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An evaluation of the inlet flow reduction for a cable in conduit conductor by rapid heating
Cryogenics 39 (1999) 939±945
An evaluation of the inlet ¯ow reduction for a cable in conduit conductor by rapid heating Makoto Sugimoto *, Takaaki Isono, Norikiyo Koizumi, Gen Nishijima, Kunihiro Matsui, Yoshihiko Nunoya, Yoshikazu Takahashi, Hiroshi Tsuji Superconducting Magnet Laboratory, Japan Atomic Energy Research Institute, 801-1 Mukouyama, Naka-machi, Naka-gun, Ibaraki-ken 311-0193, Japan Received 30 August 1999; accepted 17 November 1999
Abstract The ¯ow reduction of forced ¯ow superconducting coil with a cable in conduit (CIC) conductor has been studied for AC losses due to pulsed operation. In this paper, the ¯ow reduction by rapid heating is described for forced ¯ow superconducting coil with a CIC conductor. The phenomenon of ¯ow reduction of the forced ¯ow coil has been applied for coil quench detection and has been developed by Japan Atomic Energy Research Institute (JAERI). It is named the ``¯uid method'' and essential technology for quench detection of large-scale forced ¯ow superconducting coil as fusion magnets and superconducting magnetic energy storage (SMES) coil. In the ¯uid method, the inlet ¯ow reduction is caused by Joule heating on the normal zone of superconducting coil. The ¯uid method has no electric noise in its detection. This is an advantage for pulsed operation in comparison with other electrical quench detection systems. On the other hand, there are no quantitative considerations between the inlet ¯ow reduction and Joule heating of the coil inside in previous studies. The ¯ow reduction for the quench detection has been determined by the operation experience of forced ¯ow superconducting coil. The purpose of this paper is an estimation of the relation between the inlet ¯ow reduction and Joule heating at coil quench. First, the inlet ¯ow reduction was obtained by experiment in which the sample has an inductive heater for the quench emulation. Second, the evaluation model was proposed and its model showed good agreement between the inlet ¯ow reduction and heat generation of the coil inside by rapid heating as coil quench. Ó 2000 Elsevier Science Ltd. All rights reserved. Keywords: Cable-in-conduit conductors (A); Supercritical helium (B); Forced ¯ow (C); Quench (C); Flow meters (D)
1. Introduction Inlet ¯ow reduction was originally observed in a cable in conduit (CIC) and hollow conductors in the Demo Poloidal Coil (DPC) Project [1]. The inlet ¯ow reduction was analyzed by hydraulic evaluation [2] which is caused by the heat generation of the conductor due to AC losses in pulsed operation. And required helium mass ¯ow rate in pulsed operation was proposed for forced ¯ow superconducting coils [3]. The ¯uid method quench detection system is applied using the phenomenon of inlet ¯ow reduction caused by
*
Corresponding author. Tel.: +81-29-270-7549; fax.: +81-29-2707579. E-mail address: [email protected] (M. Sugimoto).
Joule heating on the normal zone of the superconducting coil. The ¯uid method is an essential technology for quench detection of forced ¯ow superconducting coil and originally has been developed by Japan Atomic Energy Research Institute (JAERI) [4,5]. The ¯uid method has an advantage for pulsed operation in comparison with other electrical quench detection systems because it has no electric noise in the quench detection. The inlet ¯ow reduction must be analyzed for quench detection by the ¯uid method. However, no analytical consideration has been applied between the inlet ¯ow reduction and Joule heating of the coil inside in previous studies. The paper gives an estimation between the inlet ¯ow reduction and Joule heating at coil quench due to rapid heating. The experiment was carried out for this purpose. The sample was made from Nb3 Al superconductor for ITER
0011-2275/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 1 - 2 2 7 5 ( 9 9 ) 0 0 1 2 9 - 0
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M. Sugimoto et al. / Cryogenics 39 (1999) 939±945
Toroidal Field (TF) coils [6]. The inductive heater was assembled for emulation of the coil quench on the sample. The inlet ¯ow reduction was obtained by inductive heating of the sample. Rapid and localized heating was applied to the sample. The new evaluation model is proposed based on experimental results. The evaluation model for inlet ¯ow reduction was originally proposed for heat generation by AC losses in previous studies [2,3]. The model was also applied for rapid heating. The evaluation still has a dierence in comparison with experimental data on inlet ¯ow reduction by rapid heating [1,3]. This paper gives more precise estimation of the inlet ¯ow reduction based on the new model. The new model was obtained by taking the heat conduction of helium in the conductor crosssection into account.
2. Experimental 2.1. Sample conductor The sample conductor consists of Nb3 Al superconductor with a cable in conduit con®guration. It is developed for toroidal ®eld coils of International Thermonuclear Experimental Reactor (ITER) [6]. The main parameter of the conductor is listed in Table 1. The outer diameter of the Nb3 Al strand is 0.81 mm. Chromium plating (2 lm thickness) is applied on the strand surface to reduce the strand coupling losses. Performance of Nb3 Al superconductor has already achieved the same performance as one of Nb3 Sn by recent development. The conductor consists of six sub cables and a total of 1152 Nb3 Al strands. The sub cable laps are surrounded
by Inconel 600 to reduce the coupling losses among the cables. The center channel is for helium space and small pressure drop in the cooling paths. The helium travels between the center channel and cables because the subcable lap and center channel have a gap. The jacket is made from cryogenic stainless steel (JN1HR) which is developed by JAERI for Nb3 Al cable in conduit conductors [7]. 2.2. Test sample The test sample consists of two straight conductor legs (3.6 m length) as shown in Fig. 1. Each conductor leg is connected electrically by the lower joint terminal. And the upper joint terminals are connected to forced cooled current lead [9] as the facility side by which the current is supplied. This sample is available for current sharing temperature (Tcs ) and electric joint resistance measurement by this facility [8]. The inductive heater is assembled on the sample to emulate the coil quench and rapid heating in the conductor. The length of the inductive heater is 88 mm and heating duration is a few 10 ms.
