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Thermal-hydraulic behaviour of the ITER TF system during a quench development
Fusion Engineering and Design 86 (2011) 1497–1500
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Thermal-hydraulic behaviour of the ITER TF system during a quench development S. Nicollet a,∗ , B. Lacroix a , D. Bessette b , R. Copetti a , J.L. Duchateau a , M. Coatanea-Gouachet a , F. Rodriguez-Mateos b a b
CEA/IRFM Saint-Paul-lez-Durance 13108, France ITER International Organization, Saint Paul lez Durance, France
a r t i c l e
i n f o
Article history: Available online 13 May 2011 Keywords: ITER Fusion Magnets Cable-In-Conduit Conductor Thermal-Hydraulics Quench
a b s t r a c t In order to ensure the safety of the ITER TF magnets, a primary quench detection system has been foreseen, based on voltage detection. In addition, a secondary quench detection could rely on signals of thermohydraulic nature. As a matter of fact, the development of a quench in a CICC leads to significant variations of pressure and mass flow at the quenched pancake extremities. Analyses of the quench development have thus been performed using the coupled GANDALF and FLOWER codes. This tool allows to simulate the thermo-hydraulic behaviour of one CICC with a model of the external cryogenic circuit. The study has focused on the first seconds of the quench development, supposing that the quench has not been detected earlier by the primary detector. It is shown that signals regarding pressure, mass flow and temperature reach significant high values especially in the connecting feeder associated with the helium inlet. More detailed studies will be needed to select a secondary detector in this region. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The Toroidal Field (TF) system of the ITER tokamak consists in 18 Nb3 Sn superconducting coils. In each coil, 7 Cable In Conduit Conductors (CICC) lengths are wound in 7 double-pancakes and carry a nominal current of 68 kA, which corresponds to an electromagnetic stored energy of about 40 GJ for the whole TF system. The TF system is operating in DC mode. The Gandalf-Flower model is used for quench studies, especially in order to determine the secondary thermo-hydraulic detection ability in case of a failure of the first V Voltage quench detection. This case is called an “undetected quench”. 2. Toroidal field coil model with Gandalf-Flower The thermal hydraulic model used for this study is based on the description of the quenched TF Conductor (Pancake 6) with Gandalf, the other conductors and coils as well as the cryogenic system being roughly modeled with Flower [1]. 2.1. TF conductor description The TF Conductor description is summarized in Table 1 with the hydraulic characteristics used for Gandalf input parameters. The friction factor and heat exchange coefficient have the same type
∗ Corresponding author. Tel.: +33 4 4225 4979. E-mail address: [email protected] (S. Nicollet). 0920-3796/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2011.03.102
of correlation as taken in [2]. The critical current density follows the Durham LMI law as a function of magnetic field B, temperature T and the strain [3] with the following parameters: p = 0.4741, q = 1.953, n = 2.338, v = 1.446, w = 1.936, u = -0.056, Ac0 = 24460000, Tc0m = 16.89 K, Bc20m = 28.54 T, c2 = -0.7697, c3 = -0.4913, c4 = 0.0538. It corresponds to a JnonCu of 824 A/mm2 at 12 T, 4.2 K and =−0.25%. In Gandalf 2.1 (coupled with Flower 2.1), the N-power value describing the resistive transition is by default very high. The coil is operated in steady state and the current is maintained constant equal to 68 kA during the computation time. Fig. 1 gives the corresponding distribution of magnetic field and current sharing temperature Tcs. The initial conditions are: initial uniform temperature 5 K, inlet initial pressure 0.55 MPa and mass flow rate of 8 g/s per pancake. 2.2. TF Coils circuit and external cryogenic circuit For the model of all TF Coils in the Flower scheme: - 2 TF Coils are linked to the inlet and outlet feeders respectively at V1 and V2. - all the other coils (16) are linked to feeders respectively at V12 and V15 and to cryolines at a distance corresponding to the average length value (Fig. 2 and Table 2). The meshed junctions with helium compressible flow (in Flower with 50 nodes) represent the different pancakes of the coil (length of the circuit equivalent to 14, 11 or 3 turns) multiplied by the number of corresponding pancakes (junction 1 modeled with Gandalf,
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S. Nicollet et al. / Fusion Engineering and Design 86 (2011) 1497–1500 Table 2 TF Flower model feeders and cryolines characteristics.
