- Email: [email protected]
Relaxation of internal stress generated in hydrogen absorbing alloy vessels
hf. J. Hydrogen Energy, Vol. 23, No. 10, pp. 921-929, 1998
Pergamon PII: s036&3199(97)00158-4
RELAXATION
‘p 1998International Association for Hydrogen Energy Elsevier ScienceLtd All rights reserved. Printed in Great Britain 0360-3199/98 $19.00+0.00
OF INTERNAL STRESS GENERATED ABSORBING ALLOY VESSELS K. NASAKO,*tf
Y. ITO,* N. HIROt
IN HYDROGEN
and M. OSUMIt
* Department of Fundamental Energy Science,Graduate School of Energy Science,Kyoto University, Yoshida, Sakyo-ku, Kyoto 606, Japan and t Mechatronics Research Center, Sanyo Electric Co. Ltd, I-18-13, Hashiridani, Hirakata City, Osaka, 573, Japan
Abstract-Hydrogen absorbing alloys cause internal stressin reaction vesselsdue to the expansion that occurs when they absorb hydrogen. This stressis affectednot only by the amount of reacting hydrogen but also by the ab/desorption cycles. In this paper, we analyze the reaction distribution in a reaction vessel through simulations and show that locally excess internal stress occurs near the heat media inlet. We also show that this excess stress is decreased by unifying the reaction ratio by exchanging heat between the heat media inlet and the outlet in the reaction vessel. 0 1998International Association for Hydrogen Energy
NOMENCLATURE A a1 c ct. E K k 1 m NCY n P R T v x %n I. P iH AS
f 1
Heat transfer area (m’) Conversion constant (mol. kg-’ * mass% -‘) Specific heat (J * kg-’ * K-‘) Heat capacity of reaction vessel (J * K-‘) Activation energy (J * mol-‘) Overall heat transfer coefficient (W em-* * K-‘)
S
e sl sa SS
Reaction rate constant (mass% * s-‘) Length (m) Weight of alloy (kg) Number of ab/desorption cycles Flow rate of H, (mol. s-l) Pressure(MPa) Gas constant (J *mall’ *K- ‘) Temperature (K) Flow rate of heat media (m’ *s-‘) Hydrogen content (mass%) Heat transfer coefficient (W *mm2* K-‘) Thermal conductivity (W * m-’ * Km’) Density (kg *m-‘) Stress(MPa) Reaction heat (J . mol H, ‘) Entropy change of hydriding (J *mol H; ’ * Km ‘)
Fin
Heat media Hydrogen absorbing alloy Equilibrium Between alloy and heat media Between alloy and atmosphere Between alloy bed i and N - i+ 1
1. INTRODUCTION
Subscripts a Atmosphere f: Author to whom correspondence should be addressed.Tel.: 0081 720 41 7859. Fax: 0081 720 44 2985. E-mail: nasako@ mech.rd.sanyo.co.jp. 921
Because hydrogen absorbing alloys can reversibly convert room-temperature heat into chemical energy, they hold great promise in terms of low-level energy conversion. So far, these alloys have been researched in conventional heat utilization systemssuch as heat storage [l] and heat pumps [2, 31. In previous studies, the authors have expanded the application range of the alloys, proposing a new long distance heat transport system with higher heat transport efficiency than conventional systems [4], and realizing a -20°C refrigeration system which was not possible with conventional heat-driven refrigeration systems[5, 61. On the other hand, researchconcerning the stability of these systems’ cycle performance, which is necessaryfor practical use, has been reported only from the standpoint of alloy materials, such as the hydrogen ab/desorption cycle performance, changes in the lattice structure, and pulverization of hydrogen absorption [7, 81. However, research on reaction vesselsrelated to stability with cycles, which is indispensable for estimating system endurance, has been scarcely reported [9, IO]. To
922
K. NASAKO et al.
establish the technology for heat utilization systemsusing hydrogen absorbing alloys, more detailed studies must be conducted in the 27% expansion in the alloy [7], and the generation of more than 45 MPa of stressin the alloy bed [lo] during hydrogen absorption. The authors analyzed internal stressin vesselsresulting from hydrogen absorbing alloy expansion. Namely, we assumedthat the pulverization of the alloy is a significant factor in stress generation, and we measured and analyzed the stresson reaction vesselsfor up to 100hydrogen ab/desorption cycles where alloy particle sizesare rapidly changed by pulverization. As a result, it was found that localized internal stressis generated at the bottom of the vessel at a 50 ~01% packing fraction with 1.30 mass% hydrogen ab/desorption cycles, and that this stress not only increaseswith each cycle, but continues to increase even after plastic deformation of the vessel. It was also found that the internal stress occurrence and accumulation depends on the amount of hydrogen ab/desorption. In this paper, we apply the internal stress data mentioned above to actual vessels used in heat utilization systems, that is, performing an analysis of the localized reaction ratio in the vesselthrough simulation, an analysis of the stress distribution in vessels and a study of practical vessel structures capable of relaxing excess stress.
