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Optimum design of the ITER in-vessel plasma-position reflectometry antenna coverage
G Model
ARTICLE IN PRESS
FUSION-9559; No. of Pages 5
Fusion Engineering and Design xxx (2017) xxx–xxx
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Optimum design of the ITER in-vessel plasma-position reflectometry antenna coverage H. Policarpo a,b,∗ , N. Velez a , P.B. Quental a , R. Moutinho a , R. Luís a , M.M. Neves b a b
Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
h i g h l i g h t s • • • •
Optimum design of the ITER in-vessel plasma-position reflectometry antenna coverage. Finite element optimization using adaptive single-objective optimization. Finite element optimization using adaptive multiple-objective optimization. Optimized design presents lower maximums and average temperatures and deformations.
a r t i c l e
i n f o
Article history: Received 26 September 2016 Received in revised form 16 May 2017 Accepted 16 May 2017 Available online xxx Keywords: ITER PPR antenna Optimization Temperature minimization Deformation minimization Plasma thermal radiation
a b s t r a c t The ITER plasma position reflectometry (PPR) system measures the edge electron density profile of the plasma, providing real-time supplementary contribution to the magnetic measurements of the plasmawall distance. The reflectometry antenna is one of the most critical components as it is the first in direct sight of the plasma. Its optimization is important to improve the structural performance of the antenna, here focused in the temperature and deformation. In this work, adaptive single-objective optimization (ASO) and adaptive multiple-objective optimization (AMO) are used to find optimized coverage distributions in the antenna, while maintaining its internal geometry that is relevant for microwave diagnostics. The optimized design obtained presents lower maximums and average temperatures and deformation. Hence, this design is a suitable alternative to be further considered for the ITER PPR system. © 2017 Elsevier B.V. All rights reserved.
1. Introduction The ITER PPR system [1] will be used to provide real-time estimates of the distance between the position of the magnetic separatrix and the first-wall at four pre-defined locations also known as gaps 3, 4, 5, and 6, complementing the information provided by the magnetic diagnostics. For gaps 4 and 6, the in-vessel PPR system include several components from which the antenna, see Fig. 1, to/from which the microwave signal is routed, is considered a critical component from a structural integrity point of view. The antenna is in direct sight of the plasma through cut-outs in the blanket shield modules, see A and B in Fig. 1, and is subject to plasma radiation, neutronics loads, and stray-radiation from
∗ Corresponding author at: Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal. E-mail address: [email protected] (H. Policarpo).
electron cyclotron resonance heating (ECRH) and collective Thomson scattering (CTS). These loads and radiations may cause excessive temperatures [2] and/or deformations and consequently compromise the structural integrity of the antenna and/or the accuracy and precision of the diagnostics measurement, respectively. Hence, the ideal antenna design should present simultaneously the minimum in maximum temperature Tmax and displacement Dmax , or, when not possible, the best compromise between both. Here, we report on the optimum design of the ITER PPR antenna using finite element analysis (FEA) combined with ASO or AMO, implemented in ANSYS V17 [3], to obtain suitable coverage distributions that minimize Tmax and a combination of Tmax and Dmax at the antenna, while maintaining its internal geometry, that is essential for proper microwave diagnostics. The results obtained through the analysis presented here contribute with suitable alternative antenna designs to be considered for the ITER PPR system.
http://dx.doi.org/10.1016/j.fusengdes.2017.05.075 0920-3796/© 2017 Elsevier B.V. All rights reserved.
Please cite this article in press as: H. Policarpo, et al., Optimum design of the ITER in-vessel plasma-position reflectometry antenna coverage, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.05.075
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Fig. 2. CAD model of ITER PPR antenna (w – width; h – height, t – thickness (uniform) and L – length). Table 1 Dimensions (in mm) of the ITER PPR antenna (w – width; h – height, t – thickness (uniform) and L – length). Fig. 1. Generic CAD model of PPR in-vessel components: A – upper blanket module, B – lower blanket module, C – PPR in-vessel components and D – vacuum vessel.
