Structural assessment of the ITER Fast-Ion Loss Detector

Equa ion Chap e 1 Sec ion 1 Mas e Thesis Indus ial Enginee ing S uc u al assessmen o he ITER Fas -Ion Loss De ec o Au ho : Juan Ca los Rod íguez C iado Supe iso s: Juan Manuel Ayllón Gue ola Manuel Toscano Jiménez Dep. Física Aplicada III Escuela Técnica Supe io de Ingenie ía Uni e si y o Se ille Se ille, 2018 iii Mas e Thesis Indus ial Enginee ing S uc u al assessmen o he ITER Fas -Ion Loss De ec o Au ho : Juan Ca los Rod íguez C iado Supe iso : Juan Manuel Ayllón Gue ola Assis an P o esso Manuel Toscano Jiménez Associa e P o esso Dep. de Física Aplicada III Escuela Técnica Supe io de Ingenie ía Uni e si y o Se ille Se ille, 2018 Mas e Thesis: S uc u al assessmen o he ITER Fas -Ion Loss De ec o Au ho : Juan Ca los Rod íguez C iado Supe iso : Juan Manuel Ayllón Gue ola Manuel Toscano Jiménez El ibunal nomb ado pa a juzga el P oyec o a iba indicado, compues o po los siguien es miemb os: P esiden e: Vocales: Sec e a io: Acue dan o o ga le la cali icación de: Se illa, 2018 El Sec e a io del T ibunal ii A mis pad es y Ainhoa po su ex ao dina ia ayuda ix Acknowledgmen Es e abajo no pod ía habe se ealizado sin la colabo ación de aquellas pe sonas que han es ado apoyándome du an e el anscu so de es e p oyec o. En p ime luga , ag adece a los di ec o es de es e p oyec o po habe me ayudado odo lo posible. A Manuel po habe me dado la opo unidad y a Juanma po di igi me, enseña me y da los consejos adecuados pa a pode e mina con éxi o es e abajo. No me puedo ol ida de mis compañe os de g ado y más e , en especial And és, An onio, Se gio Se ano y Se gio Mo eno; po es a siemp e apoyándonos mu uamen e an e cualquie p oblema. Po úl imo, debo menciona a aquellas pe sonas que han sido un apoyo mo al du an e el p oyec o. A oda mi amilia po p eocupa se de mi y po la e olución del p oyec o; en especial a mis pad es que me han dado su apoyo en cualquie aspec o p o esional y pe sonal. Finalmen e, dedica una mención especial pa a Ainhoa que me acompaña en es os úl imos e impo an es años, apoyándome cuando las cosas salen mal y cuando salen bien; escuchándome y dándome consejos. G acias. Juan Ca los Rod íguez C iado Julio de 2018 x ii LIST OF FIGURES Figu e 1: Nuclea usion eac ion 1 Figu e 2: ITER scheme 2 Figu e 3: Poloidal c oss-sec ion o ITER 3 Figu e 4. ITER okamak in e nal s uc u e 5 Figu e 5. FILD's loca ion 6 Figu e 6. Gene al scheme o FILD 7 Figu e 7. FILD posi ions 8 Figu e 8. Main componen s o FILD 9 Figu e 9. Schema ic o FILD p inciple 9 Figu e 10. Linea ac ua o s 10 Figu e 11. Gas chambe scheme 11 Figu e 12. Pa h o he olume ic loads om induced cu en s in passi e s uc u es 15 Figu e 13. Fo ce densi y dis ibu ion o be in e pola ed in he whole po plug (N/m3) 17 Figu e 14. FILD CAD model 18 Figu e 15. Model o elec omagne ic calcula ions ( adial ield a ia ion) 20 Figu e 16. Momen s in z-axis due o eddy cu en s 22 Figu e 17. Model o elec omagne ic calcula ions ( e ical ield a ia ion) 22 Figu e 18. Momen s in x-axis due o eddy cu en s 23 Figu e 19. Time e olu ions o he plasma cu en , e ical posi ion and poloidal halo cu en . 24 Figu e 20. Halo cu en dis ibu ed in he o oidal wid h o he EPP#08 25 Figu e 21. Dis ibu ed o ce due o Halo cu en 27 Figu e 22. Mesh in eddy cu en model 30 Figu e 23. Elemen me ics o he p e ious mesh 31 Figu e 24. Bounda y condi ions in he s uc u al s a ic model 32 Figu e 25. S ess dis ibu ion in FILD 33 Figu e 26. To al de o ma ion in FILD 34 Figu e 27. Sensi i i y analysis o he mesh. 34 Figu e 28. Equi alen s ess s leng h in hickness. Compa a i e be ween se e al meshes. 35 Figu e 29. Equi alen s ess maximum esponse su ace e sus la ge adius and hickness. 36 Figu e 30. S ess dis ibu ion in FILD (P oposed design) 37 Figu e 31. To al de o ma ion in FILD (P oposed design) 37 Figu e 32. FILD CAD model (wi h ixed pa ) 39 Figu e 33. Mesh in Halo cu en model. 39 Figu e 34. Elemen me ics o he p e ious mesh 40 Figu e 35. Augmen ed Lag ange o mula ion scheme 41 Figu e 36. Time s ep con ols. Bisec ion me hod (le ), P edic o impac ( igh ). 41 Figu e 37. Bounda y condi ions in Halo cu en model 42 Figu e 38. Equi alen s ess in FILD (concep ual phase). De ail o he pene a ion. 43 Figu e 39. Equi alen s ess maximum s leng h be ween he con ac ing and he p obe head 44 Figu e 40. S ess dis ibu ion in FILD (725 mm con ac ing) 45 Figu e 41. De o ma ion in FILD (725 mm con ac ing) 45 Figu e 42. Sensi i i y analysis o he mesh 46 Figu e 43. Equi alen s ess maximum e sus la ge adius 47 Figu e 44. S ess dis ibu ion in FILD (40 mm la ge adius) 47 Figu e 45. Equi alen s ess maximum esponse su ace e sus s ess concen a o adius and hickness. 