reaction vessel, and the amount of hydrogen abidesorption is assumedto locally exceedthe critical level. 3. REACTION AND STRESS DISTRIBUTION REACTION VESSELS
IN
3.1. Simulation of hydrogenation reaction
The ordinary heat exchanger transfers steady-state heat. On the other hand, the heat exchanger for hydrogen absorbing alloys exchanges the limited reaction heat of the alloy in the vessel. Therefore, the reaction vessel properties obtained by standardizing the packing alloy weight are useful for estimating the vesselperformance of heat utilization systems,in which the vesseltemperature is raised and lowered cyclically. In other words, the reaction vessel performance can be evaluated regardless of the heat exchanger structure by using the heat transfer coefficient per unit of alloy (1 kg) between the alloy and the heat media, the heat radiative coefficient per 1 kg of alloy from the reaction vessel, and the heat capacity per 1kg of alloy in the reaction vessel(including heat capacity of the alloy, heat exchanger and pressure container). In this study, we use the performance terms K,, * A,, K, *A, and C, for the above reason, which are the values of the heat transfer coefficient K,,, K,, multiplied by the heat transfer area A,, A,, and the value of the vesselheat capacity divided by the packing alloy weight, respectively. 2. STRESS GENERATION IN VESSELS Figure 2 shows the simulation model. Here, we adopted a vessel with an internal heat exchanger. This Hydrogen absorbing alloys generate accumulating structure is expected to have a low heat capacity for the stress by hydrogen ab/desorption cycles. This stress reaction vessel, and offer the advantage of raising or accumulation can be estimated as a two-step process in lowering the reaction vesseltemperature. We also divided which agglomeration occurs between the hydride par- the vessel in the heat media pipe direction since a temticles when the hydride packing fraction is higher than a perature difference of at least 5 K was set up in the heat critical level in the initial cycles (Step l), and then fine utilization system. powder generated by pulverization with progressing We assumed that the temperature distribution in the cycles falls down and causesthe localized packing frac- vertical direction from the heat media pipe was uniform tion at the vessel bottom to gradually increase (Step 2) in this model. This is because the effective heat con1111. ductivity of the alloy layer was improved by means such As a result of measurementswith LaNi, 55A10.45, stress as high-density fins in order to decreasethe temperature in up to 100cycles is significantly affected by the amount drop in the alloy layer. Furthermore, we used uniform of hydrogen ab/desorption as shown in Fig. 1, and it was pressure in the alloy layers and ignored the heat transfer found that this stress CJis expressed by the amount of between the divided alloy beds. hydrogen ab/desorption x and the number of cycles NC,, With the model described above, the basic simulation shown as eqn (1). equations can be expressedusing the following eqns (30-0~ = Ao = 10.4N,(x- 1.1) (1) 7). x > 1.1, 0 < NcY< 100
(2)
From this, internal stressincreased linearly at a point of 1.1 mass%. Since this critical value of 1.1 mass% is higher than the effective hydrogen transfer (0.7-0.9 mass%) of ordinary heat pumps [6], stressaccumulation is not expected to occur in an actual reaction vessel. However, in the vessels of heat utilization systems, a temperature difference of at least 5 K is needed between the heat media inlet and outlet in order to obtain thermal power. So, there is a large reaction distribution in the
-K,,
. A,,(T-
T,) = 0
(3)
dxi
iii = a, *rn;dt
>
= V-C,-p,(T,,- T,J
(5)
RELAXATION
OF INTERNAL
STRESS GENERATED
IN HYDROGEN
: LaNi4.,,
Packing
fraction of alloy
ABSORBING
ALLOY
VESSELS
923
Alo.
: 50 ~01%
(T=cTi +10.4Nq(X-1.1)
Hydrogen content x : 1.30 mass%
40
60
80
100
120
Number of cycles, A&, Fig. 1. Effect of absorbed maximum hydrogen content on vessel surface stress in one hydrogen ab/desorption
P, = func (T, x)
(6)
$=k*exp(g)*ln(y).(l-2)”
(7)
Here the heat balance eqn (3) consists of the first term as the reaction heat, the second term as the heat capacity change in the reaction vessel,the third term as the exchange heat between the alloy and the heat media, and the fourth term as the exchange heat between alloy and atmosphere. Equation (4) indicates the relationship between the hydrogen flow rate and the hydrogen content of the alloy. Equation (5) expresses the temperature change of the heat media by heat exchange between the alloy and heat transfer media. Equation (6) expressesthe fitting curve [12] of the LaNi,,,,Al,,, P-C isotherms as
G Xl
T2 x2
G
TN-I TN XN-I
&
t n Fig. 2. A model for the hydrogenation simulation of hydrogen absorbing alloy vessels.
cycle
shown in Fig. 3. In this equation, the relationship between equilibrium hydrogen pressure P, and temperature T is set according to eqn (8).
(8) Equation (7) shows the reaction rate which is induced by the shrinking core model [13, 141.In this equation, the effect of pressure on the reaction rate was adopted [(P- P,)/P,] which showed fairly good coincidence [15, 161. 3.2. Calculation results of’ reaction ratio and stress distribution
Equations (3)(7) were calculated by a differential method of minute time with 10 divided parts. Here, the alloy properties (equilibrium and dynamic) and thermophysical properties of the reaction vessel used were those of our -20°C refrigeration system [6]. These are summarized in Table 1. The initial conditions are set up as a hydrogen content of 0.20 mass%, a vessel temperature and atmosphere temperature of 2O”C, and a hydrogen pressure of 0.05 MPa. Figure 4 shows the calculated results. The horizontal axis indicates the time after the start of the reaction, the vertical axis shows the hydrogen content in each bed, and the symbol N in the figure indicates the bed numbers. From this figure, it is found that the reaction is fastest at the heat media inlet (N = l), and the latter beds follow it. Since the total reaction rate of the vessel, which is
924
K. NASAKO ef al. 10 I
Alloy : LaNi,,,,Al,,,
0.0
0.4
0.8
1.2
1.6
Hydrogen content / mass% Fig. 3. P-C isotherms of LaNi,,5A10,,, alloy.
