- Email: [email protected]
The experimental research and analysis on the quench propagation of YBCO coated conductor and coil
Physica C 484 (2013) 153–158
Contents lists available at SciVerse ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
The experimental research and analysis on the quench propagation of YBCO coated conductor and coil W.J. Lu, J. Fang ⇑, D. Li, C.Y. Wu, L.J. Guo School of Electrical Engineering, Beijing Jiaotong University, Beijing, China
a r t i c l e
i n f o
Article history: Accepted 27 March 2012 Available online 31 March 2012 Keywords: Quench characteristics Quench propagation velocity Minimum propagation current Minimum quench energy YBCO tapes and coil
a b s t r a c t Quench propagation characteristics of YBCO tapes and coils were studied in this paper. Quench propagation in each test was initiated by a NiCr wire heater mounted on the sample tape and coil. Quench propagation velocity was measured through voltage taps and temperature sensors across different zones of the tapes and coil. Voltage taps and temperature sensors are arranged in longitudinal and radial direction of the coil. The thermal stability margin, the longitudinal quench propagation velocity for the tape and coil, radial quench propagation velocity for coil and the minimum propagation current were measured. In this study, we investigated the relationship between heat inputs and normal zone propagation velocities and the impact of operating currents on normal zone propagation velocities. We also compared the longitudinal quench propagation velocity and the radial quench propagation velocity. Furthermore, we performed numerical simulations by using a computer program based on a one-dimensional heat flow equation model for YBCO tape. The temperature longitudinal distributions of YBCO tape were simulated. The simulation results also prove the relation between heat input and normal zone propagation velocities and agree with the experimental results. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction In superconducting application field, the stable operation of the superconducting magnets is necessary, so superconducting magnets as basic component of the superconducting coil must have high stability [1]. The normal zone propagation velocity (NZPV) is an important parameter to describe the stability of the superconducting magnets. In general, the NZPV of high temperature superconductor (HTS) is lower by two or three magnitude than the NZPV of low temperature superconductor (LTS) [2,3]. This is mainly due to the high thermal capacity and high critical temperature of HTS [4]. So HTS’s stability is better than LHS, but on the other hand, if the NZPV is too slow, a thermal spot can be formed in the superconductor materials. Since the heat can only spread in a small zone in HTS, permanent damage of the superconductors occurs. Generally speaking, the electrical and thermal properties during a quenching must be taken into account. Quench propagation characteristics of superconductor tapes have been studied by international scholars [5–8]. In our study, we used the YBCO coated conductor which is provided by American Superconductor Corporation, voltage and the temperature curves during a quench were drawn. According to the theoretical analysis and experimental ⇑ Corresponding author. Address: Room 508, Electrical Engineering Building, Beijing Jiaotong University, Beijing 100044, China. Tel.: +86 13911063206; fax: +86 10 51687101. E-mail addresses: [email protected] (W.J. Lu), [email protected] (J. Fang). 0921-4534/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physc.2012.03.062
data, we calculated the longitudinal quench propagation velocity and the radial quench propagation velocity of the HTS coil and compared them to each other. Many approaches and models were used to describe that transition [9–11]. In our work, a one-dimensional heat flow equation model is used to simulate the temperature longitudinal distributions during the quench process. We also studied the effects of the input energy and transfer current on quench propagation velocity. 2. Heat transfer model and velocity formula Assuming uniform temperatures over any cross section of the wire, the temperature is constant at both ends of the tape, the heat flow equation is [12]:
CðTÞ
@T @ @T ¼ kðTÞ þ QðTÞ þ Q ini WðTÞ @t @x @x
ð1Þ
where x is distance along the wire, C(T) is the specific heat of the material, k(T) is the thermal conductivity. Q(T) are the Joule losses, Qini is the initiating energy pulse (W/m3), W(T) is the heat transfer to the liquid nitrogen per unit volume. When the temperature exceeds the current-sharing temperature TCS, part of the current would flow through the silver stabilizer. When the temperature exceeds the critical temperature TC, the whole current would flow through the silver stabilizer. Then Q(T) is:
154
W.J. Lu et al. / Physica C 484 (2013) 153–158
ðT < T CS Þ
qAg JJC ðT T CS Þ=ðT C T CS Þ ðT CS 6 T < T C Þ > : qAg J2 ðT P T C Þ
ð2Þ
where qAg is the resistivity of silver, J is the current density and JC is the critical current density. According to Newton’s law of cooling, then W(T) can be simplified as follows:
WðTÞ ¼ hðTÞðT T op Þ
P A
ð3Þ
