Structural assessment of the ITER Fast-Ion Loss Detector

Equation Chapter 1 Section 1 Master Thesis Industrial Engineering Structural assessment of the ITER Fast-Ion Loss Detector Author: Juan Carlos Rodríguez Criado Supervisors: Juan Manuel Ayllón Guerola Manuel Toscano Jiménez Dep. Física Aplicada III Escuela Técnica Superior de Ingeniería University of Seville Seville, 2018 iii Master Thesis Industrial Engineering Structural assessment of the ITER Fast-Ion Loss Detector Author: Juan Carlos Rodríguez Criado Supervisor: Juan Manuel Ayllón Guerola Assistant Professor Manuel Toscano Jiménez Associate Professor Dep. de Física Aplicada III Escuela Técnica Superior de Ingeniería University of Seville Seville, 2018 v Master Thesis: Structural assessment of the ITER Fast-Ion Loss Detector Author: Juan Carlos Rodríguez Criado Supervisor: Juan Manuel Ayllón Guerola Manuel Toscano Jiménez El tribunal nombrado para juzgar el Proyecto arriba indicado, compuesto por los siguientes miembros: Presidente: Vocales: Secretario: Acuerdan otorgarle la calificación de: Sevilla, 2018 El Secretario del Tribunal vii A mis padres y Ainhoa por su extraordinaria ayuda ix Acknowledgment Este trabajo no podría haberse realizado sin la colaboración de aquellas personas que han estado apoyándome durante el transcurso de este proyecto. En primer lugar, agradecer a los directores de este proyecto por haberme ayudado todo lo posible. A Manuel por haberme dado la oportunidad y a Juanma por dirigirme, enseñarme y dar los consejos adecuados para poder terminar con éxito este trabajo. No me puedo olvidar de mis compañeros de grado y máster, en especial Andrés, Antonio, Sergio Serrano y Sergio Moreno; por estar siempre apoyándonos mutuamente ante cualquier problema. Por último, debo mencionar a aquellas personas que han sido un apoyo moral durante el proyecto. A toda mi familia por preocuparse de mi y por la evolución del proyecto; en especial a mis padres que me han dado su apoyo en cualquier aspecto profesional y personal. Finalmente, dedicar una mención especial para Ainhoa que me acompaña en estos últimos e importantes años, apoyándome cuando las cosas salen mal y cuando salen bien; escuchándome y dándome consejos. Gracias. Juan Carlos Rodríguez Criado Julio de 2018 xvii LIST OF FIGURES Figure 1: Nuclear fusion reaction 1 Figure 2: ITER scheme 2 Figure 3: Poloidal cross-section of ITER 3 Figure 4. ITER tokamak internal structure 5 Figure 5. FILD's location 6 Figure 6. General scheme of FILD 7 Figure 7. FILD positions 8 Figure 8. Main components of FILD 9 Figure 9. Schematic of FILD principle 9 Figure 10. Linear actuators 10 Figure 11. Gas chamber scheme 11 Figure 12. Path of the volumetric loads from induced currents in passive structures 15 Figure 13. Force density distribution to be interpolated in the whole port plug (N/m3) 17 Figure 14. FILD CAD model 18 Figure 15. Model for electromagnetic calculations (radial field variation) 20 Figure 16. Moments in z-axis due to eddy currents 22 Figure 17. Model for electromagnetic calculations (vertical field variation) 22 Figure 18. Moments in x-axis due to eddy currents 23 Figure 19. Time evolutions of the plasma current, vertical position and poloidal halo current. 24 Figure 20. Halo current distributed in the toroidal width of the EPP#08 25 Figure 21. Distributed force due to Halo current 27 Figure 22. Mesh in eddy current model 30 Figure 23. Element metrics of the previous mesh 31 Figure 24. Boundary conditions in the structural static model 32 Figure 25. Stress distribution in FILD 33 Figure 26. Total deformation in FILD 34 Figure 27. Sensitivity analysis of the mesh. 34 Figure 28. Equivalent stress vs length in thickness. Comparative between several meshes. 35 Figure 29. Equivalent stress maximum response surface versus larger radius and thickness. 36 Figure 30. Stress distribution in FILD (Proposed design) 37 Figure 31. Total deformation in FILD (Proposed design) 37 Figure 32. FILD CAD model (with fixed part) 39 Figure 33. Mesh in Halo current model. 39 Figure 34. Element metrics of the previous mesh 40 Figure 35. Augmented Lagrange formulation scheme 41 Figure 36. Time step controls. Bisection method (left), Predict for impact (right). 41 Figure 37. Boundary conditions in Halo current model 42 Figure 38. Equivalent stress in FILD (conceptual phase). Detail of the penetration. 43 Figure 39. Equivalent stress maximum vs length between the contact ring and the probe head 44 Figure 40. Stress distribution in FILD (725 mm contact ring) 45 Figure 41. Deformation in FILD (725 mm contact ring) 45 Figure 42. Sensitivity analysis of the mesh 46 Figure 43. Equivalent stress maximum versus larger radius 47 Figure 44. Stress distribution in FILD (40 mm larger radius) 47 Figure 45. Equivalent stress maximum response surface versus stress concentrator radius and thickness. 48 Figure 46. Stress distribution in the proposed final design 49 Figure 47. Deformation generated by own weight 49 Figure 48. Stress distribution in proposed final design (Gap 4 mm) 50 Figure 49. Details of the plastified zone 50 Figure 50. Deformation in proposed final design (Gap 4 mm) 51 1 1 INTRODUCTION 1.1 Fusion energy This is a difficult time for the energy industry. Many of the new signals emerging, disruptive digitalization, the commitment to decarbonization and desire, in some counties, for a more national focus; indicate that new frameworks for thinking are needed. The period of 1970 to 2015 was one of remarkable world economic growth: The increase in the Gross World Product, the population, and the labour force, was complemented with a high rate of productivity growth; which led to an increase in energy demand [1]. According to a recent study by U.S. Energy Information Administration [2], world energy consumption will rise 28% between 2015 and 2040. Currently, most of the energy resources that provide energy to the planet are of natural origin, especially fossil fuels; while renewable energies remain in the background due to their low efficiency and dependence on climatic conditions. What happens with fission nuclear energy is the same because of the generation of radioactive and dangerous waste. It is expected that in de coming years the consumption of renewable energies will increase, but so will fossil fuels, which is not sustainable due to the overexploitation of these resources, as well as the negative consequences on the environment. Global warming is a problem that is being addressed in key points of reports like World Energy Scenarios 2016 [1]. Given these arguments, there is a need to find a source of sustainable, safe, inexhaustible and clean energy. Nuclear fusion energy is a promising field in these aspects, but its developments as an energy source is one of the most complex scientific and technical tasks ever undertaken for non-military purposes and will still span several human generations [3]. The fusion reaction that is easiest to accomplish is the reaction between two hydrogen isotopes: deuterium, extracted from water and tritium, produced during the fusion reaction through contact with lithium. When deuterium and tritium nuclei fuse, they form a helium nucleus, a neutron and a lot of energy [4]. Figure 1: Nuclear fusion reaction The kinetic energy released is due to the mass difference between reactants and products, according to the Einstein formula (E = ∆m · c2) that can be used to generate electricity. This is the reason why so little fuel can produce so much energy: When burnt in a fusion reactor, the deuterium contained in 1 L of water (about 33 mg) will produce as much energy as burning 260 L of gasoline [3]. Introduction 2 Since 1991 several megawatts of fusion power have been released in a controlled way in deuterium-tritium experiments in JET (Joint European Torus, Culham, UK) and TFTR (Tokamak Fusion Test Reactor, Princeton, USA) [3]. These experiments are carried out in nuclear fusion reactors of tokamak type (most widespread). The tokamak is a toroidal plasma confinement system, the plasma being confined by a magnetic field. The principal magnetic field is the toroidal field. However, this field alone does not allow confinement of the plasma, it is necessary a poloidal magnetic field [5]. This Master Thesis is framed in ITER (International Thermonuclear Experimental Reactor). ITER is one of the most ambitious energy projects today. In southern France (Cadarache), 35 nations are collaborating to build the world’s largest tokamak, a magnetic fusion device that has been designed to prove the feasibility of fusion as a large-scale and carbon-free source of energy based on the same principle that powers our Sun and stars. In figure 2, a rendering of the complex where