A one-dimensional heat conduction model is employed to predict burnout of a Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8} current lead. The upper end of the lead is assumed to be at 77 K and the lower end is at 4 K. The results show that burnout always occurs at the warmer end of the lead. The lead reaches its burnout temperature in two distinct stage. Initially, the temperature rises slowly when part of the lead is in flux-flow state. As the local temperature reaches the critical temperature, it begins to increase sharply. Burnout time depends strongly on flux-flow resistivity

Cha, Y. S.

Hull, J. R.

Niemann, R. C.

Seol, S. Y.

UNT Digital Library

Prediction of Burnout of a Conduction-Cooled BSCCO Current Lead* s. Y. Seol Deparfment of Mechanical Engineering, Chonnam National University, Kwangju 700-757, Korea Y. S. Cha, R. C. Niemann, and J. R. Hull Energy Technology Division, Argonne National Laboratory, Argonne, IL 60439, USA i . '.AL ' ' ' - ' -  'a L'*eid L h  L -tB Ths submitted nunurcrlpt has been created by thc Unkrorsily d Chlugo as Opalor d Argonno Natknal Labmkuy(%Qmlw) undrConlndNo.W-31-10 -  38 with ths U.S. D.p.rtmnt ot Energy. Th. US. Ciovrnmnt retains far Hnlf. and dhen acting on its b s h w . a ~ m w r d u s k e , h r v m b b ~ P g n D a  in r i d  aftkle to reproduce. prepore derkraUve works, distribute copies to the public. and podarm pubikly and d b h v  wbl)ck bv won bshddtheoovemnd. 1. R. W. Weeks 2. R. B. Poeppel 3. U.Balachandran 4. R. A. Valentin 5 .  Authors 6. ESASection 7. B.Baudino 8. F.Y.Fradin 9. H.Drucker 10. S.Lake For presentation at 1996 Applied Superconductivity Conference, August 25-30,1996, Pittsburgh, PA, and publication in IEEE Transactions on Applied Superconductivity. *Work supported by the U.S. Department of Energy, Energy Efficiency and Renewable Energy. as part of a program to develop electric power technology, under Conaact W-31-1W-Eng-38. DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best avaiiable original document. This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employes, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or use- fulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any spe- cific commercial product, process, or service by trade name, trademark, manufac- turer, or otherwise dots not necessarily constitute or imply its endorsement, recorn- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. Prediction of Burnout of a Conduction-Cooled BSCCO Current Lead S. Y. Seol Department of Mechanical Engineering, Chonnam National University. Kwangju 700-757. Korea Y. S. Cha, R. C. Niemann, and J. R. Hull Energy Technology Division, Argonne National Laboratory, Argonne, E. 60439, USA Abstract-A one-dimensional heat conduction model is employed to predict burnout of a B i2Sr2CaCu20s  current lead. The upper end of the lead is assumed to be at 77 K and the lower end is at 4 K. The results show that burnout always occurs at the warmer end of the lead. The lead reaches its burnout temperature in two distinct stages. Initially, the temperature rises slowly when part of the lead is in flux-flow state. As  the local temperature reaches the critical temperature, it begins to increase sharply. Burnout time depends strongly on flux-flow resistivity. I. INTRODUC~ION High-temperature superconductor (HTS) current leads are advantageous because they have the potential to reduce refrigeration requirements to significantly below the best values achievable with conventional leads [ll. Various HTS materials were considered as candidates for certain applications [1]-[7]. Because of the relatively high current in the leads, any small resistance in the lead may lead to burnout by Joule heating. Burnout of current leads has k e n  studied for conventional 181, [9J and superconducting [51-[71 current Ieads. In [7], it was assumed that the entire HTS lead suddenly becomes normal, and the results represent the most conservative estimate of burnout time. However, HTSs are known to have a much wider transition region between superconducting and normal states than conventional low-temperature superconductors. In this transition (flux-flow) state, resistivity is much lower than that in the normal state. Burnout predictions in this study were carried out by including the flux-now (transition) state. A one-dimensiond heat conduction model is employed and the temperatures at upper and lower ends of the lead are assumed to be fixed. The HTS lead is BizSrzCaCuzOg (BSCCO-2212) 'and is made by a melt-casting process. MManwxrpr received August 18. 