w1
w2
w3
h1
h2
t
L
25
20
8
20
12
1
115.4
2. Numerical analysis 2.1. Finite element analysis The FEA at hand is governed by the heat transfer equation that may be expressed as [4] [C]{T˙ } + [KT ]{T } = {RT } with [KT ] = [Kk ] + [H] + [Hrad ] and
(1)
{RT } = {RB } + {Rh } + {Rhrad } + {RQ }, where [C] and [KT ] are the general global specific heat and conductivity matrices, and {RT }, {T} and {T˙ } are the general global thermal load, temperature, and the first derivative of the temperature vectors, respectively. Furthermore, [Kk ], [H] and [Hrad ] are the global conductivity, convection and radiation matrices, and {RB }, {Rh }, {Rhrad } and {RQ } are the global heat flux, convection, radiation and heat generation vectors, respectively. The FEA is established as a nonlinear transient thermal analysis (as radiation is considered and the properties of the materials are temperature dependent) that considers conduction and radiation effects (convection is not considered as the medium is vacuum, which means that [H] = {Rh } = 0) to estimate the temperature distribution along the antenna. Afterwards, a static structural FEA, which may be expressed by Eq. (2), is conducted to evaluate the respective thermal displacements on the antenna. [K]{U} = {F},
Fig. 3. Parameterized CAD model: Lc – length of the material coverage; tc – thickness of the material coverage.
The AMO combines a multi-objective genetic algorithm (MOGA), that is a hybrid variant of the non-dominated sorted genetic algorithm-II (NSGA-II) based on controlled elitism concepts, with a Kriging response surface that simulates part of the population increasing the convergence performance. The general multiobjective optimization problem may be formulated as minf(x) = (f1 (x), f2 (x), . . ., fk (x)) x
s.t. hi (x) = 0,
i = 1 to p
gj (x) ≤ 0,
j = 1 to m
(3)
where k is the number of objective functions, p and m are the number of equality and inequality constraints, respectively and f(x) is the k-dimensional vector of the objective functions.
(2)
where [K] is the global stiffness matrix, {F} is the global force vector and {U} is the global displacement vector that accounts for the thermal strain vector [4]. This two-step procedure is suited as temperature influences displacement but displacement has negligible influence on temperature. Hence, it is suited to be incorporated in the optimization analysis. 2.2. Optimization analysis Depending on whether one (e.g., temperature) or multiple objective functions (e.g., temperature and displacement) are considered, ASO [5] or AMO [5], respectively, that are implemented and available in ANSYS V17 [3] are used. A brief description of both methods follows. The ASO is a gradient-based algorithm that combines an optimal space-filling design (OSD), a Kriging response surface and a mixedinteger sequential quadratic programming (MISQP) optimization algorithm to provide a refined global optimized result.
3. CAD and finite element model A CAD model of the antenna, available in ITER’s ENOVIA, is illustrated in Fig. 2 with the respective dimensions: w – width, h – height, t – thickness (uniform) and L – length, presented in Table 1. Based on this model (see Fig. 2), a parametrized FE model, illustrated in Fig. 3, is developed to account for optimum design of the antenna coverage, considering as parameters the length of antenna coverage Lc and respective thickness tc that may vary within specific boundary values. The developed FE model, see Fig. 3, features 3D 20-node structural-thermal FEs with a four degree-of-freedom at each node (displacements in the three directions and temperature). For radiation, the radiating surfaces are considered to be the faces of the 3D FEs [3]. 4. Methodology FEA described by Eqs. (1) and (2), is combined, in ANSYS V17 [3], with adaptive optimization algorithms, considering the parameters
Please cite this article in press as: H. Policarpo, et al., Optimum design of the ITER in-vessel plasma-position reflectometry antenna coverage, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.05.075
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Fig. 6. Distribution of T for the antenna without material coverage. Fig. 4. Radiation enclosure model.
Fig. 7. Distribution of D for the antenna without material coverage.
Fig. 5. Nuclear heat load distribution on the antenna.
