On exergy losses in AMR hydrogen liquefiers

~ ) Pergamon

Int. J. Hydrogen Energy, Vol. 19, No. 5, pp. 447--452,1994 Copyright © 1994International Associationfor HydrogenEnergy Elsevier ScienceLtd Printed in Great Britain. All rights reserved 0360-3199,/94$6.00+ 0.00

ON EXERGY LOSSES IN AMR HYDROGEN LIQUEFIERS L. ZHANG,) S. A. SHER1F,JfT. N. VEZIROGLU~and J. W. SHEFFIELD~ *University of Miami, Department of Mechanical Engineering, Coral Gables, FL 33124, U.S.A. 1"University of Florida, Department of Mechanical Engineering Gainesville, FL 32611, U.S.A. ~,University of Miami, Clean Energy Research Institute, Coral Gables, Florida 33124, U.S.A. §University of Missouri-Rolla, Department of Mechanical and Aerospace Engineering, and Engineering Mechanics, Rolla, MO 65401, U.S.A. (Received for publication 7 June 1993)

Abstract-This paper reports on exergy losses and some performance features of a three-stage active magnetic regenerative (AMR) hydrogen liquefier in which the effects of material bed size, helium flow rate, heat exchanger parameters and magnetic field strength are examined. Results are presented in terms of the cooling capacity and onecycle exergy losses for the different stages.

B Qc T~ Th

NOMENCLATURE Magnetic field (tesla) Cooling load Helium fluid outlet temperature after heating the magnetic material bed (K) Hot end temperature of the auxiliary refrigerator

(K) T~ To T,c T,h Tw

Nitrogen boiling point temperature (K) Curie temperature of magnetic material (K) Stage cold temperature of magnetic liquefier (K) Stage hot temperature of magnetic liquefier (K) Helium fluid outlet temperature after cooling magnetic material bed (K)

INTRODUCTION Magnetic refrigeration research has intensified in recent years because of the potential of magnetic refrigerators for greater efficiency, high reliability and more rugged construction than the present gas-cycle refrigerators. Previous investigations are many and include those of Schroeder et al. [11, Seyfert [2"1, Helvensteijn et al. [31, Savage et al. [4], Serlemitsos et al. [5], Smith et al. [6], Numazawa et al. [71, Li et ai. [8], Kral and Barclay [91, DeGregoria et al. [10-12], Zimm et al. [13], Janda et al. [14] and Carpetis [15]. Additional details can be found in Sherif and Zhang [ 161. This paper reports on exergy losses associated with a three-stage AMR hydrogen liquefier. Effects of material bed size, helium flow rate, heat exchanger parameters and magnetic field strength are investigated.

SYSTEM DESCRIPTION The system considered in this paper is a three-stage AMR hydrogen liquefier. This system is described in some detail in Waynert et at. [171, but is modified here to the system shown in Fig. 1. Three temperature ranges of 20-40K, 40-60K and 60-77K correspond to three stages of an active magnetic regenerative cycle. For identification purposes, the lowest temperature range stage will be labeled as the first stage. Heat is rejected to a 77K liquid nitrogen boil-off tank at the third stage. The boiled-off nitrogen is used to precool the incoming hydrogen gas from 300K to near 77K in a series of heat exchangers (Sherif and Zhang [161). The modifications employed in the system in question include the addition of an auxiliary classical refrigerator's box having two classical gas-cycle refrigerators that operate between the first and second stages and between the second and third stages, and two pipes with separate valves for the two lower stages. The aim of the first modification is to reduce the helium temperature. The aim of the second modification is to ensure that helium can be cooled under the specified cooling load of each stage. Each of the three stages operates on a cycle comprised of four processes. The magnetic material bed is magnetized isentropically by applying a magnetic field, followed by releasing heat to the cycled cool helium fluid. The hot helium fluid then releases its heat to an auxiliary gascycle refrigerator. The magnetic material bed is then demagnetized and the cycled helium is cooled. Finally, the cool helium cools the hydrogen gas. Also, an offset strip plate-fin heat exchanger is employed in six heat 447

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Fig. 1. Three-stage AMR hydrogen liquefier. exchanger positions in the overall system, as suggested by Zukauskas [18]. For details pertaining to the assumptions made and calculation procedures employed, the reader should consult Sherif and Zhang FI6]. PERFORMANCE SUMMARY Since the heat released due to ortho-para conversion at different temperatures is different, the size of the magnetic material bed of the three stages should be different to satisfy the respective stage cooling load requirements.