1996. Work s u p f l e d  by the C.S. Department of Energy. Energy Efficiency and Renewable Energy. as part of J prosram to develop electric p w e r  technology. under Contract W-3 1- 109-Eng-38. II. ANALYSIS The model employed for tbe conduction-cooled current lead is shown in Fig. 1. The BSCCO-2212 rod is a solid cylinder with diameter d and length L. The cold end (lower end) is kept at TL (= 4 K), and the warm end (upper end) is at Tu. The warm-end temperature can be controlled by an intermediate heat intercept and the cold end is usually maintained at a temperature close to the saturation temperature of the cryogenic coolant. It is assumed that heat is transferred by conduction only in the axial direction of the BSCCO rod. This is a conservative assumption because no credit is taken for any heat transfer in the radial direction. The calculation of bumout time of BSCCO-2212 current lead is based on the Fourier heat conduction equation: where y is density, C is specific heat, k is thermal conductivity, p is electrical resistivity, and J is current density. The boundary conditions are Fig. 1. Schematic &gram of current lead geonletry. 2.5 P z 2  e 5 S '  )I 5 1.5 B - E i 0.5 Fig. 2. Variation of thermal conductivity with temperature for BSCCO- 2212 lead. T = T L  a tx=O T = T u  a t x = L .  In this paper, we assume that the lower end of the lead is very close to a pool of liquid helium and TL = 4 K. The upjxr end of the superconductor lead is assumed to be intercepted by liquid nitrogen and Tu = 77 K. The thermal conductivity for the BSCCO-2212 lead is shown in Fig. 2, which comes from [41. The thermal diffusivity of BSCCO-2212 can be obtained from [lo]. The specific heat of BSCCO-2212 is calculated from the data of thermal conductivity and thermal diffusivity and is approximated by C = 1.58 T, (3) where C is in J/(kg-K) and T is absolute temperature in Kelvins. The objective of the burnout analysis is to estimate the time required for the maximum temperature of the lead to reach a specified value called burnout temperature. In this paper, burnout temperature is arbitrarily defined to be Tb = 300 K. The finite-volume metbod is used to solve the partial differential equation (1) with boundary condition given by (2) .  A central difference scheme is employed for space coordinates. and a fully implicit scheme is employed for time. A. Superconducting State - - [ k ( T ) g ]  d = 0. dr (4) The temperature distribution can be obtained by integrating (4): By using the temperature dependent thermal conductivity data, we can calculate the temperature distribution in the superconducting steady state (Fig. 3). Two upper-end temperatures, T u  = 77 and 60 K, are considered. The upper curve of Fig. 3 is for Tu = 77 K, and the lower curve is for T u  = 60 K. TL = 4 K in both cases. To calculate the burnout time, the temperature profile in the steady (superconducting) state is used as an initial condition for the lead. The helium boiloff rate in the superconducting state can be calculated by [5]: where m is the helium boiloff rate (kg/s), and CL is the latent heat of vaporization for liquid helium (2.36 x lo4 Jkg). If the BSCCO-2212 rod is 15 cm long and has a diameter of 5 mm, the calculated helium boiloff rate is 0.269 mg/s for Tu = 77 K, and 0.178 mg/s for T u  = 60 K. B. Critical Current Density The critical current density is primarily a function of temperature. The following equation for critical current density is a linear fit of a small number of values provided by the manufacturer of the BSCCO-2212 rod: If the HTS lead is in the superconducting state, the resistance is zero and no Joule heat is generated. Temperature distribution along the lead can be obtained by solving (1) without the heat generation term, 0 ' ~ " " " '  ' ' 0 0.2 0.4 0.6 0.8 1 % t i  Fig. 3. Steady-state