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Simulation of current and temperature distribution in YBCO bulk's electrical contact
Physica C 412–414 (2004) 668–672 www.elsevier.com/locate/physc
Simulation of current and temperature distribution in YBCO bulk’s electrical contact T. Imaizumi a
a,d,*
, N. Yamamoto a,d, K. Sawa a, M. Tomita M. Murakami c,d, I. Hirabayashi d
b,d
,
Faculty of Science and Technology, Department of System Design Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan b Railway Technical Research Institute, 2-8-38 Hikari-cho, Kokubunji-shi, Tokyo 185-8540, Japan c Shibaura Institute of Technology, 3-9-14 Shibaura, Minato-ku, Tokyo 108-8548, Japan d ISTEC-Superconductivity Research Laboratory, 1-10-13 Shinonome, Koutou-ku, Tokyo 135-0062, Japan Received 29 October 2003; accepted 19 January 2004 Available online 2 July 2004
Abstract We have proposed a mechanical switch of high-temperature superconductor (HTS) as a mechanical persistent current switch (PCS). Two YBCO bulks are mechanically mated and the current flows through contact. However, the contact resistance was too large to work as PCS. In previous work, we polished the contact surface in order to reduce the contact resistance; however, we were not able to reduce it easily. So, in addition to polishing the contact surface, we deposited the metals on the surface to reduce the contact resistance. Accordingly, the contact resistance can be drastically reduced. Based on the experimental results, we analyzed the temperature of the switch with Finite Element Method (FEM). The axisymmetrical three-dimensional model is used, and the temperature distribution is numerically obtained as a function of the current density. We have expected that analytical results would make a contribution to reduce the contact resistance. 2004 Elsevier B.V. All rights reserved. PACS: 74.72.Bk; 74.72.)h Keywords: YBCO; Persistent current switch; Contact resistance; FEM
1. Introduction
*
Corresponding author. Address: Faculty of Science and Technology, Department of System Design Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan. Tel.: +81-45-563-1141x43057; fax: +81-45-566-1720. E-mail address: [email protected] (T. Imaizumi).
Recently, various studies of high temperature superconductor (HTS) have been made. We focused attention on superconducting magnetic energy storage system (SMES) which is one of HTS applications. In SMES a persistent current switch (PCS) is used between a power source and a superconducting coil. There are three types of
0921-4534/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.01.086
T. Imaizumi et al. / Physica C 412–414 (2004) 668–672
PCS, magnetic, thermal and mechanical ones. Among these types, a mechanical switch is thought to be better in speed and off-resistance. A mechanical switch using metallic superconducting materials has been reported in PCS applications [1]. But no mechanical switch using HTS material has been reported. Since last three years we have studied a mechanical switch using YBCO [2–4]. In such mechanical contact a transfer between a low resistance range and a high one was observed similar to quench phenomena of the superconducting material. In this paper the experimental result and the simulation of current and temperature distribution are reported.
2. Experimental 2.1. Experimental procedure A switching material is 1 cm cube of a YBCO bulk similar to the previous report [2–4]. The bulk is protected by an epoxy resin except for the contact surface. Two types of contact surface are used. One is only polished with abrasive papers (Case 1); another is polished and deposited with silver (Case 2). The contact voltage is measured by the four-terminal method. In previous reports [2–4], the details of experimental procedure are described. 2.2. Experimental results Fig. 1 shows contact resistance vs current. In Case 1, the rising current stage of the first cycle is high in resistance and peculiar in behavior. However, since the falling current stage of the first cycle, the transfer between low and high contact resistance ranges is observed every cycle. In the low resistance range its value is hoped to be zero, but actually a certain value remains, which is called ‘‘residual resistance’’ in this paper. It can be found that the residual resistance is about 0.2 mX in average. The current of the transition from the superconducting state to the normal state is about 18 A. This current is called ‘‘transfer current’’ in this paper.
669
Fig. 1. Contact resistance vs current.
In Case 2, the resistance is low and the behavior is stable since the rising current stage of first cycle. It can be found that the residual resistance is about 0.09 mX in average. The value is about half of Case 1. This is because the contact spot area increased by depositing a soft metal on the hard surface. The transition from the superconducting state to the normal state was not appeared at maximum of experimental setup 30 A in Case 2.