where Top is the operating temperature, P is the cooling perimeter, A is the cross sectional area and h(T) is the heat transfer coefficient between the YBCO tape and the liquid nitrogen. In this paper, we assume that h(T) is a constant [13], i.e. the heat is removed by liquid phase nitrogen only. In fact, the boiling heat transfer hb(T) is smaller. Therefore, W(T) is larger when h(T) is applied to calculate W(T) by Eq. (3). In the case of the coil experiment, W(T) also contains the heat absorbed by the neighboring layers of the tape, the temperature rise of the neighboring layers is negligible so that the heat absorbed by the neighboring layers of the tapes hardly affects W(T). Therefore, the value of W(T) in Eq. (1) is larger. So, with a same input energy, the experimental result T is larger than the simulation result. Furthermore, the balance between Q(T) and W(T) affects the quench energy, it is obvious that Q(T) is related to the transport current in Eq. (2). Then we can conclude that the quench energy decreases with a larger transport current. In order to further research quench propagation, a more detailed model of the coil needs to be built. Having the complete expression of the empirical laws i.e. Eqs. (1)–(3), the numerical model can be built to compute the evolution of the temperature in the sample. Assuming the normal zone cross section travel at a constant velocity, the temperature front can be regarded as a traveling wave. With the traveling wave representation n = x vt, Eq. (1) becomes:
@ @T @T kðTÞ þ v CðTÞ þ QðTÞ þ Q ini WðTÞ ¼ 0 @n @n @n
v¼
qAg k J qm C p T C T op
(a)
Heater
(b)
Heater
ð4Þ
If all the thermal parameters are taken independently of the temperature when we calculate the velocity, The heat is generated by Joule losses only in the stabilizer i.e. Q ¼ qAg J 2 , the NZPV can be calculated [14]:
layer (the 18th layer) and the nearby four layers (the 16th, 17th, 19th, 20th layers). Fig. 1a and b shows the distribution of the heater, voltage taps and temperature taps of the tape and coil respectively. Localized thermal disturbances for quench initiation are applied using short heat pulses discharged by a NiCr wire heater mounted on the sample, thus the normal zone of the sample appears near the heater. The quench propagation characteristics can be obtained by the voltage and temperature traces which are recorded by the computer.
Fig. 1. Distribution drawing of the heater, voltage taps U1–U4, and temperature taps T1–T4: (a) is the experimental setup for the tape and (b) is the experimental setup for the coil.
Solution at x = 1
92
12 ð5Þ
where qm is mass density of the material. With a larger input energy, the sum of the last three terms in Eq. (1) would be larger so that @T in Eq. (1) increases. The increase of @T would shorten the time @t @t when the temperature reaches the critical value and quench occurs earlier. From Eq. (5) we can see that the input energy does not affect the NZPV, the NZPV is related to the transport current and material parameters.
Ttap1 Ttap2 Ttap3 Ttap4 Ttap5 Ttap6 Ttap7
90 88 86
T (1,t)
Q ðTÞ ¼
8 0 > <
84 82
3. Experiment
80
Both tape and coil experiments have been done in this paper. An experiment setup of the tape is shown in Fig. 1a. The length of the tape is 20 cm. Four thermocouples (T1–T4) and four pairs of voltage taps (U1–U4) are fixed on the YBCO tape, a NiCr wire heater is mounted on the center of the tape. The experiment setup of the coil is similar to the tape. The YBCO coil we studied in this paper has 35 layers, 10 thermocouples (T1– T10) and 10 pairs of voltage taps (U1–U10) are fixed on the center
78 76
0
5
10
15
20
Time t Fig. 2. Simulation results of the tape. The distinct curves (Ttap1–Ttap7) indicate the temperature variation of 7 points which are 1–7 cm away from the heater, respectively.
155
W.J. Lu et al. / Physica C 484 (2013) 153–158
The NZPV can be calculated by the following equation: VP = L/Dt, here, L is the distance between two voltage taps, it is 4 cm for the tape and 2 cm for the coil in our study, Dt is the time-interval between two voltage traces reaching the quench voltage. In this paper, we use the 1 lV/cm criterion. 4. Results and analysis 4.1. Minimum quench energy (MQE) According to the heat flow Eq. (1), K(T) is the thermal conductivity, C(T) is the specific heat of the material. They vary with the temperature and we create the fit curves and formulas with experimental data. The MQE stands for the minimum quenching energy which can initiate a quench in the tape. The quenching means that if the local quenching caused by input energy cannot be recovered and it would propagation to overall tape [15,16].
The input energy in the experiment is calculated by E = I2Rt, where E is the input energy, I is the constant current in the heater, R is the resistance of the heater, and t is the pulse width. In Fig. 2, the distinct curves (Ttap1–Ttap7) indicate the temperature variation of 7 points which are 1–7 cm away from the heater, respectively. Fig. 3a shows the measurement result of T2 reaches the peak value 83.4 K when the input energy is 4.2 J. Fig. 3b shows the measurement result of T2 reaches the peak value 133.5 K when the input energy is 13.7 J. We also simulate the temperature curves under the same condition. When the input energy is 4.2 J and 13.7 J, the simulation results of T2 are 81.7 K and 126 K respectively. That the simulation results are slightly smaller than the experimental results because h(T) which is applied to calculate W(T) by Eq. (3) is larger, which is explained in Section 2. Fig. 4 shows the temperature at a series of input energy, we can see that the temperature reaches the critical temperature 92 K when the input energy is 5.8 J. Therefore, minimum quench energy of YBCO tape is about 5.8 J.
