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Stress and Thermal Analysis of the In-Vessel Resonant Magnetic Perturbation Coils on the J- TEXT Tokamak This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2012 Plasma Sci. Technol. 14 83 (http://iopscience.iop.org/1009-0630/14/1/18) Download details: IP Address: 115.156.252.178 The article was downloaded on 08/02/2012 at 02:11 Please note that terms and conditions apply. View the table of contents for this issue, or go to the journal homepage for more Home Search Collections Journals About Contact us My IOPscience Plasma Science and Technology, Vol.14, No.1, Jan. 2012 Stress and Thermal Analysis of the In-Vessel Resonant Magnetic Perturbation Coils on the J-TEXT Tokamak∗ HAO Changduan (郝长端)1,2, ZHANG Ming (张明)1,2, DING Yonghua (丁永华)1,2, RAO Bo (饶波)1,2, CEN Yishun (岑义顺)1,2, ZHUANG Ge (庄革)1,2 1College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China 2State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Wuhan 430074, China Abstract A set of four in-vessel saddle coils was designed to generate a helical field on the J- TEXT tokamak to study the influences of the external perturbation field on plasma. The coils are fed with alternating current up to 10 kA at frequency up to 10 kHz. Due to the special structure, complex thermal environment and limited space in the vacuum chamber, it is very important to make sure that the coils will not be damaged when undergoing the huge electromagnetic forces in the strong toroidal field, and that their temperatures don’t rise too much and destroy the in- sulation. A 3D finite element model is developed in this paper using the ANSYS code, stresses are analyzed to find the worst condition, and a mounting method is then established. The results of the stress and modal analyses show that the mounting method meets the strength require- ments. Finally, a thermal analysis is performed to study the cooling process and the temperature distribution of the coils. Keywords: J-TEXT tokamak, resonant magnetic perturbation (RMP) coils, finite ele- ment analysis (FEA) PACS: 52.55.Fa, 07.05.Fb, 07.55.Db doi: 10.1088/1009-0630/14/1/18 1 Introduction Resonant magnetic perturbations are of great impor- tance for tokamak plasma. They lead to rotation of the edge plasma, through which magnetohydrodynamic (MHD) instabilities can be studied. To produce such magnetic fields, a set of four in-vessel saddle coils is de- signed with current up to 10 kA and frequency up to 10 kHz. To control and influence the MHD instabilities, ex- ternal magnetic perturbation fields are popular among tokamak devices. DIII-D [1] installed a set of 12 internal coils with water-cooled hollows located behind protec- tive armor tiles. The ASDEX upgrade installed a set of 16 in-vessel saddle coils which were cooled by water and mounted at the passive stabilizing loop [2,3]. KSTAR succeeds in enhancing the coil system with no welding inside the vacuum vessel [4], and J-TEXT is a mid-sized tokamak with a smaller vacuum chamber [5]. Coils with internal coolant holes will be used and welded onto the inner vacuum vessel. Different methods are used to an- alyze the structural and thermal stabilities of the coils. This paper describes the structure of the coils, the de- sign process of mounting, and the stress and thermal analyses with the ANSYS code [6∼8]. 2 Coil structure In the J-TEXT tokamak, the cross-section shape of the plasma region is circular, with a major radius of 1.05 m and a minor radius of about 0.27 m. Its center- line field reaches 3 T. Due to the limited space in the vacuum chamber, the plasma region has a distance of only about 60 mm to the up vacuum-chamber wall and 73 mm to the lower field vacuum-chamber wall (near the mid-plane). The existence of the movable graphite limiter decreases the space for the mounting of the coils. Once the plasma hits the coils, they will be damaged, so the size and the structure of the coils should be se- riously considered. Currently, a set of four coils will be mounted in the vacuum-chamber wall by welding (see Fig. 1). Two coils will be placed up and down (called the up coil and down coil) close to the vacuum-chamber wall, and one coil close to the wall in the low field region (near the mid-plane, called the mid-plane coil). As can be seen, in each set there are two types of coils: the trapezoid up and down coils and the rectangular mid-plane coils. Owing to symmetry, two trapezoid coils have the same shape. The coils are made of copper conductors on the in- side and thin stainless steel pipes on the outside, and the space between them is filled with glass fiber for insu- ∗supported by the ITER Project Funds of China (No. 2010GB107004) and National Natural Science