the reactor is installed is shown. Figure 2: ITER scheme ITER is designed to produce a ten-fold return of energy (Q = 10), or 500 MW of fusion power from 50 MW of input heating power. ITER will not capture the energy it produces as electricity, but -as first of all fusion experiments in history to produce net energy gainit will prepare the way for the machine that can [6]. Other objectives can be summarized in: • Demonstrate the integrated operation of technologies for a fusion power plant. Scientist will be able to study plasmas under conditions similar to those expected in a future power plant and test technologies such as heating, control, diagnostics, cryogenics and remote maintenance. • Achieve a deuterium-tritium plasma in which the reaction is sustained through internal heating. Scientists are confident that the plasmas in ITER will not only produce much more fusion energy but will remain stable for longer periods of time. • Test tritium breeding. The world supply of tritium is not sufficient to cover the needs of future power plants. ITER will provide a unique opportunity to test mockup in-vessel tritium breeding blankets in a real fusion environment. • Demonstrate the safety characteristics of a fusion device. One of the primary goals of ITER operation is to demonstrate the control of the plasma and the fusion reactions with negligible consequences to the environment. 3 3 Structural assessment of the ITER Fast-Ion Loss Detector 1.2 The Fast-Ion Loss Detector (FILD) In ITER, fusion reactions and the use of various specific systems such as ion cyclotron heating and neutral beam injection can generate fast ions. Fast-ions are the population of ions whose energy is above the thermal energy, i.e. the bulk plasma energy. Therefore, they can be expelled from the core region to plasma edge by various instabilities. Even though they are a small fraction of the total ions population, they have a crucial effect on fusion devices performance and plasma stability because of their high energy [7]. The Fast-Ion Loss Detector (FILD) is one of the most widely used diagnostic for measuring fast ions in the plasma edge (Figure 3). A fraction of the incident fast ions is transmitted into a FILD where they encounter a scintillator and/or an array of Faraday cups. The interaction of fast ions with the scintillator provides measurements of their energy and the velocity pitch. This permits extracting information about the underlying loss process [8]. Figure 3: Poloidal cross-section of ITER Understanding the mechanisms of losses and developing procedures for their control is one of the main avenues of research in the field of fusion. An ideal Fast-Ion Loss Detector should be able to provide information on the following aspects [9]: • Type of suprathermic particles that are escaping from the plasma. • Spatial location of the losses on the first wall of the reactor. • Information about the angular distribution of the fast ions that provides information on the nature of the orbits followed by the ions. • Good resolution in energy to detect the energy range of the suprathermic particles. • Temporary resolution to follow the evolution and frequency of losses due to the presence of instabilities. • The absolute flow of particles that impact on the vessel. • The detector must be flexible and resistant to be able to withstand the harsh conditions of the hostile Introduction 4 environment of the fusion reactors in which it must operate. 1.3 Objectives and project scope ITER is an experimental nuclear fusion reactor where the aim is to achieve a technology that provides clean, safe and unlimited energy. To reach this point it is necessary to study the plasma and the physical phenomena that occur during the reaction, to finally be able to control the plasma and generate energy. Hence the experimental character of the reactor. Diagnostic systems such as FILD play an important role in understanding the process. But the fact of being incorporated in this system means that it is exposed to certain loads, such as those generated by electromagnetic disruptions. The main objective of this master thesis is to achieve a design of FILD that is capable of resisting static loads due to electromagnetic disruptions, starting from an initial concept of device. Other secondary objectives, but necessary to reach the main objective are: • The general understanding of the performance of the tokamak and its components. This allowed to acquire ease for the calculation of the loads. • Study the operation of FILD and its components to understand the conceptual design and be able to approach the design process in a realistic way. • Learn about the different types of loads that occur in tokamaks and how they are transferred to different devices. • Generate a valid model for the calculation of electromagnetic loads for FILD. • Perform a finite element model to study the behavior of FILD against previously calculated loads. 1.4 Document structure This document is composed of 5 chapters through which the objectives of the project will be completed. The following is a summary of the contents of the chapters: • Chapter 2. FILD components. In this chapter, the main components of the tokamak are explained in order to locate FILD. In addition, the different parts of this device are described in detail in its conceptual design, as well as its operation. • Chapter 3. Electromagnetic loads in FILD. The objective of this chapter is to obtain the value of the loads that act on FILD during an electromagnetic disruption. To do so, first the types of loads in tokamaks are exposed, to later detail the electromagnetic ones, exposing calculation examples and finally establishing a valid model to calculate the loads on FILD. • Chapter 4. Structural analysis of FILD. The results of the analyses with the loads obtained in chapter 3 carried out are exposed. This chapter details how the analyses have been carried out, as well as the design process followed to arrive at an optimal solution that solves the static problem by modifying as little as possible the conceptual design. • Chapter 5. Conclusions. It is dedicated to extract the conclusions of the results obtained in chapter 4 and indicate the possible future lines in which to develop new work. 5 2 FILD COMPONENTS 2.1 Introduction In this section, it is intended to show the conceptual design of FILD, with a detailed description of all its parts, as well as its operation and location. Before going into detail with FILD components, it is necessary to know the internal structure of the tokamak. In the figure 4, the main components of the ITER reactor are shown. Figure 4. ITER tokamak internal structure The main component is the Vacuum Vessel (VV). The ITER experiments will take place inside the Vacuum Vessel, a hermetically sealed steel container that houses the fusion reactions and acts as a first safety containment barrier. In its doughnut-shaped chamber, or torus, the plasma particles spiral around continuously without touching the walls [10]. Ten thousand tonnes of magnets, with a combined stored magnetic energy of 51 Gigajoules (GJ), will produce the magnetic fields that will initiate, confine, shape and control the ITER plasma. Manufactured from niobiumtin (Nb3Sn) or niobium-titanium (Nb-Ti), the magnets become superconducting when cooled with supercritical helium in the range of 4 Kelvin (-269 °C) [11]. The Vacuum Vessel provides a high-vacuum environment for the plasma, improves radiation shielding and plasma stability, acts as the primary confinement barrier for radioactivity, and provides support for in-vessel components such as the blanket and the divertor. Cooling water circulating through the vessel's double steel walls will remove the heat generated during operation. The blanket modules that cover the inner walls of the VV protect the steel structure and the superconducting toroidal field magnets from the heat and high-energy neutrons produced by the fusion reactions [12]. Situated at the bottom of the Vacuum Vessel, the divertor extracts heat and ash produced by the fusion reaction, minimizes plasma contamination, and protects the surrounding walls from thermal and neutronic loads [13]. Forty-four openings, or ports, in the Vacuum Vessel provide access for remote handling operations, diagnostics, heating, and vacuum systems. These openings are divided according to their location in Upper Port, Equatorial Port and Lower Port. FILD components 6 2.2 Location As explained previously, FILD intends to make measurements of fast ion losses at the plasma edge, so it must be placed in a situation that can perform this type of measurements. That is why FILD is integrated in an Equatorial Port Plug #08 (EPP#08). The Equatorial Port Plugs are the central structures (Figure 5) where various diagnostic systems are located such as FILD and consists of three basic parts [14]: • The diagnostic first walls (DFW) which serves as plasma facing parts of the assembly while developing the role of first neutron shielding layer and implements the necessary cutouts and apertures to the plasma required for the operation of diagnostic systems assembled in the PP. • The diagnostics shielding modules (DSM), which provide the neutron shielding to port aperture in order to minimize the activation and the dose in the Port Cell (interspace) area and ports and house diagnostic and service systems. • The EPP#08 structure as main structural element that holds the rest of components, that forms the connection to the VV being part of the primary vacuum and confinement boundaries and that provides the interface (closure plate) for all required penetrations and feedthroughs between the in-VV space and the Port Cell. a) EPP’s distribution b) FILD’s location in EPP#08 Figure 5. FILD's location The device will be installed at the EPP#08, approximately 10 cm above the midplane, oriented horizontally along the major radius of the machine [15]. The design of FILD, at conceptual design phase, is shown in figure 6, where EPP#08, DSM2 and DFW are also schematically represented. As can be seen in the figure, FILD is attached to the last vertical blade of the DSM2 by the fixed part. This fixed part serves as a support and guide for the movable part, which holds the probe head and pushes it close to the plasma for measuring. FILD EPP#08 7 Structural assessment of the ITER Fast-Ion Loss Detector Figure 6. General scheme of FILD 2.3 General description FILD is integrated into an EPP, but it is necessary to measure at the edge of the plasma to capture the fast ions. This fact presents a great disadvantage: The exposure to large thermal loads, which significantly limits the duration of the measurement. FILD is designed to operate in a fixed position during plasma discharge. The insertion length is previously defined and when the discharge is finished, the system automatically retracts. To protect both the integrity of the tokamak and FILD, there is a security protocol that allows the discharge to be aborted if the measured thermal loads exceed a limit. By providing the detector with feedback for temperature control (or other measure of thermal load) it can automatically be retracted if necessary, e. g. if the thermal loads suddenly increase due to plasma displacements. Given the time scale associated with thermal variations near the plasma, rapid displacements will be required in a short period of time, to send the FILD body to a safe position. Thus, the system will have a measurement position and a parking position (Figure 7). a) Measurement position Electromagnetic loads in FILD 14 Therefore, a rigorous treatment of these loads would require their consideration in a dynamic way to account for the inertial effects of the system. Indeed, this would be the second contribution. For the particular case of the assembled Port Plugs (but not limited to); as they are complex systems and dynamic analyses are usually cumbersome; a usual practice is to treat these loads in a static way. This requires first the identification of the peak forces developed during the transient. These peak forces are then, scaled by a dynamic amplification factor (DAF) to include the inertial effects. DAFs are normally determined using transient analysis in simplified models and their validity is subjected to the equivalence of the peak loads static and maximum dynamic responses of the system. • Inertial loads associated to Vacuum Vessel movements: Port Plugs are assembled in the Vacuum Vessel by insertion in the port extensions. Port extensions are in turn, connected to the Vacuum Vessel through the port stubs leading to double cantilevered massive system. During the evolution of electromagnetic event, the Vacuum Vessel is subjected to similar effects as those described in the first point above. This means that the Vacuum Vessel will experience movements whose effect at port stub level is the development of additional inertia loads on assembled port plug systems. These actions, which constitute the third contribution, may be readily described by point response spectra defined at the port stub. • Interface loads: Diagnostic systems inside EPPs are anchored to frame structures (EPP structure, DSM, DFW) which are actually deformable bodies. During the development of the transient electromagnetic events these structures will suffer deformations which can affect to the diagnostic components subjected to structural integrity evaluation in the form of relative displacements between the anchorage points. These interface loads would constitute the last contribution to consider in the specification of mechanical loads derived from electromagnetic events in diagnostic systems. The two first contributions described above are normally determined through dedicated electromagnetic analysis of the components under study as part of the global process of structural integrity assessment. The characterization of the Vacuum Vessel movements, inertial effects and related interface loads is obtained from a global dynamics analysis of the Tokamak including the different scenarios and particularities of the electromagnetic loads. 3.3 Volumetric loads from currents in structures The dominant mechanical loads on FILD components arise from plasma disruptions; that is why this master thesis will focus on the study of this type of loads. The rapidly changing magnetic fields associated with disruptions induce electrical eddy currents in the surrounding mechanical conductive structures which then interact with the background magnetic field, thus producing forces and torques. Unlike most mechanical loads, the load associated with the eddy currents is not simply specified but is instead dependent upon the details of the port plug hardware, including the DSM-DFW assembly, the port plug structure and how these components are electrically connected. The path of electromagnetic volumetric load is shown in figure 12: 15 Structural assessment of the ITER Fast-Ion Loss Detector Figure 12. Path of the volumetric loads from induced currents in passive structures Disruptions in ITER are simulated with the DINA code and the results of the DINA simulations for ITER are stored in IDM (ITER Document Management). Table 2 shows the categorization of these DINA simulations according to the ITER load specification document [19]. Additional analyses to determine worst events depending on the location are still on-going. Table 2. ITER plasma disruptions cases and its categorization Type of disruption Current quench time Peak TPF*Ihalo/Ip Thermal quench time Number of events MD I Exp. 22 ms 0,15 3 ms 2600 MD II Exp. 16 ms 0,15 1 ms 400 MD III Exp. 16 ms 0,15 0,5 ms - MD IV Exp. 11,3 ms 0,15 0,5 ms - MD IVslow fast - VDE II slow 50 – 100 ms 0,34/0,42 150 VDE II fast Exp. 16 ms 0,2/0,25 150 VDE III slow > 200 ms 0,75/0,6 - VDE III fast Exp. 16 ms 0,36/0,45 - VDE IV slow fast 0,6/0,75 - Electromagnetic loads in FILD 16 Eddy currents do exist in principle (with different intensities) at any time moment of any transient electromagnetic events including normal operation, but halo current is considered only at latter phase of Vertical Displacement Events (VDEs) and Major Disruption (MDs), when the separatrix touches the plasma-facing conducting wall. Maximum electromagnetic loads on the Port Plug components are caused by three kinds of abnormal terminations of plasma pulse: • A MD consists of an abnormal termination of the plasma pulse consisting of two phases, the thermal quench with a fast loss of the plasma thermal energy and the current quench with a fast drop in plasma current often accompanied by a vertical drift and compression of the plasma core. • A VDE consists of an abnormal termination of the plasma pulse initiated by a failure of vertical position control, followed by an irreversible plasma vertical drift, compression of the plasma core, the thermal quench, plasma current decay and by a further compression of the plasma core. • A MFD (Magnet Fast Discharge) is an event where the current that flows in the ITER magnets is rapidly brought to zero (usually done intentionally after the detection of a quench to protect the coils from overheating). In both VDEs and MDs the halo current can reach very large fractions of the total plasma current once the plasma touches the wall. In both cases the final stages include a plasma drift to either upper or lower part of the VV. There are two types of MFD. MFD