Table 1. The values of alloy, heat media and reaction vesselproperties used in the hydrogenation simulation Alloy properties
3.64x IO4[J*mol H;‘] 4.2 x lo4 [J . mol H; ‘1 9.1 x lo4 [mass% OS-‘1 1.43 [mass%] 4.18x103[J.kg-‘-K-l] 1.Ox 10’ [kg * m-‘1 7x 10-6[m’*s-‘]* 40 [w - K-l]* 0.05 w*K-‘I* 1000[J-K-‘]*
Heat media properties Reaction vesselproperties
* Per 1 kg of alloy
expressed by the sum of the reaction rates in each bed,
decreaseswith the progressing reaction, we switch a hydrogenation reaction to a reversereaction of dehydrogenation to perform cycle operations in heat utilization systems. If, for example, the effective hydrogen transfer is 0.9 mass%, the reaction is switched at 1390 s as shown in Fig. 4. The hydrogen content in each bed at this time is N = 1, 4, 7 and 10 at 1.26, 1.16, 1.05 and 0.93 mass%, respectively. Becausethese hydrogen content values are equal to the maximum
amount
of hydrogen
ab/de-
sorption in each bed, the stressaccumulation at 100cycles is shown in Fig. 5 from eqn (1). We therefore expect that a significant excessof stress occurs near the heat media inlet, and it is found that this stressexceedsthe proof stressfor Cu (Z 100 MPa) and is
near the proof stress for stainless steel (200 MPa) at N= 1.
4. STUDIES FOR RELAXING INTERNAL
STRESS
4.1. Relaxing stress by unifving reaction ratio in each bed
We studied ways to reduce stressaccumulation in reaction vesselsfrom the standpoint of the vessel structures. It is possible to reduce stress accumulation by unifying the reaction ratio throughout the vessel, and this can be
achieved by exchanging heat between the heat media inlet (N = 1) and the outlet (N = 10). Figure 6 shows a model that exchanges heat between alloy bed i and N-i+ 1. Here, the heat balance can be
RELAXATION
OF INTERNAL
STRESS GENERATED
IN HYDROGEN
ABSORBING
I
0
600
1200
1800
Time / s Fig. 4. Relationship
between hydrogen content and reaction time.
Part in the vessel
Fig. 5. Relationship
between inner stress and part in the vessel.
ALLOY
I
2400
VESSELS
925
926
K. NASAKO et al. Hydride bed i
T2
and show the difference by the factor of K,, *A,, which means the heat transfer between bed i and N-i+ 1. Figure 8 shows the stress distribution at 100 cycles using the sameeffective hydrogen transfer of 0.9 mass%. From this, it is found that stressis significantly reduced by a heat exchange of at least 20 W *K-’ between alloy i and N-i+ 1. 4.2. Reaction vessel structure
/
II
/
TN
TN-I
XN
XN-1
\ Hydride bed
ri t N-i+1 Fig. 6. A revised model for hydrogenation simulation of a hydrogen absorbing alloy heat exchanger turned up with the heat media inlet and outlet.
expressedby eqn (9), which consists of eqn (3) and heat transfer between bed i and N-i+ 1.
-Ka; A,Vi-
Ta)-Ks;A,(T,-
TN--I+‘) = 0
(9)
With the new model described above, we calculated the reaction ratio of each bed by eqns (9) and (4)-(7). Figure 7 shows the results through simulation using the same numbers of divided beds and the same initial conditions. In this figure, we plot only the reaction ratio at alloy bed N = 1 for which stressaccumulation is highest,
a. Heat transfer model for the heat exchanger of the hydrogen absorbing alloy vessel
The structure of a heat exchanger, which exchanges heat between the heat media inlet and outlet, can be constructed by a tube-in-fin type heat exchanger. We therefore studied the possibility of simultaneously achieving the conditions of KS,*A, = 40 W *K-’ (heat transfer between alloy bed i and heat media) and KS,+A, > 20 W * K-’ (heat transfer between alloy bed i and N-i+ 1) in an actual heat exchanger. Figure 9 shows the heat transfer model between the alloy bed i and the heat media or the facing alloy bed N - i+ 1. In this model, we simply used a flat heat transfer surface for the heat media although the heat transfer surface of the tube-in-fin type heat exchanger is actually round. We assumed that the alloy packed between the fins reacts at the volumetric center. We also supposed that the heat flux between the alloy bed and the heat media is represented from A to B, and the heat flux between alloy bed i and N-i+ 1 is represented from A to C as shown in Fig. 9 becauseof 1, <
1.4
0
600
1200
1800
2400
Time I s Fig. 7. Relationship between hydrogen content and reaction time of the revised model.