(a) 86
96.0 95.5
(T2) (T1)
84
95.0 94.5 94.0 93.5
T (K)
T ,K
82 80
93.0 92.5
Critical Value
92.0 91.5
78
91.0 90.5
76
90.0
0
5
10
15
20
25
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
Q (J)
t ,s
Fig. 4. Temperature at different input energy, the critical value is 92 K.
(b) 130
(T2) (T1)
120
40000 35000 30000
110
25000
100 U/µV
T, K
8.31J 15.16J 26.94J
90
20000 15000 10000
80
5000
70
0
5
10
t ,s
15
20
25
0 0
5
10
15
20
T/s Fig. 3. Experimental values of the temperature curves of the tape: (a) shows the result at 4.2 J and (b) shows the result at 13.7 J.
Fig. 5. Voltage curves at different input energies of the tape.
25
156
W.J. Lu et al. / Physica C 484 (2013) 153–158
(a)
(a)
(U6) (U7) (U8) I=10A
1000
U, µV/cm
100
10
1
0.1
0
20
40
60
80
100
t ,s
(b)
(b)
(U6) (U9) (U10) I=10A
1000
U, µV/cm
100
10
1
0.1
0
20
40
60
80
100
t ,s
Fig. 6. Voltage curves at each point of the coil: (a) is the voltage traces of U6, U7, U8 and (b) is the voltage traces of U6, U9, U10.
4.2. NZPV at different input energy For the superconductor tapes, Fig. 5 shows the voltage curves U2 at different input energies of the tape. We can see that quenching occurs earlier with a larger input energy, however the NZPV keeps constant since the slopes of the curves are almost the same at 60 A. For the coil, Fig. 6a and b shows the voltage characteristic curves, the transfer current is 5 A and the input energy is 398.86 J. Quench propagation appeared at T2, T5, T6, T7 and T9. NZPV is calculated by the equation v = L/Dt as introduced before. When the transfer current is 5 A and the input energy is 90.2 J, the NZPV can be calculated in the same way. Table 1 shows NZPV at different input energy. To conclude, the input energy of the superconductor tapes and coils hardly affects NZPV. With larger input energy, quench occurs earlier, however NZPV keeps constant. Quench cannot propagate when the transfer current is too small, even if the input energy is Table 1 NZPV at different input energy. Input energy (J)
v6–2 (mm/s)
v5–4
v6–7
v6–9
v9–10
90.2 398.86
0.0677 0.071
0.49 0.5
0.526 0.53
0.23 0.25
0.00853 0.008
Fig. 7. Voltage traces at I = 10 A: (a) is the voltage traces of U6, U7, U8 and (b) is the voltage traces of U6, U9, U10.
large. When the input energy stimulates a hot spot in a tiny area of the tape, a quench is triggered. When the input energy is larger, temperature increases more rapidly so that quench occurs earlier. When quenching occurs, the transfer current begins flowing through the stabilizer. Quench propagation is driven by the heat generated by the resistance in the stabilizer, rather than the input heat pulse [17,18]. Therefore, the input energy could trigger a quenching initially but has no effects on the NZPV which is affected by the heat generated by heat spot resistance of HTS tape. 4.3. NZPV at different transfer current We calculate the longitudinal and the radial quench propagation velocities of the coil at different transfer currents, Fig. 7 shows the voltage traces when the transfer current is 10 A. In the same way, we measured the velocities at different transfer currents. Table 2 Quench propagation velocities at different transfer currents. I (A)
v6–2 (mm/s)
v5–4
v6–7
v6–9
v9–10
5 10 40 45
0.0677 0.0633 0.0649 0.0837
0.49 0.808 4.694 6.666
0.526 0.916 4.202 8.368
0.23 0.14 0.14 0.695
0.00853 0.0117 0.0531 0.0659
157
W.J. Lu et al. / Physica C 484 (2013) 153–158
(a)
2.0
1.2
theoretical curve experimental curve
NZPV(cm/s) 1.5
NZPV(mm/s)
NZPV (cm/s)
1.0 0.8 0.6
1.0
0.5
0.4 0.2
0.0 0.0
0
20
40
60
80
V6-7(mm/s)
30
40
50
measured parameters are put in the formula of the quench velocity, the formula (4) can be simplified as follows:
v ¼ 0:338 104 ðI 3:75Þ
ð6Þ
Then we can get the theoretical values at different transfer currents, the numerical results are close to those of experiment values. Fig. 9 shows that the quench velocity increases with the larger transfer current. The theoretical value of the velocity is proportional to transfer current, and experiment values show the same tendency despite small errors. Both the numerical results and experimental results indicate that the superconductor tapes and coils have a low NZPV.
6
4
2
0
20
Fig. 9. Comparison between theoretical and experiment values.
NZPV (mm/s)
8
10
I (A)
I (A)
(b)
0
4.4. Comparison of the longitudinal and radial quench propagation velocity of YBCO coil
0
10
20
30
40
50
I (A) Fig. 8. Velocity curves at different transfer currents: (a) is values of the tape and (b) is the experimental values of the coil experimental.
