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Thermo-mechanical analysis of RMP coil system for EAST tokamak
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ARTICLE IN PRESS
FUSION-7432; No. of Pages 5
Fusion Engineering and Design xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Thermo-mechanical analysis of RMP coil system for EAST tokamak Songke Wang ∗ , Xiang Ji, Yuntao Song, Shanwen Zhang, Zhongwei Wang, Youwen Sun, Minzhong Qi, Xufeng Liu, Shengming Wang, Damao Yao Institute of Plasma Physics, Chinese Academy of Sciences, China
h i g h l i g h t s • • • •
Thermal design requirements for EAST RMP coils are summarized. Cooling parameters based on both theoretical and numerical solutions are determined. Compromise between thermal design and structural design is made on number of turns. Thermo-mechanical calculations are made to validate its structural performance.
a r t i c l e
i n f o
Article history: Received 15 September 2013 Received in revised form 31 March 2014 Accepted 31 March 2014 Available online xxx Keywords: EAST RMP coil Thermo-hydraulic Thermal-structural analysis
a b s t r a c t Resonant magnetic perturbation (RMP) has been proved to be an efficient approach on edge localized modes (ELMs) control, resistive wall mode (RWM) control, and error field correction (EFC), RMP coil system under design in EAST tokamak will realize the above-mentioned multi-functions. This paper focuses on the thermo-mechanical analysis of EAST RMP coil system on the basis of sensitivity analysis, both normal and off-normal working conditions are considered. The most characteristic set of coil system is chosen with a complete modelling by means of three-dimensional (3D) finite element method, thermohydraulic and thermal-structural performances are investigated adequately, both locally and globally. The compromise is made between thermal performance and structural design requirements, and the results indicate that the optimized design is feasible and reasonable. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Erosion and damage caused by ELMs is a major hurdle on the route towards achieving magnetic fusion in a reactor scale machine. RMP has been proved to be an efficient approach on ELMs control, RWM control, and EFC. By perturbing the magnetic field on the edge of the confined plasma to create RMPs, the RMP coil system produces a magnetic field perturbation spectrum characterized by a distribution in toroidal (n) and poloidal mode numbers. Perturbations with mode numbers up to n = 4 are promising for ELM suppression [1]. To investigate tearing mode control, improve plasma configuration and enhance plasma instabilities, multi-functional RMP coils will be designed by integrating the functions of ELM control, RMW control, and EFC in EAST tokamak. By controlling the current on 16 coils independently, the RMP
∗ Corresponding author. Tel.: +86 0551 65593267. E-mail address: [email protected] (S. Wang).
coils can realize above-mentioned functions smoothly. The working modes corresponding to three different functions are listed in Table 1, expected operational parameters are given to guide the design. To generate a wide range of perturbation spectrums, the RMP coils will be energized independently by DC or AC with the amplitude up to 10 kA in the frequency range of 50 Hz–1 kHz, using a real-time control system. During normal and off-normal operation life, thermal source items such as joule heat generation due to the excitation current in coil and baking out would produce a large temperature rise without a cooling system. In order to meet design criteria, coupled analyses should be performed to confirm heat removal and structural rigidity, and a trade-off on cooling design parameters should be determined based on the calculations. Therefore, thermohydraulic calculations are implemented to decide optimized cooling design parameters and thermal performance, thermostructural analyses are necessary to be carried out to validate the feasibility of the thermal design from the view of mechanical strength.
http://dx.doi.org/10.1016/j.fusengdes.2014.03.087 0920-3796/© 2014 Elsevier B.V. All rights reserved.
Please cite this article in press as: S. Wang, et al., Thermo-mechanical analysis of RMP coil system for EAST tokamak, Fusion Eng. Des. (2014), http://dx.doi.org/10.1016/j.fusengdes.2014.03.087
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Table 1 Working modes during three different functions. Function
Pulses
t (s)/pulse
Current (kAt)
Frequency (Hz)
EFC ELM RWM
25,000 5000 2500
100 100 10
1 10 1
0 0 (80%), 50 (20%) ≤1000
2. Thermal design requirements According to expected functions and foreseen working conditions for the RMP coil system, the design requirements based on thermal consideration are summarized as below: (1) The conductor with central active cooling water will work in ultrahigh vacuum, and temperature rise should be no more than 20 ◦ C when the 3 kA is imposed during normal operation [2]. (2) Insulation ability of the conductor should withstand at least 5 kV after 24 h baking out at 350 ◦ C. (3) Leakage rate of the conductor in vacuum environment should be no more than 10−10 Pa m3 s−1 . (4) The conductor and its support structure should meet the requirements on physics and lifetime under electromagnetic, thermal and structural working conditions. (5) The coils should be compatible with other internal components in EAST vacuum vessel (VV).