3. Simulation of current and temperature distribution 3.1. Modeling of contact spot The bulk and contact spot are modeled as an axisymmetrical three-dimensional structure shown in Fig. 2. The contact spot is a cylinder which is a radius of r and a length of d. According to Ref. [5], the resistance of contact spot is represented as follows
Fig. 2. Analytical model of contact spot.
670
R¼
T. Imaizumi et al. / Physica C 412–414 (2004) 668–672
qd q þ 2 pr 2r
ð1Þ
where q is a resistivity of contact spot, and the second term is a constriction resistance. In Case 1 the resistivity of contact spot is represented as follows R q¼ d þ 2r1 pr2
ð2Þ
R ¼ 0:2 mX is substituted from the experimental result. On the other hand, in Case 2 the resistivity of contact spot is represented as follows pr q¼ 1þ ð3Þ q 2d Ag where qAg is the resistivity of silver at 77 K, 1.8 · 108 · 0.2 X m.
of the normal state, and K and m are determined for the resistivity and the first derivative to be continuous at J ¼ Jc2 . The resistivity of the normal state is represented as follows q ¼ qn ¼ q0 þ aH
ð8Þ
at H P Tc
The critical current density is also dependent on a temperature, which is represented as follows 1:98 H2 Jc / 1 2 at H < Tc ð9Þ Tc Fig. 3 shows the resistivity of YBCO used for the simulation. 3.3. Current and temperature distribution by FEM The current density J satisfies the following equation
3.2. Resistivity of YBCO
div J ¼ 0
The resistivity of YBCO is dependent on current density J and temperature H. Generally the electric field E of a high temperature superconductor is represented as follows n J E ¼ Ec ð4Þ Jc
Therefore, J is represented by a current vector potential T. rot T ¼ J
ð10Þ
ð11Þ
The electric field E is static, and the followings are obtained. E ¼ qJ
ð12Þ
where Ec is an electric field at the critical current density Jc , 1.0 · 104 V/m and n is an index of a high temperature superconductor. Eq. (4) is converted to q–J equation as follows n1 J q ¼ qc ; Ec ¼ qc Jc ð5Þ Jc However, Eq. (5) represents resistivity at the rising part around the critical current. The transition from the superconducting state to the normal state should be also represented, so that the following equations are used n1 J q ¼ qc at 0 < J < Jc2 ð6Þ Jc q ¼ qn
K Jm
at Jc2 6 J
ð7Þ
Eq. (6) is connected to Eq. (7) at J ¼ Jc2 . Jc2 is current density at q ¼ 0:5 qn . qn is the resistivity
Fig. 3. Resistivity of YBCO used for the simulation.
T. Imaizumi et al. / Physica C 412–414 (2004) 668–672
rot E ¼ 0
ð13Þ
Eq. (14) can be derived from Eqs. (11)–(13) rotðqrot TÞ ¼ 0
671
Fig. 5 is the temperature distribution of the whole bulk obtained by FEM before transfer, and
ð14Þ
The Galerkin method is applied to Eq. (14) and the integration equation for obtaining an approximation solution is obtained. The current density distribution can be found by solving the integration equation by FEM. From the current density distribution, the heat generation is calculated by the equation 2 Q_ ¼ qjJj
ð15Þ
The steady-state temperature distribution is also estimated from the following equation by FEM 1 o oH o oH r j þ þ Q_ ¼ 0 ð16Þ r or or oz oz where j is a thermal conductivity. [K]
3.4. Simulation results
7.70e+01
Fig. 4 is one of the current distributions. From Fig. 4, it turns out that the current is concentrating on the contact spot.
7.84e+01
7.98e+01
8.12e+01
8.26e+01
Fig. 5. Temperature distribution of whole bulk.
[A/m2] 2.50e+05
9.68e+07
1.93e+08
2.90e+08
Fig. 4. Current distribution.
3.86e+08
Fig. 6. Temperature distribution around contact spot.
672
T. Imaizumi et al. / Physica C 412–414 (2004) 668–672
Figs. 7 and 8 that the contact spot radius of Case 1 is about 0.09 mm and that of Case 2 is more than about 0.13 mm. On the contrary, it is confirmed that the transfer current increases when the contact spot radius enlarges.
