xed at 1.1 and 1.2, respectively. It is seen that the mass ¯ow rates

are little a€ected by the size of the outer vessel for ®xed values of a and b. Therefore, it is necessary to make the outer vessel as small as possible after determining the thickness of the MLI layer. In summary, it is preferable to make the VCS close to the inner vessel and to thicken the MLI layer (bÿa ) in the manufacture of an LH2 vessel.

2.2. Vapor-cooled heat stations for reducing conduction heat in-leak In an e€ort to reduce conduction heat in-leak through a ®lling tube, the e€ect of vapour-cooled heat stations will be dealt with hereafter. Fig. 9(b) shows the schematic con®guration of three-stage vapor-cooled heat stations that are equally spaced by DL. Vaporcooled heat stations absorb conduction heat transfer by increasing sensible heat of evaporated gas. In the thermal analysis, it is assumed that heat is transferred only by steady-state one-dimensional conduction and thermophysical properties are little changed in the temperature ranges considered. As seen in Fig. 9(b), Q1 is the conduction heat transfer rate from the ambient temperature to the ®rst stage of the heat station at y = 3DL. It is thermally balanced with a sum of the heat transferred to the second stage of the heat station at y = 2DL, Q2, and the sensible heat absorbed by the boilo€ vapor passing 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 boilo€ vapor by conduction heat in-leak. _ p …Ta ÿ Tb † ˆ ks A Q1 ˆ Q2 ‡ mC

…T2 ÿ Ta † , …L ÿ 3DL†

…18†

where ks denotes the thermal conductivity of a ®lling tube. A is the cross-sectional area of the ®lling tube, A=pt(Doÿt ), where Do is the outer diameter and t is the thickness of a ®lling tube. 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 sensible heat absorbed by the vapor passing through the . second stage of the heat station, mCp(TbÿTc). _ p …Tb ÿ Tc † ˆ ks A Q2 ˆ Q3 ‡ mC

_ fg ˆ ks A Q4 ˆ mh

…Tc ÿ T1 † , DL

…21†

…Ta ÿ Tb † : DL

…19†

where hfg is the latent heat of vaporization. . Eliminating m after dividing Eqs. (18)±(20) by Eq. (21), we obtain

…Tb ÿ Tc † : DL

…20†

Cp …Ta ÿ T2 † Q1 ˆ1‡ , hfg Q4

…22†

Cp …Tb ÿ T2 † Q2 ˆ1‡ , Q4 hfg

…23†

Cp …Tc ÿ T2 † Q3 ˆ1‡ : hfg Q4

…24†

Similarly, _ p …Tc ÿ T2 † ˆ ks A Q3 ˆ Q4 ‡ mC

Here, Q4 evaporates cryogenic ¯uids.

Fig. 9. Three-stage vapor-cooled heat stations.

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 compared 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 LHe. Consequently, the vapor-cooled heat stations are

S.Y. Kim, B.H. Kang / International Journal of Hydrogen Energy 25 (2000) 133±141

Fig. 10. Temperature pro®les along the ®lling tube for various cryogenic ¯uids.

141

ance than the parallel-type DVCS. The combined insulation 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 liquid helium (LHe).

Acknowledgements This work was ®nancially supported by the Alternative Energy Program at RaCER (R&D Management Center for Energy and Resources) of Korea.

References

Fig. 11. E€ect of a vapor-cooled heat station.

preferred to apply in a cryogenic vessel for high Cp/hfg ¯uids. 3. Conclusion One-dimensional thermal analysis for three schemes of combined insulation has been carried out. For DVCS, the serial-type DVCS shows a better perform-

[1] Ewald R, Kesten M. Cryogenic equipment of liquid hydrogen powered automobiles. Adv Cryogenic Engineering 1990;35:1777±81. [2] Hasan MM, Lin CS, Van Dresar NT. Self-pressurization of a ¯ight weight liquid hydrogen storage tank subjected to low heat ¯ux, ASME HTD. Cryogenic Heat Transfer 1991;167:37±42. [3] Rudiger H. Design characteristics and performance of a liquid hydrogen tank system for motor cars. Cryogenics 1992;32 (3):327±9. [4] Peschka W. Hydrogen cryofuel in internal combustion engines. Adv Cryogenic Engineering 1994;39:35±44. [5] Michel F, Fieseler H, Meyer G, Theiben F. On-board equipment for liquid hydrogen vehicles. Int J Hydrogen Energy 1998;23 (3):191±9. [6] Timmerhaus KD, Flynn TM. Cryogenic Process Engineering. Plenum Press, 1989. [7] Flynn TM. Cryogenic Engineering. New York: Marcel Dekker, 1997.