Lc and tc , i.e., x = (Lc , tc ), to find the antenna coverage that minimizes: (i) Tmax using ASO and; (ii) a combination of the Tmax and Dmax using AMO. Following the formulation of Eq. (3), (i) and (ii) may be formulated as minT (x) x
s.t. Lc min ≤ Lc ≤ Lc max
(4)
tcmin ≤ tc ≤ tc max min(T (x), D(x)) x
s.t. Lc min ≤ Lc ≤ Lc max
(5) Fig. 8. Tmax as a function of Lc and tc .
tcmin ≤ tc ≤ tc max where Lc min , Lcmax , tcmin , tcmax are the minimum and maximum length and thickness of material coverage, respectively. A radiation power density of 500 kW/m2 [6] is assumed at the first wall (gap between A and B in Fig. 1), i.e., at the front surface of the enclosure model illustrated in Fig. 4. A constant temperature of 300 ◦ C [7] is applied to the rear side of the antenna, where it is structurally fixed, and to the inner surface of the blanket surfaces. An earth gravity acceleration of 98,066 m/s2 is considered. The PPR antenna is made of austenitic stainless steel 316L(N)-IG, with temperature dependent mechanical properties [8]. The surface emissivity of the antenna is that correspondent to a polished steel with a mean surface roughness of 5 m and the blankets emissivity is that correspondent to a clean and smooth surface (see [9] for specific values). It is further assumed that the surface emissivity is equal to the surface absortivity. The nuclear heat load distribution, induced by the neutrons and gamma photons coming from the plasma and surrounding materials, is illustrated in Fig. 5. These values are estimated using the Monte Carlo simulation program MCNP6 [10] and ITER reference neutronics models provided by the ITER Organization. Note that the thermal loads due to ECRH/CTS stray radiation are not taken into account as they are considered negligible [11]. 5. Results Initially, thermal-structural FEAs, see Eqs. (1) and (2), are conducted to identify the location of Tmax and Dmax .
Fig. 9. Dmax as a function of Lc and tc .
As illustrated by Figs. 6 and 7, Tmax and Dmax , respectively, occur at the frontal face of the antenna as expected. This is the first region, of the PPR in-vessel system, facing the plasma, hence the first to be in contact with the plasma prevenient loads, reaching a Tmax of ∼704 ◦ C, a mean temperature T¯ of ∼557 ◦ C and a Dmax (thermal expansion and displacements due to its dead weight) of ∼0.106 mm. In Figs. 8 and 9 are presented the results from the parametric studies that are conducted at these locations to infer how both Tmax and Dmax evolve with the material coverage evolution, respectively, considering 0 ≤ Lc ≤ 115.4 mm and 0 ≤ tc ≤ 3 mm.
Please cite this article in press as: H. Policarpo, et al., Optimum design of the ITER in-vessel plasma-position reflectometry antenna coverage, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.05.075
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Fig. 12. CAD model images of the antenna for tc = 3 mm obtained from: (a) ASO – Lc = 114.7 mm and; (b) AMO – Lc = 102.8 mm.
Table 2 Initial and optimized results obtained by ASO and AMO.
Fig. 10. Minimum Tmax as a function of Lc for tc = 3 mm obtained from ASO.
Fig. 11. Pareto front (in red) for the minimum Tmax and minimum Dmax as a function of Lc for tc = 3 mm obtained with AMO. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
As illustrated by Figs. 8 and 9, both Tmax and Dmax decrease as Lc and tc increase, until each reach the correspondent minimums. The minimum values of Tmax are located between Lc ∼114 mm and ∼Lc 115.4 mm for all the different tc , after which they starts to increase. Regarding the minimum values of Dmax these are located between Lc ∼ 95 mm and Lc ∼ 110 mm for all the different tc , after which they starts to increase. From the parametric studies are established the optimization intervals of each design variable (i.e., Lc and tc ) for each optimization problem, i.e., ASO and AMO. Hence, for the minimization of Tmax using ASO, see Eq. (4), Lc min = 114 mm, Lc max = 115.4 mm and tc max = 3 mm are considered. For the minimization of the combination of Tmax and Dmax using AMO, see Eq. (5), Lc min = 95 mm, Lc max = 115.4 mm and tc max = 3 mm are considered. Figs. 10 and 11 illustrate the ASO and AMO optimization results, respectively. As illustrated by Fig. 10, the minimum Tmax of 617.3 ◦ C is obtained for Lc = 114.7 mm which corresponds to 0.7 mm from the front edge originating the CAD model in Fig. 12 a. Fig. 11, illustrates the Pareto front obtained from the AMO. Considering equal weight of 50% to T and D, the optimum point obtained is illustrated in Fig. 11 by the filled circle, that corresponds to optima T and D of 631.9 ◦ C and a 0.087 mm, respectively, obtained for Lc = 102.8 mm which corresponds to 12.6 mm from the front edge of the antenna, originating the CAD model illustrated in Fig. 12b. In Table 2 are summarized the initial and optimized results obtained by ASO and AMO, where T¯ is the average temperature of the antenna.