RELAXATION
OF INTERNAL
STRESS GENERATED
IN HYDROGEN
ABSORBING
ALLOY
150 cl % .
100
f 2 50
0
1
2
3
4
5\6
7
8
9
10
P&t in the vessel
Fig. 8. Relationship
.. . Heat
between inner stress and part in the vessel of the revised model.
a.
media
>
j
:.
! Heat transfer surface
riz-I
L-4 I
1-m11111)
,
‘II.
-b’
.
fl ,
Fin Hydrogen absorbing
4 Heat media Fig. 9. Heat transfer model of heat exchanger for hydrogen absorbing alloy.
alloy
VESSELS
921
928
K. NASAKO et al.
Heat m;dia inlet # 9.9 (Heat media pipe) # 8.0 (H2 filter pipe)
A-A’ cross section
(Unit : mm)
Fig. 10. Structure of a hydrogen absorbing alloy vessel.
the resistance in alloy bed R,, fin material Rb and the contact surface between the heat transfer plate and heat media R, as shown in eqn (10). Heat resistance RAmC between alloy bed i and N-i+ 1 is similarly expressedas shown in eqn (11). In addition, the heat transfer performance per unit alloy weight KS,*A,, KS *A, is expressed as eqns (13) and (14) respectively [m: alloy weight packed in the bed i as shown in eqn (12)]. La
2 R,+Rb+R,
=
(1, - lN4 1 1 1 h’ d’
s
1 + (1,/2)d,.& + (lP/2)ddYx,
hII2
RAc = R,+ Rb,+ R,, = 2(R,+R,)
(1o)
ductivity of the fin and the alloy bed are 237 W em-’ * K-’ and 0.5 We m-’ * K-’ [ 171,respectively. The heat transfer coefficient between the heat transfer surface and the heat media cc,is assumedto be 4000 W * K-‘. From this calculation, it is found that the fin-in-tube heat exchanger can simultaneously attain the heat transfer of 40 W * K-i between the alloy and the heat media as well as the heat transfer over 20 W. K-’ between alloy beds i and N-i+ 1, which are needed in order to relax stress. The structure can be scaled up using the vessel structure shown in Fig. 10,and it is important for relaxing inner stress to set the heat media inlet and outlet closer to each other.
(11)
5. CONCLUSION
(12)
(1) The stress accumulation which occurs in hydrogen
X, *4 = UU?-B*4
(13)
KS, * A, = 1/( RA-C * m)
(14)
b. Heat exchanger for relaxing stress
If we assumea fin pitch lP of 1 mm, a fin thickness I, of 0.1 mm and an alloy bed height /,, of 13 mm as shown in Fig. 9, we get 39.5 and 36.7 W * K-’ for KS,*A, and KS,- A,, respectively, per 1 kg of alloy (apparent density: 4 x lo3 kg*m3) by using eqns (lOHl4). Here, thermal con-
absorbing alloy beds was clarified by the relationship of the ab/desorption quantity and the number of ab/desorption cycles. c-9 It was found that there is a great possibility for excess stressaccumulation to occur at the heat media inlet of an actual reaction vesselfrom the analytical results of the hydrogenation simulation. (3) We showed that heat exchange between the heat media inlet and outlet in the reaction vessel makes the local reaction more uniform, and simultaneously relaxes stress accumulation.
RELAXATION
OF INTERNAL STRESS GENERATED IN HYDROGEN ABSORBING ALLOY VESSELS
work was supported by NED0 (New Energy and Industrial Technology Development Organization) as a part of the Sunshine Project under the Ministry of International Trade and Industry of Japan. Acknowledgement-This
REFERENCES 1. Libowitz, G. G. and Blank, Z., Proceedings of the I Ith IECEC, 1976, p. 673. 2. Gruen, D. M., Mendelsohn, M. H., Sheft, I. and Lamich, G. J., Proceedings of the 2nd WHEC, Zurich, Switzerland, 1978,p. 1931. 3. 1.anoma, A., Yoneta, M., Nitta, T. and Okuda, K., Proceedings of the ASMEIJSME Conference, 1987,p. 43 1.
