EuCARD-CON-2011-057 European Coordination for Accelerator Research and Development PUBLICATION Thermal Design of an Nb3Sn High Field Accelerator Magnet Pietrowicz, S (CEA-irfu, on leave from Wroclaw University of Technology) et al 22 May 2012 The research leading to these results has received funding from the European Commission under the FP7 Research Infrastructures project EuCARD, grant agreement no. 227579. This work is part of EuCARD Work Package 7: Super-conducting High Field Magnets for higher luminosities and energies. The electronic version of this EuCARD Publication is available via the EuCARD web site <http://cern.ch/eucard> or on the CERN Document Server at the following URL : <http://cdsweb.cern.ch/record/1450241 EuCARD-CON-2011-057
THERMAL DESIGN OF AN Nb 3 Sn HIGH FIELD ACCELERATOR MAGNET S. Pietrowicz and B. Baudouy CEA, Irfu/SACM, F-91191 Gif-sur-Yvette, France ABSTRACT Within the framework of the European project EuCARD, a Nb 3 Sn high field accelerator magnet is under design to serve as a test bed for future high field magnets and to upgrade the vertical CERN cable test facility, Fresca. The Fresca 2 block coil type magnet will be operated at 1.9 K or 4.2 K and is designed to produce about 13 T. A 2D numerical thermal model was developed to determinate the temperature margin of the coil in working conditions and the appropriate cool-down scenario. The temperature margin, which is T marge =5.8 K at 1.9 K and T marge =3.5 K at 4.2 K, was investigated in steady state condition with the AC losses due to field ramp rate as input heat generation. Several cool-down scenarios were examined in order to minimize the temperature difference and therefore reducing the mechanical constraints within the structure. The paper presents the numerical model, the assumptions taken for the calculations and several results of the simulation for the cool-down and temperature distributions due to several cases of heat loads. KEYWORDS: Thermal modeling, Nb 3 Sn magnet, cool-down scenarios INTRODUCTION The High Field Magnet project, within the European project EuCARD, aims at constructing a Nb 3 Sn high field accelerator magnet, Fresca 2, to serve as a test bed for future high field magnets and to upgrade the vertical CERN cable test facility [1-2]. The Fresca 2 magnet is based on a block coil magnetic configuration with a 100 mm diameter free aperture and total length of 1600 mm. The view of the cross and horizontal sections are shown in FIGURE 1a and FIGURE 1b respectively [3]. The inner part of the magnet is inserted in an aluminum Al 2014 T6 shrinking cylinder having an outside diameter of 1030 mm and a thickness of 65 mm.
shrinking cylinder a) b) yoke free aperture pancakes vertical pad horizontal pad FIGURE 1. (1a) The cross section and (1b) horizontal section of Fresca 2 magnet [3]. The yoke, which has direct contact with the shrinking cylinder, is essentially made of Magnetil (LHC Iron). The superconducting coil of the magnet is structurally linked with the yoke through 304 stainless steel vertical and horizontal keys. Each Nb 3 Sn conductor has a bare dimension of 21.4 x 1.82 mm 2 and is surrounded by 0.2 mm thick electrical insulation (FIGURE 2). The total number of conductors is 156 in one pole. To meet the required magnetic field the superconducting cables are located in two double-pancakes [3]. The first double-pancake (blocks no. 1 and no. 2) consists of 72 (2 36) conductors, the second (block no. 3 and 4) consists of 84 conductors (2 42). All the blocks are separated from each other by a G10 layer insulation. More description about the Fresca 2 magnet can be found in [3]. STEADY STATE THERMAL MODELING Physical model and assumptions Because the kernel of the solver uses a finite volume method, the numerical model applied during calculation is based on the standard three dimensional heat conduction equation with internal heat sources and is described by the following equation, ( ( ) ) ( ( ) ) ( ( ) ) (1) but in this paper the results are produced for the 2D cross section. k(t) is the thermal conductivity of materials as a function of temperature and is the heat source distribution. For simplification, the model does not include helium. Therefore we consider only conduction in the model. The contacts between solid elements are assumed to be perfect, i.e. there is continuity in heat flux and temperature between material domains. The thermal conductivity of materials is a function of temperature and their values are taken from the literature and cryogenics data base [4-7]. During the calculations two variants of the heat load distribution in the conductors are taken into consideration. One variant considered the heat load distributed homogenously in the conductors with the total values of dissipated power of 1 W, 5 W and 10 W, as specified in [8]. The second one assumed that the heat load in each conductor is generated in the magnet by AC losses. The calculations were