Figures 2a and b show the magnetic material bed volume as functions of both the cooling capacity and exergy losses for the three stages. From Fig. 2a we can see that the cooling capacity increases almost linearly with the bed volume for all three stages. However, the rates of increase of the cooling capacity are different, with the smallest increase being associated with the lower temperature stage. Since increasing the material bed volume requires increasing the size of the superconductor magnet, the system's performance cannot be improved solely by increasing the bed size. Also, since the materials used in magnetic refrigerators are usually expensive rare metal

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compounds, increasing the material bed size is not an economical way to improve the performance. Since for the same material bed volumes the cooling capacities are different for all three stages, different volum,~ for the material bed should be used for proper operation. Results pertaining to the cooling capacity and cxergy loss for each cycle are listed in Table 1. As can be seen, the lower the Curie temperature, the larger the cooling capacity and the smaller the exergy loss. The Curie temperature should be higher than the magnetized temperature, thus limiting the minimum Curie temperature of any section by the section magnetized temperature and the magnetic field strength. Under normal circumstances, the larger the magnetic field, the larger the cooling capacity. However, in his case, the magnetic field has little effect on the cooling capacity, primarily because the internal energy at a high field and low temperature is smaller than that at a low field and high temperature. Figure 3 shows the difference between the helium output temperature and the stage cold temperature (Tc T,c) as functions of both the cooling capacities and exergy losses for each cycle of the three stages. As seen in Fig. 3a, the cooling capacity monotonically increases with the temperature difference; however, the exergy losses do not change much with increasing temperature difference (see Fig. 3b). Therefore, higher values for Tw and lower values for T¢ are normally recommended. However, T,, and Tc are dependent upon the bed heat transfer performance. Under certain circumstances, the required cooling capacity cannot be achieved due to some limitations on the heat transfer performance of the material bed [see discussion items (5) and (6) below]. Trying to remedy this problem by increasing the temperature difference leads to increasing the helium mass flow rate, which requires an increase in the helium inlet pressure and a consequent increase in the pumping power. Figure 4 demonstrates that longer isofield times help achieve higher cooling capacities. Unfortunately, the associated exergy losses are also larger. In other words,

Table 1. Cooling capacities for different Curie temperature ranges

Curie temperature range (K)

Cooling

One-cycle exergy losses

First section

Last section

capacities Q~(w)

First stage

34.0 35.0 36.0

70.0 80.0 90.0

2.67 2.71 2.28

88.10 96.87 246.3

Second stage

59.0 60.0 61.0

95.0 105.0 I ! 5.0

3.78 3.53 3.28

58.12 91.70 76.22

Third stage

83.0 84.0 85.0

114.0 122.0 131.0

3.93 3.79 3.57

30.20 44.57 37.85

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temperature and stage temperature of (a) cooling capacity of the three stages; (b) one-cycle exergy loss of the three stages.

adiabatic process time of (a) cooling capacity; (b) one-cycle exergy loss.

increasing the cooling capacity requires increasing the isofield process time, while increasing the cooling capacity and reducing exergy losses require parametric optimization for every stage. Higher operating frequencies result in larger cooling capacities and higher exergy losses (see Fig. 5). However, higher frequencies may result in higher frictional heating as well. Also, the frequency is restricted by the performance of the moving parts in the system. As stated in Sherif and Zhang [191 regarding the frequency effect, there is always an optimal operating frequency that takes into account all the heat losses. The exergy losses per cycle are the sum of the exergy losses from the four processes. Table 2 lists the exergy loss distribution of all four processes for the three stages.

As can be seen, maximum exergy losses take place during the bed demagnetization and helium heating processes. This is primarily because the bed specific heat under zero magnetic field is relatively large. A material with a relatively small zero-magnetic-field specific heat has a better performance from an exergy loss point of view.

CONCLUSIONS Based on the aforementioned performance features, one may conclude the following: (1) For a given volume of the magnetic material, the shape should be one that maximizes heat transfer between the material bed and the helium fluid.

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(2) The material Curie temperature distribution of each stage should be similar to that of the stage bed magnetization. Also, materials having small specific heats in a zero magnetic field are more likely to improve the performance of the system. (3) The lower stage material bed heat transfer performance is important in achieving higher cooling capacities. (4) To achieve lower helium outlet temperatures and larger cooling capacities, the helium mass flow rate should be increased. This requires higher helium inlet pressures. Another method is to increase the operating frequency. (5) Since increasing the duration of the isofield process results in increasing both the cooling capacity and exergy losses unevenly, optimized variables should be used for each stage with the objective of maximizing the cooling capacity and minimizing the exergy losses.

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Acknowledgements- This work was supported by a grant from the U.S. Department of Energy under Contract No. XL-918168-1. Support from the Clean Energy Research Institute and the Department of Mechanical Engineering at the University of Miami is also gratefully acknowledged. The second author would like to acknowledge the help of Mrs Alice A. Jempson of the University of Florida.