Table 1 TF Conductor hydraulic characteristics. TF Conductor Characteristics in Gandalf Cooling channel length (m) (3 types of pancake) Stainless Steel Jacket cross section AJK (m2 ) Total Insulation section AIN (m2 ) Bundle SC strands Cu/non Cu ratio Non-twisted superconducting section ASC (m2 ) Extra Cu cross section Total non-twisted section Cu AST (m2 ) Total conductor wetted perimeter PHTC (m) Helium section in Bundle region AHEB (m2 ) Bundle region hydraulic diameter DHB (m) Spiral diameter inner/outer = DHH (mm) PHTJ = PTCJ (m) Perimeter hole and bundle PHTHB (m) Helium section in central hole AHEH (m2 )
380/311/106 262.01 E-6 193.98 E-6 1 245 E-6 284.2 E-6 529.19 E-6 3.72 344.4 E-6 0.3296 E-3 8/10 62.36 E-3 31.42 E-3 78.54 E-6
Fig. 1. Distribution of magnetic field B, and current sharing temperature Tcs for pancake 6 (x = 0 conductor helium inlet), for constant current at 68 kA.
Junctions 2, 3 and 4 for the 2TF, and junctions 5, 6 and 7 for the 16 TF). For the equivalent friction factor ft the same correlation as in CS modules is considered [2]. An incompressible flow is assumed in the external pipes. Additional tubes are located at the end of the shortest length of CICC, in order to conserve the same pressure drop in normal operation. Typically for Junctions 8 and 9 (Fig. 2),
Fig. 2. TF Coil model with Gandalf-Flower.
Flower Name
Length (m)
Section (m2 )
DH (m)
Comments
J12 J13 J14 J15 J16
17 110 5 1 30
2513.2 E-6 10054 E-6 5027 E-6 1200 E-6 20 E-3
0.03998 0.08011 M = 2 kg/s F = 1E-6 40.0 E-3
J17 J18 J19 J20 J21 J22
110 17 75 17 17 75
10054 E-6 2513.2 E-6 8937 E-6 20105 E-6 20105 E-6 8937 E-6
0.08011 0.03998 0.08011 0.03998 0.03998 0.08011
Outlet feeder 2TF Outlet CryoL 2TF Circulating pump Control valve Heat exchanger Pw = 2.0, T = 5 K Inlet CryoL 2TF Inlet feeder 2TF Inlet CryoL 16TF Inlet feeder 16TF Out feeder 16TF Out CryoL 16TF
Table 3 TF Flower model volumes characteristics. Flower Name
Volume (m3)
V1, V2 V3, V4, V8, V11, V16 V5, V6, V7 V9, V10, V13, V14 V12, V15 V17, V18 V19 V20 V21
13333 E-6 80216 E-6 140216 E-6 1 E-6 106666 E-6 0.02 0.1 0.2 400
the additional lengths have been adjusted respectively at 69 m and 274 m and the hydraulic diameter is 11.6 10−3 m. For junctions 10 and 11, the length being the same, the hydraulic diameter found is 25 10−3 m. The check valves are connected to the extremities of the feeders and will open at an inlet pressure of 2.0 MPa. The envisaged sensors location for the secondary detection is V8 (inlet of the inlet feeder, inside Cold Termination Box). The pressure, temperature and mass flow rate are computed for the conductor J1, and between V8 and V1 for the inlet feeder. Table 2 gives the characteristics of the Flower junctions, especially cryolines and feeders as well as pump, valve and heat exchanger. Table 3 presents the value of the different volumes in the Flower Model. The Quench calculations are performed with Gandalf on Pancake 6 (J1, with 11 turns and a length of 380 m). This model has some limitations: the quench propagation may be slower due to the lack of radial plates, propagation to adjacent pancake of the same DP is not modeled, the heat diffusion from one turn to the other is not modeled. It was asked by ITER IO to especially focus on the case when only one pancake receives an external energy and quenches. The quench is triggered at the innermost turn of pancake 6. A heat power of 200 W/m (same as in [4], case 4) is deposited along 6 m
Fig. 3. Distribution of the conductor temperature during a quench.
S. Nicollet et al. / Fusion Engineering and Design 86 (2011) 1497–1500
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Fig. 7. Time evolution of mass flow in Pancake 6, and in inlet and outlet feeders during quench. Fig. 4. Evolution vs. time of Resistance and Voltage for Pancake 6 of TF1 during a quench.