Funds of China (No. 50907029) Plasma Science and Technology, Vol.14, No.1, Jan. 2012 lation. The gap in the glass fiber is stuffed with epoxy resin to strengthen its mechanical properties, such as wear-resisting property. The copper conductor is made of oxygen-free copper with a radius of 8 mm and a wall thickness of 4 mm (see Fig. 2). Fig.1 Schematic diagram of the in-vessel saddle coils Fig.2 The trapezoid up and down coils 3 Stress analysis The electromagnetic force can be obtained by j×B. The current consists of two parts: the normal 10 kA current and the induced current caused by the plasma disruption. In extreme circumstances, the induced cur- rent flows instantaneously along the same path in the same direction as the nominal 10 kA current, which contributes to a significant electromagnetic force in the coil. Besides, due to the different positions where the coils will be placed, the currents induced in them will be different and each coil bears a different force. So, the up and down coils and the mid-plane coils, during the ramping and disruption of the plasma current, will be separately analyzed by electromagnetic-stress analysis. 3.1 Plasma disruption and the induced current There are two main types of plasma disruption sce- narios: plasma-centered disruption and the vertical dis- placement event. When a disruption happens, the plasma current soon quenches, leading to a large flux change in the coils. According to Lenz’s law, the in- duced current will be generated. In a normal shot, the plasma current rises in about 0.05 s and falls off in about 0.2 s. However, when the plasma current dis- rupts, it falls off so quickly that it leads to a large flux change in the coils in a very short time, which induces large voltages in the coils. Meanwhile, huge induced currents occur because the resistances of the coils are very small. On the basis of the experimental current waves for plasma on J-TEXT, it takes more than 0.01 s to dis- rupt. A typical plasma current curve versus time is shown in Fig. 3. In the worst condition, the plasma current disruption happens as quickly as 0.01 s, during which time the total flux φ in the coil changes tremen- dously and produces great instant current, resulting in a huge electromagnetic force [9,10]. By applying Stokes’ theorem, the flux of a coil is calculated through a line integral of magnetic vector potential A around a closed contour along the coil by φ = ∮ s B · dS = ∮ l A · dl. (1) If R and L represent the coil’s resistance and induc- tance, ϕ represent the variation of the coil’s magnetic flux during the plasma disruption, the induced current Iinduced can be calculated by Einduced= dϕ dt =IinducedR+ L dIinduced dt . (2) To reduce the amount of calculation needed, only part of the plasma region is built (see Fig. 4). The closed loop below represents the down-coil plane. As the mechanism of plasma disruption is not clear so far, it is simply assumed that the plasma moves towards the coil and them disrupts. Fig.3 Plasma current versus time during a disruption Fig.4 Coil plane and the plasma area (color online) 84 HAO Changduan et al.: Stress and Thermal Analysis of the In-Vessel RMP Coils on the J-TEXT Tokamak When the plasma region moves towards the down- coil plane in the vertical direction (see Fig. 4), the flux in the coil increases at first and then decreases. When the plasma moves towards the mid-plane in the hori- zontal direction, the coil’s flux increases continuously. During this process, the maximum magnetic flux vari- ation of the coil reaches 0.2188× 10−1 Wb. According to Eqs. (1) and (2), the induced current is Iinduced = 9.84 × 103(1 − e−202.4t) A (R = 22.23 × 10−5 Ω, L = 1.0976 × 10−6 H). In this condition, the maximum in- stant total current in the copper conductor may reach 19.84 kA due to superposition. 3.2 Simplified stress calculation model In order to reduce the computational complexity and obtained an accurate result, part of the coil is built (see Fig. 5). Both ends of the pipe are the strength- ening parts, which are welded onto the inner surface of the vacuum-chamber wall through their up-sides. To achieve a reasonable outcome, the coils are meshed with hexahedral-shaped elements. The strengthening parts and the air layer are meshed freely with tetrahedral- shaped elements. The solution involves two parts: the electromagnetic solution and the stress solution. In the electromagnetic analysis, the total current is applied to the copper conductor. The imposed external mag- netic field (that represents the 3 T toroidal magnetic field) is vertical to the current. Then magnetic forces are obtained through j×B; in the stress analysis, the electromagnetic force is transferred as the load. The proper