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REFERENCES 1. E. Schroeder, G. Green and J. Chafe, Performance prediction of a magnetocaloric refrigerator using a finite element model. Adv. Cryogenic EnonO35, 1149-1155 (1990). 2. P. Seyfert, Research on magnetic refrigeration at CEA Grenoble. Adv. Cryogenic Enon0 35, 1087-1096 (1990). 3. B. P. M. Helvensteijn and A. Kashani, Conceptual design of a 0.1 W magnetic refrigerator for operation between 10K and 2K. Adv. Cryogenic Enon0 35, 1105 1123 (1990). 4. M. L. Savage, P. Kittel and T. Rocllig, Salt materials testing for a spacecraft adiabatic demagnetizaion refrigerator. Adv. Cryogenic Enono 35, 1439-1446 (1990). 5. A. T. Serlemitsos, B. A. Warner, S. Castles, S. R. Breon, M. San Sebastian and T. Hair, Adiabatic demagnetization refrigerator for space use. Adv. Cryogenic Engno 35, 1431-1438 (1990).

Table 2. Exergy loss distribution for one cycle First stage Bed magnetization and cooling by helium Hot helium heat release to the refrigerator Bed demagnetization and helium heating Heat removal from hydrogen by the cold helium

10.25 0.0012

Second stage 1 !.39 0.0004

Third stage 12.25 0.0002

70.13

40.81

14.89

8.73

4.55

3.07

452

L. ZHANG et al.

6. J. L. Smith, Jr, Y. lwasa and F. J. Cog,swell, Material and cycle considerations for regenerative magnetic refrigeration. Adv. Cryogenic Enono 35, 1157-1164 (1990). 7. T. Numazawa, H. Kimura, M. Sato, H. Maeda, M. Takahashi and H. Nakagnme, Analysis of a magnetic refrigerator operating temperature between 10K and 1.4K. Proc. Sixth Int. Cryocoolers Conf., Plymouth, MA, Voi. 2, pp. 199-213 (1990). 8. R. Li, O. Yoshida, T. Hashimoto, T. Kuriyama and H. Nakagom¢, Measurement of ineffectiveness on regenerators packed with magnetic regenerator materials between 4 and 35K. Adv. Cryogenic Engng 35, 1183-1190 (1990). 9. S. F. Kral and J. A. Barclay, Magnetic refrigeration: a large cooling power cryogenic refrigeration technology. Proc. Cryo '90 Conf., Binghampton, NY. Plenum Press, New York (1990). 10. A.J. DeGregoria, J. A. Barclay, P. J. Claybaker, S. R. Jaeger, S. F. Kral, R. A. Pax, J. R. Rowe and C. B. Zimm, Preliminary design of a 100W 1.8K to 4.7K regenerative magnetic refrigerator. Adv. Cryogenic Enong 35, 1125-1131 0990). 11. A. J. DeGregoria, P. J. Claybaker, J. R. Trueblood, R. A. Pax, T. M. Stankey, S. F. Kral and J. A. Barclay, Initial test results of an active magnetic regenerative refrigerator. Proc. Fourth lnteragency Meeting of Cryocoolers, Plymouth, MA, pp. 277-290 (1990). 12. A. J. DeGregnria, L. J. Feuling, J. F. Laatsch, J. R. Rowe, J. R. Trueblood and A. A. Wang, Test results of an active magnetic regenerative refrigerator. Adv. Cryogenic EnonO 37B, 875-882 (1992).

13. C. B. Zimm, E. M. Ludeman, M. C. Severson and T. A. Henning, Materials for regenerative magnetic cooling spanning 20K to 80K. Adv. Cryogenic Engno 3715, 883-890 (1992). 14. D. Janda, A. J. DeGregoria, J. Johnson and S. Krai, Design of an active magnetic regenerative hydrogen liquefier. Adv. Cryogenic Engno 37, 891-898 (1992). 15. C. Carpetis, A preliminary numerical study of magnetic refrigeration, Proc. Sixth Int. Cryocoolers Conf., Plymouth, MA, Vol. 2, pp. 215-230 (1990). 16. S.A. Sherif and L. Zhang, Exergy analysis of AMR liquefaction systems, in T. N. Veziro~u (Ed.) Solar Hydrogen Energy System. Annual Progress Report, Contract No. DOE # XL-9-18168-1; prepared for the U.S. Department of Energy/Solar Energy Research Institute by the Clean Energy Research Institute, University of Miami, FL, C2.1-C2.30 (1991). 17. J. A. Waynert, A. J. DcGregoria, R. A. Foster and J. A. Barclay, Magnetic heat pumps for hydrogen liquefaction, l lOth ASME Winter Annual Meeting, Industrial Heat Pump Session, San Francisco, CA (1989). 18. A. Zukauskas, High Performance Sinole-phase Heat Exchangers. Hemisphere, New York (1989). 19. S. A. Sherif and L. Zhang, Magnetic liquefaction, in T. N. Veziro~u (Ed.) Solar Hydrogen Energy System, Annual Progress Report, Contract No. DOE #XL-9-18168-1; Prepared for the U.S. Department of Energy/SERI by the Clean Energy Research Institute, University of Miami, FL, C2.1-C2.69 (1990).