48 Figu e 46. S ess dis ibu ion in he p oposed inal design 49 Figu e 47. De o ma ion gene a ed by own weigh 49 Figu e 48. S ess dis ibu ion in p oposed inal design (Gap 4 mm) 50 Figu e 49. De ails o he plas i ied zone 50 Figu e 50. De o ma ion in p oposed inal design (Gap 4 mm) 51 1 1 INTRODUCTION 1.1 Fusion ene gy This is a di icul ime o he ene gy indus y. Many o he new signals eme ging, dis up i e digi aliza ion, he commi men o deca boniza ion and desi e, in some coun ies, o a mo e na ional ocus; indica e ha new amewo ks o hinking a e needed. The pe iod o 1970 o 2015 was one o ema kable wo ld economic g ow h: The inc ease in he G oss Wo ld P oduc , he popula ion, and he labou o ce, was complemen ed wi h a high a e o p oduc i i y g ow h; which led o an inc ease in ene gy demand [1]. Acco ding o a ecen s udy by U.S. Ene gy In o ma ion Adminis a ion [2], wo ld ene gy consump ion will ise 28% be ween 2015 and 2040. Cu en ly, mos o he ene gy esou ces ha p o ide ene gy o he plane a e o na u al o igin, especially ossil uels; while enewable ene gies emain in he backg ound due o hei low e iciency and dependence on clima ic condi ions. Wha happens wi h ission nuclea ene gy is he same because o he gene a ion o adioac i e and dange ous was e. I is expec ed ha in de coming yea s he consump ion o enewable ene gies will inc ease, bu so will ossil uels, which is no sus ainable due o he o e exploi a ion o hese esou ces, as well as he nega i e consequences on he en i onmen . Global wa ming is a p oblem ha is being add essed in key poin s o epo s like Wo ld Ene gy Scena ios 2016 [1]. Gi en hese a gumen s, he e is a need o ind a sou ce o sus ainable, sa e, inexhaus ible and clean ene gy. Nuclea usion ene gy is a p omising ield in hese aspec s, bu i s de elopmen s as an ene gy sou ce is one o he mos complex scien i ic and echnical asks e e unde aken o non-mili a y pu poses and will s ill span se e al human gene a ions [3]. The usion eac ion ha is easies o accomplish is he eac ion be ween wo hyd ogen iso opes: deu e ium, ex ac ed om wa e and i ium, p oduced du ing he usion eac ion h ough con ac wi h li hium. When deu e ium and i ium nuclei use, hey o m a helium nucleus, a neu on and a lo o ene gy [4]. Figu e 1: Nuclea usion eac ion The kine ic ene gy eleased is due o he mass di e ence be ween eac an s and p oduc s, acco ding o he Eins ein o mula (E = ∆m · c2) ha can be used o gene a e elec ici y. This is he eason why so li le uel can p oduce so much ene gy: When bu n in a usion eac o , he deu e ium con ained in 1 L o wa e (abou 33 mg) will p oduce as much ene gy as bu ning 260 L o gasoline [3]. In oduc ion 2 Since 1991 se e al megawa s o usion powe ha e been eleased in a con olled way in deu e ium- i ium expe imen s in JET (Join Eu opean To us, Culham, UK) and TFTR (Tokamak Fusion Tes Reac o , P ince on, USA) [3]. These expe imen s a e ca ied ou in nuclea usion eac o s o okamak ype (mos widesp ead). The okamak is a o oidal plasma con inemen sys em, he plasma being con ined by a magne ic ield. The p incipal magne ic ield is he o oidal ield. Howe e , his ield alone does no allow con inemen o he plasma, i is necessa y a poloidal magne ic ield [5]. This Mas e Thesis is amed in ITER (In e na ional The monuclea Expe imen al Reac o ). ITER is one o he mos ambi ious ene gy p ojec s oday. In sou he n F ance (Cada ache), 35 na ions a e collabo a ing o build he wo ld’s la ges okamak, a magne ic usion de ice ha has been designed o p o e he easibili y o usion as a la ge-scale and ca bon- ee sou ce o ene gy based on he same p inciple ha powe s ou Sun and s a s. In igu e 2, a ende ing o he complex whe e he eac o is ins alled is shown. Figu e 2: ITER scheme ITER is designed o p oduce a en- old e u n o ene gy (Q = 10), o 500 MW o usion powe om 50 MW o inpu hea ing powe . ITER will no cap u e he ene gy i p oduces as elec ici y, bu -as i s o all usion expe imen s in his o y o p oduce ne ene gy gain- i will p epa e he way o he machine ha can [6]. O he objec i es can be summa ized in: • Demons a e he in eg a ed ope a ion o echnologies o a usion powe plan . Scien is will be able o s udy plasmas unde condi ions simila o hose expec ed in a u u e powe plan and es echnologies such as hea ing, con ol, diagnos ics, c yogenics and emo e main enance. • Achie e a deu e ium- i ium plasma in which he eac ion is sus ained h ough in e nal hea ing. Scien is s a e con iden ha he plasmas in ITER will no only p oduce much mo e usion ene gy bu will emain s able o longe pe iods o ime. • Tes i ium b eeding. The wo ld supply o i ium is no su icien o co e he needs o u u e powe plan s. ITER will p o ide a unique oppo uni y o es mockup in- essel i ium b eeding blanke s in a eal usion en i onmen . • Demons a e he sa e y cha ac e is ics o a usion de ice. One o he p ima y goals o ITER ope a ion is o demons a e he con ol o he plasma and he usion eac ions wi h negligible consequences o he en i onmen . 3 3 S uc u al assessmen o he ITER Fas -Ion Loss De ec o 1.2 The Fas -Ion Loss De ec o (FILD) In ITER, usion eac ions and he use o a ious speci ic sys ems such as ion cyclo on hea ing and neu al beam injec ion can gene a e as ions. Fas -ions a e he popula ion o ions whose ene gy is abo e he he mal ene gy, i.e. he bulk plasma ene gy. The e o e, hey can be expelled om he co e egion o plasma edge by a ious ins abili ies. E en hough hey a e a small ac ion o he o al ions popula ion, hey ha e a c ucial e ec on usion de ices pe o mance and plasma s abili y because o hei high ene gy [7]. The Fas -Ion Loss De ec o (FILD) is one o he mos widely used diagnos ic o measu ing as ions in he plasma edge (Figu e 3). A ac ion o he inciden as ions is ansmi ed in o a FILD whe e hey encoun e a scin illa o and/o an a ay o Fa aday cups. The in e ac ion o as ions wi h he scin illa o p o ides measu emen s o hei ene gy and he eloci y pi ch. This pe mi s ex ac ing in o ma ion abou he unde lying loss p ocess [8]. Figu e 3: Poloidal c oss-sec ion o ITER Unde s anding he mechanisms o losses