length between the strengthening parts is ob- tained through this analysis. Fig.5 Simplified finite element model (color online) 3.3 Electromagnetic-stress analysis re- sults The purpose of the analysis is to determine the length of the strengthening parts arranged along the coils. Its main limit is the mechanical properties of the stainless steel pipe, which has a yield limit of 170∼210 MPa, and thus a minimal stress limit of SA = 170/2.2 = 77.27 MPa. As can be seen from Table 1, the maximum magnetic flux variation and induced cur- rent in the up and down coils are much bigger than the mid-plane coils when the plasma current breaks off. This occurs because the mid-plane coils are rect- angular, and plenty of the magnetic fluxes flow in and then out again. The up and down coils are trapezoid, with their long sides much wider than their short sides, so they don’t work out as up and down coils. Conse- quently, the induced currents vary obviously and their stress analysis should be considered separately. The re- sults of the stress analysis are shown in Table 2. The mounting distance means the conductor distance be- tween the strengthening parts. It is shown in Table 2 that the maximum mounting distance is 0.12 m for the up and down coils, and their maximum equivalent stress is 75.13 MPa at the two ends of the conductor, which is smaller than the permissible value. The maximum deformation takes place in the center of the conductor with a value of 0.0176 mm. As for the mid-plane coils, the mounting distance can be much larger. The proper distance is 0.135 m, the maximum equivalent stress is 71.28 MPa and the maximum deformation is 0.01873 mm at the middle of the coils. Table 1. The magnetic flux and induced currents in the coils when the plasma currents disrupted Maximum Maximum induced flux (Wb) current (kA) Up and down coils 0.02188 9.840 Mid-plane coils 0.01269 4.447 Table 2. The maximum equivalent stress and deforma- tion Fix Maximum equivalent Maximum distance stress deformation (m) (MPa) (mm) Up and 0.120 75.13 0.0176 down coils Mid-plane 0.135 71.28 0.0187 coils In conclusion, the mounting distance of the up and down coils should be no more than 0.12 m, and 0.135 m for the mid-plane coils, otherwise the allowable stress of the steel shell will be exceeded and the coils will be damaged [11]. Fig. 6 shows the stress distribution of a 0.08 m long down-coil. The maximum stress, 31.9 MPa, happens 85 Plasma Science and Technology, Vol.14, No.1, Jan. 2012 at the ends of the coil and the maximum deformation, 0.0052 mm, at the center, which agrees well with the law of mechanics. Fig.6 The stress distribution of a pipe 0.08 m in length (color online) 3.4 Design verification According to the electromagnetic-stress analysis, a mounting plan is formulated, and a full model of the down coil with strengthening parts is built to verify its stress distribution, deformation and natural frequency. The whole model is shown in Fig. 7. The strengthening parts are arranged so that one is inserted almost every 90 mm, shorter than the 120 mm analyzed above. So there are 13 strengthening parts for the down coils, with their top sides welded onto the inner wall of the vacuum vessel chamber. Fig. 8 shows the results of the electromagnetic and stress analyses of the down coil. As can be seen from Fig. 8(d), the maximum stress is 5.08 MPa, which is very small. The maximum stresses happen in places where the strengthening parts are arranged, while the maximum deformations occur in places between two strengthening parts with a value of 0.000278 mm. Stress and deformation in two of the four sides of the coil are obviously larger than the other two, for the currents flow in are almost vertical to the 3 T toroidal field. Fig.7 The fixing of the down coil (color online) To make sure the coils will not be damaged because of resonance incurred by the electromagnetic forces, a modal analysis is carried out using the model shown in Fig. 7. Results show that the basic natural frequency of the coil is 4521 Hz. It indicates that during opera- tion, currents with a frequency near 4.5 kHz should be avoided. Fig.8 The electromagnetic and stress analysis results: (a) the current distribution in the copper conductor of the coil, (b) the magnetic field (Tesla) distribution in the coil, (c) the magnetic force distribution of the coil and (d) the equivalent stress of the down coil (color online) 86 HAO Changduan et al.: Stress and Thermal Analysis of the In-Vessel RMP Coils on the J-TEXT Tokamak 4 Thermal analysis [12] The thermal environment in the vacuum chamber is very complex. During operation, the coils are mainly heated by three heat sources: the Joule heat of the 10 kA normal current, the Joule heat