4. Conclusion
Fig. 7. Simulation result of transfer current vs contact spot radius in Case 1.
Two YBCO bulks were mechanically mated and the current flowed through the contact. This phenomenon was simulated by using an axisymmetrical three-dimensional model. The current and the temperature distributions of the switch were obtained by FEM. The temperature distribution showed that the heat generated at the contact spot has stayed without diffusing. The contact spot radius was able to be estimated from the simulation. In order to reduce the residual resistance and to increase the transfer current through the experiment and the simulation, it was reconfirmed that the contact spot area must be enlarged.
Acknowledgements
Fig. 8. Simulation result of transfer current vs contact spot radius in Case 2.
the temperature distribution around the contact spot is shown in Fig. 6. It seems that the temperature of the whole bulk is 77 K of liquid nitrogen temperature. However, the temperature only around the contact spot is rising. Figs. 7 and 8 show the transfer current vs contact spot radius in Case 1 and Case 2 obtained by FEM. The dotted lines in Figs. 7 and 8 show the experimental transfer current. Although the contact spot radius of experiment is a certain fixed value, it cannot be specified. It is guessed from
This work was supported by the New Energy and Industrial Technology Development Organization (NEDO) as Collaborative Research and Development of Fundamental Technologies for Superconductivity Applications.
References [1] S. Ohtsuka, H. Ohtsubo, T. Nakamura, J. Suehiro, M. Hara, Cryog. Jpn. 32 (10) (1997) 473 (in Japanese). [2] K. Sawa, M. Suzuki, M. Tomita, M. Murakami, IEEE Trans. 25 (3) (2002) 415. [3] T. Sakai, N. Yamamoto, K. Sawa, M. Tomita, M. Murakami, In: Proc. 48th IEEE Holm Conf., 2002, pp. 206–211. [4] N. Yamamoto, T. Sakai, K. Sawa, M. Tomita, M. Murakami, Physica C: Supercond. 392–396 (Part 1) (2003) 729. [5] R. Holm, Electrical Contacts, Fourth ed., Springer, New York, 1979, chapter 1, pp. 1–18.
Simulation of current and temperature distribution in YBCO bulk’s electrical contact T. Imaizumi a
a,d,*
, N. Yamamoto a,d, K. Sawa a, M. Tomita M. Murakami c,d, I. Hirabayashi d
b,d
,
Faculty of Science and Technology, Department of System Design Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan b Railway Technical Research Institute, 2-8-38 Hikari-cho, Kokubunji-shi, Tokyo 185-8540, Japan c Shibaura Institute of Technology, 3-9-14 Shibaura, Minato-ku, Tokyo 108-8548, Japan d ISTEC-Superconductivity Research Laboratory, 1-10-13 Shinonome, Koutou-ku, Tokyo 135-0062, Japan Received 29 October 2003; accepted 19 January 2004 Available online 2 July 2004
Abstract We have proposed a mechanical switch of high-temperature superconductor (HTS) as a mechanical persistent current switch (PCS). Two YBCO bulks are mechanically mated and the current flows through contact. However, the contact resistance was too large to work as PCS. In previous work, we polished the contact surface in order to reduce the contact resistance; however, we were not able to reduce it easily. So, in addition to polishing the contact surface, we deposited the metals on the surface to reduce the contact resistance. Accordingly, the contact resistance can be drastically reduced. Based on the experimental results, we analyzed the temperature of the switch with Finite Element Method (FEM). The axisymmetrical three-dimensional model is used, and the temperature distribution is numerically obtained as a function of the current density. We have expected that analytical results would make a contribution to reduce the contact resistance. 2004 Elsevier B.V. All rights reserved. PACS: 74.72.Bk; 74.72.)h Keywords: YBCO; Persistent current switch; Contact resistance; FEM
1. Introduction
*
Corresponding author. Address: Faculty of Science and Technology, Department of System Design Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan. Tel.: +81-45-563-1141x43057; fax: +81-45-566-1720. E-mail address: [email protected] (T. Imaizumi).