and de eloping p ocedu es o hei con ol is one o he main a enues o esea ch in he ield o usion. An ideal Fas -Ion Loss De ec o should be able o p o ide in o ma ion on he ollowing aspec s [9]: • Type o sup a he mic pa icles ha a e escaping om he plasma. • Spa ial loca ion o he losses on he i s wall o he eac o . • In o ma ion abou he angula dis ibu ion o he as ions ha p o ides in o ma ion on he na u e o he o bi s ollowed by he ions. • Good esolu ion in ene gy o de ec he ene gy ange o he sup a he mic pa icles. • Tempo a y esolu ion o ollow he e olu ion and equency o losses due o he p esence o ins abili ies. • The absolu e low o pa icles ha impac on he essel. • The de ec o mus be lexible and esis an o be able o wi hs and he ha sh condi ions o he hos ile In oduc ion 4 en i onmen o he usion eac o s in which i mus ope a e. 1.3 Objec i es and p ojec scope ITER is an expe imen al nuclea usion eac o whe e he aim is o achie e a echnology ha p o ides clean, sa e and unlimi ed ene gy. To each his poin i is necessa y o s udy he plasma and he physical phenomena ha occu du ing he eac ion, o inally be able o con ol he plasma and gene a e ene gy. Hence he expe imen al cha ac e o he eac o . Diagnos ic sys ems such as FILD play an impo an ole in unde s anding he p ocess. Bu he ac o being inco po a ed in his sys em means ha i is exposed o ce ain loads, such as hose gene a ed by elec omagne ic dis up ions. The main objec i e o his mas e hesis is o achie e a design o FILD ha is capable o esis ing s a ic loads due o elec omagne ic dis up ions, s a ing om an ini ial concep o de ice. O he seconda y objec i es, bu necessa y o each he main objec i e a e: • The gene al unde s anding o he pe o mance o he okamak and i s componen s. This allowed o acqui e ease o he calcula ion o he loads. • S udy he ope a ion o FILD and i s componen s o unde s and he concep ual design and be able o app oach he design p ocess in a ealis ic way. • Lea n abou he di e en ypes o loads ha occu in okamaks and how hey a e ans e ed o di e en de ices. • Gene a e a alid model o he calcula ion o elec omagne ic loads o FILD. • Pe o m a ini e elemen model o s udy he beha io o FILD agains p e iously calcula ed loads. 1.4 Documen s uc u e This documen is composed o 5 chap e s h ough which he objec i es o he p ojec will be comple ed. The ollowing is a summa y o he con en s o he chap e s: • Chap e 2. FILD componen s. In his chap e , he main componen s o he okamak a e explained in o de o loca e FILD. In addi ion, he di e en pa s o his de ice a e desc ibed in de ail in i s concep ual design, as well as i s ope a ion. • Chap e 3. Elec omagne ic loads in FILD. The objec i e o his chap e is o ob ain he alue o he loads ha ac on FILD du ing an elec omagne ic dis up ion. To do so, i s he ypes o loads in okamaks a e exposed, o la e de ail he elec omagne ic ones, exposing calcula ion examples and inally es ablishing a alid model o calcula e he loads on FILD. • Chap e 4. S uc u al analysis o FILD. The esul s o he analyses wi h he loads ob ained in chap e 3 ca ied ou a e exposed. This chap e de ails how he analyses ha e been ca ied ou , as well as he design p ocess ollowed o a i e a an op imal solu ion ha sol es he s a ic p oblem by modi ying as li le as possible he concep ual design. • Chap e 5. Conclusions. I is dedica ed o ex ac he conclusions o he esul s ob ained in chap e 4 and indica e he possible u u e lines in which o de elop new wo k. 5 2 FILD COMPONENTS 2.1 In oduc ion In his sec ion, i is in ended o show he concep ual design o FILD, wi h a de ailed desc ip ion o all i s pa s, as well as i s ope a ion and loca ion. Be o e going in o de ail wi h FILD componen s, i is necessa y o know he in e nal s uc u e o he okamak. In he igu e 4, he main componen s o he ITER eac o a e shown. Figu e 4. ITER okamak in e nal s uc u e The main componen is he Vacuum Vessel (VV). The ITER expe imen s will ake place inside he Vacuum Vessel, a he me ically sealed s eel con aine ha houses he usion eac ions and ac s as a i s sa e y con ainmen ba ie . In i s doughnu -shaped chambe , o o us, he plasma pa icles spi al a ound con inuously wi hou ouching he walls [10]. Ten housand onnes o magne s, wi h a combined s o ed magne ic ene gy o 51 Gigajoules (GJ), will p oduce he magne ic ields ha will ini ia e, con ine, shape and con ol he ITER plasma. Manu ac u ed om niobium- in (Nb3Sn) o niobium- i anium (Nb-Ti), he magne s become supe conduc ing when cooled wi h supe c i ical helium in he ange o 4 Kel in (-269 °C) [11]. The Vacuum Vessel p o ides a high- acuum en i onmen o he plasma, imp o es adia ion shielding and plasma s abili y, ac s as he p ima y con inemen ba ie o adioac i i y, and p o ides suppo o in- essel componen s such as he blanke and he di e o . Cooling wa e ci cula ing h ough he essel's double s eel walls will emo e he hea gene a ed du ing ope a ion. The blanke modules ha co e he inne walls o he VV p o ec he s eel s uc u e and he supe conduc ing o oidal ield magne s om he hea and high-ene gy neu ons p oduced by he usion eac ions [12]. Si ua ed a he bo om o he Vacuum Vessel, he di e o ex ac s hea and ash p oduced by he usion eac ion, minimizes plasma con amina ion, and p o ec s he su ounding walls om he mal and neu onic loads [13]. Fo y- ou openings, o po s, in he Vacuum Vessel p o ide access o emo e handling ope a