I which corresponds to a fast discharge of the CS (Central Solenoid) and PFC (Poloidal Field Coils) only, or MFD II where all coils are discharged. During a MFD I, the eddy currents created are similar to those generated during plasma initiation. During MFD II, larger loads will occur. Nevertheless, these loads are considered very small because the IVCs (in-vessel components) are not electrically connected in the toroidal and Poloidal direction. Besides, the load due to MFD is not really superimposed to the disruption loads because the current decay of MFD is much longer than the plasma disruption time. 3.4 Analysis techniques for calculation of electromagnetic loads Below are exposed several methods used in a multitude of systems to calculate electromagnetic loads. Procedure 1: Approach based on DINA inputs. The general approach for calculation of EM loads is based on the EM transient analysis of the components where the eddy and halo currents are usually calculated with different kinds of inputs [14]: • Typical input for the calculation of eddy currents caused by diamagnetic flux loss at the time of thermal quench is a current waveform in a set of poloidal loops located in plasma volume. These loops form a toroidal solenoid. The variation of the diamagnetic flux is prescribed by the DINA code. Some resultant variations of plasma shape, plasma current and the Poloidal magnetic field take place at the time of thermal quench. • Typical input for the calculation of eddy currents caused by plasma current quench is a set of current waveforms in the toroidal coaxial loops which represent plasma evolution (time dependent net current, position, shape and current density profile). The current waveforms in these loops are provided by DINA. • Typical input for calculation of halo currents is the time dependent poloidal profile of halo current density on the surface where the halo current intercepts the PFCs. This profile is provided by DINA. • EM loads on the Port plug system components, as output of 3D EM transient numerical analysis, are initially represented in the form of distributed force density. These results are then transmitted further for the supporting stress-strain static and dynamic analysis of the components. The EM loads applied to each component are summarized as 6 time-dependent orthogonal components: 3 integral moments and 3 integral forces. 17 Structural assessment of the ITER Fast-Ion Loss Detector • Typically, EM analysis and load integration are done separately for eddy and halo current related loads, giving as output 6+6=12 time-dependent integral load components. The time dependent graphics of such integral loads indicate the peaks of each component and the time moment when each peak occurs. Note that the peaks of different load components can be reached at different times and even in different plasma events. Electromagnetic (EM) loads (either by eddy currents or by a sum of eddy and halo) exist in each conductive part of the machine during each transient EM event. They can be represented as time-dependent 3-D vector field of force density (F=J x B), where B is time-dependent vector sum of magnetic fields by all sources at each spot and J is vector of sum current densities at each spot. Procedure 2: Approach based on previous magnetic field solutions An alternative approach much easier to apply in the one based on the maps of the magnetic field evolution in space envelope where components sit. The loads due to the induced currents are mostly dominated by the plasma transients and the large CS, PF and TF currents, hardly affected by the local variation in effective conductivity. Given the maps of evolution of the magnetic field in the region of interest the electromagnetic loads can be estimated using a local electromagnetic model of the assembled components in the PP including the components under study can be used. The fields provided as inputs can be interpolated in the local finite element mesh. Figure 13 shows the volumetric force density in an entire port plug [20]. Figure 13. Force density distribution to be interpolated in the whole port plug (N/m3) This interpolation depends on the formulation of the electromagnetic analysis, nevertheless it would be performed as imposed boundary conditions in the whole domain simulated considering the particular degrees of freedom in consistency with the formulation chosen. Volumetric electromagnetic forces may be the determined as a time-dependent 3-D vector field of force density (F= J x B). However, these activities have not been performed for the Fast-Ion Loss Detector. Therefore, the electromagnetic loads presented in this master thesis have to be valid estimates for the conceptual design review. The following sections show this estimate, starting with the definition of the geometry and later the calculation Electromagnetic loads in FILD 18 models based on the Lorentz law. On the sensors, eddy currents will be induced as a result of the induced voltages in the structures because of the variation of the fields during the transient events. As a result, torques will appear. In addition to that, a shared current with the supporting structure (DSM) will produce net forces on the in-port cameras. 3.5 FILD geometry for electromagnetic analysis The geometry under study consists of the probe head, the support of the probe head and the support of the rollers; that is to say the movable part. The fixed part will only be taken into account in case there are large deformations, so it is necessary to study the interaction between the fixed and movable part. To facilitate the calculation of electromagnetic loads, as well as finite element analysis; a simplified CAD model has been used. In this model, unnecessary elements such as the detailed shape of the probe head have been eliminated or rounding has been added in the foreseeable tension concentrator. Figure 14-a shows an overview of the CAD model of FILD, and figure 14-b shows a cross section of the movable part under study. a) FILD CAD model general view b) Cross section in the medium plane. The dimensions are shown un millimeters. All roundings have radius of 7,5 mm. Figure 14. FILD CAD model 19 Structural assessment of the ITER Fast-Ion Loss Detector 3.6 Estimation of electromagnetic loads Once the geometry to be studied is defined, it is intended to calculate the electromagnetic loads that must be supported by FILD during a disruption event. As explained above, detailed electromagnetic analyses of disruptions over FILD and EPP # 08 have not been performed yet. Therefore, electromagnetic loads must be estimated from values obtained from analyses carried out in other zones of ITER or in other diagnostic systems. The main objective of these estimations is to verify the structural integrity of FILD in a first study against electromagnetic disruptions, and thus be able to validate or make the opportune changes in the conceptual design in front of this type of loads. The first step for estimating is to create a physical model of the problem, on which applying the various physical laws is simple. Later, translating that model to the FILD geometry, decomposing it in several parts to facilitate the calculation. The next step is to obtain the current that circulates through FILD, which can be of two types: • Eddy current induced by the mechanism of conservation of the magnetic fluxes crossing the electrically conducting parts. They are closed current loops that being inside a magnetic field causes torques to appear on FILD by the Lorentz law (which acts like a loop). • Halo currents flow in loop formed partly by conducting structures and partly by the plasma scrape-off layer. This current inside a magnetic field causes forces in FILD by the Lorentz law (which acts like a conductor). The last step is to calculate these loads which are the beginning of the mechanical problem. 