Fig. 8. Evolution vs. time of Joule Energy of Pancake 6 during quench. Fig. 5. Zoom at early quench time on conductor inlet (V1) Pressure and Temperature (Pancake 6).
(from 23.6 m to 29.6 m where the temperature margin is minimum, see Fig. 1), and during 1 s (from 0.1 to 1.1 s). Note that at 180 W/m the conductor recovers. 3. Quench propagation and detection results 3.1. Description of the studied case and results in terms of temperature, voltage and resistance Fig. 3 presents the distribution of temperature along pancake 6. The peak temperature reaches 160 K only 10 s after the beginning of the quench. The voltage and resistance along the pancake follow the same power function since the current is constant (Fig. 4). In this “undetected quench” case, the current remains high, the voltage increases very rapidly and reaches 1 V, 0.5 s after quench beginning. Nevertheless the temperature in V1 at time equal 4 s (3 s after quench beginning) is only 6 K (Fig. 5), instead of 5 K at initial conditions.
Fig. 6. Distribution of helium pressure along Pancake 6 during quench.
The pressure (in V1) at the conductor inlet reaches only 0.56 MPa at time = 4 s (3 s after quench beginning) in comparison with 0.55 MPa at initial conditions (Fig. 5). 3.2. Quench results in terms of pressure and mass flow Higher pressure values are reached along the conductor at time = 10 s, and the corresponding maximum is nearly 15 MPa at x = 100 m (Fig. 6). Such a pressure profile was already encountered in [5]. Fig. 7 presents the evolution of mass flow rate: there is an important reverse mass flow at the inlet of conductor (P6 x = 0m) reaching – 300 g/s in comparison with + 8 g/s (normal operation). At time = 4 s, the maximum reverse flow is -600 g/s in comparison with + 220 g/s at initial conditions. Such reverse flow was already calculated for the ITER CS Quench [6]. In case of undetected voltage signal, the temperature, pressure and mass flow in V1 and V8 could be used. The real conditions of V8 can be reached only in
Fig. 9. Evolution vs. time of Normal Length and quench propagation velocity along Pancake 6.
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Fig. 10. Evolution vs. time of Pressure at different abscissa from the inlet feeder (x = 0 corresponds to the volume V8).
of the feeder is taken equal to 17 m and so the spatial mesh length is 0.34 m. At abscissa x = 0 m of the inlet of inlet feeder (V8), the pressure only increases from 0.55 MPa to 0.65 MPa in 20 s. It is however interesting to see (Fig. 10) that, at an abscissa x = 3.4 m, a pressure sensor could reach 0.6 MPa within only 5 s. In volume V1 (corresponding to abscissa x = 17 m of the inlet feeder), the pressure reaches 0.7 MPa at time = 5 s (instead of 0.587 MPa with uncompressible helium in feeders). These results could be explained by the pressure wave propagating in the counter flow direction, thus showing higher and more realistic values. The mass flow rate at the inlet of inlet feeder, in Cold Termination Box (CTB) could be used also as secondary quench detection system (important reverse flow: -0.3 kg/s at t = 5 s, Fig. 11). 4. Conclusion
Fig. 11. Evolution vs. time of Mass flow rate at the inlet of inlet feeder (J18)(corresponds to the volume V8).