ions, diagnos ics, hea ing, and acuum sys ems. These openings a e di ided acco ding o hei loca ion in Uppe Po , Equa o ial Po and Lowe Po . FILD componen s 6 2.2 Loca ion As explained p e iously, FILD in ends o make measu emen s o as ion losses a he plasma edge, so i mus be placed in a si ua ion ha can pe o m his ype o measu emen s. Tha is why FILD is in eg a ed in an Equa o ial Po Plug #08 (EPP#08). The Equa o ial Po Plugs a e he cen al s uc u es (Figu e 5) whe e a ious diagnos ic sys ems a e loca ed such as FILD and consis s o h ee basic pa s [14]: • The diagnos ic i s walls (DFW) which se es as plasma acing pa s o he assembly while de eloping he ole o i s neu on shielding laye and implemen s he necessa y cu ou s and ape u es o he plasma equi ed o he ope a ion o diagnos ic sys ems assembled in he PP. • The diagnos ics shielding modules (DSM), which p o ide he neu on shielding o po ape u e in o de o minimize he ac i a ion and he dose in he Po Cell (in e space) a ea and po s and house diagnos ic and se ice sys ems. • The EPP#08 s uc u e as main s uc u al elemen ha holds he es o componen s, ha o ms he connec ion o he VV being pa o he p ima y acuum and con inemen bounda ies and ha p o ides he in e ace (closu e pla e) o all equi ed pene a ions and eed h oughs be ween he in-VV space and he Po Cell. a) EPP’s dis ibu ion b) FILD’s loca ion in EPP#08 Figu e 5. FILD's loca ion The de ice will be ins alled a he EPP#08, app oxima ely 10 cm abo e he midplane, o ien ed ho izon ally along he majo adius o he machine [15]. The design o FILD, a concep ual design phase, is shown in igu e 6, whe e EPP#08, DSM2 and DFW a e also schema ically ep esen ed. As can be seen in he igu e, FILD is a ached o he las e ical blade o he DSM2 by he ixed pa . This ixed pa se es as a suppo and guide o he mo able pa , which holds he p obe head and pushes i close o he plasma o measu ing. FILD EPP#08 7 S uc u al assessmen o he ITER Fas -Ion Loss De ec o Figu e 6. Gene al scheme o FILD 2.3 Gene al desc ip ion FILD is in eg a ed in o an EPP, bu i is necessa y o measu e a he edge o he plasma o cap u e he as ions. This ac p esen s a g ea disad an age: The exposu e o la ge he mal loads, which signi ican ly limi s he du a ion o he measu emen . FILD is designed o ope a e in a ixed posi ion du ing plasma discha ge. The inse ion leng h is p e iously de ined and when he discha ge is inished, he sys em au oma ically e ac s. To p o ec bo h he in eg i y o he okamak and FILD, he e is a secu i y p o ocol ha allows he discha ge o be abo ed i he measu ed he mal loads exceed a limi . By p o iding he de ec o wi h eedback o empe a u e con ol (o o he measu e o he mal load) i can au oma ically be e ac ed i necessa y, e. g. i he he mal loads suddenly inc ease due o plasma displacemen s. Gi en he ime scale associa ed wi h he mal a ia ions nea he plasma, apid displacemen s will be equi ed in a sho pe iod o ime, o send he FILD body o a sa e posi ion. Thus, he sys em will ha e a measu emen posi ion and a pa king posi ion (Figu e 7). a) Measu emen posi ion Elec omagne ic loads in FILD 14 The e o e, a igo ous ea men o hese loads would equi e hei conside a ion in a dynamic way o accoun o he ine ial e ec s o he sys em. Indeed, his would be he second con ibu ion. Fo he pa icula case o he assembled Po Plugs (bu no limi ed o); as hey a e complex sys ems and dynamic analyses a e usually cumbe some; a usual p ac ice is o ea hese loads in a s a ic way. This equi es i s he iden i ica ion o he peak o ces de eloped du ing he ansien . These peak o ces a e hen, scaled by a dynamic ampli ica ion ac o (DAF) o include he ine ial e ec s. DAFs a e no mally de e mined using ansien analysis in simpli ied models and hei alidi y is subjec ed o he equi alence o he peak loads s a ic and maximum dynamic esponses o he sys em. • Ine ial loads associa ed o Vacuum Vessel mo emen s: Po Plugs a e assembled in he Vacuum Vessel by inse ion in he po ex ensions. Po ex ensions a e in u n, connec ed o he Vacuum Vessel h ough he po s ubs leading o double can ile e ed massi e sys em. Du ing he e olu ion o elec omagne ic e en , he Vacuum Vessel is subjec ed o simila e ec s as hose desc ibed in he i s poin abo e. This means ha he Vacuum Vessel will expe ience mo emen s whose e ec a po s ub le el is he de elopmen o addi ional ine ia loads on assembled po plug sys ems. These ac ions, which cons i u e he hi d con ibu ion, may be eadily desc ibed by poin esponse spec a de ined a he po s ub. • In e ace loads: Diagnos ic sys ems inside EPPs a e ancho ed o ame s uc u es (EPP s uc u e, DSM, DFW) which a e ac ually de o mable bodies. Du ing he de elopmen o he ansien elec omagne ic e en s hese s uc u es will su e de o ma ions which can a ec o he diagnos ic componen s subjec ed o s uc u al in eg i y e alua ion in he o m o ela i e displacemen s be ween he ancho age poin s. These in e ace loads would cons i u e he las con ibu ion o conside in he speci ica ion o mechanical loads de i ed om elec omagne ic e en s in diagnos ic sys ems. The wo i s con ibu ions desc ibed abo e a e no mally de e mined h ough dedica ed elec omagne ic analysis o he componen s unde s udy as pa o he global p ocess o s uc u al in eg i y assessmen . The cha ac e iza ion o he Vacuum Vessel mo emen s, ine ial e ec s and ela ed in e ace loads is ob ained om a global dynamics analysis o he Tokamak including he di e en scena ios and pa icula i ies o he elec omagne ic loads. 