Recently, various studies of high temperature superconductor (HTS) have been made. We focused attention on superconducting magnetic energy storage system (SMES) which is one of HTS applications. In SMES a persistent current switch (PCS) is used between a power source and a superconducting coil. There are three types of
0921-4534/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.01.086
T. Imaizumi et al. / Physica C 412–414 (2004) 668–672
PCS, magnetic, thermal and mechanical ones. Among these types, a mechanical switch is thought to be better in speed and off-resistance. A mechanical switch using metallic superconducting materials has been reported in PCS applications [1]. But no mechanical switch using HTS material has been reported. Since last three years we have studied a mechanical switch using YBCO [2–4]. In such mechanical contact a transfer between a low resistance range and a high one was observed similar to quench phenomena of the superconducting material. In this paper the experimental result and the simulation of current and temperature distribution are reported.
2. Experimental 2.1. Experimental procedure A switching material is 1 cm cube of a YBCO bulk similar to the previous report [2–4]. The bulk is protected by an epoxy resin except for the contact surface. Two types of contact surface are used. One is only polished with abrasive papers (Case 1); another is polished and deposited with silver (Case 2). The contact voltage is measured by the four-terminal method. In previous reports [2–4], the details of experimental procedure are described. 2.2. Experimental results Fig. 1 shows contact resistance vs current. In Case 1, the rising current stage of the first cycle is high in resistance and peculiar in behavior. However, since the falling current stage of the first cycle, the transfer between low and high contact resistance ranges is observed every cycle. In the low resistance range its value is hoped to be zero, but actually a certain value remains, which is called ‘‘residual resistance’’ in this paper. It can be found that the residual resistance is about 0.2 mX in average. The current of the transition from the superconducting state to the normal state is about 18 A. This current is called ‘‘transfer current’’ in this paper.
669
Fig. 1. Contact resistance vs current.
In Case 2, the resistance is low and the behavior is stable since the rising current stage of first cycle. It can be found that the residual resistance is about 0.09 mX in average. The value is about half of Case 1. This is because the contact spot area increased by depositing a soft metal on the hard surface. The transition from the superconducting state to the normal state was not appeared at maximum of experimental setup 30 A in Case 2.
3. Simulation of current and temperature distribution 3.1. Modeling of contact spot The bulk and contact spot are modeled as an axisymmetrical three-dimensional structure shown in Fig. 2. The contact spot is a cylinder which is a radius of r and a length of d. According to Ref. [5], the resistance of contact spot is represented as follows
Fig. 2. Analytical model of contact spot.
670
R¼
T. Imaizumi et al. / Physica C 412–414 (2004) 668–672
qd q þ 2 pr 2r
ð1Þ
where q is a resistivity of contact spot, and the second term is a constriction resistance. In Case 1 the resistivity of contact spot is represented as follows R q¼ d þ 2r1 pr2
ð2Þ
R ¼ 0:2 mX is substituted from the experimental result. On the other hand, in Case 2 the resistivity of contact spot is represented as follows pr q¼ 1þ ð3Þ q 2d Ag where qAg is the resistivity of silver at 77 K, 1.8 · 108 · 0.2 X m.
of the normal state, and K and m are determined for the resistivity and the first derivative to be continuous at J ¼ Jc2 . The resistivity of the normal state is represented as follows q ¼ qn ¼ q0 þ aH
ð8Þ
at H P Tc
The critical current density is also dependent on a temperature, which is represented as follows 1:98 H2 Jc / 1 2 at H < Tc ð9Þ Tc Fig. 3 shows the resistivity of YBCO used for the simulation. 3.3. Current and temperature distribution by FEM The current density J satisfies the following equation
3.2. Resistivity of YBCO
div J ¼ 0
The resistivity of YBCO is dependent on current density J and temperature H. Generally the electric field E of a high temperature superconductor is represented as follows n J E ¼ Ec ð4Þ Jc
Therefore, J is represented by a current vector potential T. rot T ¼ J
ð10Þ
ð11Þ
The electric field E is static, and the followings are obtained. E ¼ qJ
ð12Þ
where Ec is an electric field at the critical current density Jc , 1.0 · 104 V/m and n is an index of a high temperature superconductor. Eq. (4) is converted to q–J equation as follows n1 J q ¼ qc ; Ec ¼ qc Jc ð5Þ Jc However, Eq. (5) represents resistivity at the rising part around the critical current. The transition from the superconducting state to the normal state should be also represented, so that the following equations are used n1 J q ¼ qc at 0 < J < Jc2 ð6Þ Jc q ¼ qn
K Jm
at Jc2 6 J
ð7Þ
Eq. (6) is connected to Eq. (7) at J ¼ Jc2 . Jc2 is current density at q ¼ 0:5 qn . qn is the resistivity
Fig. 3. Resistivity of YBCO used for the simulation.