Table 1 Main parameters of the Nb3 Al ITER±TF conductor Strand Diameter Cu/Non Cu ratio RRR Surface Critical current density (Non-Cu) Conductor Number of strands Con®guration Outer diameter Inner diameter Outer diameter of center channel Inner diameter of center channel Strand cross-section Helium cross-section Void fraction Wet perimeter Hydraulic diameter Jacket material
0.81 mm 1.5 120 2 lm Cr plating 600±680 A/mm2 at 12 T Average 620 A/mm2 1152 34446 42.5 mm 38.5 mm 12 mm 10 mm 594 mm2 554 mm2 36% at cable space 3100 mm 0.72 mm Stainless steel: JN1HR
Fig. 1. Test sample with the current lead. Test sample consists of two straight superconductors.
M. Sugimoto et al. / Cryogenics 39 (1999) 939±945
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2.3. Sensor location The sensor location is shown in Fig. 2 for the test sample. Supercritical helium (SHe) coolant is supplied from the upper terminal side to the conductor. The sensors which are a ¯ow meter (ori®ce type), temperature sensor (carbon graphite resistor) and pressure tap are located on the helium-supply plumbing. The inlet ¯ow reduction was measured by this ¯ow meter in the experiment. SHe travels on the sample conductor and is returned to the refrigerator from the lower joint. The temperature sensor and pressure tap are also installed on the return helium plumbing. 2.4. Test facility Flow reduction experiment was carried out at the superconducting performance test facility for large-current conductor of fusion machine which has been developed by JAERI and named Ic test stand [8]. The test sample is connected both mechanically and electrically by bolts on the upper terminal to the test facility (Fig. 1). The transport current of the sample is available up to 60 kA on Ic test stand. SHe coolant is supplied from a 5 kW helium refrigerator and 20 000 l helium storage tank. Cryogenic system of the Ic test stand is shown in Fig. 3. The supply temperature of the coolant is increased by the resistive heater which is installed on the plumbing. The coolant
Fig. 3. Cryogenic system of the Ic test stand. Supercritical helium (SHe) is supplied to the sample from a 5 kW refrigerator. SHe is cooled by the heat exchanger which is installed in the helium reservoir. SHe is heated and the supply temperature controlled by the resistive heater which is assembled on the supply plumbing. SHe after traveling over the sample is supplied to the helium reservoir. The upper and current lead terminal is also cooled by SHe.
after traveling over the conductor is supplied to the helium reservoir. The coolant also cools on the upper terminal and current lead and ®nally it is returned to gas bags. Available coolant conditions on the sample are: pressure 0.3±1.0 MPa, temperature 5±16 K, mass ¯ow rate 6 10 g/s. The sample well is located in the middle of the helium reservoir. The sample well is a vacuum environment during the experiments in which the sample was installed. Superconducting split coils are installed on the helium reservoir and they apply the magnetic ¯ux density to the sample. 2.5. Experimental results ± Inlet ¯ow reduction by rapid heating
Fig. 2. Sensor location of the test sample. The ¯ow reduction experiment was carried out by using the conductor on the positive side and inductive heater. There was no transport current or applied magnetic ®eld during this experiment.
The experimental results of inlet ¯ow reduction due to the rapid heating are shown in Fig. 4. The heating duration of the inductive heater was 40 ms. The coolant conditions, pressure, mass ¯ow rate are the parameters of the experiment. No transport current and magnetic ®elds were applied to the sample on this experiment for inlet ¯ow reduction. The inlet ¯ow reduction was measured by the ¯ow meter (ori®ce type) which was installed on the supply helium plumbing. The correlation of heat input to the sample was calibrated by the calorimetric method [10]. Heat input is described as total heat inputs divided by unit volume of superconducting strands and it is present by term of ``strand'' in the unit of horizontal axis in Fig. 4.
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Estrand
Ahe Astrand
Z
T1
T0
qCP dT
2
where Estrand is the heat input per unit volume of superconducting strands (J/m3 ), Ahe is the helium crosssection of the conductor(m2 ), Astrand is the cross-section of superconducting strands (m2 ), q is the helium density (kg/m3 ), CP is the helium speci®c heat at constant pressure (J/(kg K)), T is the helium temperature (K), T0 is the helium temperature before heating (K), and T1 is the Helium temperature after heating (K). The experimental results are summarized by heat input per unit volume of superconducting strands as shown in Fig. 4. Then the heat capacity of the jacket material is neglected in Eq. (2). The inlet ¯ow reduction is expressed Eq. (3) from the equation of continuity [1,3] u L 1ÿ ln q0 ÿ ln q1 3 u0 2 Dt u0
Fig. 4. Experimental results of the inlet ¯ow reduction due to the rapid heating. Symbols represent the data and lines show the empirical correlation as listed in Table 2. The heating was by inductive heater and the heating duration was 40 ms in the experiment. Heat input in horizontal axis is described a total heat inputs divided by unit volume of superconducting strands and its presents by term of ``strand'' in the unit.
where u0 is the initial helium velocity (m/s), Du is the velocity change due to the heating (m/s), u is the velocity after heating (u u0 ÿ Du < u0 ), L is the heating length (m), Dt is the heating duration (s), and q0 and q1 is the helium density at temperature T0 and T1 .