Fig. 2. A typical RMP coil with its supports.
also to reinforce mechanical strength. An MgO layer is adopted to electrically and thermally insulate inner conductor from steel tube. The oxygen-free copper (OFC) cylinder with a hollow structure is used to carry excitation current. Finally, active cooling by flowing water in the central pipe would improve coil protection against overheating and possible failure of the insulation system. It would ensure timely removal of the pulsed heat loads between pulses.
4. Thermo-hydraulic analysis 3. Design description of RMP coils The coil configuration adopted in Fig. 1 consists of a 16-coil array arranged in two toroidal belts around the plasma, distributed roughly symmetrical in respect to the mid-plane, and rigidly mounted to the ribs inside VV. The coils are mechanically grouped in eight sets, and each set consists of two coils that share the same vertical neck tube. The in-vessel coils require a robust design due to high cyclic thermal stress and temperature up to 350 ◦ C during vessel baking. Fig. 2 shows a typical design of RMP coils with its own supports and large support structure mounted to VV. The RMP coil will be connected to a closed loop of deionized water. Demineralized water from a water treatment system is used, to minimize leakage of current. The adopted coil design is a watercooled hollow copper conductor insulated by MgO and housed inside a stainless steel tube that forms a vacuum boundary (Fig. 3). To prevent insulation materials outgassing to ultra-high vacuum in VV, the coils are finally designed as a multi-layers structure [3]: the outmost layer is stainless steel (SS) 316L tube which is used as isolated layer between insulation materials and ambient vacuum, and
Fig. 1. EAST RMP coils with passive stabilization plates.
During its operation life, RMP coils should endure thermal loads depending on different working modes, the baking out will last for several days to get higher vacuum. Joule heat generation by applied current will produce a significant temperature rise, the critical condition occurs at 10 kA DC mode, and corresponding cooling system inside coil should remove heat timely to satisfy the design requirements. Because the coil is located at the back of passive stabilization plate, the vast majority of eddy current occurring on SS jacket and the heat flux radiated from plasma will be blocked substantially. Meanwhile, radiation effects are ignored in the present case for simplicity of analysis.
4.1. Theoretical solution In order to correctly evaluate the temperature distribution on OFC, an accurate estimation of the convective heat transfer coefficient h between the hollow structure and the coolant is required. The h correlations are usually expressed in terms of dimensionless
Fig. 3. Cross section of RMP coil.
Please cite this article in press as: S. Wang, et al., Thermo-mechanical analysis of RMP coil system for EAST tokamak, Fusion Eng. Des. (2014), http://dx.doi.org/10.1016/j.fusengdes.2014.03.087
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3
parameters including the Nusselt (Nu), Reynolds number (ReD ) and Prandtl (Pr) numbers in Eq. (1): ReD =
um D 4/5
NuD = 0.023ReD Pr n Pr =
cp k
NuD =
(1)
hD k
where is the density of the fluid, um the average velocity in the coil, dynamic viscosity, D the hydraulic diameter, cp specific heat, and k thermal conductivity of coolant. The Dittus–Boelter equation is used here and n = 2/5 due to heated coolant. Because ReD > 2300 and L/D > 10, (L is the length of the coil) the cooling water flow can be considered as a fully developed turbulent flow in a cylindrical smooth pipe. To evaluate the coolant temperature rise, Joule heat generation rate at DC mode should be computed using Joule’s law, 3 kA per turn is taken as a conservative value accounting for current loss along the coil. For current design, the total length for typical coil is 21.5 m. The heat transfer coefficient of 1.55 × 104 W/m2 corresponds to a velocity of 4 m/s and the heat generation rate is approximately 5.09 × 106 W/m3 [4]. Number of turns is a crucial parameter in RMP coil design. Less turns will result in larger conductor and higher current, although this will bring more convenience on support design and shorter cooling path, it leads to a series of problems such as more difficulties on manufacturing, lower adjustment sensitivity of current, and especially more waste of large current on long feeder coil and so on. However, too many turns will occupy more space in the already crowded VV and bring more challenges on conductor bending, higher voltage and support design. Hence compromise should be made to balance the benefits and challenges for better design. Considering the constrains in the VV, three schemes, one, two, and four turns, are studied to check strength, rigidity, and cooling requirements etc. The results indicate that more turns can have a better performance with smaller diameter and applied current, and that four turn coils are forseen to be used in the present design. The coil will experience about 40 ◦ C during normal operation and 350 ◦ C during baking out. To maintain the insulation and the jacket strength, MgO and SS layer is set up to a thickness of 3 mm and 2 mm, respectively. The dimension of hollow structure of OFC determines the cooling capacity and heat generation rate. Skin effect causes the effective resistance of the conductor to increase at higher frequencies where the skin depth is smaller, thus reducing the effective cross-section of the conductor. skin depth ı can be attained by the following formulation:
ı=
2 ω
averaged temperature at outlet, and Tin averaged temperature of velocity inlet. Several schemes of hollow structure are purposed to determine most reasonable and compact cross-section. As shown in Fig. 4, temperature rise versus cooling water velocity under different hollow structure are illustrated, five schemes with internal and external diameter of hollow structure are included, the results indicate that Scheme 3, with an internal diameter of 10 mm and an external diameter of 18 mm, can get a temperature rise of 14.7 ◦ C when the coil conductor system is engineered to operate up to 3 kA DC steady-state with cooling water flow of 4 m/s, which can meet the design requirement very well based on thermal stress consideration. Enough margin has been retained due to the rough cooling pipe and possible radiation from VV environment. Heat transfer rate from OFC to cooling water can be equivalent to power on internal surface of hollow structure, is about 19248 W. Pressure drop to sustain the internal flow which determines pump power requirement should be focused on during engineering design, it can then be evaluated as: P = f
u2m L 2 D
(4)
where is the density of the fluid, um the average velocity in the pipe, f the friction factor, L the length of the pipe, and D the pipe −1/5 diameter. Here empirical correlation f = 0.184ReD is used to identify the Darcy friction factor. At the same time, eighteen 90◦ bends are used because of their much stronger turbulent flow and therefore larger equivalent length, 30 is taken for the value of L/D to evaluate pressure loss, and 0.413 MPa is obtained.
(2) 4.2. Numerical solution
where is resistivity of the conductor, ω angular frequency of current, and absolute magnetic permeability of the conductor. For RWM mode 1000 Hz corresponds to a skin depth of 2.1 mm, while 50 Hz corresponds to 9.4 mm, so a intervening thickness can be adopted. In a simplified assumption, external boundary of OFC is considered as thermal insulation, but thermal conduction and radiation with ambient is ignored. Convection from cooling water will take away equivalent heat generation in hollow structure, which causes temperature equilibrium state quickly, it can be described as: ˙ out − Tin ) Q = cp m(T
Fig. 4. Temperature rise versus water velocity inlet.
(3)
where Q is amount of heat generation in hollow structure in unit ˙ averaged mass flow rate, Tout time, cp specific heat of the fluid, m
To determine the cooling parameters ensuring required temperature condition, ANSYS Fluent model of the cooling system is developed to simulate the 3D incompressible turbulent flow. The following boundary conditions are taken in the hydraulic analysis: - Velocity inlet including velocity magnitude of 4 m/s and water temperature 20 ◦ C are used at flow inlet. - Outflow is adopted to get overall mass balance correction. - Heat generation rate 5.09 × 106 W/m3 is set as the source item in solid cell zone. The standard k– model is chosen as turbulence model, the turbulence intensity at the core of the fully developed duct flow can
Please cite this article in press as: S. Wang, et al., Thermo-mechanical analysis of RMP coil system for EAST tokamak, Fusion Eng. Des. (2014), http://dx.doi.org/10.1016/j.fusengdes.2014.03.087
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Fig. 7. Stress intensity on OFC. Fig. 5. Temperature distribution on OFC.
be estimated from the following formula derived from an empirical correlation for pipe flows [5]: I ≡ 0.16(ReD )−1/8
(5)
At the Reynolds number of 47,000, the turbulence intensity will be 4.2% according to this formula, and hydraulic diameter is 10 mm. According to the initial solution in CFD analysis, temperature distribution on OFC is shown in Fig. 5, temperature increases along the flowing path, the area-weighted average temperature on outflow is 34.9 ◦ C, temperature rise of the cooling water is about 14.9 ◦ C, which is slightly larger than analytical solution, the possible reason is that the internal wall of hollow structure is assumed as totally smooth in theoretical calculation, but turbulent effect and wall resistance are recovered in numerical simulation, thus the flow will be weaker and will take away less heat. The result of the relative pressure on water is shown in Fig. 6, which shows that pressure losses calculated in FLUENT is 0.415 MPa which is in good agreement with the analytical solution [6]. Heat transfer rate on internal surface of hollow structure is 19,208 W, proving that the heat balance is kept within the range of errors permitted. RMP coils are fully heated during each bake cycle to 350 ◦ C. With this type of thermal cycling, the thermal stresses sustain acceptable levels without temperature gradient [7].