3.6.1 Eddy currents The eddy currents tend to dominate in the thermal quench phase, at the beginning of disruption event and their time scale is small. The electromagnetic loads due to eddy currents can be calculated considering: • The magnetic field components and their variation in time in region in which they are located. • The current induced estimated by assuming a conductor loop with all the material lumped around the perimeter loop. The area of the flux can be considered as the area facing the variation of the field. Because there is no magnetic field variation data in Equatorial Port Plug #08, these values are approximated by taking them from another region similar to where FILD is located. Specifically, there are electromagnetic analysis results in the Equatorial Port Plug #01 that provide an estimate of the magnetic field variation, as well as the value of the static toroidal magnetic field (Table 3). Table 3. Estimation of static toroidal field Bt and the variation of electromagnetic field in EPP #01 Equatorial Port #01 Cameras Variation of radial field dBx/dt (T/s) Variation of vertical field dBz/dt (T/s) Static toroidal field Bt (T) 11,1 70,9 5,6 The values provided in the previous table are enveloping all the electromagnetic events, as the maximum static and variation of field has been taken in each case. This is a very conservative assumption, as the maximum static field and field variation values can happen in different disruption events or time instant. As can be seen in table 3, there are magnetic field variation values in both the radial and vertical directions. This generates that current is induced in two different directions, and therefore there are torques in two directions Electromagnetic loads in FILD 20 which are calculated independently. 3.6.1.1 Eddy current due to variation of radial field The model used to calculate the eddy currents due to the variation of the radial field is an open tube whose longitudinal direction is parallel to the field variation (which is known). That is why, according to Faraday’s law, the induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux enclosed by the circuit. To carry out the calculations, cylindrical differential elements (dr) of radius r and length L will be taken as shown in the figure 15. Figure 15. Model for electromagnetic calculations (radial field variation) Radial field variation induces an electromotive force, and by symmetry the induced currents (I eddy; figure 15) will have the shape of circles centered on the axis of the cylinder. The flow (Φ) through one of these cylindrical elements is the magnetic field multiplied by the area that faces the magnetic flux variation. Φ=𝐵∙𝜋∙𝑟2 The electromotive force induced (ε) in the element of radius r is: ε=−𝑑Φ 𝑑𝑡 =−𝜋∙𝑟2∙𝐵󰇗𝑥 As can be seen from the previous equation the induced electromotive force (emf) is variable depending on the radius. The negative sign of ε means that the direction of the induced current is such that it opposes the flow variation, therefore, the direction of the induced current is shown in figure 15 and the negative sign will be eliminated in the next expressions. This emf is the one that sets in motion the charge carriers contained in the cylindrical layer volume of length L between r and r + dr, originating a current: 𝑑𝑖=ε 𝑑𝑅𝑒 being 𝑑𝑅𝑒 the resistance of a tube of length 2∙𝜋∙𝑟 and section 𝐿∙𝑑𝑟, through which the current flows. The resistance is: 𝑑𝑅𝑒=𝜌2∙𝜋∙𝑟 𝐿∙𝑑𝑟 21 Structural assessment of the ITER Fast-Ion Loss Detector where 𝜌 is the resistivity of the material. The current flowing in the differential section is: 𝑑𝑖=𝜋∙𝑟2∙𝐵󰇗𝑥∙𝐿∙𝑑𝑟 2∙𝜌∙𝜋∙𝑟 =𝐵󰇗𝑥∙𝐿∙𝑟∙𝑑𝑟 2∙𝜌 Once obtained the differential expression of the intensity, the next step is to integrate it between the major and minor radius (b and a, respectively) to calculate the total intensity that circulates through the tube. 𝐼=∫ 𝐵󰇗𝑥∙𝐿∙𝑟 2∙𝜌 𝑑𝑟=𝐵󰇗𝑥∙𝐿 4∙𝜌 𝑏 𝑎∙[𝑏2−𝑎2] With the calculation of the induced intensity, the proposed model is solved, so it will be necessary to transfer the model to FILD geometry. Comparing figures 14 and 15, it is concluded that FILD con be modeled as two cylinders of different dimensions in which two intensities will circulate. First, the intensity (I1) that flows through the larger cylinder (radius 54 and 44 mm) is calculated: 𝐼1=3324 𝐴 On the other hand, the intensity that circulates through the smaller cylinder (radius 25 and 17 mm) is: 𝐼2=1437 𝐴 These intensities that circulate through FILD as if it were a loop, are immersed in a toroidal static magnetic field, so by the Lorentz law there are moments. The moment can be expressed as a vector product of two vectors, the magnetic moment vector 𝑚 󰇍 󰇍 and the magnetic field vector 𝐵 󰇍 . The modulus of the magnetic moment vector is the product of the intensity by the area of the loop (it is considered the largest area to be conservative, and all the material in a single loop). Its direction is perpendicular to the plane of the loop and it is determined by the progress of a corkscrew that rotates as the current does in the loop. The magnetic field vector is the static toroidal field which is shown in figure 16. Performing the vector product described above, the following expression is obtained to calculate the moment: 𝑀=𝑆∙𝐼∙𝐵𝑡 being S, the surface of the loop (largest surface); I, the intensity previously calculated; and Bt, the static magnetic field. Particularizing for the two intensities, the moments M1 and M2 result with the directions shown in figure 16. 𝑀1=171 𝑁∙𝑚 𝑀2=16 𝑁∙𝑚 The resulting moments are bending moments in the z-axis applied to the principle of the major and minor cylinders. Electromagnetic loads in FILD 22 Figure 16. Moments in z-axis due to eddy currents 3.6.1.2 Eddy current due to variation of vertical field The model used to calculate the eddy currents due to the variation of the vertical field is a closed tube (to close the circuit) whose longitudinal direction is perpendicular to the field variation (which is known). In this case, to perform the calculations, sheets have been taken along the z-axis of thickness dz. The length of the cylinder is L. The width of the sheet in x direction depends on the distance z of the sheet and is 2∙√𝑅2−𝑧2. Finally, the thickness in the y direction is δ. The model is shown in the figure 17: Figure 17. Model for electromagnetic calculations (vertical field variation) The magnetic flux defined by the magnetic field multiplied by the area facing the variation of magnetic field: Φ=𝐵∙2∙√𝑅2−𝑧2 ∙𝐿 By performing the same procedure as in the previous case, the induced electromotive force is calculated: 23 Structural assessment of the ITER Fast-Ion Loss Detector ε=−𝑑Φ 𝑑𝑡 =−𝐵󰇗𝑧∙2∙√𝑅2−𝑧2 ∙𝐿 The induced electromotive force is opposed to the effect of magnetic flux variation hence the negative sign and direction of induced intensity (I eddy) shown in figure 17. The resistance of each of the sheets of dr is calculated taking into account a length of (4∙√𝑅2−𝑧2+2∙𝐿) and a section of δ∙dz. 𝑑𝑅𝑒=𝜌∙(4∙√𝑅2−𝑧2+2∙𝐿) δ∙dz The intensity in one of the differential loops is the emf divided by the electrical resistance: 𝑑𝑖=𝐵󰇗𝑧∙2∙√𝑅2−𝑧2 ∙𝐿∙δ 𝜌∙(4∙√𝑅2−𝑧2+2∙𝐿) ∙dz To obtain the intensity that circulates through the tube it is necessary to integrate all the sheets between -R and R (along the z-axis): 𝐼=∫ 𝐵󰇗𝑧∙2∙√𝑅2−𝑧2 ∙𝐿∙δ 𝜌∙(4∙√𝑅2−𝑧2+2∙𝐿) ∙dz 𝑅 −𝑅 Due to the complexity of solving this integral analytically, a numerical calculation software has been used to solve it. Therefore, the model has been transferred directly to FILD dimensions in the same way as in the previous section. An intensity has been calculated for the outer diameter tube 54 mm (I1) and another for the 25 mm diameter (I2): 𝐼1=3987 𝐴 𝐼2=726 𝐴 In the same way as previously, the torques that generate the induced intensities on FILD are calculated. Again, two separate loops are considered so that two torques will be obtained, in this case of torsion (Figure 18) 𝑀1=2181 𝑁∙𝑚 𝑀2=232 𝑁∙𝑚 Figure 18. Moments in x-axis due to eddy currents Structural analysis of FILD 30 4.3 Eddy current loads analysis In this section the static analysis of FILD will be carried out to ensure the structural integrity against of the loads generated by eddy currents. Then, the different aspects of the model (meshing, boundary conditions) will be discussed before commenting on the results. 