Table 2 shows that the NZPV increases with the larger transfer current. The longitudinal quench propagation velocities v5–4, v6–7 are much larger than the radial quench propagation velocities v6–2, v6–9, v9–10. Based on this, researches of the minimum transfer current (Imp) for the superconductor tape and coil have been done. Since the minimum transfer current is difficult to measure, in our study, we calculated velocities at different transfer currents, and create the fit curve as is shown in Fig. 8a and b. The intersection point with the horizontal axis represents the minimum transfer current. When I Imp, the normal zone would shrink and quench cannot propagate. This phenomenon can be explained as a result of heat exchange between YBCO tapes and liquid nitrogen. If the transfer current is smaller than the critical value (Imp), the heat generated by the resistance in the stabilizer would be carried away by liquid nitrogen and HTS tape around hot spot so that the temperature drops below the critical temperature and the quenching cannot propagate. Therefore, the stability of the superconductor would be better at a smaller transfer current. Furthermore, we calculate the quench velocity of the coil theoretically on the basis of the formula we analyzed in Section 2. The
From the experimental data in Tables 1 and 2, we can conclude that the longitudinal quench propagation velocity is much greater than the radial quench propagation velocity, and quench propagation velocity of the part close to the heater is larger. The process of quench propagation in YBCO coil can be described as follows. As soon as the input energy triggered a quench, the quenching propagates along the longitudinal and radial directions of the coil. When quenching energy propagates to the adjacent layer and the temperature of the adjacent layer increases to the critical temperature, a hot spot is generated in the adjacent layer and normal zone begins to propagate along the radial direction. Because there is a insulation boundary layer on YBCO tape, such insulating materials slow down the radial quench propagation velocity of YBCO coil. In longitudinal direction, quench propagate along the stabilizer of YBCO tape so that the longitudinal propagate velocity is much larger than the radial propagate velocity. 5. Conclusions The stability and quench behavior of YBCO tapes and coils at self-field has been investigated over a range of input energy and transfer currents. The experimental results show that with the input energy increase, quench propagate becomes earlier, but the input energy hardly affects the velocity. Higher transport current accelerates the NZPV. Minimum quench energy (MQE) and minimum propagate current (Imp) have been studied as well, the MQE increased as the transport current decreased. We have numerically
158
W.J. Lu et al. / Physica C 484 (2013) 153–158
investigated the characteristics of the thermal behavior and NZPV during a quench, the results are close to the experimental results. It is an valuable tool for coil design for HTS applications. Acknowledgments This project was founded by the National High Technology Research and Development Program of China (863 Program), and under charge of Prof. Jin Fang. References [1] J.R. Hull, Rep. Prog. Phys. 66 (2003) 1865. [2] A. Ishiyama, H. Ueda, T. Ando, H. Naka, S. Bam, Y. Shiohara, IEEE Trans. Appl. Supercond. 17 (2007) 2430. [3] X. Wang, A.R. Caruso, M. Breschi, G. Zhang, U.P. Trociewitz, H.W. Weijers, J. Schwartz, IEEE Trans. Appl. Supercond. 15 (2005) 2586. [4] Hae-Yong Park, A. Rong Kim, Minwon Park, In-Keun Yu, Beom-Yong Eom, JunHan Bae, Seok-Ho Kim, Kideok Sim, Myung-Hwan Sohn, IEEE Trans. Appl. Supercond. 20 (2010) 1339.
[5] T. Huang, A. Johnston, Y. Yang, C. Beduz, C. Friend, IEEE Trans. Appl. Supercond. 15 (2005) 1647. [6] Z. Bai, X. Wu, C. Wu, J. Wang, Physica C 436 (2006) 99. [7] E. Martínez, F. Lera, M. Martinez-López, Y. Yang, S.I. Schlachter, P. Lezza, P. Kováè, Supercond. Sci. Technol. 19 (2006) 143. [8] H.-I. Du, M.-J. Kim, Y.-J. Kim, D.-H. Lee, B.-S. Han, S.-S. Song, Physica C 470 (2010) 1626. [9] M.N. Wilson, R. Wolf, IEEE Trans. Appl. Supercond. 7 (1997) 950. [10] F. Roy, Ph.D. Thesis, École Polytechnique Fé dé rale de Lausanne (EPFL), 2010. [11] M. Prester, Supercond. Sci. Technol. 11 (1998) 333. [12] I. Aranson, A. Gurevich, V. Vinokur, Phys. Rev. Lett. 87 (2001) 1. [13] J. Mosqueira, O. Cabeza, M.X. François, C. Torrón, F. Vidal, Supercond. Sci. Technol. 6 (1993) 584. [14] M. Tinkham, Introduction to Superconductivity, second ed., Dover Publications Inc., Mineola, NY, 2004. [15] E.A. Young, C.M. Friend, Y. Yang, IEEE Trans. Appl. Supercond. 19 (2009) 2500. [16] N.Y. Kwon, H.S. Kim, K.L. Kim, S. Hahn, H.-R. Kim, O.-B. Hyun, H.M. Kim, W.S. Kim, C. Park, H.G. Lee, IEEE Trans. Appl. Supercond. 20 (2010) 1246. [17] Honghai Song, Justin Schwartz, IEEE Trans. Appl. Supercond. 19 (2009) 3735. [18] Minyi Fu, Xiaofeng Xu, Zhengkuan Jiao, H. Kumakura, K. Togano, Physica C 402 (2004) 234.