3.3 Volume ic loads om cu en s in s uc u es The dominan mechanical loads on FILD componen s a ise om plasma dis up ions; ha is why his mas e hesis will ocus on he s udy o his ype o loads. The apidly changing magne ic ields associa ed wi h dis up ions induce elec ical eddy cu en s in he su ounding mechanical conduc i e s uc u es which hen in e ac wi h he backg ound magne ic ield, hus p oducing o ces and o ques. Unlike mos mechanical loads, he load associa ed wi h he eddy cu en s is no simply speci ied bu is ins ead dependen upon he de ails o he po plug ha dwa e, including he DSM-DFW assembly, he po plug s uc u e and how hese componen s a e elec ically connec ed. The pa h o elec omagne ic olume ic load is shown in igu e 12: 15 S uc u al assessmen o he ITER Fas -Ion Loss De ec o Figu e 12. Pa h o he olume ic loads om induced cu en s in passi e s uc u es Dis up ions in ITER a e simula ed wi h he DINA code and he esul s o he DINA simula ions o ITER a e s o ed in IDM (ITER Documen Managemen ). Table 2 shows he ca ego iza ion o hese DINA simula ions acco ding o he ITER load speci ica ion documen [19]. Addi ional analyses o de e mine wo s e en s depending on he loca ion a e s ill on-going. Table 2. ITER plasma dis up ions cases and i s ca ego iza ion Type o dis up ion Cu en quench ime Peak TPF*Ihalo/Ip The mal quench ime Numbe o e en s 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 as - VDE II slow 50 – 100 ms 0,34/0,42 150 VDE II as Exp. 16 ms 0,2/0,25 150 VDE III slow > 200 ms 0,75/0,6 - VDE III as Exp. 16 ms 0,36/0,45 - VDE IV slow as 0,6/0,75 - Elec omagne ic loads in FILD 16 Eddy cu en s do exis in p inciple (wi h di e en in ensi ies) a any ime momen o any ansien elec omagne ic e en s including no mal ope a ion, bu halo cu en is conside ed only a la e phase o Ve ical Displacemen E en s (VDEs) and Majo Dis up ion (MDs), when he sepa a ix ouches he plasma- acing conduc ing wall. Maximum elec omagne ic loads on he Po Plug componen s a e caused by h ee kinds o abno mal e mina ions o plasma pulse: • A MD consis s o an abno mal e mina ion o he plasma pulse consis ing o wo phases, he he mal quench wi h a as loss o he plasma he mal ene gy and he cu en quench wi h a as d op in plasma cu en o en accompanied by a e ical d i and comp ession o he plasma co e. • A VDE consis s o an abno mal e mina ion o he plasma pulse ini ia ed by a ailu e o e ical posi ion con ol, ollowed by an i e e sible plasma e ical d i , comp ession o he plasma co e, he he mal quench, plasma cu en decay and by a u he comp ession o he plasma co e. • A MFD (Magne Fas Discha ge) is an e en whe e he cu en ha lows in he ITER magne s is apidly b ough o ze o (usually done in en ionally a e he de ec ion o a quench o p o ec he coils om o e hea ing). In bo h VDEs and MDs he halo cu en can each e y la ge ac ions o he o al plasma cu en once he plasma ouches he wall. In bo h cases he inal s ages include a plasma d i o ei he uppe o lowe pa o he VV. The e a e wo ypes o MFD. MFD I which co esponds o a as discha ge o he CS (Cen al Solenoid) and PFC (Poloidal Field Coils) only, o MFD II whe e all coils a e discha ged. Du ing a MFD I, he eddy cu en s c ea ed a e simila o hose gene a ed du ing plasma ini ia ion. Du ing MFD II, la ge loads will occu . Ne e heless, hese loads a e conside ed e y small because he IVCs (in- essel componen s) a e no elec ically connec ed in he o oidal and Poloidal di ec ion. Besides, he load due o MFD is no eally supe imposed o he dis up ion loads because he cu en decay o MFD is much longe han he plasma dis up ion ime. 3.4 Analysis echniques o calcula ion o elec omagne ic loads Below a e exposed se e al me hods used in a mul i ude o sys ems o calcula e elec omagne ic loads. P ocedu e 1: App oach based on DINA inpu s. The gene al app oach o calcula ion o EM loads is based on he EM ansien analysis o he componen s whe e he eddy and halo cu en s a e usually calcula ed wi h di e en kinds o inpu s [14]: • Typical inpu o he calcula ion o eddy cu en s caused by diamagne ic lux loss a he ime o he mal quench is a cu en wa e o m in a se o poloidal loops loca ed in plasma olume. These loops o m a o oidal solenoid. The a ia ion o he diamagne ic lux is p esc ibed by he DINA code. Some esul an a ia ions o plasma shape, plasma cu en and he Poloidal magne ic ield ake place a he ime o he mal quench. • Typical inpu o he calcula ion o eddy cu en s caused by plasma cu en quench is a se o cu en wa e o ms in he o oidal coaxial loops which ep esen plasma e olu ion ( ime dependen ne cu en , posi ion, shape and cu en densi y p o ile). The cu en wa e o ms in hese loops a e p o ided by DINA. • Typical inpu o calcula ion o halo cu en s is he ime dependen poloidal p o ile o halo cu en densi y on he su ace whe e he halo cu en in e cep s he PFCs. This p o ile is p o ided by DINA. • EM loads on he Po plug sys em componen s, as ou pu o 3D EM ansien nume ical analysis, a e ini ially ep esen ed in he o m o dis ibu ed o ce densi y. These esul s a e hen ansmi ed u he o he suppo ing s ess-s ain s a ic and dynamic analysis o he componen s. The EM loads applied o each componen a e summa ized as 6 ime-dependen o hogonal componen s: 3 in eg al momen s and 3 in eg al o ces. 17 S uc u al assessmen o he ITER Fas -Ion Loss De ec o • Typically, EM analysis and load in eg a ion a e done sepa a ely o eddy and halo cu en ela ed loads, gi ing as ou pu 6+6=12 ime-dependen in eg al load componen s. The ime dependen g aphics o such in eg al loads indica e he peaks o each componen and he ime momen when each peak occu s. No e ha he peaks o di e en load componen s can be eached a di e en imes and e en in di e en plasma e en s. Elec omagne ic (EM) loads (ei he by eddy cu en s o by a sum o eddy and halo) exis in each conduc i e pa o he machine du ing each ansien EM e en . They can be ep esen ed as ime-dependen 3-D ec o ield o o ce densi y (F=J x B), whe e B is ime-dependen ec o sum o magne ic ields by all sou ces a each spo and J is ec o o sum cu en densi ies a each spo . P ocedu e 2: App oach based on p e ious magne ic ield solu ions An al e na i e app oach much easie o apply in he one based on he maps o he magne ic ield e olu ion in space en elope whe e componen s si . The loads due o he induced cu en s a e mos ly domina ed by he plasma ansien s and he la ge CS, PF and TF cu en s, ha dly a ec ed by he local a ia ion in e ec i e conduc i i y. Gi en he maps o e olu ion o he magne ic ield in he egion o in e es he elec omagne ic loads can be es ima ed using a local elec omagne ic model o he assembled componen s in he PP including he componen s unde s udy can be used. The ields p o ided as inpu s can be in e pola ed in he local ini e elemen mesh. Figu e 13 shows he olume ic o ce densi y in an en i e po plug [20]. Figu e 13. Fo ce densi y dis ibu ion o be in e pola ed in he whole po plug (N/m3) This in e pola ion depends on he o mula ion o he elec omagne ic analysis, ne e heless i would be pe o med as imposed bounda y condi ions in he whole domain simula ed conside ing he pa icula deg ees o eedom in consis ency wi h he o mula ion chosen. Volume ic elec omagne ic o ces may be he de e mined as a ime-dependen 3-D ec o ield o o ce densi y (F= J x B). Howe e , hese ac i i ies ha e no been pe o med o he Fas -Ion Loss De ec o . The e o e, he elec omagne ic loads p esen ed in his mas e hesis ha e o be alid es ima es o he concep ual design e iew. The ollowing sec ions show his es ima e, s a ing wi h he de ini ion o he geome y and la e he calcula ion Elec omagne ic loads in FILD 18 models based on he Lo en z law. On he senso s, eddy cu en s will be induced as a esul o he induced ol ages in he s uc u es because o he a ia ion o he ields du ing he ansien e en s. As a esul , o ques will appea . In addi ion o ha , a sha ed cu en wi h he suppo ing s uc u e (DSM) will p oduce ne o ces on he in-po came as. 3.5 FILD geome y o elec omagne ic analysis The geome y unde s udy consis s o he p obe head, he suppo o he p obe head and he suppo o he olle s; ha is o say he mo able pa . The ixed pa will only be aken in o accoun in case he e a e la ge de o ma ions, so i is necessa y o s udy he in e ac ion be ween he ixed and mo able pa . To acili a e he calcula ion o elec omagne ic loads, as well as ini e elemen analysis; a simpli ied CAD model has been used. In his model, unnecessa y elemen s such as he de ailed shape o he p obe head ha e been elimina ed o ounding has been added in he o eseeable ension concen a o . Figu e 14-a shows an o e iew o he CAD model o FILD, and igu e 14-b shows a c oss sec ion o he mo able pa unde s udy. a) FILD CAD model gene al iew b) C oss sec ion in he medium plane. The dimensions a e shown un millime e s. All oundings ha e adius o 7,5 mm. Figu e 14. FILD CAD model 19 S uc u al assessmen o he ITER Fas -Ion Loss De ec o 3.6 Es ima ion o elec omagne ic loads Once he geome y o be s udied is de ined, i is in ended o calcula e he elec omagne ic loads ha mus be suppo ed by FILD du ing a dis up ion e en . As explained abo e, de ailed elec omagne ic analyses o dis up ions o e FILD and EPP # 08 ha e no been pe o med ye . The e o e, elec omagne ic loads mus be es ima ed om alues ob ained om analyses ca ied ou in o he zones o ITER o in o he diagnos ic sys ems. The main objec i e o hese es ima ions is o e i y he s uc u al in eg i y o FILD in a i s s udy agains elec omagne ic dis up ions, and hus be able o alida e o make he oppo une changes in he concep ual design in on o his ype o loads. The i s s ep o es ima ing is o c ea e a physical model o he p oblem, on which applying he a ious physical laws is simple. La e , ansla ing ha model o he FILD geome y, decomposing i in se e al pa s o acili a e he calcula ion. The nex s ep is o ob ain he cu en ha ci cula es h ough FILD, which can be o wo ypes: • Eddy cu en induced by he mechanism o conse a ion o he magne ic luxes c ossing he elec ically conduc ing pa s. They a e closed cu en loops ha being inside a magne ic ield causes o ques o appea on FILD by he Lo en z law (which ac s like a loop). • Halo cu en s low in loop o med pa ly by conduc ing s uc u es and pa ly by he plasma sc ape-o laye . This cu en inside a magne ic ield causes o ces in FILD by he Lo en z law (which ac s like a conduc o ). The las s ep is o calcula e hese loads which a e he beginning o he mechanical p oblem. 