4.3.1 Mesh Meshing can be considered the most important process in the calculation with finite elements, since the results and their reliability will depend on the chosen mesh. The factors to take into account in this process are the type of element with which it will be meshed, and their distribution in the geometry. The choice of the type of element is linked to the results wanted to extract with the analysis in question, since each of them is programmed for a specific purpose. The distribution in the geometry refers to the use of different element sizes (mesh refinement) to take advantage of computational resources and refine the calculation in areas of interest for the obtaining results, or else, in which important stress/strain gradients are produced to guarantee their correct transmission. On the other hand, it also depends on the distribution of elements, their quality, since a uniform and orderly distribution gives rise to elements with better aspect ratio (less deformation), improving the results obtained. Tetrahedral elements can fit better complex geometry. However, the integration of the shape functions with points of Gauss is less accurate than hexahedral elements. In addition, one of the factors that determines the quality of the mesh is the distortion of the elements. As the geometry to be studied is not very complicated, mostly hexahedral elements (Hex20 element) have been used. The idea of meshing is to generate a regular mesh, without distortions and faithfully reproduce the geometry. For this it is necessary that the mesh can be refined a lot, but it is also possible, through sensitivity analysis, to obtain a compromise between coarse mesh (lower computational cost) and precision of calculations. Figure 22 shows an example of fine hexahedral mesh, although throughout the evolution of the analysis a thicker mesh with similar stress results will be sought. The details of the stress concentrator are also shown, because they are areas where a high element density is necessary to capture the stress concentration effect. The mesh shown has 233100 elements. Figure 22. Mesh in eddy current model 31 Structural assessment of the ITER Fast-Ion Loss Detector There are two parameters that give an idea of the quality of the mesh and these are: • Element quality: A value of 1 indicates a perfect cube or square while a value of 0 indicates that the element has a zero or negative volume. • Aspect ratio: The aspect ratio is the ratio between its largest and smallest dimension. Element quality (Figure 23 – a) and aspect ratio (Figure 23 – b) of the previous mesh are shown un Figure 23. The element quality average is 0,87 and the aspect ratio average is 1,88. There are few elements that have a high aspect ratio, but this is not worrisome, since they are few elements and located in areas of low stress. Such elements will not necessarily produce bad results – that depends on the loading and boundary conditions of the problem – but do introduce the potential for trouble. 4.3.2 Boundary conditions The boundary conditions are other important aspects to comment before performing the static analysis since the results depend on its application. First, the support of the rollers can be modeled as a fixed support, because this only allows the movement in the longitudinal axis (x-axis), on which loads do no act. Second, the device’s own weight has been considered, because it can have a significant influence on a 2 m cantilever. The mass of the device is 39,465 kg and the centroid in on xaxis (953,5 mm). Finally, the loads generated by eddy currents calculated in the previous chapter are applied as point moments. The load of flexion in the small cylinder is totally negligible (16 𝑁∙𝑚) compared to the rest, but to be on the safety side it is joined with the loads applied to the larger cylinder. The torsion loads are applied on the centroins of each cylinder. Figure 24 shows the boundary conditions on FILD a) Element quality b) Aspect ratio Figure 23. Element metrics of the previous mesh Structural analysis of FILD 32 Figure 24. Boundary conditions in the structural static model A good practice to check that the boundary conditions are well applied is to obtain the reactions in the fixed support. These results are shown in table 5. Table 5. Force and moments reactions in the fixed support Fx (N) Fy (N) Fz (N) Mx (𝑁∙𝑚) My (𝑁∙𝑚) Mz (𝑁∙𝑚) 0 0 387 2413 369 187 The reaction forces on the x and y axes are zero and on the z-axis is the weight of FILD. On the other hand, the reaction moments of torsion (x axis) is equal to the sum of the moments applied, and the same happens with the flexion in the z-axis. There is also a moment in the y-axis due to the application of the weight in the center of gravity of FILD. The obtained values coincide with the theoretical ones so the next step is to perform the static analysis. 4.3.3 Static structural analysis In this section, once the mesh and the boundary conditions are explained, the results of the static analysis will be displayed. To check the feasibility of the design, the results of the equivalent Von-Misses stress will be compared with the elastic limit of the material (270 MPa). Plasticity is an undesirable situation because it generates a permanent deformation that can affect the structural integrity and in addition to the measurement made. But the plasticity of small areas very localized is accepted as long as it does not compromise the entire section. Figure 25 shows the stress distribution in FILD. In this figure, cross sections are shown because the predominant effect is the torsion that generates the same tension on the surface but varies in thickness. With a cross section it can be seen a representation of the stress variation. There are two conflicting zones that are potential stress concentrators. The union of cylinder 1 (larger cylinder) and cylinder 2 (smaller cylinder) and the union of cylinder 2 with the roller support. These zones will be analyzed in detail and shown in figure 25 b – c. 33 Structural assessment of the ITER Fast-Ion Loss Detector a) Stress distribution in FILD (general view) b) Stress in the stress concentrator 1 c) Stress in the stress concentrator 2 Figure 25. Stress distribution in FILD The first conclusion that is obtained from this figure is that there is plastification because the maximum stress is 288,73 MPa that occurs in the stress concentrator 2. In general, it can be seen that cylinder 1, as is logical, hardly supports stress due to its greater diameter and therefore greater inertia. However, cylinder 2 (smaller), is exposed to a stress around 224 MPa on its surface. In the stress concentrator 1 (Figure 25 – b) there is no problem because the stress simply varies between the value of cylinder 1 and cylinder 2 and does not increase. In the stress concentrator 2 (Figure 25 – c) the same does not happen. Due to the proximity to the support and after a cantilever of 2 meters, the stress is concentrated in a localized area. This zone will be the one that limits the design, although if it is in a localized area, the only thing that would happen wild be a small superficial plastification in the stress concentrator and a hardening by deformation. Another interesting aspect is to verify that there are no excessive deformations. Figure 26 shows the total deformations in FILD. Structural analysis of FILD 34 a) Total deformation (toroidal view) b) Total deformation (radial view) Figure 26. Total deformation in FILD The total deformation generated especially by the torsion torque and the own weight reaches a peak of 18,12 mm. Because this state is inadmissible, it is necessary to change the current design to obtain a result in which stresses and deformations are adequate, without the conceptual design being substantially modified. Before modifying the design, it is important to verify the mesh used in the previous case. To do this, a sensitivity analysis of the mesh is performed, varying the number of elements and checking the value of the maximum equivalent Von-Misses stress (Figure 27). Figure 27. Sensitivity analysis of the mesh. 35 Structural assessment of the ITER Fast-Ion Loss Detector This analysis has been done by varying the number of elements between approximately 30000 elements and 230000. In this graph, it can be observed, as expected, an increase in the maximum stress as the number of elements increases and finally the convergence around a value of 288,7 MPa. This is why the mesh used for the previous analysis is valid and will be used for the following ones. In addition, to complete this analysis the variation of the stress along the thickness has been studied in the area where it is maximum, at the beginning of the rounding of the stress concentrator. By varying the size of the mesh, it is intended to validate the result along the thickness. This is important because a very high stress on the surface may be acceptable if plastification does not occur in the entire section. This analysis has been carried out taking into account the last three meshes of the sensitivity analysis, when the maximum stress value has already stabilized. The data of the meshes are the following: • Mesh 1: 233100 elements / 1134358 nodes. • Mesh 2: 173204 elements / 861634 nodes. • Mesh 3: 142272 elements / 718220 nodes. Figure 28 shows the stress-length (along the thickness) curves for the previously described meshes. Figure 28. Equivalent stress vs length in thickness. Comparative between several meshes. In this figure it can be seen that the results are very similar for the different meshes so it can be concluded that the mesh used previously not only calculates correctly the maximum equivalent stress, but also the stresses along the thickness. In addition, an important fact that can be extracted from this graph is that only the first 0.5 mm (approximately) of the thickness (8 mm) are plastified in said region. Structural