done with a cross contact resistance R c of 0.5 μω, an adjacent resistance R a of 0.5 μω and a ramp-rate of 0.015 T/s [9]. The total dissipated power is 0.2 W in the whole coil. Boundary conditions and meshing Due to the symmetrical location of the conductors, the calculations domain can be reduced to a quarter of magnet (FIGURE 2). Two sets of calculations were performed for each heat load, one for the base temperature of 1.9 K and one at 4.2 K. For each temperature two types of boundary conditions are applied. The first condition is an imposed constant temperature (1.9 K or 4.2 K) at the boundaries (dot lines in FIGURE 2) simulating a direct contact between liquid helium and the magnet parts. The second boundary is symmetry and is applied to the other parts (the line with triangles in FIGURE 2). The calculation region was divided into 19 domains and meshed in ANSYS ICEM Software with the total numbers of 988260 nodes and 714868 elements [10]. The example of the central part mesh with conductors, insulations and G10 layers and explanation of blocks configuration is shown in FIGURE 2. T emperature evolution Symmetry conductor insulation 115 156 Block 4 Block 3 73 114 37 72 Block 2 Block 1 1 36 G10 layer FIGURE 2. Quarter of magnet considered during calculations with boundary conditions, details of structural mesh applied in the central part of magnet - conductors, insulations and G10 layers and numbering of double - pancakes. Results The calculations are performed in ANSYS CFX solver which uses Finite Volume Method (FVM) techniques [11]. The results at a bath temperature of 1.9 K are shown in FIGURE 3 and for 4.2 K in FIGURE 4. For all simulations with the assumption of homogenous heat generation, the maximum temperature is located at the same location in the middle of the block 2 (the dots in FIGURE 3a and FIGURE 4a). A small displacement can be observed with increasing heat load; the maximum temperature is shifted towards the central part of the magnet along OY axie. For the heat load due to AC losses, the localization of the maximum temperature is in block 3 as it is depicted in FIGURE 3b and FIGURE 4b. With increasing value of heat load, the temperature generated in the magnet structure increases as well. The highest heat load of 10 W causes the highest temperature increase of about 4.0 K at 1.9 K and 2.2 K at 4.2 K. All results obtained during numerical calculations are summarized in TABLE 1.
a) b) FIGURE 3. The contours of temperature field with the localization of maximum temperature for a) 10 W, and b) AC losses model at 1.9 K bath temperature. a) b) FIGURE 4. The contours of temperature field with the localization of maximum temperature for a) 10 W, and b) AC losses model at 4.2 K bath temperature. TABLE 1. The values of maximum temperature differences at 1.9 and 4.2 K for all variants of simulations Bath temperature Model of heat load Unit AC losses Margin of Homogenous model model critical Total W 0.199 1 5 10 temperature By length of (K) W/m 0.106 0.529 2.646 5.292 conductor (at B=13.5 T By volume and I=10.5 W/m 3 4.341 21.775 108.876 217.751 of conductor ka) Maximum temperature difference @ 1.9 K 0.2 1.1 2.9 4.0 5.8 @ 4.2 K 0.1 0.4 1.3 2.2 3.5 The heat load is presented in W, W/m of conductor length and W/m 3 of conductor volume. In the nominal working conditions, for the current of 10.5 ka and the magnetic field of 13 T, a critical temperature is to be 7.7 K [12] and provides a temperature margin of 5.8 K for a bath temperature of 1.9 K and 3.5 K for a bath temperature of 4.2 K. The simulations confirmed that for the considered values of heat load the magnet will still be safe. MAGNET COOL-DOWN - TRANSIENT PROCESS It is important to determine the thermal behavior of the magnet during its cool-down since the thermal gradients created within the magnet structure can cause internal thermal