Thermal Engineering Joint
4. Nasako, K., Yonesaki, T., Yonezu, I., Fujitani, S., Saito, T., Moroto, M., Osumi, M. and Furukawa, N., Proceedings qf the ISES Solar World Congress, Vol. 2. Pergamon Press, Oxford, 1990,p. 1343. 5. Nasako, K., Yonesaki, T., Satoh, K., Imoto, T., Fujitani, S., Hiro, N., Hirose, N., Fukushima, K., Saito, T. and Yonezu, I., Z. Phys. Chem., 1994,183,235. 6. Nasako, K., Hiro, N., Fukushima, K., Fujitani. S., Yonezu,
929
I. andosumi, M.. Solar Engineering(ASME, G00837), 1994, p. 313. 7. van Vucht, J. H. N., Kuijpers, F. A. and Bruning, H. C. A. M.. Philias Res. Rents. 1970.25. 133. 8. Osumi, Y., Suzuki: H., Kafo, A. and Oguro, K.. J. LessCommon Met., 1983,89, 287. 9. Lynch, F. E., J. Less-Common Met., 1980,74. 411. IO. Kawamura, M., Ono, S. and Mizuno, Y., Proceedings of the Miami Inter. Symp. on Metal-Hydride Systems. Pergamon Press,Oxford, 1981, p. 489. 11. Nasako, K., Ito, Y., Hire, N. and Osumi, M., J. Alloys and Comoounds, 1998.264.211. 12. Fujitani, S., Nakamura, H., Furukawa, A., Nasako, K., Satoh, K., Imoto, T., Saito, T. and Yonezu. I., Z. Phys. Chem., 1993,179,29. 13. Miyamoto, M., Yamaji, K. and Nakata, Y., J. Less-Comman Met., 1983,89, 111. 14. Reilly, J. J., Josephy, Y. and Johnson, J. R.. Z. Phys. Chem., 1989,164, 1241. 15. Groll, M., Supper. W. and Werner, R., 2. Phys. Chem., 1989,164, 1485. 16. Imoto, T., Yonesaki, T., Fujitani, S., Yonezu, I., Hiro, N., Nasako, K. and Saito, T., Int. J. Hydrogen Energ.y, 1996, 21,451. 17. Suds, S., Kobayashi, N. and Yoshida, K.. Inr. J. Hydrogen Energy. 198 1, 6, 521.
Pergamon PII: s036&3199(97)00158-4
RELAXATION
‘p 1998International Association for Hydrogen Energy Elsevier ScienceLtd All rights reserved. Printed in Great Britain 0360-3199/98 $19.00+0.00
OF INTERNAL STRESS GENERATED ABSORBING ALLOY VESSELS K. NASAKO,*tf
Y. ITO,* N. HIROt
IN HYDROGEN
and M. OSUMIt
* Department of Fundamental Energy Science,Graduate School of Energy Science,Kyoto University, Yoshida, Sakyo-ku, Kyoto 606, Japan and t Mechatronics Research Center, Sanyo Electric Co. Ltd, I-18-13, Hashiridani, Hirakata City, Osaka, 573, Japan
Abstract-Hydrogen absorbing alloys cause internal stressin reaction vesselsdue to the expansion that occurs when they absorb hydrogen. This stressis affectednot only by the amount of reacting hydrogen but also by the ab/desorption cycles. In this paper, we analyze the reaction distribution in a reaction vessel through simulations and show that locally excess internal stress occurs near the heat media inlet. We also show that this excess stress is decreased by unifying the reaction ratio by exchanging heat between the heat media inlet and the outlet in the reaction vessel. 0 1998International Association for Hydrogen Energy
NOMENCLATURE A a1 c ct. E K k 1 m NCY n P R T v x %n I. P iH AS
f 1
Heat transfer area (m’) Conversion constant (mol. kg-’ * mass% -‘) Specific heat (J * kg-’ * K-‘) Heat capacity of reaction vessel (J * K-‘) Activation energy (J * mol-‘) Overall heat transfer coefficient (W em-* * K-‘)
S
e sl sa SS
Reaction rate constant (mass% * s-‘) Length (m) Weight of alloy (kg) Number of ab/desorption cycles Flow rate of H, (mol. s-l) Pressure(MPa) Gas constant (J *mall’ *K- ‘) Temperature (K) Flow rate of heat media (m’ *s-‘) Hydrogen content (mass%) Heat transfer coefficient (W *mm2* K-‘) Thermal conductivity (W * m-’ * Km’) Density (kg *m-‘) Stress(MPa) Reaction heat (J . mol H, ‘) Entropy change of hydriding (J *mol H; ’ * Km ‘)
Fin
Heat media Hydrogen absorbing alloy Equilibrium Between alloy and heat media Between alloy and atmosphere Between alloy bed i and N - i+ 1
1. INTRODUCTION
Subscripts a Atmosphere f: Author to whom correspondence should be addressed.Tel.: 0081 720 41 7859. Fax: 0081 720 44 2985. E-mail: nasako@ mech.rd.sanyo.co.jp. 921
Because hydrogen absorbing alloys can reversibly convert room-temperature heat into chemical energy, they hold great promise in terms of low-level energy conversion. So far, these alloys have been researched in conventional heat utilization systemssuch as heat storage [l] and heat pumps [2, 31. In previous studies, the authors have expanded the application range of the alloys, proposing a new long distance heat transport system with higher heat transport efficiency than conventional systems [4], and realizing a -20°C refrigeration system which was not possible with conventional heat-driven refrigeration systems[5, 61. On the other hand, researchconcerning the stability of these systems’ cycle performance, which is necessaryfor practical use, has been reported only from the standpoint of alloy materials, such as the hydrogen ab/desorption cycle performance, changes in the lattice structure, and pulverization of hydrogen absorption [7, 81. However, research on reaction vesselsrelated to stability with cycles, which is indispensable for estimating system endurance, has been scarcely reported [9, IO]. To
922
K. NASAKO et al.
establish the technology for heat utilization systemsusing hydrogen absorbing alloys, more detailed studies must be conducted in the 27% expansion in the alloy [7], and the generation of more than 45 MPa of stressin the alloy bed [lo] during hydrogen absorption. The authors analyzed internal stressin vesselsresulting from hydrogen absorbing alloy expansion. Namely, we assumedthat the pulverization of the alloy is a significant factor in stress generation, and we measured and analyzed the stresson reaction vesselsfor up to 100hydrogen ab/desorption cycles where alloy particle sizesare rapidly changed by pulverization. As a result, it was found that localized internal stressis generated at the bottom of the vessel at a 50 ~01% packing fraction with 1.30 mass% hydrogen ab/desorption cycles, and that this stress not only increaseswith each cycle, but continues to increase even after plastic deformation of the vessel. It was also found that the internal stress occurrence and accumulation depends on the amount of hydrogen ab/desorption. In this paper, we apply the internal stress data mentioned above to actual vessels used in heat utilization systems, that is, performing an analysis of the localized reaction ratio in the vesselthrough simulation, an analysis of the stress distribution in vessels and a study of practical vessel structures capable of relaxing excess stress.