is connected to VV. Since the displacement on the bottom face of support is negligible, degrees of freedom are set as zero, it can be considered as a conservative estimation. The ANSYS code is used to transfer body temperature from thermal analysis result to structural analysis, gravity and electromagnetic force on coils are also taken into consideration. Local non-uniformities in the heat distribution will cause large temperature difference, resulting in a high thermal stress. 3D thermal-structural analysis has been performed to estimate the thermal stresses and to verify the structural integrity of the RMP coils [8]. The period during ELM function is the worst case, as shown in Figs. 7 and 8, the maximum von Mises stress on OFC and SS jacket is 44 MPa and 119 MPa. Large Lorenz force will generate on poloidal coil due to larger toroidal magnetic field, however it is difficult to add a support at inter-turn transition part. So the largest deformation happens at inter-turn transition due to torque, which agrees well with laws of mechanics. As shown in Table 2, the classified stress should satisfy the criterion Pm + Pb < 1.5Sm and Pm + Pb + Q < 3Sm , where Pm , Pb , Sm and Q mean primary membrane stress, bending stress, allowable stress, and secondary stress, respectively, according to ASME Section VIII, Division II. And the results meet the criterion very well. The design seems to be rather well covered from the perspective of thermomechanical analysis.
5. Thermo-mechanical analysis The 3-layer coil support will be bolt connected to fasten four turns before being welded together with support structure which
Fig. 8. Stress intensity on SS jacket.
Table 2 Stress classification on OFC and SS jacket.
Fig. 6. Relative pressure on cooling water.
Unit: MPa
Pm + Pb
Pm + Pb + Q
Sm
OFC SS jacket
26 81
44 119
40 147
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6. Conclusion The specified thermal design requirements are summarized to instruct the following design, the preliminary design of RMP coils is demonstrated from view of thermal design, the number of turns of RMP is designed as a compromise of the complex relevant factor, and 4 turns is taken as the chosen design due to their good compatibility. Sensitive calculations are accomplished to obtain optimized design parameter, the cross-section of conductor and the cooling design parameters are derived from the analytical solution, finite element calculations based on ANSYS software have been performed to simulate the working conditions, thermo-hydraulic analysis by FLUENT is performed to validate cooling design scheme, the resultant values of temperature rise and pressure drop are in good agreement with analytical calculations, thermo-mechanical analyses have been carried out to confirm heat removal and structural rigidity and the main results indicate that the present design is reasonable and feasible. The conductor and its support structure should meet the requirements on physics and life expectancy under working conditions including electromagnetic, thermal and structural loads, weight constraints imposed by the existing EAST equipment and
5
operational requirements should also be satisfied. Corresponding test platforms are also established to validate the strength and rigidity of the RMP coils, and all the results show the chosen design can work well after optimizations. Up to now the prototype has been finished and all the RMP coils should be assembled into the EAST VV before the end of 2014. References [1] R. Baker, A. Brooks, P. Carman, M. Cole, T. Edlington, T. Evans, et al., JET ELM control coil feasibility study: final report, 2010, January. [2] Y. Sun, Physical design of RMP coil on EAST, ASIPP internal report, 2012, October. [3] T. Bohm, A. Brooks, L. Bryant, J. Chrzanowski, E. Daly, R. Feder, et al., Final report on the preliminary design of the ITER in-vessel coil system, US ITER 1081001TD0001-R00, 2011, June. [4] M. Onozuka, K. Ioki, G. Sannazzaro, Y. Utin, H. Yoshimura, Design and thermalhydraulic characteristics of the ITER-FEAT vacuum vessel, Fusion Eng. Des. 58–59 (2001) 857–861. [5] ANSYS FLUENT help, release notes 14.0, ANSYS Inc. [6] P. Chaudhuri, C. Danani, V. Chaudhari, C. Chakrapani, R. Srinivasan, I. Sandeep, et al., Thermal hydraulic and thermo-structural analysis of first wall for Indian DEMO blanket module, Fusion Eng. Des. 84 (2009) 573–577. [7] P.M. Anderson, C.B. Baxi, A.G. Kellman, E.E. Reis, Design, fabrication, installation, testing and initial results of in-vessel control coils for DIII-D, in: 20th IEEE/NPSS Symposium on Fusion Engineering, 2003. [8] ANSYS Mechanical APDL application help, Release notes 14.0, ANSYS Inc.