stress and in extreme cases, for high values, cracks and eventually magnet failure. Knowledge of the temperature evolution within the magnet can also be useful for optimizing the cool-down process, reducing the working hours and in consequence reducing the amount of coolant (helium). It is considered that the cool-down process can be done in two indirect and direct cooling steps. In indirect cooling, the magnet will be cooled from 300 K to 20 K via eight external cooling tubes placed on the shrinking cylinder (FIGURE 5). When the temperature of the magnet will reach 20 K, the cool-down will continue by direct cooling where helium is supplied around the internal and external magnet structures. The mathematical formula of unsteady heat conduction process can be applied to model the physical process during the cool-down, ( ) * ( ( ) ) ( ( ) ) ( ( ) )+ (2) where is the density, c p (T) the thermal capacity as a function of temperature [4-7] and k(t) is thermal conductivity as a function of temperature [4-7]. Indirect cool-down method assumptions and boundary conditions To accelerate the calculation process, some simplifications were done. The helium is treated as a solid element where only heat transfer via conduction is considered. In the real process, buoyancy flow would appear increasing the amount of heat transfers via helium and decreasing the temperature difference. Thus, the calculations presented in this paper can be considered as a conservative case of cool-down. The simulations are performed for four durations of indirect cool-down: 1.5, 2, 3 and 4 days. As it was proposed in [13], the indirect cool-down of the magnet will be realized in four steps: step 1 - cool-down from 300 K to 80 K, step 2 - electrical integrity test at 80 K, step 3 - cool-down from 80 K to 20 K and step 4 - electrical integrity test at 20 K. In practice this process can be carried out by controlling of the inlet temperature and mass flow rate in the external pipes. Because the numerical calculations are considered for a 2D geometry, the modeling of internal flow in the cooling tubes is replaced by the evolution of temperature on external side of shrinking cylinder, that we call cooling functions (FIGURE 5 and FIGURE 6). a) b) FIGURE 5. a) The idea of indirect cool-down using external cooling tubes, b) numerical model with simplification and boundary conditions.
Maximum thermal gradient in magnet (K) Temperature of cooling function (K) We assumed that during the first and third steps the temperature is decreasing linearly and stays constant during electrical integrity test (2 and 4 steps) with respect to the time as it is described in FIGURE 6. The electrical integrity tests will take about 6 hours and the cool-down from 80 K to 20 K at least 12 hours. On the other external sides of the shrinking cylinder adiabatic condition is applied. On the rests, symmetry condition is used. During all calculations the same computational time step of 10 minutes is used. Results In FIGURE 6 the evolution of the maximum temperature differences in the magnet with the cooling function is presented. The maximum differences are created between the cooling tubes and the central part of the magnet in conductor block number 1. Within the first and third steps, the evolution of the maximum thermal gradient can be characterized by rapid increasing and after reaching a maximum value, gradually decreasing. During the electrical integrity tests the maximum thermal gradient is continuously decreasing and at the end of those steps reaches almost zero. The maximum value of 60 K is obtained for the faster cool-down i.e. 1.5 days, and as expected the lowest value of 10 K is for 4 days of indirect cooling. As it was mentioned above, to keep the magnet safe during the cool-down the thermal gradient created within the magnet structure cannot be higher than the critical thermal gradient. From gained experience obtained during the design process of the LHC main magnets at CERN, the safety maximum thermal gradient which can be acceptable during cool-down was estimated to be around 75 K [14]. Because Fresca 2 magnet has a different structure than main LHC magnet, therefore the critical temperature gradient during the cool-down was decided [8] to be 30 K. To satisfy that condition, the magnet has to be cooled down over more than 2 days. The critical value of thermal gradient has to be confirmed by thermo-mechanical calculations. The simulations of the last indirect phase of cool-down from 80 K to 20 K shows that the evolution of the maximum thermal gradient has the same maximum value which does not exceed 8 K and is almost three times smaller than the critical temperature gradient. 60,0 50,0 40,0 30,0 1.5 days 2 days 3 days 4 days cooling function 1.5 days cooling function 2 days cooling function 3 days cooling function 4 days 300 250 200 150 20,0 100 10,0 50 0,0 0 20 40 60 80 Time of indirect cool-down (hour) 0 FIGURE 6. Evolutions of maximum thermal gradient (solid lines) with the cooling functions for all considered variants of indirect cool - down.