reaction vessel, and the amount of hydrogen abidesorption is assumedto locally exceedthe critical level. 3. REACTION AND STRESS DISTRIBUTION REACTION VESSELS
IN
3.1. Simulation of hydrogenation reaction
The ordinary heat exchanger transfers steady-state heat. On the other hand, the heat exchanger for hydrogen absorbing alloys exchanges the limited reaction heat of the alloy in the vessel. Therefore, the reaction vessel properties obtained by standardizing the packing alloy weight are useful for estimating the vesselperformance of heat utilization systems,in which the vesseltemperature is raised and lowered cyclically. In other words, the reaction vessel performance can be evaluated regardless of the heat exchanger structure by using the heat transfer coefficient per unit of alloy (1 kg) between the alloy and the heat media, the heat radiative coefficient per 1 kg of alloy from the reaction vessel, and the heat capacity per 1kg of alloy in the reaction vessel(including heat capacity of the alloy, heat exchanger and pressure container). In this study, we use the performance terms K,, * A,, K, *A, and C, for the above reason, which are the values of the heat transfer coefficient K,,, K,, multiplied by the heat transfer area A,, A,, and the value of the vesselheat capacity divided by the packing alloy weight, respectively. 2. STRESS GENERATION IN VESSELS Figure 2 shows the simulation model. Here, we adopted a vessel with an internal heat exchanger. This Hydrogen absorbing alloys generate accumulating structure is expected to have a low heat capacity for the stress by hydrogen ab/desorption cycles. This stress reaction vessel, and offer the advantage of raising or accumulation can be estimated as a two-step process in lowering the reaction vesseltemperature. We also divided which agglomeration occurs between the hydride par- the vessel in the heat media pipe direction since a temticles when the hydride packing fraction is higher than a perature difference of at least 5 K was set up in the heat critical level in the initial cycles (Step l), and then fine utilization system. powder generated by pulverization with progressing We assumed that the temperature distribution in the cycles falls down and causesthe localized packing frac- vertical direction from the heat media pipe was uniform tion at the vessel bottom to gradually increase (Step 2) in this model. This is because the effective heat con1111. ductivity of the alloy layer was improved by means such As a result of measurementswith LaNi, 55A10.45, stress as high-density fins in order to decreasethe temperature in up to 100cycles is significantly affected by the amount drop in the alloy layer. Furthermore, we used uniform of hydrogen ab/desorption as shown in Fig. 1, and it was pressure in the alloy layers and ignored the heat transfer found that this stress CJis expressed by the amount of between the divided alloy beds. hydrogen ab/desorption x and the number of cycles NC,, With the model described above, the basic simulation shown as eqn (1). equations can be expressedusing the following eqns (30-0~ = Ao = 10.4N,(x- 1.1) (1) 7). x > 1.1, 0 < NcY< 100
(2)
From this, internal stressincreased linearly at a point of 1.1 mass%. Since this critical value of 1.1 mass% is higher than the effective hydrogen transfer (0.7-0.9 mass%) of ordinary heat pumps [6], stressaccumulation is not expected to occur in an actual reaction vessel. However, in the vessels of heat utilization systems, a temperature difference of at least 5 K is needed between the heat media inlet and outlet in order to obtain thermal power. So, there is a large reaction distribution in the
-K,,
. A,,(T-
T,) = 0
(3)
dxi
iii = a, *rn;dt
>
= V-C,-p,(T,,- T,J
(5)
RELAXATION
OF INTERNAL
STRESS GENERATED
IN HYDROGEN
: LaNi4.,,
Packing
fraction of alloy
ABSORBING
ALLOY
VESSELS
923
Alo.
: 50 ~01%
(T=cTi +10.4Nq(X-1.1)
Hydrogen content x : 1.30 mass%
40
60
80
100
120
Number of cycles, A&, Fig. 1. Effect of absorbed maximum hydrogen content on vessel surface stress in one hydrogen ab/desorption
P, = func (T, x)
(6)
$=k*exp(g)*ln(y).(l-2)”
(7)
Here the heat balance eqn (3) consists of the first term as the reaction heat, the second term as the heat capacity change in the reaction vessel,the third term as the exchange heat between the alloy and the heat media, and the fourth term as the exchange heat between alloy and atmosphere. Equation (4) indicates the relationship between the hydrogen flow rate and the hydrogen content of the alloy. Equation (5) expresses the temperature change of the heat media by heat exchange between the alloy and heat transfer media. Equation (6) expressesthe fitting curve [12] of the LaNi,,,,Al,,, P-C isotherms as
G Xl
T2 x2
G
TN-I TN XN-I
&
t n Fig. 2. A model for the hydrogenation simulation of hydrogen absorbing alloy vessels.
cycle
shown in Fig. 3. In this equation, the relationship between equilibrium hydrogen pressure P, and temperature T is set according to eqn (8).