Please cite this article in press as: S. Wang, et al., Thermo-mechanical analysis of RMP coil system for EAST tokamak, Fusion Eng. Des. (2014), http://dx.doi.org/10.1016/j.fusengdes.2014.03.087
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FUSION-7432; No. of Pages 5
Fusion Engineering and Design xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Thermo-mechanical analysis of RMP coil system for EAST tokamak Songke Wang ∗ , Xiang Ji, Yuntao Song, Shanwen Zhang, Zhongwei Wang, Youwen Sun, Minzhong Qi, Xufeng Liu, Shengming Wang, Damao Yao Institute of Plasma Physics, Chinese Academy of Sciences, China
h i g h l i g h t s • • • •
Thermal design requirements for EAST RMP coils are summarized. Cooling parameters based on both theoretical and numerical solutions are determined. Compromise between thermal design and structural design is made on number of turns. Thermo-mechanical calculations are made to validate its structural performance.
a r t i c l e
i n f o
Article history: Received 15 September 2013 Received in revised form 31 March 2014 Accepted 31 March 2014 Available online xxx Keywords: EAST RMP coil Thermo-hydraulic Thermal-structural analysis
a b s t r a c t Resonant magnetic perturbation (RMP) has been proved to be an efficient approach on edge localized modes (ELMs) control, resistive wall mode (RWM) control, and error field correction (EFC), RMP coil system under design in EAST tokamak will realize the above-mentioned multi-functions. This paper focuses on the thermo-mechanical analysis of EAST RMP coil system on the basis of sensitivity analysis, both normal and off-normal working conditions are considered. The most characteristic set of coil system is chosen with a complete modelling by means of three-dimensional (3D) finite element method, thermohydraulic and thermal-structural performances are investigated adequately, both locally and globally. The compromise is made between thermal performance and structural design requirements, and the results indicate that the optimized design is feasible and reasonable. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Erosion and damage caused by ELMs is a major hurdle on the route towards achieving magnetic fusion in a reactor scale machine. RMP has been proved to be an efficient approach on ELMs control, RWM control, and EFC. By perturbing the magnetic field on the edge of the confined plasma to create RMPs, the RMP coil system produces a magnetic field perturbation spectrum characterized by a distribution in toroidal (n) and poloidal mode numbers. Perturbations with mode numbers up to n = 4 are promising for ELM suppression [1]. To investigate tearing mode control, improve plasma configuration and enhance plasma instabilities, multi-functional RMP coils will be designed by integrating the functions of ELM control, RMW control, and EFC in EAST tokamak. By controlling the current on 16 coils independently, the RMP
∗ Corresponding author. Tel.: +86 0551 65593267. E-mail address: [email protected] (S. Wang).
coils can realize above-mentioned functions smoothly. The working modes corresponding to three different functions are listed in Table 1, expected operational parameters are given to guide the design. To generate a wide range of perturbation spectrums, the RMP coils will be energized independently by DC or AC with the amplitude up to 10 kA in the frequency range of 50 Hz–1 kHz, using a real-time control system. During normal and off-normal operation life, thermal source items such as joule heat generation due to the excitation current in coil and baking out would produce a large temperature rise without a cooling system. In order to meet design criteria, coupled analyses should be performed to confirm heat removal and structural rigidity, and a trade-off on cooling design parameters should be determined based on the calculations. Therefore, thermohydraulic calculations are implemented to decide optimized cooling design parameters and thermal performance, thermostructural analyses are necessary to be carried out to validate the feasibility of the thermal design from the view of mechanical strength.
http://dx.doi.org/10.1016/j.fusengdes.2014.03.087 0920-3796/© 2014 Elsevier B.V. All rights reserved.
Please cite this article in press as: S. Wang, et al., Thermo-mechanical analysis of RMP coil system for EAST tokamak, Fusion Eng. Des. (2014), http://dx.doi.org/10.1016/j.fusengdes.2014.03.087
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Table 1 Working modes during three different functions. Function
Pulses
t (s)/pulse
Current (kAt)
Frequency (Hz)
EFC ELM RWM
25,000 5000 2500
100 100 10
1 10 1
0 0 (80%), 50 (20%) ≤1000
2. Thermal design requirements According to expected functions and foreseen working conditions for the RMP coil system, the design requirements based on thermal consideration are summarized as below: (1) The conductor with central active cooling water will work in ultrahigh vacuum, and temperature rise should be no more than 20 ◦ C when the 3 kA is imposed during normal operation [2]. (2) Insulation ability of the conductor should withstand at least 5 kV after 24 h baking out at 350 ◦ C. (3) Leakage rate of the conductor in vacuum environment should be no more than 10−10 Pa m3 s−1 . (4) The conductor and its support structure should meet the requirements on physics and lifetime under electromagnetic, thermal and structural working conditions. (5) The coils should be compatible with other internal components in EAST vacuum vessel (VV).