temperature profile of conduction-cooled BSCCO-2212 current lead. Jc(A I cm2 = 10728- 116.64T. (7) Although (7) gives critical temperature T, = 91.9 K, Tc is assumed to be 90 IC in this paper for conservative results. Although the temperature of the superconductor is lower than the critical temperature, the conductor becomes resistive if the operating current density J becomes higher than the critical current density J,(T). Consider an HTS current lead with a temperature distribution like that shown in Fig. 3. If the o p t i n g  current is greater than the critical current at Tu, part of the lead near the upper end becomes resistive. The temperature in the resistive region will increase and beat will be conducted toward the lower end of the lead where the temperature is lower. This increase in temperature will further lower the critical current density, and the resistive region will propagate toward the lower end of the lead. In this paper, the resistive regime is also referred to as the flux- flow regime, which is a transition regime between the superconducting and normal regimes. To calculate the temperature response, we must know the flux-flow resistivity of the BSCCO rod. C. Flux-Flaw Resistivity In general, flux-flow resistivity pff is a function of temperature, and only limited data [l 11 indicate that flux-flow resistivity increases with temperature. However, there are little or no data on flux-flow resistivity of a BSCCO-2212 superconductor. We have conducted experiments to measure the flux-flow resistivity of the BSCCO-2212 rod at 77 K (liquid nitrogen) and 87 K (liquid argon), and the results are shown in Fig. 4. The slope of the E-J curve gives the flux- flow resistivity (pg=  dEldJ). From the data shown in Fig. 4, the flux-flow resistivity of the BSCCO-2212 rod is estimated to be -loe6 R-cm and appears to be fairly insensitive to temperatures between 77 and 87 K. Because there is a lack of data, the uncertainty in the flux-flow resistivity is relatively large. Therefore, in this paper, calculations are carried out by parametrically varying the flux-flow resistivity from 10-5 to 10-7 R-cm. In the numerical calculation, it is assumed that the lead is in the superconducting state if Tc T, and Jc J,(T), and the resistivity is zero. The lead is assumed to be in the resistive (tlux-flow) state if T c T, and J > Jc(T) and the resistivity is equal to pfi The lead is in normal state if T < T, and the resistivity is equal to the normal state resistivity pn. Resistivity of the BSCCO rod under normal state is 2.5 x $2-cm at 92 K. Between 92 and 300 K, normal state resistivity is calculated by linear interpolation. fl-cm at 300 K ,urd 0.8 x 800 I “ 1  4 i 700 9 -1 600 k 0 - 7 - d 3 5 500 5 - 10 100 1000 10000 J, A/cmZ Fig. 4. E-J characteristics of melt-cast BSCCO-2212 rod. m. RESULTS AND DISCUSSION Fig. 5 shows change of temperature with time by using a flux-flow resistivity of R-cm and an operating current of 400 A. Because heat generation is concentrated near the wanner end, temperature rise is also concentrated there. Initially, the rise in temperature is very slow due to the relatively low resistivity of flux flow state. When the temperature reaches the critical point, (90 K), it rises rapidly because there is a sudden increase in resistivity. Once the warmer end becomes normal, the lead reaches its burnout temperature (300 K) in a very short time, as s h o h  in Fig. 5. While 2.8 s are needed for the temperature to rise from 77 K to 90 K, only 0.1 s is needed for the temperature to rise from 90 K to 300 K. At 77 K, critical current density is 1747 A/cm2; this corresponds to a critical current of 343 A. For an operating current of 400 A, the current density is 2037 A/cm2. Therefore, the wanner end of the lead is in the resistive regime and begins to heat up. An operating current of 350 A corresponds to a Current density of 1783 A/cm2. This is slightly higher than the critical current density at 77 K and the lead will heat up also but at a slower rate. The calculated burnout time is 5.8 s, twice that for the 0.13 0.134 0.138 0.142 0.146 0.15 x. m Fig. 5. Temperature cli.