The inlet ¯ow reduction depends on the initial mass ¯ow rate in comparison with the helium pressure. This means much initial helium ¯ow causes a small inlet ¯ow reduction rate. Also helium pressure is not dominant for the inlet ¯ow reduction. The empirical equations between the heat input and inlet ¯ow reduction are described in Eq. (1) as shown in Fig. 4. u f eg Einput 1 u0
3.2. Eective heating duration Let us make precise evaluation of the heating duration (Dt) in Eq. (3) as follows. The heat conduction in the cross-section of the conductor takes the heating duration into account. A forced ¯ow superconductor like a CIC conductor, which is a coolant path, is modeled as plumbing which has an inner diameter of hydraulic diameter (Dh ) as shown in Fig. 5. It is assumed that the coolant SHe travels on the inner diameter of Dh and is heated on the tube wall in this model. In the experimental situation, the superconducting strands are heated by rapid heating and the heat is transferred to the cross-section of the conductor by heat conduction. It is evaluated that the tube wall is heated by rapid heating and heat is transferred to the cross-section of the conductor by heat conduction in this model. The heat conduction Eq. (4) is applied to the cross-section of the conductor and the
where u=u0 is the ¯ow reduction rate(non-dimensional number), and Einput is the heat input per unit volume of superconducting strands (mJ/cm3 -strands). The coecients f and g in Eq. (1) are listed in Table 2. 3. Analysis 3.1. Governmental equation The temperature rise and heat input are evaluated by Eq. (2) in the heating zone [1,3] Table 2 Coecients in the empirical equation (Eq. (1)) u=u0 f eg Einput a Experimental condition
Correlation
Pressure (MPa)
Flow rate (g/s)
f
g
Residual
0.40 0.33 0.20 0.19 0.78
4.0 10 4.0 5.7 4.0
0.95 0.93 0.90 0.92 0.99
ÿ2:1 10ÿ4 ÿ3:2 10ÿ5 ÿ1:7 10ÿ4 ÿ6:3 10ÿ5 ÿ1:2 10ÿ4
0.99 0.98 0.97 0.98 0.98
a
Experimental results of the inlet ¯ow reduction due to rapid heating. Einput shows heat input per unit volume of superconducting strands and its has a unit of mJ/cm3 -strands.
M. Sugimoto et al. / Cryogenics 39 (1999) 939±945
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Fig. 5. Model of the cooling path for a forced ¯ow superconductor. Hydraulic diameter Dh is applied to the cooling tube.
heating duration is modi®ed by the heat conduction in cross-section q CP
oT o2 T k 2 ot oy
4
where t is the time (s), k is the thermal conductivity of helium (W/m K), and y is the axis on the cross-section of conductor (m). The initial condition of Eq. (4) is assumed by Dirac's delta function as shown in Eq. (5): T y; 0 f y f y lim de y 0 e!0 1=e jyj < e=2 de y 0 jyj > e=2
5
where f y is the Dirac's delta function. The analytical solution is obtained Eq. (6) by the liner assumption of Eq. (4) and the initial condition of Eq. (5) [11]: 1 2 T y; t p eÿy = 4jt 2 pjt k j CP q
6
The helium temperature at the center of the cooling tube in this model is expressed by Eq. (7) which has maximum distance from the tube wall as the heating zone 1 2 T Dh =2; t p eÿDh = 16jt 2 pjt
7
The maximum helium temperature at the position y Dh =2 is obtained from Eq. (7) after heating from the tube wall. The pro®le of the helium temperature is shown in Fig. 6 for this model. 2
oT Dh =2; t p ÿ2jt Dh =2 D2 = 16jt 0 ot t jpt 3=2 8e h teff
D2 D2 CP q h h 8j 8k
8
Eective heating duration (teff ) is de®ned by Eq. (8).
Fig. 6. De®nition of the eective heating duration as described by Eq. (8) based on the temperature pro®le in the cross-section of the conductor.
The evaluation of ¯ow reduction is modi®ed as in Eq. (9) by eective heating duration (teff ) instead of heating duration (Dt) on Eq. (3) u L 1ÿ ln q0 ÿ ln q1 u0 2 teff u0
9
4. Discussion The eective heating duration as de®ned by Eq. (8) is evaluated for the experimental conditions as described in Section 2.5. The eective heating duration is described as a function of speci®c heat at constant pressure (CP ), thermal conductivity (k) and density (q) for helium coolant. It is well know that speci®c heat of helium has a maximum value near the 4 K region as shown in Fig. 7. The eective heating duration also has a maximum value as shown in Fig. 8 near the 4 K region. In the experimental conditions, the eective heating duration as de®ned by Eq. (8) is evaluated as a few seconds. The heating duration of the inductive heater was 40 ms in all experiments. The heat generation on the superconducting strands was also of the same time duration. The heat is transferred to all of the helium
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M. Sugimoto et al. / Cryogenics 39 (1999) 939±945
Fig. 7. Speci®c heat at constant pressure of helium [12]. It is well known that speci®c heat has a maximum value near the 4 K region.