Contents lists available at SciVerse ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
The experimental research and analysis on the quench propagation of YBCO coated conductor and coil W.J. Lu, J. Fang ⇑, D. Li, C.Y. Wu, L.J. Guo School of Electrical Engineering, Beijing Jiaotong University, Beijing, China
a r t i c l e
i n f o
Article history: Accepted 27 March 2012 Available online 31 March 2012 Keywords: Quench characteristics Quench propagation velocity Minimum propagation current Minimum quench energy YBCO tapes and coil
a b s t r a c t Quench propagation characteristics of YBCO tapes and coils were studied in this paper. Quench propagation in each test was initiated by a NiCr wire heater mounted on the sample tape and coil. Quench propagation velocity was measured through voltage taps and temperature sensors across different zones of the tapes and coil. Voltage taps and temperature sensors are arranged in longitudinal and radial direction of the coil. The thermal stability margin, the longitudinal quench propagation velocity for the tape and coil, radial quench propagation velocity for coil and the minimum propagation current were measured. In this study, we investigated the relationship between heat inputs and normal zone propagation velocities and the impact of operating currents on normal zone propagation velocities. We also compared the longitudinal quench propagation velocity and the radial quench propagation velocity. Furthermore, we performed numerical simulations by using a computer program based on a one-dimensional heat flow equation model for YBCO tape. The temperature longitudinal distributions of YBCO tape were simulated. The simulation results also prove the relation between heat input and normal zone propagation velocities and agree with the experimental results. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction In superconducting application field, the stable operation of the superconducting magnets is necessary, so superconducting magnets as basic component of the superconducting coil must have high stability [1]. The normal zone propagation velocity (NZPV) is an important parameter to describe the stability of the superconducting magnets. In general, the NZPV of high temperature superconductor (HTS) is lower by two or three magnitude than the NZPV of low temperature superconductor (LTS) [2,3]. This is mainly due to the high thermal capacity and high critical temperature of HTS [4]. So HTS’s stability is better than LHS, but on the other hand, if the NZPV is too slow, a thermal spot can be formed in the superconductor materials. Since the heat can only spread in a small zone in HTS, permanent damage of the superconductors occurs. Generally speaking, the electrical and thermal properties during a quenching must be taken into account. Quench propagation characteristics of superconductor tapes have been studied by international scholars [5–8]. In our study, we used the YBCO coated conductor which is provided by American Superconductor Corporation, voltage and the temperature curves during a quench were drawn. According to the theoretical analysis and experimental ⇑ Corresponding author. Address: Room 508, Electrical Engineering Building, Beijing Jiaotong University, Beijing 100044, China. Tel.: +86 13911063206; fax: +86 10 51687101. E-mail addresses: [email protected] (W.J. Lu), [email protected] (J. Fang). 0921-4534/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physc.2012.03.062
data, we calculated the longitudinal quench propagation velocity and the radial quench propagation velocity of the HTS coil and compared them to each other. Many approaches and models were used to describe that transition [9–11]. In our work, a one-dimensional heat flow equation model is used to simulate the temperature longitudinal distributions during the quench process. We also studied the effects of the input energy and transfer current on quench propagation velocity. 2. Heat transfer model and velocity formula Assuming uniform temperatures over any cross section of the wire, the temperature is constant at both ends of the tape, the heat flow equation is [12]:
CðTÞ
@T @ @T ¼ kðTÞ þ QðTÞ þ Q ini WðTÞ @t @x @x
ð1Þ
where x is distance along the wire, C(T) is the specific heat of the material, k(T) is the thermal conductivity. Q(T) are the Joule losses, Qini is the initiating energy pulse (W/m3), W(T) is the heat transfer to the liquid nitrogen per unit volume. When the temperature exceeds the current-sharing temperature TCS, part of the current would flow through the silver stabilizer. When the temperature exceeds the critical temperature TC, the whole current would flow through the silver stabilizer. Then Q(T) is:
154
W.J. Lu et al. / Physica C 484 (2013) 153–158
ðT < T CS Þ
qAg JJC ðT T CS Þ=ðT C T CS Þ ðT CS 6 T < T C Þ > : qAg J2 ðT P T C Þ
ð2Þ
where qAg is the resistivity of silver, J is the current density and JC is the critical current density. According to Newton’s law of cooling, then W(T) can be simplified as follows:
WðTÞ ¼ hðTÞðT T op Þ
P A
ð3Þ