Initial ASO AMO
Lc (mm)
tc (mm)
Tmax (◦ C)
T¯ (◦ C)
Dmax (mm)
0 114.7 102.8
0 3 3
703.7 617.3 631.9
556.7 500.5 492.6
0.106 – 0.087
As presented in Table 2, relatively to the initial design the results obtained by: ASO correspond to a decrease in Tmax and T¯ of 86.4 ◦ C (12.3%) and 56.2 ◦ C (10.1%), respectively and; AMO correspond to a decrease in Tmax , T¯ and Dmax of 71.8 ◦ C (10.2%), 64.1 ◦ C (11.5%) and 0.019 mm (17.9%), respectively. In both cases, the decrease in Tmax and T¯ is justified by the fact that conduction is the most sensible heat transfer method in regards to the parameters considered in the analyses. Hence, as the material available to dissipate heat to the back side of the antenna increases, i.e., Lc and tc increase, the conduction heat flux also increases and consequently Tmax and T¯ decrease. The fact that the optimum Tmax obtained using ASO, see Table 2, corresponds to Lc = 114.7 mm is related to the higher conduction heat flux previously explained, and to the lower plasma heat radiation that this surface is exposed to by being located 0.7 mm from the front edge of the antenna. Regarding the fact that the optimum Dmax obtained using AMO, see Table 2, decreases is related to the increase in the stiffness of the antenna. 6. Conclusions Parametric studies show that Tmax and Dmax of the antenna decrease with the increase of tc and Lc until the optimum Lc . With design optimization one obtains with: ASO a Tmax and T¯ decrease of 12.3% and 10.1%, respectively and; AMO a Tmax , T¯ and Dmax of 10.2%, 11.5% and 17.9%, respectively. With lower values of Tmax and T¯ , the lifetime of the antenna is extended, less maintainability is required and hence, the availability of the antenna is increased. With lower Dmax , the signal attenuation is improved and more accurate estimations for the plasma position are expected. Finally, it is suggested, as future works, to apply similar design optimization methodologies to other PPR components. Acknowledgments The work leading to this publication has received financial support from Fundac¸ão para a Ciência e a Tecnologia (FCT) through project UID/FIS/50010/2013. Authors further acknowledge the data provided by Fusion for Energy under F4E-FPA-375-04. References [1] P. Varela, 55.F3 PPR: System Design Description Document (DDD), ITER D SGCQ2S v2.0, July 2016.
Please cite this article in press as: H. Policarpo, et al., Optimum design of the ITER in-vessel plasma-position reflectometry antenna coverage, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.05.075
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[2] B.P. Quental, H. Policarpo, R. Luís, P. Varela, Thermal analysis of the in-vessel components of the ITER plasma-position reflectometry, Rev. Sci. Instrum. 87 (2016) 11E720, http://dx.doi.org/10.1063/1.4960493. [3] ANSYS Academic Research, Release 17.0, 2016. [4] R.D. Cook, D.S. Malkus, M.E. Plesha, R.J. Witt, Concepts and Applications of Finite Element Analysis, John Willy & Sons, Inc., 2002. [5] Ansys DesignXplorer User’s Guide v17, 2016. [6] C. Vacas, 55.F3 – PPR: Load Specification for In-vessel Components, ITER D 9QWLQ8, January 2015. [7] H. Policarpo, F4E-FPA-375-SG04: Plan for the Thermal Analysis of the PPR In-vessel Components, F4E D 25B8L7 v1.1, July 2016.
[8] Appendix A, Materials Design Limit Data, ITER D 222RLN, January 2013. [9] 316L(N)-IG Stainless Steel Emissivity, ITER Material Properties Handbook, ITER D 223FGA, May 2011. [10] G.W. McKinney, F.B. Brown, et al., MCNP 6.1.1 – new features demonstrated, in: IEEE 2014 Nuclear Science Symposium, Seattle, November 8–15, 2014, LA-UR-14-23108. [11] A. Silva, H. Policarpo, P. Varela, Assessment of Stray-Radiation Protection Needs for the PPR In-vessel Components, F4E D 24LLE8, March 2016.