generated by the eddy currents in the stainless steel pipe, and the plasma radiation. The currents flowing in the coil contribute to most of the temperature rise. So the other two parts are ignored in this analysis. Heat accumulation will damage the insulation if the heat does not dissipate in time. What’s even worse, great thermal stress will oc- cur if the temperature of the coil keeps rising, which is not expected to be seen. The analysis includes two stages. First the initial temperature of the coil is measured, and second the amount of water needed to cool the coil is determined. In J-TEXT, the duration of one discharge is about 500 ms. Normally, it takes about 5 minutes before the next discharge. Water in the coil is supposed to remove all the heat in the interval between the two shots. A two- dimensional FEA model is used here to analyze the cooling process. In the thermal analysis, the maximum temperature rise is 12◦C (see Fig. 9). Then the tem- perature is taken as the initial temperature of the coil in the transient computational fluid dynamics (CFD) analysis. Fig.9 The temperature distribution of the coil in one shot (color online) In the transient CFD analysis, it is supposed that the average temperature of the coil is 316 K. Water flows into the pipe through the inlet with an initial temper- ature of 303 K and a velocity of 1 m/s. The cooling water is taken as turbulent uncompressible fluid. The results are shown in Fig. 10, where TEMP 2 represents the temperature shift at a node in the coil inlet, while TEMP 3 represents a node at the coil outlet. Clearly, the temperature fall at the outlet is much slower than the inlet, as the water is heated through the coil and leads to a low heat exchange rate at the outlet. After about 2 minutes, the coil temperature falls to 303 K, indicating that the heat caused by the current has been taken away. This time is shorter than 5 minutes and satisfies the cooling demand. Fig.10 The cool-down of the inlet and the outlet 5 Summary This paper described the structure of resonant mag- netic coils and verified their stress and thermal instabil- ities. Several factors influence the design: the structure and space of the J-TEXT tokamak device, the desired magnetic field in the device, the electromagnetic force the coils will undertake, the thermal environment in the vacuum chamber, the difficulty level of installation, and so on. What is mainly discussed includes three parts: firstly, a mounting distance is obtained through an electromagnetic-stress analysis. It is recommended that the fixing distance should be no more than 0.12 m for the up and down coils and 0.135 m for the mid-plane coils. Secondly, a verification of the designed mount- ing plan is carried out to obtained the stress distribu- tion and the natural frequencies of the coils. The re- sults show that it is safe enough to mount in this way. Besides, the modal analysis indicates that the current should avoid the frequency of 4.5 kHz in case resonance occurs. Finally, a thermal analysis is performed. The coil temperature is demonstrated by the analysis to fall to the environmental level in about 2 minutes, which keeps the coils at low temperature and meets the cool- ing requirements. References 1 Anderson P, Baxi C, Kellman A, et al. 2004, Fusion Science and Technology, 66∼68: 791 2 Rott M, Seidel U, Streibl B, et al. 2009, Fusion Engi- neering and Design, 84: 1653 3 Vierle T, Streibl B, Rott M, et al. 2009, Fusion Engi- neering and Design, 84: 1928 4 Kim H K, Yang H L, Kim G H, et al. 2009, Fusion Engineering and Design, 84: 1029 5 University of TEXAS at Austin. 1976, Proposal for a fusion plasma research facility. Fusion Research Cen- ter, Austin 6 Deng Fanpin. 2006, Self-study Manual of Finite El- ement Analysis Using Ansys 10.0. People’s Post and Telecommunication Publishing House, Beijing (in Chi- nese) 87 Plasma Science and Technology, Vol.14, No.1, Jan. 2012 7 Kong Mingli. 2007, Tutorial with examples to Finite Element Analysis of electromagnetic Using Ansys 10.0. Machinery Industry Press, Bejing (in Chinese) 8 Wang Jiangjiang. 2008, Finite Element Analysis of structure and thermodynamics Using Ansys 10.0. Ma- chinery Industry Press, Bejing(in Chinese) 9 Xie Chufang. 2006, Electromagnetic. High Education Press, Bejing (in Chinese) 10 Ni Qiao. 2007, Mechanics of Materials. Press of Huazhong Unversity of Science and Technology, Wuhan (in Chinese) 11 Long Yuqiu. 1999, Tutorial of Structure Mechanics. High Education Press, Bejing (in Chinese) 12 Yang Shiming. 2006, Theory of Heat Transfer. High Education Press, Bejing (in Chinese) (Manuscript received 6 August 2011) (Manuscript accepted 20 October 2011) E-mail address of HAO Changduan: hchangduan@163.com 88