3.6.1 Eddy cu en s The eddy cu en s end o domina e in he he mal quench phase, a he beginning o dis up ion e en and hei ime scale is small. The elec omagne ic loads due o eddy cu en s can be calcula ed conside ing: • The magne ic ield componen s and hei a ia ion in ime in egion in which hey a e loca ed. • The cu en induced es ima ed by assuming a conduc o loop wi h all he ma e ial lumped a ound he pe ime e loop. The a ea o he lux can be conside ed as he a ea acing he a ia ion o he ield. Because he e is no magne ic ield a ia ion da a in Equa o ial Po Plug #08, hese alues a e app oxima ed by aking hem om ano he egion simila o whe e FILD is loca ed. Speci ically, he e a e elec omagne ic analysis esul s in he Equa o ial Po Plug #01 ha p o ide an es ima e o he magne ic ield a ia ion, as well as he alue o he s a ic o oidal magne ic ield (Table 3). Table 3. Es ima ion o s a ic o oidal ield B and he a ia ion o elec omagne ic ield in EPP #01 Equa o ial Po #01 Came as Va ia ion o adial ield dBx/d (T/s) Va ia ion o e ical ield dBz/d (T/s) S a ic o oidal ield B (T) 11,1 70,9 5,6 The alues p o ided in he p e ious able a e en eloping all he elec omagne ic e en s, as he maximum s a ic and a ia ion o ield has been aken in each case. This is a e y conse a i e assump ion, as he maximum s a ic ield and ield a ia ion alues can happen in di e en dis up ion e en s o ime ins an . As can be seen in able 3, he e a e magne ic ield a ia ion alues in bo h he adial and e ical di ec ions. This gene a es ha cu en is induced in wo di e en di ec ions, and he e o e he e a e o ques in wo di ec ions Elec omagne ic loads in FILD 20 which a e calcula ed independen ly. 3.6.1.1 Eddy cu en due o a ia ion o adial ield The model used o calcula e he eddy cu en s due o he a ia ion o he adial ield is an open ube whose longi udinal di ec ion is pa allel o he ield a ia ion (which is known). Tha is why, acco ding o Fa aday’s law, he induced elec omo i e o ce in any closed ci cui is equal o he nega i e o he ime a e o change o he magne ic lux enclosed by he ci cui . To ca y ou he calcula ions, cylind ical di e en ial elemen s (d ) o adius and leng h L will be aken as shown in he igu e 15. Figu e 15. Model o elec omagne ic calcula ions ( adial ield a ia ion) Radial ield a ia ion induces an elec omo i e o ce, and by symme y he induced cu en s (I eddy; igu e 15) will ha e he shape o ci cles cen e ed on he axis o he cylinde . The low (Φ) h ough one o hese cylind ical elemen s is he magne ic ield mul iplied by he a ea ha aces he magne ic lux a ia ion. Φ=𝐵∙𝜋∙𝑟2 The elec omo i e o ce induced (ε) in he elemen o adius is: ε=−𝑑Φ 𝑑𝑡 =−𝜋∙𝑟2∙𝐵󰇗𝑥 As can be seen om he p e ious equa ion he induced elec omo i e o ce (em ) is a iable depending on he adius. The nega i e sign o ε means ha he di ec ion o he induced cu en is such ha i opposes he low a ia ion, he e o e, he di ec ion o he induced cu en is shown in igu e 15 and he nega i e sign will be elimina ed in he nex exp essions. This em is he one ha se s in mo ion he cha ge ca ie s con ained in he cylind ical laye olume o leng h L be ween and + d , o igina ing a cu en : 𝑑𝑖=ε 𝑑𝑅𝑒 being 𝑑𝑅𝑒 he esis ance o a ube o leng h 2∙𝜋∙𝑟 and sec ion 𝐿∙𝑑𝑟, h ough which he cu en lows. The esis ance is: 𝑑𝑅𝑒=𝜌2∙𝜋∙𝑟 𝐿∙𝑑𝑟 21 S uc u al assessmen o he ITER Fas -Ion Loss De ec o whe e 𝜌 is he esis i i y o he ma e ial. The cu en lowing in he di e en ial sec ion is: 𝑑𝑖=𝜋∙𝑟2∙𝐵󰇗𝑥∙𝐿∙𝑑𝑟 2∙𝜌∙𝜋∙𝑟 =𝐵󰇗𝑥∙𝐿∙𝑟∙𝑑𝑟 2∙𝜌 Once ob ained he di e en ial exp ession o he in ensi y, he nex s ep is o in eg a e i be ween he majo and mino adius (b and a, espec i ely) o calcula e he o al in ensi y ha ci cula es h ough he ube. 𝐼=∫ 𝐵󰇗𝑥∙𝐿∙𝑟 2∙𝜌 𝑑𝑟=𝐵󰇗𝑥∙𝐿 4∙𝜌 𝑏 𝑎∙[𝑏2−𝑎2] Wi h he calcula ion o he induced in ensi y, he p oposed model is sol ed, so i will be necessa y o ans e he model o FILD geome y. Compa ing igu es 14 and 15, i is concluded ha FILD con be modeled as wo cylinde s o di e en dimensions in which wo in ensi ies will ci cula e. Fi s , he in ensi y (I1) ha lows h ough he la ge cylinde ( adius 54 and 44 mm) is calcula ed: 𝐼1=3324 𝐴 On he o he hand, he in ensi y ha ci cula es h ough he smalle cylinde ( adius 25 and 17 mm) is: 𝐼2=1437 𝐴 These in ensi ies ha ci cula e h ough FILD as i i we e a loop, a e imme sed in a o oidal s a ic magne ic ield, so by he Lo en z law he e a e momen s. The momen can be exp essed as a ec o p oduc o wo ec o s, he magne ic momen ec o 𝑚 󰇍 󰇍 and he magne ic ield ec o 𝐵 󰇍 . The modulus o he magne ic momen ec o is he p oduc o he in ensi y by he a ea o he loop (i is conside ed he la ges a ea o be conse a i e, and all he ma e ial in a single loop). I s di ec ion is pe pendicula o he plane o he loop and i is de e mined by he p og ess o a co ksc ew ha o a es as he cu en does in he loop. The magne ic ield ec o is he s a ic o oidal ield which is shown in igu e 16. Pe o ming he ec o p oduc desc ibed abo e, he ollowing exp ession is ob ained o calcula e he momen : 𝑀=𝑆∙𝐼∙𝐵𝑡 being S, he su ace o he loop (la ges su ace); I, he in ensi y p e iously calcula ed; and B , he s a ic magne ic ield. Pa icula izing o he wo in ensi ies, he momen s M1 and M2 esul wi h he di ec ions shown in igu e 16. 