&buuon.q of BSCCO-2212 lead at different times frw p,y= la6 W-cm and operating Lvrrent of NO A. case with an operating current of 400 A. If the operating current is below 343 A, the lead will be superconducting everywhere and there is no temperature rise, so &e temperature distribution is l i e  that shown in Fig. 3. Fig. 6 shows the variation of maximum temperature with time for various flux flow resistivities and operating current I=  400 A. Burnout time varies strongly with flux-flow resistivity. The flux-flow resistivity must be measured more accurately in order to predict correctiy the bumout time. Fig. 7 shows the variation of maximum temperature with time for various flux-flow resistivities and an operating current of I = 350 A. The results are similar to that shown in Fig. 6 for I = 400 A, except the burnout time is longer for I = 350 A. IV. CONCLUSIONS Transient behavior and burnout time of a conduction- cooled BSCCO-2212 current lead are predicted by numerically solving a one-dimensional heat conduction equation. The results show that the temperature rise of the superconductor lead exhibited two distinct stages when the operating current density is greater than the critical current density. The temperature at the warmer end of the lead begins to rise slowly because the superconductor is in the dissipative (flux- flow) state. As soon as the local temperature reaches the critical temperature, the temperature begins to increase sharply and approaches the burnout temperature in a relatively short period of time because the normal state resistivity is much higher than the flux-flow resistivity of the superconductor. The time to reach burnout temperature depends strongly on tbe flux-flow resistivity, and there is a general lack of available data on the flux-flow resistivity of high-temperature superconductors. REFERENCES J. R. Hull, "High temperature superconducting current leads," IEEE J. R. Hull, "High temperature superconducting current leads for cryogenic apparatus," Cryogenics, vol. 29, pp. 11 16 1123, 1989. R. C. Niemann. Y. S. Cha. J. R. Hull, W. E. Buckles, and M. L. Daugherty, "High remperature superconducting current leads for micro-SMES applicatioaq." IEEE Trans. Magn., vol. 30, pp. 1,589- 2592. 1994. P. F. Herrmann. et al., "European project for the development of high TC cxtrrent Irails." IEEE Trans. Appl. Supermod.. vol. 3, no. 1, pp. 876-880, 1993. S. Y. Scol and I. R. Hull. "Transient analysis ancl burnout of high temperature superconducting current leach," Cryogenics. vol. 33, pp. 1X6-975. 1993. Trans. Awl. S U ~ ~ ~ C O I I ~ . .  VO . 3, pp  869-875, 1995. 7 0  0.01 0.1 1 10 100 Time. s Fig. 6. Variations of maximum temperature with time for different values of flux-flow resistivity with I = 400 A. 100 90 8 0  Y P a 8 c' 3 a i  1 ,  ' ' l l ' l l . i  ' ' O , A  * ' ' , . * , , ,J  ' '- 0.01 1 100 Fig. 7. Variations of maximum temperature with time for different values of flux-flow resistivity with I = 350 A. Time. s [6] S. Y. Seol, I. R Hull, and M. C. Chyu, "Optimization of high- temperature superconductor current leads," IEEE Trans. Appl. H. Fujishiro, et al., "Low t h e d  conductive Bi-2223 tapes sheathed with Ag-Au alloys," IEEE Trans. Magn., vol. 30, pp. 1645-1650, 1994. A. Bejan and E. M. Cluss, "Criterion for burn-up conditions in gas cooled cryogenic current leads," Cryogenics, vol. 16, pp. 515-518, 1976. Yu. L. Buyanov. "Current leads for use in cryogenic devices. Principle of design and formulae for design calculations," Cryogenics. vol. 23, pp. 94-1 10, 1985. [lo] X. D. Wu. J. R. Fanion, G. S. Kino, S. Ryu, D. B. ,Mitzi. and A. Hapitulnik, 'Thermal diffkivity of Bi2sr2Cacu208 single cryst&." Physica C, vol. 218. pp. 417-423.1993. T. R. Askew, J. G. Nestell. R B. Flippen, D. M. Groski. and .\I. McN. Alford. "Dynamic measurement of flux flow resistivity in Y B a ~ C u 3 0 7  wires." IEEE Trans. Appl. Supercond.. vol. 3. pp. S ~ r c o n d . ,  VOI. 5,  DO. 2. pp. 785-788, 1995. [7] 18) [9] [ i l l  1398-1401. 1993. 

Prediction of burnout of a conduction-cooled BSCCO current lead

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Prediction of burnout of a conduction-cooled BSCCO current lead

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