Please cite this article in press as: H. Policarpo, et al., Optimum design of the ITER in-vessel plasma-position reflectometry antenna coverage, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.05.075
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ARTICLE IN PRESS
FUSION-9559; No. of Pages 5
Fusion Engineering and Design xxx (2017) xxx–xxx
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Optimum design of the ITER in-vessel plasma-position reflectometry antenna coverage H. Policarpo a,b,∗ , N. Velez a , P.B. Quental a , R. Moutinho a , R. Luís a , M.M. Neves b a b
Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
h i g h l i g h t s • • • •
Optimum design of the ITER in-vessel plasma-position reflectometry antenna coverage. Finite element optimization using adaptive single-objective optimization. Finite element optimization using adaptive multiple-objective optimization. Optimized design presents lower maximums and average temperatures and deformations.
a r t i c l e
i n f o
Article history: Received 26 September 2016 Received in revised form 16 May 2017 Accepted 16 May 2017 Available online xxx Keywords: ITER PPR antenna Optimization Temperature minimization Deformation minimization Plasma thermal radiation
a b s t r a c t The ITER plasma position reflectometry (PPR) system measures the edge electron density profile of the plasma, providing real-time supplementary contribution to the magnetic measurements of the plasmawall distance. The reflectometry antenna is one of the most critical components as it is the first in direct sight of the plasma. Its optimization is important to improve the structural performance of the antenna, here focused in the temperature and deformation. In this work, adaptive single-objective optimization (ASO) and adaptive multiple-objective optimization (AMO) are used to find optimized coverage distributions in the antenna, while maintaining its internal geometry that is relevant for microwave diagnostics. The optimized design obtained presents lower maximums and average temperatures and deformation. Hence, this design is a suitable alternative to be further considered for the ITER PPR system. © 2017 Elsevier B.V. All rights reserved.
1. Introduction The ITER PPR system [1] will be used to provide real-time estimates of the distance between the position of the magnetic separatrix and the first-wall at four pre-defined locations also known as gaps 3, 4, 5, and 6, complementing the information provided by the magnetic diagnostics. For gaps 4 and 6, the in-vessel PPR system include several components from which the antenna, see Fig. 1, to/from which the microwave signal is routed, is considered a critical component from a structural integrity point of view. The antenna is in direct sight of the plasma through cut-outs in the blanket shield modules, see A and B in Fig. 1, and is subject to plasma radiation, neutronics loads, and stray-radiation from
∗ Corresponding author at: Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal. E-mail address: [email protected] (H. Policarpo).
electron cyclotron resonance heating (ECRH) and collective Thomson scattering (CTS). These loads and radiations may cause excessive temperatures [2] and/or deformations and consequently compromise the structural integrity of the antenna and/or the accuracy and precision of the diagnostics measurement, respectively. Hence, the ideal antenna design should present simultaneously the minimum in maximum temperature Tmax and displacement Dmax , or, when not possible, the best compromise between both. Here, we report on the optimum design of the ITER PPR antenna using finite element analysis (FEA) combined with ASO or AMO, implemented in ANSYS V17 [3], to obtain suitable coverage distributions that minimize Tmax and a combination of Tmax and Dmax at the antenna, while maintaining its internal geometry, that is essential for proper microwave diagnostics. The results obtained through the analysis presented here contribute with suitable alternative antenna designs to be considered for the ITER PPR system.
http://dx.doi.org/10.1016/j.fusengdes.2017.05.075 0920-3796/© 2017 Elsevier B.V. All rights reserved.
Please cite this article in press as: H. Policarpo, et al., Optimum design of the ITER in-vessel plasma-position reflectometry antenna coverage, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.05.075
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Fig. 2. CAD model of ITER PPR antenna (w – width; h – height, t – thickness (uniform) and L – length). Table 1 Dimensions (in mm) of the ITER PPR antenna (w – width; h – height, t – thickness (uniform) and L – length). Fig. 1. Generic CAD model of PPR in-vessel components: A – upper blanket module, B – lower blanket module, C – PPR in-vessel components and D – vacuum vessel.