Fig. 2. A typical RMP coil with its supports.
also to reinforce mechanical strength. An MgO layer is adopted to electrically and thermally insulate inner conductor from steel tube. The oxygen-free copper (OFC) cylinder with a hollow structure is used to carry excitation current. Finally, active cooling by flowing water in the central pipe would improve coil protection against overheating and possible failure of the insulation system. It would ensure timely removal of the pulsed heat loads between pulses.
4. Thermo-hydraulic analysis 3. Design description of RMP coils The coil configuration adopted in Fig. 1 consists of a 16-coil array arranged in two toroidal belts around the plasma, distributed roughly symmetrical in respect to the mid-plane, and rigidly mounted to the ribs inside VV. The coils are mechanically grouped in eight sets, and each set consists of two coils that share the same vertical neck tube. The in-vessel coils require a robust design due to high cyclic thermal stress and temperature up to 350 ◦ C during vessel baking. Fig. 2 shows a typical design of RMP coils with its own supports and large support structure mounted to VV. The RMP coil will be connected to a closed loop of deionized water. Demineralized water from a water treatment system is used, to minimize leakage of current. The adopted coil design is a watercooled hollow copper conductor insulated by MgO and housed inside a stainless steel tube that forms a vacuum boundary (Fig. 3). To prevent insulation materials outgassing to ultra-high vacuum in VV, the coils are finally designed as a multi-layers structure [3]: the outmost layer is stainless steel (SS) 316L tube which is used as isolated layer between insulation materials and ambient vacuum, and
Fig. 1. EAST RMP coils with passive stabilization plates.
During its operation life, RMP coils should endure thermal loads depending on different working modes, the baking out will last for several days to get higher vacuum. Joule heat generation by applied current will produce a significant temperature rise, the critical condition occurs at 10 kA DC mode, and corresponding cooling system inside coil should remove heat timely to satisfy the design requirements. Because the coil is located at the back of passive stabilization plate, the vast majority of eddy current occurring on SS jacket and the heat flux radiated from plasma will be blocked substantially. Meanwhile, radiation effects are ignored in the present case for simplicity of analysis.
4.1. Theoretical solution In order to correctly evaluate the temperature distribution on OFC, an accurate estimation of the convective heat transfer coefficient h between the hollow structure and the coolant is required. The h correlations are usually expressed in terms of dimensionless
Fig. 3. Cross section of RMP coil.
Please cite this article in press as: S. Wang, et al., Thermo-mechanical analysis of RMP coil system for EAST tokamak, Fusion Eng. Des. (2014), http://dx.doi.org/10.1016/j.fusengdes.2014.03.087
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3
parameters including the Nusselt (Nu), Reynolds number (ReD ) and Prandtl (Pr) numbers in Eq. (1): ReD =
um D 4/5
NuD = 0.023ReD Pr n Pr =
cp k
NuD =
(1)
hD k
where is the density of the fluid, um the average velocity in the coil, dynamic viscosity, D the hydraulic diameter, cp specific heat, and k thermal conductivity of coolant. The Dittus–Boelter equation is used here and n = 2/5 due to heated coolant. Because ReD > 2300 and L/D > 10, (L is the length of the coil) the cooling water flow can be considered as a fully developed turbulent flow in a cylindrical smooth pipe. To evaluate the coolant temperature rise, Joule heat generation rate at DC mode should be computed using Joule’s law, 3 kA per turn is taken as a conservative value accounting for current loss along the coil. For current design, the total length for typical coil is 21.5 m. The heat transfer coefficient of 1.55 × 104 W/m2 corresponds to a velocity of 4 m/s and the heat generation rate is approximately 5.09 × 106 W/m3 [4]. Number of turns is a crucial parameter in RMP coil design. Less turns will result in larger conductor and higher current, although this will bring more convenience on support design and shorter cooling path, it leads to a series of problems such as more difficulties on manufacturing, lower adjustment sensitivity of current, and especially more waste of large current on long feeder coil and so on. However, too many turns will occupy more space in the already crowded VV and bring more challenges on conductor bending, higher voltage and support design. Hence compromise should be made to balance the benefits and challenges for better design. Considering the constrains in the VV, three schemes, one, two, and four turns, are studied to check strength, rigidity, and cooling requirements etc. The results indicate that more turns can have a better performance with smaller diameter and applied current, and that four turn coils are forseen to be used in the present design. The coil will experience about 40 ◦ C during normal operation and 350 ◦ C during baking out. To maintain the insulation and the jacket strength, MgO and SS layer is set up to a thickness of 3 mm and 2 mm, respectively. The dimension of hollow structure of OFC determines the cooling capacity and heat generation rate. Skin effect causes the effective resistance of the conductor to increase at higher frequencies where the skin depth is smaller, thus reducing the effective cross-section of the conductor. skin depth ı can be attained by the following formulation:
ı=
2 ω
averaged temperature at outlet, and Tin averaged temperature of velocity inlet. Several schemes of hollow structure are purposed to determine most reasonable and compact cross-section. As shown in Fig. 4, temperature rise versus cooling water velocity under different hollow structure are illustrated, five schemes with internal and external diameter of hollow structure are included, the results indicate that Scheme 3, with an internal diameter of 10 mm and an external diameter of 18 mm, can get a temperature rise of 14.7 ◦ C when the coil conductor system is engineered to operate up to 3 kA DC steady-state with cooling water flow of 4 m/s, which can meet the design requirement very well based on thermal stress consideration. Enough margin has been retained due to the rough cooling pipe and possible radiation from VV environment. Heat transfer rate from OFC to cooling water can be equivalent to power on internal surface of hollow structure, is about 19248 W. Pressure drop to sustain the internal flow which determines pump power requirement should be focused on during engineering design, it can then be evaluated as: P = f
u2m L 2 D
(4)
where is the density of the fluid, um the average velocity in the pipe, f the friction factor, L the length of the pipe, and D the pipe −1/5 diameter. Here empirical correlation f = 0.184ReD is used to identify the Darcy friction factor. At the same time, eighteen 90◦ bends are used because of their much stronger turbulent flow and therefore larger equivalent length, 30 is taken for the value of L/D to evaluate pressure loss, and 0.413 MPa is obtained.
(2) 4.2. Numerical solution
where is resistivity of the conductor, ω angular frequency of current, and absolute magnetic permeability of the conductor. For RWM mode 1000 Hz corresponds to a skin depth of 2.1 mm, while 50 Hz corresponds to 9.4 mm, so a intervening thickness can be adopted. In a simplified assumption, external boundary of OFC is considered as thermal insulation, but thermal conduction and radiation with ambient is ignored. Convection from cooling water will take away equivalent heat generation in hollow structure, which causes temperature equilibrium state quickly, it can be described as: ˙ out − Tin ) Q = cp m(T
Fig. 4. Temperature rise versus water velocity inlet.
(3)
where Q is amount of heat generation in hollow structure in unit ˙ averaged mass flow rate, Tout time, cp specific heat of the fluid, m
To determine the cooling parameters ensuring required temperature condition, ANSYS Fluent model of the cooling system is developed to simulate the 3D incompressible turbulent flow. The following boundary conditions are taken in the hydraulic analysis: - Velocity inlet including velocity magnitude of 4 m/s and water temperature 20 ◦ C are used at flow inlet. - Outflow is adopted to get overall mass balance correction. - Heat generation rate 5.09 × 106 W/m3 is set as the source item in solid cell zone. The standard k– model is chosen as turbulence model, the turbulence intensity at the core of the fully developed duct flow can
Please cite this article in press as: S. Wang, et al., Thermo-mechanical analysis of RMP coil system for EAST tokamak, Fusion Eng. Des. (2014), http://dx.doi.org/10.1016/j.fusengdes.2014.03.087
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Fig. 7. Stress intensity on OFC. Fig. 5. Temperature distribution on OFC.
be estimated from the following formula derived from an empirical correlation for pipe flows [5]: I ≡ 0.16(ReD )−1/8
(5)
At the Reynolds number of 47,000, the turbulence intensity will be 4.2% according to this formula, and hydraulic diameter is 10 mm. According to the initial solution in CFD analysis, temperature distribution on OFC is shown in Fig. 5, temperature increases along the flowing path, the area-weighted average temperature on outflow is 34.9 ◦ C, temperature rise of the cooling water is about 14.9 ◦ C, which is slightly larger than analytical solution, the possible reason is that the internal wall of hollow structure is assumed as totally smooth in theoretical calculation, but turbulent effect and wall resistance are recovered in numerical simulation, thus the flow will be weaker and will take away less heat. The result of the relative pressure on water is shown in Fig. 6, which shows that pressure losses calculated in FLUENT is 0.415 MPa which is in good agreement with the analytical solution [6]. Heat transfer rate on internal surface of hollow structure is 19,208 W, proving that the heat balance is kept within the range of errors permitted. RMP coils are fully heated during each bake cycle to 350 ◦ C. With this type of thermal cycling, the thermal stresses sustain acceptable levels without temperature gradient [7].