analysis of FILD 36 Once these checks are made, the next step is to make changes in the design optimally so that the stresses are below the elastic limit and get less deformations. To make these necessary changes in an optimal way, an ANSYS tool called response surface has been used. This tool is capable of starting from one or several input parameters, establishing several design points, adjusting one or several output variables by means of a curve or surface. Translating this idea to the FILD model, the output variable is clear, the maximum equivalent stress. To select the input parameters, variables that increase the inertia of the cylinder 2 have been used as criteria. Therefore, the variables selected to perform the parametric analysis are the outer radius and the thickness of the cylinder 2. These variables have been assigned a range within which the tool normally offers 10 design points. In this case to better capture the response has been modified to 20 design points and the variables oscillating in the following range: • Larger radius: Between 25 mm (conceptual design) and 35 mm. • Thickness: Between 8 mm (conceptual design) and 15 mm. The result is a 3D surface where the x-axis is the largest radius, the y-axis the thickness and the z-axis the maximum equivalent stress (Figure 29). Figure 29. Equivalent stress maximum response surface versus larger radius and thickness. A consequence of observing the previous figure is that the increase in the greater radius decreases more the maximum equivalent stress than the increase of thickness. So, the most decisive is to increase the radius. Another aspect that can be visually extracted is that many of the different configurations are below the elastic limit (270 MPa). So, the goal now is to get as little as possible to modify the conceptual design so as not to exceed the elastic limit. First, the option to modify the thickness is rejected, since it has little influence. Second, modify the radius by interpolations of the previous curve to obtain an optimal result. These interpolations are made with ANSYS, which, like a 3D curve, can show a curve with the only influence of the greater radius. In this curve maximum stress – greater radius; the optimal point is sought. As a result of these interpolations it is obtained that a radius of 30 mm can provide a good behavior increasing this dimension only 5 mm. The expected result is only an interpolation, so to be sure that the behavior is as expected is necessary to perform 37 Structural assessment of the ITER Fast-Ion Loss Detector the static analysis with these conditions. The results of the equivalent Von-Misses stress are shown in Figure 30. Figure 30. Stress distribution in FILD (Proposed design) As can be seen in the previous figure, the maximum stress has decreased to below 200 MPa with only an increase of 5 mm radius. Not only the maximum stress in the stress concentrator has decreased, but in the cylinder 2 the stresses are in a range between 100 and 150 MPa (approximately). This result is good for structural integrity because with a proposed change of 16,7% in the radius of cylinder 2, the maximum stress has been reduced by 32,7%, leaving it totally out of risk of entering the plastic zone. To complete the comparison between the conceptual and proposed design, Figure 31 shows the total deformation results in FILD both in toroidal view (Figure 31 – a) and in radial view (Figure 31 – b). a) Total deformation (toroidal view) b) Total deformation (radial view) Figure 31. Total deformation in FILD (Proposed design) Structural analysis of FILD 38 The results of the total deformations are also favorable. With this change, the maximum deformation has been reduced by almost 50%. A deformation of 1 cm is totally acceptable and normal in this type of devices. In fact, in the preliminary design of the Upper Launcher (PBS 52.U#. P) similar deformations are obtained [21]. 4.4 Halo current loads analysis In this section the static analysis of FILD will be carried out to ensure the structural integrity against of the loads generated by Halo currents. Then, the different aspects of the model (meshing, boundary conditions) will be discussed before commenting on the results. Before going into detail explaining the mesh and the boundary conditions, it is necessary to explain an important detail of this load case. The loads calculated in chapter 3 for Halo currents, a distributed load of a value of 14,4 kN/m, are so large that they generate stresses that indicate that the device is not capable of supporting this load (approximately 9000 MPa). Given this result, making changes in the design, as in the previous section, does not provide any substantial advantage that causes the stresses to approach the elastic limit. Therefore, the solution proposed is to take into account the fixed part to reinforce the system, so that when FILD is deformed, there is a contact that helps resist stresses. This contact will be made through a ring on the body of FILD. Figure 32 shows the geometry of the fixed part and the contact ring. a) FILD CAD model general view 39 Structural assessment of the ITER Fast-Ion Loss Detector b) Cross section in the medium plane. Units in mm. Figure 32. FILD CAD model (with fixed part) This change in the model brings with it several consequences, among which is the existence of a contact that makes the problem non-linear and modeling the union of the movable and fixed part. This is explained in the boundary conditions, but before it is important to describe the mesh. 4.4.1 Mesh Including the fixed part in the model means that the mesh is made for this part. The meshing philosophy is the same as in the previous section, using hexahedral elements. On the other hand, the strategy is different, mainly due to the existence of a non-linear contact problem. If the mesh was a very important aspect in the analysis of the previous section (linear), in a non-linear problem it is much more, not only for capturing the result properly, but also for the convergence to a solution. In addition, computing time is increased by the use of iterative methods. For these reasons, the meshing strategy has been the following: • Use a large mesh size on the fixed part. The results in this part are not the main object of study, so knowing exactly the stress distribution in this element would increase the computational cost. • Refine the mesh size in the stress concentrator 2. It is known that the most conflictive area is the stress concentrator; therefore, a finer mesh has been used in this place to correctly capture the maximum stress. • A medium mesh size for the rest of the body of FILD. To speed up the calculation time, without giving up a good result. Figure 33 shows the type of mesh used in this model (61933 elements). Figure 33. Mesh in Halo current model. Structural analysis of FILD 46 Figure 42. Sensitivity analysis of the mesh From 50000 to 80000 elements approximately, there is a clear convergence in which the stress fluctuates around 1 MPa. The convergence is obtained for a smaller number of elements (with respect to the mesh of eddy currents model) thanks to the optimization of the mesh, with a very refined mesh in the stress concentrator, medium size in the body of FILD and large size in the fixed part. With this result it is concluded that the mesh used in the last static analysis is valid because it is within the convergence range, although if a slightly thicker mesh is used it could decrease the calculation time and obtain a reliable result. In order to continue with the design and that the device can resist the loads, the procedure outlined in the design of FILD in the case of eddy current loads is followed. In this case the only parameter to study is the outer radius, keeping the thickness fixed since it adds weight and does not influence as much as the radius. Maintaining the same idea as in the contact ring analysis, the following study is based on studying the structural behavior of the system against changes in the external radius. A thick mesh will be used to capture the behavior, and then at the optimum point it is refined to obtain a valid result. The variation range is between a radius of 25 mm (conceptual design) and 40 mm (maximum modification considered to not substantially change the conceptual design). Figure 43 shows the results of this analysis. 