w1
w2
w3
h1
h2
t
L
25
20
8
20
12
1
115.4
2. Numerical analysis 2.1. Finite element analysis The FEA at hand is governed by the heat transfer equation that may be expressed as [4] [C]{T˙ } + [KT ]{T } = {RT } with [KT ] = [Kk ] + [H] + [Hrad ] and
(1)
{RT } = {RB } + {Rh } + {Rhrad } + {RQ }, where [C] and [KT ] are the general global specific heat and conductivity matrices, and {RT }, {T} and {T˙ } are the general global thermal load, temperature, and the first derivative of the temperature vectors, respectively. Furthermore, [Kk ], [H] and [Hrad ] are the global conductivity, convection and radiation matrices, and {RB }, {Rh }, {Rhrad } and {RQ } are the global heat flux, convection, radiation and heat generation vectors, respectively. The FEA is established as a nonlinear transient thermal analysis (as radiation is considered and the properties of the materials are temperature dependent) that considers conduction and radiation effects (convection is not considered as the medium is vacuum, which means that [H] = {Rh } = 0) to estimate the temperature distribution along the antenna. Afterwards, a static structural FEA, which may be expressed by Eq. (2), is conducted to evaluate the respective thermal displacements on the antenna. [K]{U} = {F},
Fig. 3. Parameterized CAD model: Lc – length of the material coverage; tc – thickness of the material coverage.
The AMO combines a multi-objective genetic algorithm (MOGA), that is a hybrid variant of the non-dominated sorted genetic algorithm-II (NSGA-II) based on controlled elitism concepts, with a Kriging response surface that simulates part of the population increasing the convergence performance. The general multiobjective optimization problem may be formulated as minf(x) = (f1 (x), f2 (x), . . ., fk (x)) x
s.t. hi (x) = 0,
i = 1 to p
gj (x) ≤ 0,
j = 1 to m
(3)
where k is the number of objective functions, p and m are the number of equality and inequality constraints, respectively and f(x) is the k-dimensional vector of the objective functions.
(2)
where [K] is the global stiffness matrix, {F} is the global force vector and {U} is the global displacement vector that accounts for the thermal strain vector [4]. This two-step procedure is suited as temperature influences displacement but displacement has negligible influence on temperature. Hence, it is suited to be incorporated in the optimization analysis. 2.2. Optimization analysis Depending on whether one (e.g., temperature) or multiple objective functions (e.g., temperature and displacement) are considered, ASO [5] or AMO [5], respectively, that are implemented and available in ANSYS V17 [3] are used. A brief description of both methods follows. The ASO is a gradient-based algorithm that combines an optimal space-filling design (OSD), a Kriging response surface and a mixedinteger sequential quadratic programming (MISQP) optimization algorithm to provide a refined global optimized result.
3. CAD and finite element model A CAD model of the antenna, available in ITER’s ENOVIA, is illustrated in Fig. 2 with the respective dimensions: w – width, h – height, t – thickness (uniform) and L – length, presented in Table 1. Based on this model (see Fig. 2), a parametrized FE model, illustrated in Fig. 3, is developed to account for optimum design of the antenna coverage, considering as parameters the length of antenna coverage Lc and respective thickness tc that may vary within specific boundary values. The developed FE model, see Fig. 3, features 3D 20-node structural-thermal FEs with a four degree-of-freedom at each node (displacements in the three directions and temperature). For radiation, the radiating surfaces are considered to be the faces of the 3D FEs [3]. 4. Methodology FEA described by Eqs. (1) and (2), is combined, in ANSYS V17 [3], with adaptive optimization algorithms, considering the parameters
Please cite this article in press as: H. Policarpo, et al., Optimum design of the ITER in-vessel plasma-position reflectometry antenna coverage, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.05.075
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Fig. 6. Distribution of T for the antenna without material coverage. Fig. 4. Radiation enclosure model.
Fig. 7. Distribution of D for the antenna without material coverage.
Fig. 5. Nuclear heat load distribution on the antenna.