Fig. 8. Eective heating duration as described in Eq. (8).
cross-sections in a few seconds. This takes more than hundred times longer than with inductive heating. For example, speci®c heat at constant pressure is 25.5 J/g K at 0.33 MPa, 5.7 K as shown in Fig. 7. It is a maximum value at 0.33 MPa of helium pressure. At 0.33 MPa and 4.5 K, it is 4.4 J/g K. Eective heating duration as described Eq. (8) is slightly changed from 1.7 s at 4.5 K to a maximum value of 5.7 s at 5.8 K. Helium temperature was always increased by inductive heating in the experiments. The speci®c heat and eective heating durations have a maximum value in heating. The maximum value of eective heating duration is dominant for the inlet ¯ow reduction. The effective heating duration is required for a maximum value near the 4 K temperature region. It is also modi®ed for the inlet ¯ow reduction by Eq. (10) instead of (9). u L 1ÿ ln q0 ÿ ln q1 ; u0 2 teff max u0
10
Fig. 9. Comparison between experimental and analytical ¯ow reduction. Analytical ¯ow reduction is evaluated by Eq. (10). Symbols represent the experimental results. Lines show the analytical results.
where teff max is the maximum value of eective heating duration near 4 K. Analytical inlet ¯ow reduction as described by Eq. (10) is determined in comparison with experimental results as shown in Section 2.5. Heat input is also described by Eq. (2). Experimental inlet ¯ow reduction depended on the initial helium ¯ow rate. Comparison is made for three independent initial ¯ow rates from the experimental results as shown in Fig. 9. Analytical ¯ow reduction has good agreement with the experimental results for large initial helium ¯ow rate. Also, for small heat input (<3000 mJ/cm3 -strand), it agrees well with the experiment. For large heat input (>3000 mJ/cm3 -strand), there are dierences between the experimental and analytical results. Actual heating length may be longer than the calculation because of the heat conduction of the helium on large heat input condition. The maximum value of the eective heating duration is reasonable for the inlet ¯ow reduction by rapid heating as de®ned by Eq. (10). In the rapid heating, the heat from the superconducting strand as a heating zone may travel to the helium coolant in seconds and cause the inlet ¯ow reduction. The inlet ¯ow is reduced to zero in a few seconds. Duration for the inlet ¯ow reduction also is a few seconds in previous experimental research for cable in conduit conductor [1,5]. These experimental results also support the evaluation of inlet ¯ow reduction by eective heating duration.
5. Conclusions The inlet ¯ow reduction of cable in conduit conductor was described on the view points of the experiment and analysis in the rapid heating. There have been no quantitative studies in the past regarding the relation-
M. Sugimoto et al. / Cryogenics 39 (1999) 939±945
ship between the inlet ¯ow reduction and heat generation in the conductor. The relationship between them was determined quantitatively by experiment and analysis in this paper. The conclusions are summarized as follows. · Experimental data of inlet ¯ow reduction were obtained for Nb3 Al superconductor for ITER-TF coils. An inductive heater was installed on the conductor for the rapid heating. Conditions of the helium coolant, pressure and mass ¯ow rate were experimental parameters for ¯ow reduction. It was also found that the inlet ¯ow reduction depends on the initial mass ¯ow rate in experimental results. · The eective heating duration (teff ) for inlet ¯ow reduction by rapid heating was introduced for determining heat generation in cable in conduit conductor as follows: oT Dh =2; t 0 ot teff
D2h D2h CP 8j 8k
· Inlet ¯ow reduction by rapid heating is predicted by applying to the equation the maximum eective heating duration u L 1ÿ ln q0 ÿ ln q1 u0 2 teff max u0 · In rapid heating, the inlet ¯ow is reduced to zero in a few seconds. Duration for the inlet ¯ow reduction is also a few seconds. The heat from the superconducting strand as a heating zone may travel to the helium coolant in seconds as de®ned by the eective heating duration. · The inlet ¯ow reduction as a function of heat generation on the conductor was predicted by experimental and analytical investigation of rapid heating. Amount of the normal zone generation can be determined by the inlet ¯ow reduction directly during the coil quench. This makes quench detection method reliable for a forced ¯ow superconducting coil.
945
Acknowledgements The authors would like to thank Prof. S. Shimamoto (Tohoku University), Drs. M. Ohta (JAERI), S. Matsuda and Y. Seki for their continuing encouragement during this work. We would like to express our gratitude to all the sta members of Superconducting Magnet Laboratory of JAERI who contributed to this experiment.