where Top is the operating temperature, P is the cooling perimeter, A is the cross sectional area and h(T) is the heat transfer coefficient between the YBCO tape and the liquid nitrogen. In this paper, we assume that h(T) is a constant [13], i.e. the heat is removed by liquid phase nitrogen only. In fact, the boiling heat transfer hb(T) is smaller. Therefore, W(T) is larger when h(T) is applied to calculate W(T) by Eq. (3). In the case of the coil experiment, W(T) also contains the heat absorbed by the neighboring layers of the tape, the temperature rise of the neighboring layers is negligible so that the heat absorbed by the neighboring layers of the tapes hardly affects W(T). Therefore, the value of W(T) in Eq. (1) is larger. So, with a same input energy, the experimental result T is larger than the simulation result. Furthermore, the balance between Q(T) and W(T) affects the quench energy, it is obvious that Q(T) is related to the transport current in Eq. (2). Then we can conclude that the quench energy decreases with a larger transport current. In order to further research quench propagation, a more detailed model of the coil needs to be built. Having the complete expression of the empirical laws i.e. Eqs. (1)–(3), the numerical model can be built to compute the evolution of the temperature in the sample. Assuming the normal zone cross section travel at a constant velocity, the temperature front can be regarded as a traveling wave. With the traveling wave representation n = x vt, Eq. (1) becomes:
@ @T @T kðTÞ þ v CðTÞ þ QðTÞ þ Q ini WðTÞ ¼ 0 @n @n @n
v¼
qAg k J qm C p T C T op
(a)
Heater
(b)
Heater
ð4Þ
If all the thermal parameters are taken independently of the temperature when we calculate the velocity, The heat is generated by Joule losses only in the stabilizer i.e. Q ¼ qAg J 2 , the NZPV can be calculated [14]:
layer (the 18th layer) and the nearby four layers (the 16th, 17th, 19th, 20th layers). Fig. 1a and b shows the distribution of the heater, voltage taps and temperature taps of the tape and coil respectively. Localized thermal disturbances for quench initiation are applied using short heat pulses discharged by a NiCr wire heater mounted on the sample, thus the normal zone of the sample appears near the heater. The quench propagation characteristics can be obtained by the voltage and temperature traces which are recorded by the computer.
Fig. 1. Distribution drawing of the heater, voltage taps U1–U4, and temperature taps T1–T4: (a) is the experimental setup for the tape and (b) is the experimental setup for the coil.
Solution at x = 1
92
12 ð5Þ
where qm is mass density of the material. With a larger input energy, the sum of the last three terms in Eq. (1) would be larger so that @T in Eq. (1) increases. The increase of @T would shorten the time @t @t when the temperature reaches the critical value and quench occurs earlier. From Eq. (5) we can see that the input energy does not affect the NZPV, the NZPV is related to the transport current and material parameters.
Ttap1 Ttap2 Ttap3 Ttap4 Ttap5 Ttap6 Ttap7
90 88 86
T (1,t)
Q ðTÞ ¼
8 0 > <
84 82
3. Experiment
80
Both tape and coil experiments have been done in this paper. An experiment setup of the tape is shown in Fig. 1a. The length of the tape is 20 cm. Four thermocouples (T1–T4) and four pairs of voltage taps (U1–U4) are fixed on the YBCO tape, a NiCr wire heater is mounted on the center of the tape. The experiment setup of the coil is similar to the tape. The YBCO coil we studied in this paper has 35 layers, 10 thermocouples (T1– T10) and 10 pairs of voltage taps (U1–U10) are fixed on the center
78 76
0
5
10
15
20
Time t Fig. 2. Simulation results of the tape. The distinct curves (Ttap1–Ttap7) indicate the temperature variation of 7 points which are 1–7 cm away from the heater, respectively.
155
W.J. Lu et al. / Physica C 484 (2013) 153–158
The NZPV can be calculated by the following equation: VP = L/Dt, here, L is the distance between two voltage taps, it is 4 cm for the tape and 2 cm for the coil in our study, Dt is the time-interval between two voltage traces reaching the quench voltage. In this paper, we use the 1 lV/cm criterion. 4. Results and analysis 4.1. Minimum quench energy (MQE) According to the heat flow Eq. (1), K(T) is the thermal conductivity, C(T) is the specific heat of the material. They vary with the temperature and we create the fit curves and formulas with experimental data. The MQE stands for the minimum quenching energy which can initiate a quench in the tape. The quenching means that if the local quenching caused by input energy cannot be recovered and it would propagation to overall tape [15,16].
The input energy in the experiment is calculated by E = I2Rt, where E is the input energy, I is the constant current in the heater, R is the resistance of the heater, and t is the pulse width. In Fig. 2, the distinct curves (Ttap1–Ttap7) indicate the temperature variation of 7 points which are 1–7 cm away from the heater, respectively. Fig. 3a shows the measurement result of T2 reaches the peak value 83.4 K when the input energy is 4.2 J. Fig. 3b shows the measurement result of T2 reaches the peak value 133.5 K when the input energy is 13.7 J. We also simulate the temperature curves under the same condition. When the input energy is 4.2 J and 13.7 J, the simulation results of T2 are 81.7 K and 126 K respectively. That the simulation results are slightly smaller than the experimental results because h(T) which is applied to calculate W(T) by Eq. (3) is larger, which is explained in Section 2. Fig. 4 shows the temperature at a series of input energy, we can see that the temperature reaches the critical temperature 92 K when the input energy is 5.8 J. Therefore, minimum quench energy of YBCO tape is about 5.8 J.
(a) 86
96.0 95.5
(T2) (T1)
84
95.0 94.5 94.0 93.5
T (K)
T ,K
82 80
93.0 92.5
Critical Value
92.0 91.5
78
91.0 90.5
76
90.0
0
5
10
15
20
25
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
Q (J)
t ,s
Fig. 4. Temperature at different input energy, the critical value is 92 K.