(8) Equation (7) shows the reaction rate which is induced by the shrinking core model [13, 141.In this equation, the effect of pressure on the reaction rate was adopted [(P- P,)/P,] which showed fairly good coincidence [15, 161. 3.2. Calculation results of’ reaction ratio and stress distribution
Equations (3)(7) were calculated by a differential method of minute time with 10 divided parts. Here, the alloy properties (equilibrium and dynamic) and thermophysical properties of the reaction vessel used were those of our -20°C refrigeration system [6]. These are summarized in Table 1. The initial conditions are set up as a hydrogen content of 0.20 mass%, a vessel temperature and atmosphere temperature of 2O”C, and a hydrogen pressure of 0.05 MPa. Figure 4 shows the calculated results. The horizontal axis indicates the time after the start of the reaction, the vertical axis shows the hydrogen content in each bed, and the symbol N in the figure indicates the bed numbers. From this figure, it is found that the reaction is fastest at the heat media inlet (N = l), and the latter beds follow it. Since the total reaction rate of the vessel, which is
924
K. NASAKO ef al. 10 I
Alloy : LaNi,,,,Al,,,
0.0
0.4
0.8
1.2
1.6
Hydrogen content / mass% Fig. 3. P-C isotherms of LaNi,,5A10,,, alloy.
Table 1. The values of alloy, heat media and reaction vesselproperties used in the hydrogenation simulation Alloy properties
3.64x IO4[J*mol H;‘] 4.2 x lo4 [J . mol H; ‘1 9.1 x lo4 [mass% OS-‘1 1.43 [mass%] 4.18x103[J.kg-‘-K-l] 1.Ox 10’ [kg * m-‘1 7x 10-6[m’*s-‘]* 40 [w - K-l]* 0.05 w*K-‘I* 1000[J-K-‘]*
Heat media properties Reaction vesselproperties
* Per 1 kg of alloy
expressed by the sum of the reaction rates in each bed,
decreaseswith the progressing reaction, we switch a hydrogenation reaction to a reversereaction of dehydrogenation to perform cycle operations in heat utilization systems. If, for example, the effective hydrogen transfer is 0.9 mass%, the reaction is switched at 1390 s as shown in Fig. 4. The hydrogen content in each bed at this time is N = 1, 4, 7 and 10 at 1.26, 1.16, 1.05 and 0.93 mass%, respectively. Becausethese hydrogen content values are equal to the maximum
amount
of hydrogen
ab/de-
sorption in each bed, the stressaccumulation at 100cycles is shown in Fig. 5 from eqn (1). We therefore expect that a significant excessof stress occurs near the heat media inlet, and it is found that this stressexceedsthe proof stressfor Cu (Z 100 MPa) and is
near the proof stress for stainless steel (200 MPa) at N= 1.
4. STUDIES FOR RELAXING INTERNAL
STRESS
4.1. Relaxing stress by unifving reaction ratio in each bed
We studied ways to reduce stressaccumulation in reaction vesselsfrom the standpoint of the vessel structures. It is possible to reduce stress accumulation by unifying the reaction ratio throughout the vessel, and this can be
achieved by exchanging heat between the heat media inlet (N = 1) and the outlet (N = 10). Figure 6 shows a model that exchanges heat between alloy bed i and N-i+ 1. Here, the heat balance can be
RELAXATION
OF INTERNAL
STRESS GENERATED
IN HYDROGEN
ABSORBING
I
0
600
1200
1800
Time / s Fig. 4. Relationship
between hydrogen content and reaction time.
Part in the vessel
Fig. 5. Relationship
between inner stress and part in the vessel.
ALLOY
I
2400
VESSELS
925
926
K. NASAKO et al. Hydride bed i
T2
and show the difference by the factor of K,, *A,, which means the heat transfer between bed i and N-i+ 1. Figure 8 shows the stress distribution at 100 cycles using the sameeffective hydrogen transfer of 0.9 mass%. From this, it is found that stressis significantly reduced by a heat exchange of at least 20 W *K-’ between alloy i and N-i+ 1. 4.2. Reaction vessel structure
/
II
/
TN
TN-I
XN
XN-1
\ Hydride bed
ri t N-i+1 Fig. 6. A revised model for hydrogenation simulation of a hydrogen absorbing alloy heat exchanger turned up with the heat media inlet and outlet.
expressedby eqn (9), which consists of eqn (3) and heat transfer between bed i and N-i+ 1.