a compressible model for feeders (presented in 3.4). In that case, even if the pressure at the feeder’s inlet increases (maximal value equal to 0.9 MPa), it does not exceed 2.0 MPa, and therefore there is no massflow through the two relief valves (J23 and J24). Further calculations are needed to confirm this result. 3.3. Joule energy and quench propagation This quench corresponds to a relatively low external heat deposition: 200 W/m along 6 m and during 1 s, (total external energy of 1.2 kJ). The Joule heating developed during the quench is much higher and reaches 1 MJ (at time = 5 s, Fig. 8). The whole pancake conductor length (380 m) is resistive after nearly 19 s. The average quench velocity is 20 m/s with some peaks at a maximum value 70 m/s; each peak corresponds to one more turn quenched (Fig. 9). 3.4. Influence of compressible helium flow in feeders A more refined model has been studied to better describe the pressure wave. This Flower model is identical to the previous one, but with compressible helium flow in the inlet (junction J18) and outlet feeders (junction J12) of the 2 studied coils. The number of nodes (50) is the same as for the TF coil pancakes; the total length
The Gandalf-Flower model used for quench study is presented associated with the hypothesis concerning the conductor (Gandalf), and the thermal-hydraulics (Flower). One of ITER IO objective is to determine the feasibility of a secondary quench detection, in case of a failure of primary V detection. The calculation and results presented here are about the so called “undetected quench”, corresponding to the lowest possible initial and external deposited energy (1.2 kJ). In this case the current is maintained at 68 kA, the Joule heating is high and the quench propagates with an average velocity of 20 m/s. The temperature, the mass flow and the pressure in V1 (inlet of conductor) are increasing in this “undetected quench” case, but there is no possible access for sensors. Sensors may be installed in the CTB corresponding to V8, at the inlet of inlet feeder, and at this location pressure sensor and mass flow rate could be used as secondary quench detection (with the model described in 3.4 with compressible feeders). Calculations are planned in order to characterize other quench propagation cases. Acknowledgments This work was performed within ITER IO contract CT/08/1049. The views and opinions expressed herein do not necessarily reflect those of the ITER Organization. References [1] L. Bottura, et al., A numerical model for the simulation of quench in the ITER magnets, J.Comput. Phys. 125 (1996) 26–41. [2] S. Nicollet, et al., Cross checking of Gandalf and Vincenta on the CS behaviour during ITER reference scenario, in: Proceedings Advances in Cryogenic Engineering, 2010, pp. 1402–1409. [3] D.J. Taylor, The scaling law for the strain-dependence of the critical current density in Nb3 Sn superconducting wires, Supercond. Sci. Technol. 18 (2005) S241–252. [4] D. Bessette, Fast Discharge and Quench Simulation of the TF Coils with the Vincenta Model, ITER IO Document, IDM UID 35DQUL, 04 march 2010. [5] S. Nicollet, Quench Study, presented at JT-60SA TF Design Review Meeting, 13th June 2007, Frascati, Italy. [6] S. Nicollet, et al., Quench of Central Solenoid: Thermo-Hydraulic detection and main impact on cryogenic system, in: presented at ICEC 23rd Conference, July, 2010.
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Thermal-hydraulic behaviour of the ITER TF system during a quench development S. Nicollet a,∗ , B. Lacroix a , D. Bessette b , R. Copetti a , J.L. Duchateau a , M. Coatanea-Gouachet a , F. Rodriguez-Mateos b a b
CEA/IRFM Saint-Paul-lez-Durance 13108, France ITER International Organization, Saint Paul lez Durance, France
a r t i c l e
i n f o
Article history: Available online 13 May 2011 Keywords: ITER Fusion Magnets Cable-In-Conduit Conductor Thermal-Hydraulics Quench
a b s t r a c t In order to ensure the safety of the ITER TF magnets, a primary quench detection system has been foreseen, based on voltage detection. In addition, a secondary quench detection could rely on signals of thermohydraulic nature. As a matter of fact, the development of a quench in a CICC leads to significant variations of pressure and mass flow at the quenched pancake extremities. Analyses of the quench development have thus been performed using the coupled GANDALF and FLOWER codes. This tool allows to simulate the thermo-hydraulic behaviour of one CICC with a model of the external cryogenic circuit. The study has focused on the first seconds of the quench development, supposing that the quench has not been detected earlier by the primary detector. It is shown that signals regarding pressure, mass flow and temperature reach significant high values especially in the connecting feeder associated with the helium inlet. More detailed studies will be needed to select a secondary detector in this region. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The Toroidal Field (TF) system of the ITER tokamak consists in 18 Nb3 Sn superconducting coils. In each coil, 7 Cable In Conduit Conductors (CICC) lengths are wound in 7 double-pancakes and carry a nominal current of 68 kA, which corresponds to an electromagnetic stored energy of about 40 GJ for the whole TF system. The TF system is operating in DC mode. The Gandalf-Flower model is used for quench studies, especially in order to determine the secondary thermo-hydraulic detection ability in case of a failure of the first V Voltage quench detection. This case is called an “undetected quench”. 2. Toroidal field coil model with Gandalf-Flower The thermal hydraulic model used for this study is based on the description of the quenched TF Conductor (Pancake 6) with Gandalf, the other conductors and coils as well as the cryogenic system being roughly modeled with Flower [1]. 2.1. TF conductor description The TF Conductor description is summarized in Table 1 with the hydraulic characteristics used for Gandalf input parameters. The friction factor and heat exchange coefficient have the same type
∗ Corresponding author. Tel.: +33 4 4225 4979. E-mail address: [email protected] (S. Nicollet). 0920-3796/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2011.03.102
of correlation as taken in [2]. The critical current density follows the Durham LMI law as a function of magnetic field B, temperature T and the strain [3] with the following parameters: p = 0.4741, q = 1.953, n = 2.338, v = 1.446, w = 1.936, u = -0.056, Ac0 = 24460000, Tc0m = 16.89 K, Bc20m = 28.54 T, c2 = -0.7697, c3 = -0.4913, c4 = 0.0538. It corresponds to a JnonCu of 824 A/mm2 at 12 T, 4.2 K and =−0.25%. In Gandalf 2.1 (coupled with Flower 2.1), the N-power value describing the resistive transition is by default very high. The coil is operated in steady state and the current is maintained constant equal to 68 kA during the computation time. Fig. 1 gives the corresponding distribution of magnetic field and current sharing temperature Tcs. The initial conditions are: initial uniform temperature 5 K, inlet initial pressure 0.55 MPa and mass flow rate of 8 g/s per pancake. 2.2. TF Coils circuit and external cryogenic circuit For the model of all TF Coils in the Flower scheme: - 2 TF Coils are linked to the inlet and outlet feeders respectively at V1 and V2. - all the other coils (16) are linked to feeders respectively at V12 and V15 and to cryolines at a distance corresponding to the average length value (Fig. 2 and Table 2). The meshed junctions with helium compressible flow (in Flower with 50 nodes) represent the different pancakes of the coil (length of the circuit equivalent to 14, 11 or 3 turns) multiplied by the number of corresponding pancakes (junction 1 modeled with Gandalf,
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S. Nicollet et al. / Fusion Engineering and Design 86 (2011) 1497–1500 Table 2 TF Flower model feeders and cryolines characteristics.
Table 1 TF Conductor hydraulic characteristics. TF Conductor Characteristics in Gandalf Cooling channel length (m) (3 types of pancake) Stainless Steel Jacket cross section AJK (m2 ) Total Insulation section AIN (m2 ) Bundle SC strands Cu/non Cu ratio Non-twisted superconducting section ASC (m2 ) Extra Cu cross section Total non-twisted section Cu AST (m2 ) Total conductor wetted perimeter PHTC (m) Helium section in Bundle region AHEB (m2 ) Bundle region hydraulic diameter DHB (m) Spiral diameter inner/outer = DHH (mm) PHTJ = PTCJ (m) Perimeter hole and bundle PHTHB (m) Helium section in central hole AHEH (m2 )
380/311/106 262.01 E-6 193.98 E-6 1 245 E-6 284.2 E-6 529.19 E-6 3.72 344.4 E-6 0.3296 E-3 8/10 62.36 E-3 31.42 E-3 78.54 E-6
Fig. 1. Distribution of magnetic field B, and current sharing temperature Tcs for pancake 6 (x = 0 conductor helium inlet), for constant current at 68 kA.
Junctions 2, 3 and 4 for the 2TF, and junctions 5, 6 and 7 for the 16 TF). For the equivalent friction factor ft the same correlation as in CS modules is considered [2]. An incompressible flow is assumed in the external pipes. Additional tubes are located at the end of the shortest length of CICC, in order to conserve the same pressure drop in normal operation. Typically for Junctions 8 and 9 (Fig. 2),
Fig. 2. TF Coil model with Gandalf-Flower.