47 Structural assessment of the ITER Fast-Ion Loss Detector Figure 43. Equivalent stress maximum versus larger radius The influence of the radius on the stresses that occur is completely clear since it increases the inertia of the weakest section. The decrease in the maximum stress between the conceptual design and the maximum radius value considered is approximately 30 %. However, even for a radius of 40 mm the stresses that are expected are still excessive, around 320 MPa, but with a thick mesh, which when refined (entering the convergence zone) will be expected to be more stresses. For these reasons, the outer radius is set at 40 mm to advance the design, but not complete it, because it is necessary to reduce more the stress. To know exactly where the stresses occur and with what value a static analysis is made with a sufficiently fine mesh to be in the convergence zone (Figure 44). Figure 44. Stress distribution in FILD (40 mm larger radius) Structural analysis of FILD 48 Figure 44 shows a similar distribution of stresses with respect to the one obtained previously in the conceptual design, with the difference of a lower stress peak (375 MPa). It should be noted that the stress in the contact as well as in the base of the support of the fixed part has increased its influence, but in no case it exceeds the stresses that occur in the stress concentrator 2 (only place where plastification exists). Although the stress peak occurs in a very specific area, and not the entire section is plastified, it is convenient to reduce the stress in this area of conflict. For it, and because in general the stresses that appear on the body of FILD are very acceptable, the influence of parameters that reduce the stress in a localized way will be studied. These parameters are the following: • Stress concentrator radius: This parameter is one of the most influential in the stress that is reached in a stress concentrator and still remains at a low value (7,5 mm) which can be increased to a maximum considered amount of 15 mm and observe the structural behavior. • Thickness: The thickness of the area between the stress concentrator and the contact of the two parts can influence that there is a greater concentration of stresses in the curvature. In order to better distribute the stresses in this area, the increase in thickness from 8 mm to 15 mm will be studied. This study is carried out by means of the response surface of the maximum stress (z-axis) in front of these two parameters (Figure 45). Figure 45. Equivalent stress maximum response surface versus stress concentrator radius and thickness. The first consequence of this study is that it can be determined that the radius of the stress concentrator influences more than the thickness to reduce the stress. Another consequence is that a large part of the surface is below the 270 MPa limit. Any point that could provide a maximum stress value of less than 270 MPa could be obtained, but because with little variation of the two parameters the result is much improved, the maximum value (15 mm) has been chosen for these variables (around 220 MPa of maximum equivalent stress). Figure 46 shows the stress distribution for this configuration. 49 Structural assessment of the ITER Fast-Ion Loss Detector Figure 46. Stress distribution in the proposed final design The simulation shows a peak stress of 221 MPa which is significantly below the critical 3Sm value of 270 MPa. It can be observed how the stress is distributed more in the contact and in the support of the fixed part. Finally, a valid model has been obtained that supports the loads applied with a wide margin of safety to avoid plastification. But there is one final aspect to keep in mind: The separation between the contact ring and the fixed part is 1 mm, while the own weight of FILD, in this last configuration generates a flexion of approximately 2 mm (Figure 47) which would cause a permanent contact which is not allowed because it exists relative movement in vacuum to change from the measurement position to a parking position (it is allowed in case of loads of Halo currents). Figure 47. Deformation generated by own weight To solve this problem, it is proposed to extend the diameter of the fixed part to a value greater than 2 mm, so that FILD’s own weight does not cause permanent contact. Increasing the diameter leads to an increase in the stresses since there is a longer time when the loads are only supported by FILD, therefore a configuration is proposed so that there is a separation of 4 mm. Structural analysis of FILD 50 Figure 48. Stress distribution in proposed final design (Gap 4 mm) In the previous figure it can be seen the distribution of stresses in this configuration. The peak stress that occurs in the voltage concentrator 2 is 277 MPa, so there is a small plastification in a very small and superficial area. For more detail in Figure 49 the most affected area is shown. a) Detail 1 of the plastified zone b) Detail 2 of the plastified zone Figure 49. Details of the plastified zone Taking into account the low plastification value (Figure 48), the small plastic area (Figure 49 – a) and the little penetration in the thickness (Figure 49 – b), it can be concluded that the only phenomenon that can occur is a small permanent deformation at the surface level, which will also generate a hardening by deformation avoiding successive permanent deformations. For these reasons, a valid design is considered structurally and functionally since it avoids the permanent contact generated by the own weight. Finally, the deformations that occur in this model are shown in figure 50 below. 51 Structural assessment of the ITER Fast-Ion Loss Detector Figure 50. Deformation in proposed final design (Gap 4 mm) The deformations that occur are large in general, with a peak of about 3 cm. But considering the value of the loads to which FILD is exposed and that it is a cantilever of 2 m, these deformations are considered admissible. 53 5 CONCLUSIONS 5.1 Conclusions Starting from the objective of this master thesis, the structural design of FILD against the loads generated by electromagnetic disruptions in ITER, the following conclusions are obtained: • A design capable of supporting the loads generated by Halo currents has been proposed modifying the conceptual design as little as possible. This design resist, in addition, the case of loading by eddy currents, less severe, since the final design proposed for Halo currents, includes the proposed design for the case of Eddy currents. • A design is proposed not only with good structural integrity, but also functional. The permanent contact in vacuum is not allowed, so taking into account that the conceptual design of FILD deflects 15 mm and in the final design 2 mm by the own weight, has been solved increasing the slack between the movable and fixed part. • Models have been generated to calculate induced electromotive force, induced intensity and applied moments in devices such as FILD. In addition, these models have been moved to another FILD currently being designed for the tokamak JT 60-SA (Japan). • Throughout the development of this project, knowledge of the general operation of ITER, its components, diagnostic systems and, in particular FILD has been acquired. Another objective fulfilled is to understand the loads that act on internal components to develop the necessary models. • The expansion of knowledge of the ANSYS tool, so important in the field of mechanical engineering and design, as well as the development of a simulation tool that can be adapted to future design easily. 5.2 Future works ITER includes many restrictions and the design process is very complex. Currently the design is in conceptual phase so the estimates made are valid, but it is necessary to corroborate them with other methods. From this presented model, several lines of work are opened: • Check the estimation of electromagnetic loads due to disruption events by obtaining a 3D map of forces (in an Equatorial Port Plug) and interpolating the model in this region. This map can be obtained from a previous solution of a dedicated electromagnetic analysis carried out by other groups, or by carrying out the study itself in the region of interest. • Deepen the knowledge of Halo currents. There are conflicting opinions about the existence of Halo currents in this type of devices, one of the worst load case. In addition, more detailed studies can be carried out on the retraction system and if it is able to prevent Halo currents from entering FILD. • Weight optimization. The weight of the set of the fixed and movable part is around 167 kg. It is an improvable weight for a cantilever of 2 m so an important aspect to investigate in the future is to realize a lightened design that properly supports the loads. • Check the design in other loads cases. The proposed design correctly supports electromagnetic loads, but the same cannot be said about other cases of loads, such as seismic. 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