(b) 130
(T2) (T1)
120
40000 35000 30000
110
25000
100 U/µV
T, K
8.31J 15.16J 26.94J
90
20000 15000 10000
80
5000
70
0
5
10
t ,s
15
20
25
0 0
5
10
15
20
T/s Fig. 3. Experimental values of the temperature curves of the tape: (a) shows the result at 4.2 J and (b) shows the result at 13.7 J.
Fig. 5. Voltage curves at different input energies of the tape.
25
156
W.J. Lu et al. / Physica C 484 (2013) 153–158
(a)
(a)
(U6) (U7) (U8) I=10A
1000
U, µV/cm
100
10
1
0.1
0
20
40
60
80
100
t ,s
(b)
(b)
(U6) (U9) (U10) I=10A
1000
U, µV/cm
100
10
1
0.1
0
20
40
60
80
100
t ,s
Fig. 6. Voltage curves at each point of the coil: (a) is the voltage traces of U6, U7, U8 and (b) is the voltage traces of U6, U9, U10.
4.2. NZPV at different input energy For the superconductor tapes, Fig. 5 shows the voltage curves U2 at different input energies of the tape. We can see that quenching occurs earlier with a larger input energy, however the NZPV keeps constant since the slopes of the curves are almost the same at 60 A. For the coil, Fig. 6a and b shows the voltage characteristic curves, the transfer current is 5 A and the input energy is 398.86 J. Quench propagation appeared at T2, T5, T6, T7 and T9. NZPV is calculated by the equation v = L/Dt as introduced before. When the transfer current is 5 A and the input energy is 90.2 J, the NZPV can be calculated in the same way. Table 1 shows NZPV at different input energy. To conclude, the input energy of the superconductor tapes and coils hardly affects NZPV. With larger input energy, quench occurs earlier, however NZPV keeps constant. Quench cannot propagate when the transfer current is too small, even if the input energy is Table 1 NZPV at different input energy. Input energy (J)
v6–2 (mm/s)
v5–4
v6–7
v6–9
v9–10
90.2 398.86
0.0677 0.071
0.49 0.5
0.526 0.53
0.23 0.25
0.00853 0.008
Fig. 7. Voltage traces at I = 10 A: (a) is the voltage traces of U6, U7, U8 and (b) is the voltage traces of U6, U9, U10.
large. When the input energy stimulates a hot spot in a tiny area of the tape, a quench is triggered. When the input energy is larger, temperature increases more rapidly so that quench occurs earlier. When quenching occurs, the transfer current begins flowing through the stabilizer. Quench propagation is driven by the heat generated by the resistance in the stabilizer, rather than the input heat pulse [17,18]. Therefore, the input energy could trigger a quenching initially but has no effects on the NZPV which is affected by the heat generated by heat spot resistance of HTS tape. 4.3. NZPV at different transfer current We calculate the longitudinal and the radial quench propagation velocities of the coil at different transfer currents, Fig. 7 shows the voltage traces when the transfer current is 10 A. In the same way, we measured the velocities at different transfer currents. Table 2 Quench propagation velocities at different transfer currents. I (A)
v6–2 (mm/s)
v5–4
v6–7
v6–9
v9–10
5 10 40 45
0.0677 0.0633 0.0649 0.0837
0.49 0.808 4.694 6.666
0.526 0.916 4.202 8.368
0.23 0.14 0.14 0.695
0.00853 0.0117 0.0531 0.0659
157
W.J. Lu et al. / Physica C 484 (2013) 153–158
(a)
2.0
1.2
theoretical curve experimental curve
NZPV(cm/s) 1.5
NZPV(mm/s)
NZPV (cm/s)
1.0 0.8 0.6
1.0
0.5
0.4 0.2
0.0 0.0
0
20
40
60
80
V6-7(mm/s)
30
40
50
measured parameters are put in the formula of the quench velocity, the formula (4) can be simplified as follows:
v ¼ 0:338 104 ðI 3:75Þ
ð6Þ
Then we can get the theoretical values at different transfer currents, the numerical results are close to those of experiment values. Fig. 9 shows that the quench velocity increases with the larger transfer current. The theoretical value of the velocity is proportional to transfer current, and experiment values show the same tendency despite small errors. Both the numerical results and experimental results indicate that the superconductor tapes and coils have a low NZPV.
6
4
2
0
20
Fig. 9. Comparison between theoretical and experiment values.
NZPV (mm/s)
8
10
I (A)
I (A)
(b)
0
4.4. Comparison of the longitudinal and radial quench propagation velocity of YBCO coil
0
10
20
30
40
50
I (A) Fig. 8. Velocity curves at different transfer currents: (a) is values of the tape and (b) is the experimental values of the coil experimental.