is connected to VV. Since the displacement on the bottom face of support is negligible, degrees of freedom are set as zero, it can be considered as a conservative estimation. The ANSYS code is used to transfer body temperature from thermal analysis result to structural analysis, gravity and electromagnetic force on coils are also taken into consideration. Local non-uniformities in the heat distribution will cause large temperature difference, resulting in a high thermal stress. 3D thermal-structural analysis has been performed to estimate the thermal stresses and to verify the structural integrity of the RMP coils [8]. The period during ELM function is the worst case, as shown in Figs. 7 and 8, the maximum von Mises stress on OFC and SS jacket is 44 MPa and 119 MPa. Large Lorenz force will generate on poloidal coil due to larger toroidal magnetic field, however it is difficult to add a support at inter-turn transition part. So the largest deformation happens at inter-turn transition due to torque, which agrees well with laws of mechanics. As shown in Table 2, the classified stress should satisfy the criterion Pm + Pb < 1.5Sm and Pm + Pb + Q < 3Sm , where Pm , Pb , Sm and Q mean primary membrane stress, bending stress, allowable stress, and secondary stress, respectively, according to ASME Section VIII, Division II. And the results meet the criterion very well. The design seems to be rather well covered from the perspective of thermomechanical analysis.
5. Thermo-mechanical analysis The 3-layer coil support will be bolt connected to fasten four turns before being welded together with support structure which
Fig. 8. Stress intensity on SS jacket.
Table 2 Stress classification on OFC and SS jacket.
Fig. 6. Relative pressure on cooling water.
Unit: MPa
Pm + Pb
Pm + Pb + Q
Sm
OFC SS jacket
26 81
44 119
40 147
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6. Conclusion The specified thermal design requirements are summarized to instruct the following design, the preliminary design of RMP coils is demonstrated from view of thermal design, the number of turns of RMP is designed as a compromise of the complex relevant factor, and 4 turns is taken as the chosen design due to their good compatibility. Sensitive calculations are accomplished to obtain optimized design parameter, the cross-section of conductor and the cooling design parameters are derived from the analytical solution, finite element calculations based on ANSYS software have been performed to simulate the working conditions, thermo-hydraulic analysis by FLUENT is performed to validate cooling design scheme, the resultant values of temperature rise and pressure drop are in good agreement with analytical calculations, thermo-mechanical analyses have been carried out to confirm heat removal and structural rigidity and the main results indicate that the present design is reasonable and feasible. The conductor and its support structure should meet the requirements on physics and life expectancy under working conditions including electromagnetic, thermal and structural loads, weight constraints imposed by the existing EAST equipment and
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operational requirements should also be satisfied. Corresponding test platforms are also established to validate the strength and rigidity of the RMP coils, and all the results show the chosen design can work well after optimizations. Up to now the prototype has been finished and all the RMP coils should be assembled into the EAST VV before the end of 2014. References [1] R. Baker, A. Brooks, P. Carman, M. Cole, T. Edlington, T. Evans, et al., JET ELM control coil feasibility study: final report, 2010, January. [2] Y. Sun, Physical design of RMP coil on EAST, ASIPP internal report, 2012, October. [3] T. Bohm, A. Brooks, L. Bryant, J. Chrzanowski, E. Daly, R. Feder, et al., Final report on the preliminary design of the ITER in-vessel coil system, US ITER 1081001TD0001-R00, 2011, June. [4] M. Onozuka, K. Ioki, G. Sannazzaro, Y. Utin, H. Yoshimura, Design and thermalhydraulic characteristics of the ITER-FEAT vacuum vessel, Fusion Eng. Des. 58–59 (2001) 857–861. [5] ANSYS FLUENT help, release notes 14.0, ANSYS Inc. [6] P. Chaudhuri, C. Danani, V. Chaudhari, C. Chakrapani, R. Srinivasan, I. Sandeep, et al., Thermal hydraulic and thermo-structural analysis of first wall for Indian DEMO blanket module, Fusion Eng. Des. 84 (2009) 573–577. [7] P.M. Anderson, C.B. Baxi, A.G. Kellman, E.E. Reis, Design, fabrication, installation, testing and initial results of in-vessel control coils for DIII-D, in: 20th IEEE/NPSS Symposium on Fusion Engineering, 2003. [8] ANSYS Mechanical APDL application help, Release notes 14.0, ANSYS Inc.
Please cite this article in press as: S. Wang, et al., Thermo-mechanical analysis of RMP coil system for EAST tokamak, Fusion Eng. Des. (2014), http://dx.doi.org/10.1016/j.fusengdes.2014.03.087