Lc and tc , i.e., x = (Lc , tc ), to find the antenna coverage that minimizes: (i) Tmax using ASO and; (ii) a combination of the Tmax and Dmax using AMO. Following the formulation of Eq. (3), (i) and (ii) may be formulated as minT (x) x
s.t. Lc min ≤ Lc ≤ Lc max
(4)
tcmin ≤ tc ≤ tc max min(T (x), D(x)) x
s.t. Lc min ≤ Lc ≤ Lc max
(5) Fig. 8. Tmax as a function of Lc and tc .
tcmin ≤ tc ≤ tc max where Lc min , Lcmax , tcmin , tcmax are the minimum and maximum length and thickness of material coverage, respectively. A radiation power density of 500 kW/m2 [6] is assumed at the first wall (gap between A and B in Fig. 1), i.e., at the front surface of the enclosure model illustrated in Fig. 4. A constant temperature of 300 ◦ C [7] is applied to the rear side of the antenna, where it is structurally fixed, and to the inner surface of the blanket surfaces. An earth gravity acceleration of 98,066 m/s2 is considered. The PPR antenna is made of austenitic stainless steel 316L(N)-IG, with temperature dependent mechanical properties [8]. The surface emissivity of the antenna is that correspondent to a polished steel with a mean surface roughness of 5 m and the blankets emissivity is that correspondent to a clean and smooth surface (see [9] for specific values). It is further assumed that the surface emissivity is equal to the surface absortivity. The nuclear heat load distribution, induced by the neutrons and gamma photons coming from the plasma and surrounding materials, is illustrated in Fig. 5. These values are estimated using the Monte Carlo simulation program MCNP6 [10] and ITER reference neutronics models provided by the ITER Organization. Note that the thermal loads due to ECRH/CTS stray radiation are not taken into account as they are considered negligible [11]. 5. Results Initially, thermal-structural FEAs, see Eqs. (1) and (2), are conducted to identify the location of Tmax and Dmax .
Fig. 9. Dmax as a function of Lc and tc .
As illustrated by Figs. 6 and 7, Tmax and Dmax , respectively, occur at the frontal face of the antenna as expected. This is the first region, of the PPR in-vessel system, facing the plasma, hence the first to be in contact with the plasma prevenient loads, reaching a Tmax of ∼704 ◦ C, a mean temperature T¯ of ∼557 ◦ C and a Dmax (thermal expansion and displacements due to its dead weight) of ∼0.106 mm. In Figs. 8 and 9 are presented the results from the parametric studies that are conducted at these locations to infer how both Tmax and Dmax evolve with the material coverage evolution, respectively, considering 0 ≤ Lc ≤ 115.4 mm and 0 ≤ tc ≤ 3 mm.
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Fig. 12. CAD model images of the antenna for tc = 3 mm obtained from: (a) ASO – Lc = 114.7 mm and; (b) AMO – Lc = 102.8 mm.
Table 2 Initial and optimized results obtained by ASO and AMO.
Fig. 10. Minimum Tmax as a function of Lc for tc = 3 mm obtained from ASO.
Fig. 11. Pareto front (in red) for the minimum Tmax and minimum Dmax as a function of Lc for tc = 3 mm obtained with AMO. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
As illustrated by Figs. 8 and 9, both Tmax and Dmax decrease as Lc and tc increase, until each reach the correspondent minimums. The minimum values of Tmax are located between Lc ∼114 mm and ∼Lc 115.4 mm for all the different tc , after which they starts to increase. Regarding the minimum values of Dmax these are located between Lc ∼ 95 mm and Lc ∼ 110 mm for all the different tc , after which they starts to increase. From the parametric studies are established the optimization intervals of each design variable (i.e., Lc and tc ) for each optimization problem, i.e., ASO and AMO. Hence, for the minimization of Tmax using ASO, see Eq. (4), Lc min = 114 mm, Lc max = 115.4 mm and tc max = 3 mm are considered. For the minimization of the combination of Tmax and Dmax using AMO, see Eq. (5), Lc min = 95 mm, Lc max = 115.4 mm and tc max = 3 mm are considered. Figs. 10 and 11 illustrate the ASO and AMO optimization results, respectively. As illustrated by Fig. 10, the minimum Tmax of 617.3 ◦ C is obtained for Lc = 114.7 mm which corresponds to 0.7 mm from the front edge originating the CAD model in Fig. 12 a. Fig. 11, illustrates the Pareto front obtained from the AMO. Considering equal weight of 50% to T and D, the optimum point obtained is illustrated in Fig. 11 by the filled circle, that corresponds to optima T and D of 631.9 ◦ C and a 0.087 mm, respectively, obtained for Lc = 102.8 mm which corresponds to 12.6 mm from the front edge of the antenna, originating the CAD model illustrated in Fig. 12b. In Table 2 are summarized the initial and optimized results obtained by ASO and AMO, where T¯ is the average temperature of the antenna.