References [1] Sugimoto M, Kato T, Kawano K, Hiyama T, et al. Test results of the DPC-TJ: thermal and hydraulic performance. Cryogenics 1993;33(6):597±602. [2] Sugimoto M, Kato T, Isono T, Yoshida K, Tsuji H. Flow reduction by AC losses for a forced ¯ow superconducting coil with a cable in conduit conductor. Cryogenics 1999;39(4):323±30. [3] Sugimoto M, Isono T, Yoshida K, Tsuji H, et al. An evaluation of the inlet ¯ow reduction for a cable-in-conduit conductor in pulsed operation. Cryogenics 1998;38(10):989±94. [4] Yoshida K, Quench detection methods of superconducting coil for the fusion reactor. Cryo Eng 1989;24(5):276±82 (in Japanese). [5] Yoshida K, Stability and protection of forced cooling conductor for large superconducting magnet. JAERI-M 1992;92±119 (in Japanese). [6] Yamada Y, Ayai N, Mikumo A, Ito M, Hayashi K, et al. Development fo Nb3 Al superconductors for International Thermonuclear Experimental Reactor (ITER). Cryogenics 1999;39:115±22. [7] Nakajima H, Nunoya Y, Nozawa M, Ivano O, et al. Development of high strength austenitic stainless steel for conduit of Nb3 Al conductor. Adv Cryo Eng 1996;42:323±30. [8] Takahashi Y, Oshikiri M, Kawano K, Hanawa H, et al. Superconducting performance test facility for large-current conductor of fusion machine. Cryo Eng 1998;33(5):323±33 (in Japanese). [9] Takahashi Y, Sugimoto M, Matsui K, Takano K, et al. Experimental results and design of 50 kA forced-cooled current leads for fusion machine. In: Proceedings of the ICEC16/ICMC, Kitakyushu, Japan, 1996:795±98. [10] Hamada K, Takahashi Y, Koizumi N, Tsuji H, et al. Thermal and hydraulic measurement in the ITER Quell experiments. Adv Cryo Eng 1998;43:197±204. [11] Carslaw HS, Jaeger JC, Conduction of heat in solids. 2nd ed. Oxford: Oxford University Press, 1959:53±8. [12] Arp VD, McCarty RD. Thermophysical properties of Helium-4 from 0.8 to 1500 K with pressures to 2000 MPa, NIST Technical Note 1334, US Government printing oce, 1989.
An evaluation of the inlet ¯ow reduction for a cable in conduit conductor by rapid heating Makoto Sugimoto *, Takaaki Isono, Norikiyo Koizumi, Gen Nishijima, Kunihiro Matsui, Yoshihiko Nunoya, Yoshikazu Takahashi, Hiroshi Tsuji Superconducting Magnet Laboratory, Japan Atomic Energy Research Institute, 801-1 Mukouyama, Naka-machi, Naka-gun, Ibaraki-ken 311-0193, Japan Received 30 August 1999; accepted 17 November 1999
Abstract The ¯ow reduction of forced ¯ow superconducting coil with a cable in conduit (CIC) conductor has been studied for AC losses due to pulsed operation. In this paper, the ¯ow reduction by rapid heating is described for forced ¯ow superconducting coil with a CIC conductor. The phenomenon of ¯ow reduction of the forced ¯ow coil has been applied for coil quench detection and has been developed by Japan Atomic Energy Research Institute (JAERI). It is named the ``¯uid method'' and essential technology for quench detection of large-scale forced ¯ow superconducting coil as fusion magnets and superconducting magnetic energy storage (SMES) coil. In the ¯uid method, the inlet ¯ow reduction is caused by Joule heating on the normal zone of superconducting coil. The ¯uid method has no electric noise in its detection. This is an advantage for pulsed operation in comparison with other electrical quench detection systems. On the other hand, there are no quantitative considerations between the inlet ¯ow reduction and Joule heating of the coil inside in previous studies. The ¯ow reduction for the quench detection has been determined by the operation experience of forced ¯ow superconducting coil. The purpose of this paper is an estimation of the relation between the inlet ¯ow reduction and Joule heating at coil quench. First, the inlet ¯ow reduction was obtained by experiment in which the sample has an inductive heater for the quench emulation. Second, the evaluation model was proposed and its model showed good agreement between the inlet ¯ow reduction and heat generation of the coil inside by rapid heating as coil quench. Ó 2000 Elsevier Science Ltd. All rights reserved. Keywords: Cable-in-conduit conductors (A); Supercritical helium (B); Forced ¯ow (C); Quench (C); Flow meters (D)
1. Introduction Inlet ¯ow reduction was originally observed in a cable in conduit (CIC) and hollow conductors in the Demo Poloidal Coil (DPC) Project [1]. The inlet ¯ow reduction was analyzed by hydraulic evaluation [2] which is caused by the heat generation of the conductor due to AC losses in pulsed operation. And required helium mass ¯ow rate in pulsed operation was proposed for forced ¯ow superconducting coils [3]. The ¯uid method quench detection system is applied using the phenomenon of inlet ¯ow reduction caused by
*
Corresponding author. Tel.: +81-29-270-7549; fax.: +81-29-2707579. E-mail address: [email protected] (M. Sugimoto).
Joule heating on the normal zone of the superconducting coil. The ¯uid method is an essential technology for quench detection of forced ¯ow superconducting coil and originally has been developed by Japan Atomic Energy Research Institute (JAERI) [4,5]. The ¯uid method has an advantage for pulsed operation in comparison with other electrical quench detection systems because it has no electric noise in the quench detection. The inlet ¯ow reduction must be analyzed for quench detection by the ¯uid method. However, no analytical consideration has been applied between the inlet ¯ow reduction and Joule heating of the coil inside in previous studies. The paper gives an estimation between the inlet ¯ow reduction and Joule heating at coil quench due to rapid heating. The experiment was carried out for this purpose. The sample was made from Nb3 Al superconductor for ITER
0011-2275/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 1 - 2 2 7 5 ( 9 9 ) 0 0 1 2 9 - 0
940
M. Sugimoto et al. / Cryogenics 39 (1999) 939±945
Toroidal Field (TF) coils [6]. The inductive heater was assembled for emulation of the coil quench on the sample. The inlet ¯ow reduction was obtained by inductive heating of the sample. Rapid and localized heating was applied to the sample. The new evaluation model is proposed based on experimental results. The evaluation model for inlet ¯ow reduction was originally proposed for heat generation by AC losses in previous studies [2,3]. The model was also applied for rapid heating. The evaluation still has a dierence in comparison with experimental data on inlet ¯ow reduction by rapid heating [1,3]. This paper gives more precise estimation of the inlet ¯ow reduction based on the new model. The new model was obtained by taking the heat conduction of helium in the conductor crosssection into account.