-Ka; A,Vi-
Ta)-Ks;A,(T,-
TN--I+‘) = 0
(9)
With the new model described above, we calculated the reaction ratio of each bed by eqns (9) and (4)-(7). Figure 7 shows the results through simulation using the same numbers of divided beds and the same initial conditions. In this figure, we plot only the reaction ratio at alloy bed N = 1 for which stressaccumulation is highest,
a. Heat transfer model for the heat exchanger of the hydrogen absorbing alloy vessel
The structure of a heat exchanger, which exchanges heat between the heat media inlet and outlet, can be constructed by a tube-in-fin type heat exchanger. We therefore studied the possibility of simultaneously achieving the conditions of KS,*A, = 40 W *K-’ (heat transfer between alloy bed i and heat media) and KS,+A, > 20 W * K-’ (heat transfer between alloy bed i and N-i+ 1) in an actual heat exchanger. Figure 9 shows the heat transfer model between the alloy bed i and the heat media or the facing alloy bed N - i+ 1. In this model, we simply used a flat heat transfer surface for the heat media although the heat transfer surface of the tube-in-fin type heat exchanger is actually round. We assumed that the alloy packed between the fins reacts at the volumetric center. We also supposed that the heat flux between the alloy bed and the heat media is represented from A to B, and the heat flux between alloy bed i and N-i+ 1 is represented from A to C as shown in Fig. 9 becauseof 1, <
1.4
0
600
1200
1800
2400
Time I s Fig. 7. Relationship between hydrogen content and reaction time of the revised model.
RELAXATION
OF INTERNAL
STRESS GENERATED
IN HYDROGEN
ABSORBING
ALLOY
150 cl % .
100
f 2 50
0
1
2
3
4
5\6
7
8
9
10
P&t in the vessel
Fig. 8. Relationship
.. . Heat
between inner stress and part in the vessel of the revised model.
a.
media
>
j
:.
! Heat transfer surface
riz-I
L-4 I
1-m11111)
,
‘II.
-b’
.
fl ,
Fin Hydrogen absorbing
4 Heat media Fig. 9. Heat transfer model of heat exchanger for hydrogen absorbing alloy.
alloy
VESSELS
921
928
K. NASAKO et al.
Heat m;dia inlet # 9.9 (Heat media pipe) # 8.0 (H2 filter pipe)
A-A’ cross section
(Unit : mm)
Fig. 10. Structure of a hydrogen absorbing alloy vessel.
the resistance in alloy bed R,, fin material Rb and the contact surface between the heat transfer plate and heat media R, as shown in eqn (10). Heat resistance RAmC between alloy bed i and N-i+ 1 is similarly expressedas shown in eqn (11). In addition, the heat transfer performance per unit alloy weight KS,*A,, KS *A, is expressed as eqns (13) and (14) respectively [m: alloy weight packed in the bed i as shown in eqn (12)]. La
2 R,+Rb+R,
=
(1, - lN4 1 1 1 h’ d’
s
1 + (1,/2)d,.& + (lP/2)ddYx,
hII2
RAc = R,+ Rb,+ R,, = 2(R,+R,)
(1o)
ductivity of the fin and the alloy bed are 237 W em-’ * K-’ and 0.5 We m-’ * K-’ [ 171,respectively. The heat transfer coefficient between the heat transfer surface and the heat media cc,is assumedto be 4000 W * K-‘. From this calculation, it is found that the fin-in-tube heat exchanger can simultaneously attain the heat transfer of 40 W * K-i between the alloy and the heat media as well as the heat transfer over 20 W. K-’ between alloy beds i and N-i+ 1, which are needed in order to relax stress. The structure can be scaled up using the vessel structure shown in Fig. 10,and it is important for relaxing inner stress to set the heat media inlet and outlet closer to each other.
(11)
5. CONCLUSION
(12)
(1) The stress accumulation which occurs in hydrogen
X, *4 = UU?-B*4
(13)
KS, * A, = 1/( RA-C * m)
(14)
b. Heat exchanger for relaxing stress
If we assumea fin pitch lP of 1 mm, a fin thickness I, of 0.1 mm and an alloy bed height /,, of 13 mm as shown in Fig. 9, we get 39.5 and 36.7 W * K-’ for KS,*A, and KS,- A,, respectively, per 1 kg of alloy (apparent density: 4 x lo3 kg*m3) by using eqns (lOHl4). Here, thermal con-
absorbing alloy beds was clarified by the relationship of the ab/desorption quantity and the number of ab/desorption cycles. c-9 It was found that there is a great possibility for excess stressaccumulation to occur at the heat media inlet of an actual reaction vesselfrom the analytical results of the hydrogenation simulation. (3) We showed that heat exchange between the heat media inlet and outlet in the reaction vessel makes the local reaction more uniform, and simultaneously relaxes stress accumulation.
RELAXATION
OF INTERNAL STRESS GENERATED IN HYDROGEN ABSORBING ALLOY VESSELS
work was supported by NED0 (New Energy and Industrial Technology Development Organization) as a part of the Sunshine Project under the Ministry of International Trade and Industry of Japan. Acknowledgement-This
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Thermal Engineering Joint
4. Nasako, K., Yonesaki, T., Yonezu, I., Fujitani, S., Saito, T., Moroto, M., Osumi, M. and Furukawa, N., Proceedings qf the ISES Solar World Congress, Vol. 2. Pergamon Press, Oxford, 1990,p. 1343. 5. Nasako, K., Yonesaki, T., Satoh, K., Imoto, T., Fujitani, S., Hiro, N., Hirose, N., Fukushima, K., Saito, T. and Yonezu, I., Z. Phys. Chem., 1994,183,235. 6. Nasako, K., Hiro, N., Fukushima, K., Fujitani. S., Yonezu,
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