Maximum temperature gradient in magnet (K) Temperature of cooling function (K) Direct cool down method assumptions and boundary conditions After indirect cool-down to 20 K via external tubes, a direct cooling method from 20 K to 4.2 K is applied. The helium directly cools the internal and external magnet structure as it is shown in FIGURE 2 with the dotted lines. For that reason the same computational domains and mesh are used. The flow of helium is simplified to an evolution of surface temperature as presented in FIGURE 7 with the dotted line. The cooldown from 20 K to 4.2 K has the same scenarios for all variants - from 20 K to 4.2 K and lasts 2 hours with an electrical integrity test of 3 hours. The computational time step is equal to 5 minutes. Also it is assumed that from 20 K to 4.2 K, the temperature of the helium is decreasing linearly (the dot line in FIGURE 7). On the other sides of the computation region, a symmetry condition is used. The initial distributions of temperature in the domains are taken from the last calculation results of the indirect cool-down. Results In comparison to the indirect cool-down method, the direct cooling process generates very small thermal gradients in the magnet structure. The evolutions of maximum temperature difference within the magnet structure are almost the same and the maximum value is reached in half an hour after starting the process and equals 0.47 K. The evolution of maximum thermal gradient created in the magnet during direct method of cooling process is presented in FIGURE 7. 0,5 20 0,4 0,3 0,2 0,1 0 after 1.5 days after 2 days after 3 days after 4 days Cooling function 0 1 2 3 4 5 Time of direct cool-down (hour) 18 16 14 12 10 8 6 4 2 0 FIGURE 7. Evolutions of maximum thermal gradient (solid lines) with the cooling functions for all considered variants of direct cool - down.
CONCLUSION The numerical calculations using FVM (Finite Volume Method) have been performed for steady and transient processes. According to the calculations, the magnet will be kept safe even for a heat load of 10 W (5.292 W per one meter of conductor) and for bath temperatures of 1.9 K and 4.2 K. It is worth mentioning that, for LHC upgrade magnet, the expected value of the heat load is 2 W/m. That relatively high value of the temperature margin in Fresca 2 is a consequence of the amount of helium occupying free spaces within the magnet structure, especially in the space between the coil pack and the yoke. The cool-down of the magnet has to be done in more than 2 days with external tube indirect method. For that case, the generated maximum thermal gradient will be lower than 30 K. The estimated critical value of 30 K is based on the knowledge obtained from LHC design experience but has to be confirmed for Fresca 2 magnet by thermomechanical calculation with the results obtained in this study as input data. ACKNOWLEDGEMENTS We acknowledge the support of the European Community-Research Infrastructure Activity under the FP7 program (EuCARD, contract number 227579). S. Pietrowicz is on leave from Wroclaw University of Technology, Poland. REFERENCES 1. http://eucard.web.cern.ch/eucard/activities/research/wp7/ 2. De Rijk G., New European Accelerator Project EuCARD: Work Package on High Field Magnets, IEEE/CSC & ESAS European Superconductivity News Forum, No. 8, April 2009. 3. Milanese A., Manil P.,et al, Design of the EuCARD high field model dipole magnet FRESCA2, in IEEE Trans. Applied Superconductivity, to be published. 4. Cryocomp Software, Properties version 3.06, User interface version 3.01. 5. Metalpak Software, version 1.00, January 14, 1997. 6. http://cryogenics.nist.gov/mpropsmay/polyimide%20kapton/polyimidekapton_rev.htm 7. Baudouy B., Cryogenics 43, pp. 667 672 (2003). 8. De Rijk G., FRESCA2 magnet specification for thermal modeling, CERN, private communication, October 2009. 9. de Rapper, W. M., Estimation of AC loss due to ISCC losses in the HFM conductor and coil, CERN TE-Note-2010-004, 2010; 10. Pietrowicz S., Baudouy B., Thermal modeling of Fresca2 magnet, CERN report, EuCARD-REP-2011-004, 2011. 11. ANSYS CFX 12.1, documentation. 12. Bottura L., J C (B,T,ε) Parameterizations for the ITER Nb 3 Sn Production, CERN-ITER Collaboration Report Version 2, April 2, 2008. 13. Bajko M., de Rijk G., Specification for the cryostat for the EuCARD Fresca2 magnet in the vertical test station SM18, private communication, October 2009. 14. Bruning O., et al, LHC Design Report, Volume I The LHC Main Ring, CERN-2004-003, 4 June 2004.