2. Experimental 2.1. Sample conductor The sample conductor consists of Nb3 Al superconductor with a cable in conduit con®guration. It is developed for toroidal ®eld coils of International Thermonuclear Experimental Reactor (ITER) [6]. The main parameter of the conductor is listed in Table 1. The outer diameter of the Nb3 Al strand is 0.81 mm. Chromium plating (2 lm thickness) is applied on the strand surface to reduce the strand coupling losses. Performance of Nb3 Al superconductor has already achieved the same performance as one of Nb3 Sn by recent development. The conductor consists of six sub cables and a total of 1152 Nb3 Al strands. The sub cable laps are surrounded
by Inconel 600 to reduce the coupling losses among the cables. The center channel is for helium space and small pressure drop in the cooling paths. The helium travels between the center channel and cables because the subcable lap and center channel have a gap. The jacket is made from cryogenic stainless steel (JN1HR) which is developed by JAERI for Nb3 Al cable in conduit conductors [7]. 2.2. Test sample The test sample consists of two straight conductor legs (3.6 m length) as shown in Fig. 1. Each conductor leg is connected electrically by the lower joint terminal. And the upper joint terminals are connected to forced cooled current lead [9] as the facility side by which the current is supplied. This sample is available for current sharing temperature (Tcs ) and electric joint resistance measurement by this facility [8]. The inductive heater is assembled on the sample to emulate the coil quench and rapid heating in the conductor. The length of the inductive heater is 88 mm and heating duration is a few 10 ms.
Table 1 Main parameters of the Nb3 Al ITER±TF conductor Strand Diameter Cu/Non Cu ratio RRR Surface Critical current density (Non-Cu) Conductor Number of strands Con®guration Outer diameter Inner diameter Outer diameter of center channel Inner diameter of center channel Strand cross-section Helium cross-section Void fraction Wet perimeter Hydraulic diameter Jacket material
0.81 mm 1.5 120 2 lm Cr plating 600±680 A/mm2 at 12 T Average 620 A/mm2 1152 34446 42.5 mm 38.5 mm 12 mm 10 mm 594 mm2 554 mm2 36% at cable space 3100 mm 0.72 mm Stainless steel: JN1HR
Fig. 1. Test sample with the current lead. Test sample consists of two straight superconductors.
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2.3. Sensor location The sensor location is shown in Fig. 2 for the test sample. Supercritical helium (SHe) coolant is supplied from the upper terminal side to the conductor. The sensors which are a ¯ow meter (ori®ce type), temperature sensor (carbon graphite resistor) and pressure tap are located on the helium-supply plumbing. The inlet ¯ow reduction was measured by this ¯ow meter in the experiment. SHe travels on the sample conductor and is returned to the refrigerator from the lower joint. The temperature sensor and pressure tap are also installed on the return helium plumbing. 2.4. Test facility Flow reduction experiment was carried out at the superconducting performance test facility for large-current conductor of fusion machine which has been developed by JAERI and named Ic test stand [8]. The test sample is connected both mechanically and electrically by bolts on the upper terminal to the test facility (Fig. 1). The transport current of the sample is available up to 60 kA on Ic test stand. SHe coolant is supplied from a 5 kW helium refrigerator and 20 000 l helium storage tank. Cryogenic system of the Ic test stand is shown in Fig. 3. The supply temperature of the coolant is increased by the resistive heater which is installed on the plumbing. The coolant
Fig. 3. Cryogenic system of the Ic test stand. Supercritical helium (SHe) is supplied to the sample from a 5 kW refrigerator. SHe is cooled by the heat exchanger which is installed in the helium reservoir. SHe is heated and the supply temperature controlled by the resistive heater which is assembled on the supply plumbing. SHe after traveling over the sample is supplied to the helium reservoir. The upper and current lead terminal is also cooled by SHe.
after traveling over the conductor is supplied to the helium reservoir. The coolant also cools on the upper terminal and current lead and ®nally it is returned to gas bags. Available coolant conditions on the sample are: pressure 0.3±1.0 MPa, temperature 5±16 K, mass ¯ow rate 6 10 g/s. The sample well is located in the middle of the helium reservoir. The sample well is a vacuum environment during the experiments in which the sample was installed. Superconducting split coils are installed on the helium reservoir and they apply the magnetic ¯ux density to the sample. 2.5. Experimental results ± Inlet ¯ow reduction by rapid heating
Fig. 2. Sensor location of the test sample. The ¯ow reduction experiment was carried out by using the conductor on the positive side and inductive heater. There was no transport current or applied magnetic ®eld during this experiment.
The experimental results of inlet ¯ow reduction due to the rapid heating are shown in Fig. 4. The heating duration of the inductive heater was 40 ms. The coolant conditions, pressure, mass ¯ow rate are the parameters of the experiment. No transport current and magnetic ®elds were applied to the sample on this experiment for inlet ¯ow reduction. The inlet ¯ow reduction was measured by the ¯ow meter (ori®ce type) which was installed on the supply helium plumbing. The correlation of heat input to the sample was calibrated by the calorimetric method [10]. Heat input is described as total heat inputs divided by unit volume of superconducting strands and it is present by term of ``strand'' in the unit of horizontal axis in Fig. 4.