Table 2 shows that the NZPV increases with the larger transfer current. The longitudinal quench propagation velocities v5–4, v6–7 are much larger than the radial quench propagation velocities v6–2, v6–9, v9–10. Based on this, researches of the minimum transfer current (Imp) for the superconductor tape and coil have been done. Since the minimum transfer current is difficult to measure, in our study, we calculated velocities at different transfer currents, and create the fit curve as is shown in Fig. 8a and b. The intersection point with the horizontal axis represents the minimum transfer current. When I Imp, the normal zone would shrink and quench cannot propagate. This phenomenon can be explained as a result of heat exchange between YBCO tapes and liquid nitrogen. If the transfer current is smaller than the critical value (Imp), the heat generated by the resistance in the stabilizer would be carried away by liquid nitrogen and HTS tape around hot spot so that the temperature drops below the critical temperature and the quenching cannot propagate. Therefore, the stability of the superconductor would be better at a smaller transfer current. Furthermore, we calculate the quench velocity of the coil theoretically on the basis of the formula we analyzed in Section 2. The
From the experimental data in Tables 1 and 2, we can conclude that the longitudinal quench propagation velocity is much greater than the radial quench propagation velocity, and quench propagation velocity of the part close to the heater is larger. The process of quench propagation in YBCO coil can be described as follows. As soon as the input energy triggered a quench, the quenching propagates along the longitudinal and radial directions of the coil. When quenching energy propagates to the adjacent layer and the temperature of the adjacent layer increases to the critical temperature, a hot spot is generated in the adjacent layer and normal zone begins to propagate along the radial direction. Because there is a insulation boundary layer on YBCO tape, such insulating materials slow down the radial quench propagation velocity of YBCO coil. In longitudinal direction, quench propagate along the stabilizer of YBCO tape so that the longitudinal propagate velocity is much larger than the radial propagate velocity. 5. Conclusions The stability and quench behavior of YBCO tapes and coils at self-field has been investigated over a range of input energy and transfer currents. The experimental results show that with the input energy increase, quench propagate becomes earlier, but the input energy hardly affects the velocity. Higher transport current accelerates the NZPV. Minimum quench energy (MQE) and minimum propagate current (Imp) have been studied as well, the MQE increased as the transport current decreased. We have numerically
158
W.J. Lu et al. / Physica C 484 (2013) 153–158
investigated the characteristics of the thermal behavior and NZPV during a quench, the results are close to the experimental results. It is an valuable tool for coil design for HTS applications. Acknowledgments This project was founded by the National High Technology Research and Development Program of China (863 Program), and under charge of Prof. Jin Fang. References [1] J.R. Hull, Rep. Prog. Phys. 66 (2003) 1865. [2] A. Ishiyama, H. Ueda, T. Ando, H. Naka, S. Bam, Y. Shiohara, IEEE Trans. Appl. Supercond. 17 (2007) 2430. [3] X. Wang, A.R. Caruso, M. Breschi, G. Zhang, U.P. Trociewitz, H.W. Weijers, J. Schwartz, IEEE Trans. Appl. Supercond. 15 (2005) 2586. [4] Hae-Yong Park, A. Rong Kim, Minwon Park, In-Keun Yu, Beom-Yong Eom, JunHan Bae, Seok-Ho Kim, Kideok Sim, Myung-Hwan Sohn, IEEE Trans. Appl. Supercond. 20 (2010) 1339.
[5] T. Huang, A. Johnston, Y. Yang, C. Beduz, C. Friend, IEEE Trans. Appl. Supercond. 15 (2005) 1647. [6] Z. Bai, X. Wu, C. Wu, J. Wang, Physica C 436 (2006) 99. [7] E. Martínez, F. Lera, M. Martinez-López, Y. Yang, S.I. Schlachter, P. Lezza, P. Kováè, Supercond. Sci. Technol. 19 (2006) 143. [8] H.-I. Du, M.-J. Kim, Y.-J. Kim, D.-H. Lee, B.-S. Han, S.-S. Song, Physica C 470 (2010) 1626. [9] M.N. Wilson, R. Wolf, IEEE Trans. Appl. Supercond. 7 (1997) 950. [10] F. Roy, Ph.D. Thesis, École Polytechnique Fé dé rale de Lausanne (EPFL), 2010. [11] M. Prester, Supercond. Sci. Technol. 11 (1998) 333. [12] I. Aranson, A. Gurevich, V. Vinokur, Phys. Rev. Lett. 87 (2001) 1. [13] J. Mosqueira, O. Cabeza, M.X. François, C. Torrón, F. Vidal, Supercond. Sci. Technol. 6 (1993) 584. [14] M. Tinkham, Introduction to Superconductivity, second ed., Dover Publications Inc., Mineola, NY, 2004. [15] E.A. Young, C.M. Friend, Y. Yang, IEEE Trans. Appl. Supercond. 19 (2009) 2500. [16] N.Y. Kwon, H.S. Kim, K.L. Kim, S. Hahn, H.-R. Kim, O.-B. Hyun, H.M. Kim, W.S. Kim, C. Park, H.G. Lee, IEEE Trans. Appl. Supercond. 20 (2010) 1246. [17] Honghai Song, Justin Schwartz, IEEE Trans. Appl. Supercond. 19 (2009) 3735. [18] Minyi Fu, Xiaofeng Xu, Zhengkuan Jiao, H. Kumakura, K. Togano, Physica C 402 (2004) 234.