Initial ASO AMO
Lc (mm)
tc (mm)
Tmax (◦ C)
T¯ (◦ C)
Dmax (mm)
0 114.7 102.8
0 3 3
703.7 617.3 631.9
556.7 500.5 492.6
0.106 – 0.087
As presented in Table 2, relatively to the initial design the results obtained by: ASO correspond to a decrease in Tmax and T¯ of 86.4 ◦ C (12.3%) and 56.2 ◦ C (10.1%), respectively and; AMO correspond to a decrease in Tmax , T¯ and Dmax of 71.8 ◦ C (10.2%), 64.1 ◦ C (11.5%) and 0.019 mm (17.9%), respectively. In both cases, the decrease in Tmax and T¯ is justified by the fact that conduction is the most sensible heat transfer method in regards to the parameters considered in the analyses. Hence, as the material available to dissipate heat to the back side of the antenna increases, i.e., Lc and tc increase, the conduction heat flux also increases and consequently Tmax and T¯ decrease. The fact that the optimum Tmax obtained using ASO, see Table 2, corresponds to Lc = 114.7 mm is related to the higher conduction heat flux previously explained, and to the lower plasma heat radiation that this surface is exposed to by being located 0.7 mm from the front edge of the antenna. Regarding the fact that the optimum Dmax obtained using AMO, see Table 2, decreases is related to the increase in the stiffness of the antenna. 6. Conclusions Parametric studies show that Tmax and Dmax of the antenna decrease with the increase of tc and Lc until the optimum Lc . With design optimization one obtains with: ASO a Tmax and T¯ decrease of 12.3% and 10.1%, respectively and; AMO a Tmax , T¯ and Dmax of 10.2%, 11.5% and 17.9%, respectively. With lower values of Tmax and T¯ , the lifetime of the antenna is extended, less maintainability is required and hence, the availability of the antenna is increased. With lower Dmax , the signal attenuation is improved and more accurate estimations for the plasma position are expected. Finally, it is suggested, as future works, to apply similar design optimization methodologies to other PPR components. Acknowledgments The work leading to this publication has received financial support from Fundac¸ão para a Ciência e a Tecnologia (FCT) through project UID/FIS/50010/2013. Authors further acknowledge the data provided by Fusion for Energy under F4E-FPA-375-04. References [1] P. Varela, 55.F3 PPR: System Design Description Document (DDD), ITER D SGCQ2S v2.0, July 2016.
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[2] B.P. Quental, H. Policarpo, R. Luís, P. Varela, Thermal analysis of the in-vessel components of the ITER plasma-position reflectometry, Rev. Sci. Instrum. 87 (2016) 11E720, http://dx.doi.org/10.1063/1.4960493. [3] ANSYS Academic Research, Release 17.0, 2016. [4] R.D. Cook, D.S. Malkus, M.E. Plesha, R.J. Witt, Concepts and Applications of Finite Element Analysis, John Willy & Sons, Inc., 2002. [5] Ansys DesignXplorer User’s Guide v17, 2016. [6] C. Vacas, 55.F3 – PPR: Load Specification for In-vessel Components, ITER D 9QWLQ8, January 2015. [7] H. Policarpo, F4E-FPA-375-SG04: Plan for the Thermal Analysis of the PPR In-vessel Components, F4E D 25B8L7 v1.1, July 2016.
[8] Appendix A, Materials Design Limit Data, ITER D 222RLN, January 2013. [9] 316L(N)-IG Stainless Steel Emissivity, ITER Material Properties Handbook, ITER D 223FGA, May 2011. [10] G.W. McKinney, F.B. Brown, et al., MCNP 6.1.1 – new features demonstrated, in: IEEE 2014 Nuclear Science Symposium, Seattle, November 8–15, 2014, LA-UR-14-23108. [11] A. Silva, H. Policarpo, P. Varela, Assessment of Stray-Radiation Protection Needs for the PPR In-vessel Components, F4E D 24LLE8, March 2016.
Please cite this article in press as: H. Policarpo, et al., Optimum design of the ITER in-vessel plasma-position reflectometry antenna coverage, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2017.05.075
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