Flower Name
Length (m)
Section (m2 )
DH (m)
Comments
J12 J13 J14 J15 J16
17 110 5 1 30
2513.2 E-6 10054 E-6 5027 E-6 1200 E-6 20 E-3
0.03998 0.08011 M = 2 kg/s F = 1E-6 40.0 E-3
J17 J18 J19 J20 J21 J22
110 17 75 17 17 75
10054 E-6 2513.2 E-6 8937 E-6 20105 E-6 20105 E-6 8937 E-6
0.08011 0.03998 0.08011 0.03998 0.03998 0.08011
Outlet feeder 2TF Outlet CryoL 2TF Circulating pump Control valve Heat exchanger Pw = 2.0, T = 5 K Inlet CryoL 2TF Inlet feeder 2TF Inlet CryoL 16TF Inlet feeder 16TF Out feeder 16TF Out CryoL 16TF
Table 3 TF Flower model volumes characteristics. Flower Name
Volume (m3)
V1, V2 V3, V4, V8, V11, V16 V5, V6, V7 V9, V10, V13, V14 V12, V15 V17, V18 V19 V20 V21
13333 E-6 80216 E-6 140216 E-6 1 E-6 106666 E-6 0.02 0.1 0.2 400
the additional lengths have been adjusted respectively at 69 m and 274 m and the hydraulic diameter is 11.6 10−3 m. For junctions 10 and 11, the length being the same, the hydraulic diameter found is 25 10−3 m. The check valves are connected to the extremities of the feeders and will open at an inlet pressure of 2.0 MPa. The envisaged sensors location for the secondary detection is V8 (inlet of the inlet feeder, inside Cold Termination Box). The pressure, temperature and mass flow rate are computed for the conductor J1, and between V8 and V1 for the inlet feeder. Table 2 gives the characteristics of the Flower junctions, especially cryolines and feeders as well as pump, valve and heat exchanger. Table 3 presents the value of the different volumes in the Flower Model. The Quench calculations are performed with Gandalf on Pancake 6 (J1, with 11 turns and a length of 380 m). This model has some limitations: the quench propagation may be slower due to the lack of radial plates, propagation to adjacent pancake of the same DP is not modeled, the heat diffusion from one turn to the other is not modeled. It was asked by ITER IO to especially focus on the case when only one pancake receives an external energy and quenches. The quench is triggered at the innermost turn of pancake 6. A heat power of 200 W/m (same as in [4], case 4) is deposited along 6 m
Fig. 3. Distribution of the conductor temperature during a quench.
S. Nicollet et al. / Fusion Engineering and Design 86 (2011) 1497–1500
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Fig. 7. Time evolution of mass flow in Pancake 6, and in inlet and outlet feeders during quench. Fig. 4. Evolution vs. time of Resistance and Voltage for Pancake 6 of TF1 during a quench.
Fig. 8. Evolution vs. time of Joule Energy of Pancake 6 during quench. Fig. 5. Zoom at early quench time on conductor inlet (V1) Pressure and Temperature (Pancake 6).
(from 23.6 m to 29.6 m where the temperature margin is minimum, see Fig. 1), and during 1 s (from 0.1 to 1.1 s). Note that at 180 W/m the conductor recovers. 3. Quench propagation and detection results 3.1. Description of the studied case and results in terms of temperature, voltage and resistance Fig. 3 presents the distribution of temperature along pancake 6. The peak temperature reaches 160 K only 10 s after the beginning of the quench. The voltage and resistance along the pancake follow the same power function since the current is constant (Fig. 4). In this “undetected quench” case, the current remains high, the voltage increases very rapidly and reaches 1 V, 0.5 s after quench beginning. Nevertheless the temperature in V1 at time equal 4 s (3 s after quench beginning) is only 6 K (Fig. 5), instead of 5 K at initial conditions.
Fig. 6. Distribution of helium pressure along Pancake 6 during quench.
The pressure (in V1) at the conductor inlet reaches only 0.56 MPa at time = 4 s (3 s after quench beginning) in comparison with 0.55 MPa at initial conditions (Fig. 5). 3.2. Quench results in terms of pressure and mass flow Higher pressure values are reached along the conductor at time = 10 s, and the corresponding maximum is nearly 15 MPa at x = 100 m (Fig. 6). Such a pressure profile was already encountered in [5]. Fig. 7 presents the evolution of mass flow rate: there is an important reverse mass flow at the inlet of conductor (P6 x = 0m) reaching – 300 g/s in comparison with + 8 g/s (normal operation). At time = 4 s, the maximum reverse flow is -600 g/s in comparison with + 220 g/s at initial conditions. Such reverse flow was already calculated for the ITER CS Quench [6]. In case of undetected voltage signal, the temperature, pressure and mass flow in V1 and V8 could be used. The real conditions of V8 can be reached only in
Fig. 9. Evolution vs. time of Normal Length and quench propagation velocity along Pancake 6.