T. Imaizumi et al. / Physica C 412–414 (2004) 668–672
rot E ¼ 0
ð13Þ
Eq. (14) can be derived from Eqs. (11)–(13) rotðqrot TÞ ¼ 0
671
Fig. 5 is the temperature distribution of the whole bulk obtained by FEM before transfer, and
ð14Þ
The Galerkin method is applied to Eq. (14) and the integration equation for obtaining an approximation solution is obtained. The current density distribution can be found by solving the integration equation by FEM. From the current density distribution, the heat generation is calculated by the equation 2 Q_ ¼ qjJj
ð15Þ
The steady-state temperature distribution is also estimated from the following equation by FEM 1 o oH o oH r j þ þ Q_ ¼ 0 ð16Þ r or or oz oz where j is a thermal conductivity. [K]
3.4. Simulation results
7.70e+01
Fig. 4 is one of the current distributions. From Fig. 4, it turns out that the current is concentrating on the contact spot.
7.84e+01
7.98e+01
8.12e+01
8.26e+01
Fig. 5. Temperature distribution of whole bulk.
[A/m2] 2.50e+05
9.68e+07
1.93e+08
2.90e+08
Fig. 4. Current distribution.
3.86e+08
Fig. 6. Temperature distribution around contact spot.
672
T. Imaizumi et al. / Physica C 412–414 (2004) 668–672
Figs. 7 and 8 that the contact spot radius of Case 1 is about 0.09 mm and that of Case 2 is more than about 0.13 mm. On the contrary, it is confirmed that the transfer current increases when the contact spot radius enlarges.
4. Conclusion
Fig. 7. Simulation result of transfer current vs contact spot radius in Case 1.
Two YBCO bulks were mechanically mated and the current flowed through the contact. This phenomenon was simulated by using an axisymmetrical three-dimensional model. The current and the temperature distributions of the switch were obtained by FEM. The temperature distribution showed that the heat generated at the contact spot has stayed without diffusing. The contact spot radius was able to be estimated from the simulation. In order to reduce the residual resistance and to increase the transfer current through the experiment and the simulation, it was reconfirmed that the contact spot area must be enlarged.
Acknowledgements
Fig. 8. Simulation result of transfer current vs contact spot radius in Case 2.
the temperature distribution around the contact spot is shown in Fig. 6. It seems that the temperature of the whole bulk is 77 K of liquid nitrogen temperature. However, the temperature only around the contact spot is rising. Figs. 7 and 8 show the transfer current vs contact spot radius in Case 1 and Case 2 obtained by FEM. The dotted lines in Figs. 7 and 8 show the experimental transfer current. Although the contact spot radius of experiment is a certain fixed value, it cannot be specified. It is guessed from
This work was supported by the New Energy and Industrial Technology Development Organization (NEDO) as Collaborative Research and Development of Fundamental Technologies for Superconductivity Applications.
References [1] S. Ohtsuka, H. Ohtsubo, T. Nakamura, J. Suehiro, M. Hara, Cryog. Jpn. 32 (10) (1997) 473 (in Japanese). [2] K. Sawa, M. Suzuki, M. Tomita, M. Murakami, IEEE Trans. 25 (3) (2002) 415. [3] T. Sakai, N. Yamamoto, K. Sawa, M. Tomita, M. Murakami, In: Proc. 48th IEEE Holm Conf., 2002, pp. 206–211. [4] N. Yamamoto, T. Sakai, K. Sawa, M. Tomita, M. Murakami, Physica C: Supercond. 392–396 (Part 1) (2003) 729. [5] R. Holm, Electrical Contacts, Fourth ed., Springer, New York, 1979, chapter 1, pp. 1–18.