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M. Sugimoto et al. / Cryogenics 39 (1999) 939±945
Estrand
Ahe Astrand
Z
T1
T0
qCP dT
2
where Estrand is the heat input per unit volume of superconducting strands (J/m3 ), Ahe is the helium crosssection of the conductor(m2 ), Astrand is the cross-section of superconducting strands (m2 ), q is the helium density (kg/m3 ), CP is the helium speci®c heat at constant pressure (J/(kg K)), T is the helium temperature (K), T0 is the helium temperature before heating (K), and T1 is the Helium temperature after heating (K). The experimental results are summarized by heat input per unit volume of superconducting strands as shown in Fig. 4. Then the heat capacity of the jacket material is neglected in Eq. (2). The inlet ¯ow reduction is expressed Eq. (3) from the equation of continuity [1,3] u L 1ÿ ln q0 ÿ ln q1 3 u0 2 Dt u0
Fig. 4. Experimental results of the inlet ¯ow reduction due to the rapid heating. Symbols represent the data and lines show the empirical correlation as listed in Table 2. The heating was by inductive heater and the heating duration was 40 ms in the experiment. Heat input in horizontal axis is described a total heat inputs divided by unit volume of superconducting strands and its presents by term of ``strand'' in the unit.
where u0 is the initial helium velocity (m/s), Du is the velocity change due to the heating (m/s), u is the velocity after heating (u u0 ÿ Du < u0 ), L is the heating length (m), Dt is the heating duration (s), and q0 and q1 is the helium density at temperature T0 and T1 .
The inlet ¯ow reduction depends on the initial mass ¯ow rate in comparison with the helium pressure. This means much initial helium ¯ow causes a small inlet ¯ow reduction rate. Also helium pressure is not dominant for the inlet ¯ow reduction. The empirical equations between the heat input and inlet ¯ow reduction are described in Eq. (1) as shown in Fig. 4. u f eg Einput 1 u0
3.2. Eective heating duration Let us make precise evaluation of the heating duration (Dt) in Eq. (3) as follows. The heat conduction in the cross-section of the conductor takes the heating duration into account. A forced ¯ow superconductor like a CIC conductor, which is a coolant path, is modeled as plumbing which has an inner diameter of hydraulic diameter (Dh ) as shown in Fig. 5. It is assumed that the coolant SHe travels on the inner diameter of Dh and is heated on the tube wall in this model. In the experimental situation, the superconducting strands are heated by rapid heating and the heat is transferred to the cross-section of the conductor by heat conduction. It is evaluated that the tube wall is heated by rapid heating and heat is transferred to the cross-section of the conductor by heat conduction in this model. The heat conduction Eq. (4) is applied to the cross-section of the conductor and the
where u=u0 is the ¯ow reduction rate(non-dimensional number), and Einput is the heat input per unit volume of superconducting strands (mJ/cm3 -strands). The coecients f and g in Eq. (1) are listed in Table 2. 3. Analysis 3.1. Governmental equation The temperature rise and heat input are evaluated by Eq. (2) in the heating zone [1,3] Table 2 Coecients in the empirical equation (Eq. (1)) u=u0 f eg Einput a Experimental condition
Correlation
Pressure (MPa)
Flow rate (g/s)
f
g
Residual
0.40 0.33 0.20 0.19 0.78
4.0 10 4.0 5.7 4.0
0.95 0.93 0.90 0.92 0.99
ÿ2:1 10ÿ4 ÿ3:2 10ÿ5 ÿ1:7 10ÿ4 ÿ6:3 10ÿ5 ÿ1:2 10ÿ4
0.99 0.98 0.97 0.98 0.98
a
Experimental results of the inlet ¯ow reduction due to rapid heating. Einput shows heat input per unit volume of superconducting strands and its has a unit of mJ/cm3 -strands.
M. Sugimoto et al. / Cryogenics 39 (1999) 939±945
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Fig. 5. Model of the cooling path for a forced ¯ow superconductor. Hydraulic diameter Dh is applied to the cooling tube.
heating duration is modi®ed by the heat conduction in cross-section q CP
oT o2 T k 2 ot oy
4
where t is the time (s), k is the thermal conductivity of helium (W/m K), and y is the axis on the cross-section of conductor (m). The initial condition of Eq. (4) is assumed by Dirac's delta function as shown in Eq. (5): T y; 0 f y f y lim de y 0 e!0 1=e jyj < e=2 de y 0 jyj > e=2
5
where f y is the Dirac's delta function. The analytical solution is obtained Eq. (6) by the liner assumption of Eq. (4) and the initial condition of Eq. (5) [11]: 1 2 T y; t p eÿy = 4jt 2 pjt k j CP q
6
The helium temperature at the center of the cooling tube in this model is expressed by Eq. (7) which has maximum distance from the tube wall as the heating zone 1 2 T Dh =2; t p eÿDh = 16jt 2 pjt
7
The maximum helium temperature at the position y Dh =2 is obtained from Eq. (7) after heating from the tube wall. The pro®le of the helium temperature is shown in Fig. 6 for this model. 2
oT Dh =2; t p ÿ2jt Dh =2 D2 = 16jt 0 ot t jpt 3=2 8e h teff
D2 D2 CP q h h 8j 8k
8
Eective heating duration (teff ) is de®ned by Eq. (8).
Fig. 6. De®nition of the eective heating duration as described by Eq. (8) based on the temperature pro®le in the cross-section of the conductor.