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S. Nicollet et al. / Fusion Engineering and Design 86 (2011) 1497–1500
Fig. 10. Evolution vs. time of Pressure at different abscissa from the inlet feeder (x = 0 corresponds to the volume V8).
of the feeder is taken equal to 17 m and so the spatial mesh length is 0.34 m. At abscissa x = 0 m of the inlet of inlet feeder (V8), the pressure only increases from 0.55 MPa to 0.65 MPa in 20 s. It is however interesting to see (Fig. 10) that, at an abscissa x = 3.4 m, a pressure sensor could reach 0.6 MPa within only 5 s. In volume V1 (corresponding to abscissa x = 17 m of the inlet feeder), the pressure reaches 0.7 MPa at time = 5 s (instead of 0.587 MPa with uncompressible helium in feeders). These results could be explained by the pressure wave propagating in the counter flow direction, thus showing higher and more realistic values. The mass flow rate at the inlet of inlet feeder, in Cold Termination Box (CTB) could be used also as secondary quench detection system (important reverse flow: -0.3 kg/s at t = 5 s, Fig. 11). 4. Conclusion
Fig. 11. Evolution vs. time of Mass flow rate at the inlet of inlet feeder (J18)(corresponds to the volume V8).
a compressible model for feeders (presented in 3.4). In that case, even if the pressure at the feeder’s inlet increases (maximal value equal to 0.9 MPa), it does not exceed 2.0 MPa, and therefore there is no massflow through the two relief valves (J23 and J24). Further calculations are needed to confirm this result. 3.3. Joule energy and quench propagation This quench corresponds to a relatively low external heat deposition: 200 W/m along 6 m and during 1 s, (total external energy of 1.2 kJ). The Joule heating developed during the quench is much higher and reaches 1 MJ (at time = 5 s, Fig. 8). The whole pancake conductor length (380 m) is resistive after nearly 19 s. The average quench velocity is 20 m/s with some peaks at a maximum value 70 m/s; each peak corresponds to one more turn quenched (Fig. 9). 3.4. Influence of compressible helium flow in feeders A more refined model has been studied to better describe the pressure wave. This Flower model is identical to the previous one, but with compressible helium flow in the inlet (junction J18) and outlet feeders (junction J12) of the 2 studied coils. The number of nodes (50) is the same as for the TF coil pancakes; the total length
The Gandalf-Flower model used for quench study is presented associated with the hypothesis concerning the conductor (Gandalf), and the thermal-hydraulics (Flower). One of ITER IO objective is to determine the feasibility of a secondary quench detection, in case of a failure of primary V detection. The calculation and results presented here are about the so called “undetected quench”, corresponding to the lowest possible initial and external deposited energy (1.2 kJ). In this case the current is maintained at 68 kA, the Joule heating is high and the quench propagates with an average velocity of 20 m/s. The temperature, the mass flow and the pressure in V1 (inlet of conductor) are increasing in this “undetected quench” case, but there is no possible access for sensors. Sensors may be installed in the CTB corresponding to V8, at the inlet of inlet feeder, and at this location pressure sensor and mass flow rate could be used as secondary quench detection (with the model described in 3.4 with compressible feeders). Calculations are planned in order to characterize other quench propagation cases. Acknowledgments This work was performed within ITER IO contract CT/08/1049. The views and opinions expressed herein do not necessarily reflect those of the ITER Organization. References [1] L. Bottura, et al., A numerical model for the simulation of quench in the ITER magnets, J.Comput. Phys. 125 (1996) 26–41. [2] S. Nicollet, et al., Cross checking of Gandalf and Vincenta on the CS behaviour during ITER reference scenario, in: Proceedings Advances in Cryogenic Engineering, 2010, pp. 1402–1409. [3] D.J. Taylor, The scaling law for the strain-dependence of the critical current density in Nb3 Sn superconducting wires, Supercond. Sci. Technol. 18 (2005) S241–252. [4] D. Bessette, Fast Discharge and Quench Simulation of the TF Coils with the Vincenta Model, ITER IO Document, IDM UID 35DQUL, 04 march 2010. [5] S. Nicollet, Quench Study, presented at JT-60SA TF Design Review Meeting, 13th June 2007, Frascati, Italy. [6] S. Nicollet, et al., Quench of Central Solenoid: Thermo-Hydraulic detection and main impact on cryogenic system, in: presented at ICEC 23rd Conference, July, 2010.