The evaluation of ¯ow reduction is modi®ed as in Eq. (9) by eective heating duration (teff ) instead of heating duration (Dt) on Eq. (3) u L 1ÿ ln q0 ÿ ln q1 u0 2 teff u0
9
4. Discussion The eective heating duration as de®ned by Eq. (8) is evaluated for the experimental conditions as described in Section 2.5. The eective heating duration is described as a function of speci®c heat at constant pressure (CP ), thermal conductivity (k) and density (q) for helium coolant. It is well know that speci®c heat of helium has a maximum value near the 4 K region as shown in Fig. 7. The eective heating duration also has a maximum value as shown in Fig. 8 near the 4 K region. In the experimental conditions, the eective heating duration as de®ned by Eq. (8) is evaluated as a few seconds. The heating duration of the inductive heater was 40 ms in all experiments. The heat generation on the superconducting strands was also of the same time duration. The heat is transferred to all of the helium
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M. Sugimoto et al. / Cryogenics 39 (1999) 939±945
Fig. 7. Speci®c heat at constant pressure of helium [12]. It is well known that speci®c heat has a maximum value near the 4 K region.
Fig. 8. Eective heating duration as described in Eq. (8).
cross-sections in a few seconds. This takes more than hundred times longer than with inductive heating. For example, speci®c heat at constant pressure is 25.5 J/g K at 0.33 MPa, 5.7 K as shown in Fig. 7. It is a maximum value at 0.33 MPa of helium pressure. At 0.33 MPa and 4.5 K, it is 4.4 J/g K. Eective heating duration as described Eq. (8) is slightly changed from 1.7 s at 4.5 K to a maximum value of 5.7 s at 5.8 K. Helium temperature was always increased by inductive heating in the experiments. The speci®c heat and eective heating durations have a maximum value in heating. The maximum value of eective heating duration is dominant for the inlet ¯ow reduction. The effective heating duration is required for a maximum value near the 4 K temperature region. It is also modi®ed for the inlet ¯ow reduction by Eq. (10) instead of (9). u L 1ÿ ln q0 ÿ ln q1 ; u0 2 teff max u0
10
Fig. 9. Comparison between experimental and analytical ¯ow reduction. Analytical ¯ow reduction is evaluated by Eq. (10). Symbols represent the experimental results. Lines show the analytical results.
where teff max is the maximum value of eective heating duration near 4 K. Analytical inlet ¯ow reduction as described by Eq. (10) is determined in comparison with experimental results as shown in Section 2.5. Heat input is also described by Eq. (2). Experimental inlet ¯ow reduction depended on the initial helium ¯ow rate. Comparison is made for three independent initial ¯ow rates from the experimental results as shown in Fig. 9. Analytical ¯ow reduction has good agreement with the experimental results for large initial helium ¯ow rate. Also, for small heat input (<3000 mJ/cm3 -strand), it agrees well with the experiment. For large heat input (>3000 mJ/cm3 -strand), there are dierences between the experimental and analytical results. Actual heating length may be longer than the calculation because of the heat conduction of the helium on large heat input condition. The maximum value of the eective heating duration is reasonable for the inlet ¯ow reduction by rapid heating as de®ned by Eq. (10). In the rapid heating, the heat from the superconducting strand as a heating zone may travel to the helium coolant in seconds and cause the inlet ¯ow reduction. The inlet ¯ow is reduced to zero in a few seconds. Duration for the inlet ¯ow reduction also is a few seconds in previous experimental research for cable in conduit conductor [1,5]. These experimental results also support the evaluation of inlet ¯ow reduction by eective heating duration.
5. Conclusions The inlet ¯ow reduction of cable in conduit conductor was described on the view points of the experiment and analysis in the rapid heating. There have been no quantitative studies in the past regarding the relation-
M. Sugimoto et al. / Cryogenics 39 (1999) 939±945
ship between the inlet ¯ow reduction and heat generation in the conductor. The relationship between them was determined quantitatively by experiment and analysis in this paper. The conclusions are summarized as follows. · Experimental data of inlet ¯ow reduction were obtained for Nb3 Al superconductor for ITER-TF coils. An inductive heater was installed on the conductor for the rapid heating. Conditions of the helium coolant, pressure and mass ¯ow rate were experimental parameters for ¯ow reduction. It was also found that the inlet ¯ow reduction depends on the initial mass ¯ow rate in experimental results. · The eective heating duration (teff ) for inlet ¯ow reduction by rapid heating was introduced for determining heat generation in cable in conduit conductor as follows: oT Dh =2; t 0 ot teff
D2h D2h CP 8j 8k
· Inlet ¯ow reduction by rapid heating is predicted by applying to the equation the maximum eective heating duration u L 1ÿ ln q0 ÿ ln q1 u0 2 teff max u0 · In rapid heating, the inlet ¯ow is reduced to zero in a few seconds. Duration for the inlet ¯ow reduction is also a few seconds. The heat from the superconducting strand as a heating zone may travel to the helium coolant in seconds as de®ned by the eective heating duration. · The inlet ¯ow reduction as a function of heat generation on the conductor was predicted by experimental and analytical investigation of rapid heating. Amount of the normal zone generation can be determined by the inlet ¯ow reduction directly during the coil quench. This makes quench detection method reliable for a forced ¯ow superconducting coil.
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Acknowledgements The authors would like to thank Prof. S. Shimamoto (Tohoku University), Drs. M. Ohta (JAERI), S. Matsuda and Y. Seki for their continuing encouragement during this work. We would like to express our gratitude to all the sta members of Superconducting Magnet Laboratory of JAERI who contributed to this experiment.
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