𝑀1=171 𝑁∙𝑚 𝑀2=16 𝑁∙𝑚 The esul ing momen s a e bending momen s in he z-axis applied o he p inciple o he majo and mino cylinde s. Elec omagne ic loads in FILD 22 Figu e 16. Momen s in z-axis due o eddy cu en s 3.6.1.2 Eddy cu en due o a ia ion o e ical ield The model used o calcula e he eddy cu en s due o he a ia ion o he e ical ield is a closed ube ( o close he ci cui ) whose longi udinal di ec ion is pe pendicula o he ield a ia ion (which is known). In his case, o pe o m he calcula ions, shee s ha e been aken along he z-axis o hickness dz. The leng h o he cylinde is L. The wid h o he shee in x di ec ion depends on he dis ance z o he shee and is 2∙√𝑅2−𝑧2. Finally, he hickness in he y di ec ion is δ. The model is shown in he igu e 17: Figu e 17. Model o elec omagne ic calcula ions ( e ical ield a ia ion) The magne ic lux de ined by he magne ic ield mul iplied by he a ea acing he a ia ion o magne ic ield: Φ=𝐵∙2∙√𝑅2−𝑧2 ∙𝐿 By pe o ming he same p ocedu e as in he p e ious case, he induced elec omo i e o ce is calcula ed: 23 S uc u al assessmen o he ITER Fas -Ion Loss De ec o ε=−𝑑Φ 𝑑𝑡 =−𝐵󰇗𝑧∙2∙√𝑅2−𝑧2 ∙𝐿 The induced elec omo i e o ce is opposed o he e ec o magne ic lux a ia ion hence he nega i e sign and di ec ion o induced in ensi y (I eddy) shown in igu e 17. The esis ance o each o he shee s o d is calcula ed aking in o accoun a leng h o (4∙√𝑅2−𝑧2+2∙𝐿) and a sec ion o δ∙dz. 𝑑𝑅𝑒=𝜌∙(4∙√𝑅2−𝑧2+2∙𝐿) δ∙dz The in ensi y in one o he di e en ial loops is he em di ided by he elec ical esis ance: 𝑑𝑖=𝐵󰇗𝑧∙2∙√𝑅2−𝑧2 ∙𝐿∙δ 𝜌∙(4∙√𝑅2−𝑧2+2∙𝐿) ∙dz To ob ain he in ensi y ha ci cula es h ough he ube i is necessa y o in eg a e all he shee s be ween -R and R (along he z-axis): 𝐼=∫ 𝐵󰇗𝑧∙2∙√𝑅2−𝑧2 ∙𝐿∙δ 𝜌∙(4∙√𝑅2−𝑧2+2∙𝐿) ∙dz 𝑅 −𝑅 Due o he complexi y o sol ing his in eg al analy ically, a nume ical calcula ion so wa e has been used o sol e i . The e o e, he model has been ans e ed di ec ly o FILD dimensions in he same way as in he p e ious sec ion. An in ensi y has been calcula ed o he ou e diame e ube 54 mm (I1) and ano he o he 25 mm diame e (I2): 𝐼1=3987 𝐴 𝐼2=726 𝐴 In he same way as p e iously, he o ques ha gene a e he induced in ensi ies on FILD a e calcula ed. Again, wo sepa a e loops a e conside ed so ha wo o ques will be ob ained, in his case o o sion (Figu e 18) 𝑀1=2181 𝑁∙𝑚 𝑀2=232 𝑁∙𝑚 Figu e 18. Momen s in x-axis due o eddy cu en s S uc u al analysis o FILD 30 4.3 Eddy cu en loads analysis In his sec ion he s a ic analysis o FILD will be ca ied ou o ensu e he s uc u al in eg i y agains o he loads gene a ed by eddy cu en s. Then, he di e en aspec s o he model (meshing, bounda y condi ions) will be discussed be o e commen ing on he esul s. 4.3.1 Mesh Meshing can be conside ed he mos impo an p ocess in he calcula ion wi h ini e elemen s, since he esul s and hei eliabili y will depend on he chosen mesh. The ac o s o ake in o accoun in his p ocess a e he ype o elemen wi h which i will be meshed, and hei dis ibu ion in he geome y. The choice o he ype o elemen is linked o he esul s wan ed o ex ac wi h he analysis in ques ion, since each o hem is p og ammed o a speci ic pu pose. The dis ibu ion in he geome y e e s o he use o di e en elemen sizes (mesh e inemen ) o ake ad an age o compu a ional esou ces and e ine he calcula ion in a eas o in e es o he ob aining esul s, o else, in which impo an s ess/s ain g adien s a e p oduced o gua an ee hei co ec ansmission. On he o he hand, i also depends on he dis ibu ion o elemen s, hei quali y, since a uni o m and o de ly dis ibu ion gi es ise o elemen s wi h be e aspec a io (less de o ma ion), imp o ing he esul s ob ained. Te ahed al elemen s can i be e complex geome y. Howe e , he in eg a ion o he shape unc ions wi h poin s o Gauss is less accu a e han hexahed al elemen s. In addi ion, one o he ac o s ha de e mines he quali y o he mesh is he dis o ion o he elemen s. As he geome y o be s udied is no e y complica ed, mos ly hexahed al elemen s (Hex20 elemen ) ha e been used. The idea o meshing is o gene a e a egula mesh, wi hou dis o ions and ai h ully ep oduce he geome y. Fo his i is necessa y ha he mesh can be e ined a lo , bu i is also possible, h ough sensi i i y analysis, o ob ain a comp omise be ween coa se mesh (lowe compu a ional cos ) and p ecision o calcula ions. Figu e 22 shows an example o ine hexahed al mesh, al hough h oughou he e olu ion o he analysis a hicke mesh wi h simila s ess esul s will be sough . The de ails o he s ess concen a o a e also shown, because hey a e a eas whe e a high elemen densi y is necessa y o cap u e he s ess concen a ion e ec . The mesh shown has 233100 elemen s. Figu e 22. Mesh in eddy cu en model 31 S uc u al assessmen o he ITER Fas -Ion Loss De ec o The e a e wo pa ame e s ha gi e an idea o he quali y o he mesh and hese a e: • Elemen quali y: A alue o 1 indica es a pe ec cube o squa e while a alue o 0 indica es ha he elemen has a ze o o nega i e olume. • Aspec a io: The aspec a io is he a io be ween i s la ges and smalles dimension. Elemen quali y (Figu e 23 – a) and aspec a io (Figu e 23 – b) o he p e ious mesh a e shown un Figu e 23. The elemen quali y a e age is 0,87 and he aspec a io a e age is 1,88. The e a e ew elemen s ha ha e a high aspec a io, bu his is no wo isome, since hey a e ew elemen s and loca ed in a eas o low s ess. Such elemen s will no necessa ily p oduce bad esul s – ha depends on he loading and bounda y condi ions o he p oblem – bu do in oduce he po en ial o ouble. 4.3.2 Bounda y condi ions The bounda y condi ions a e o he impo an aspec s o commen be o e pe o ming he s a ic analysis since he esul s depend on i s applica ion. Fi s , he suppo o he olle s can be modeled as a ixed suppo , because his only allows he mo emen in he longi udinal axis (x-axis), on which loads do no ac . Second, he de ice’s own weigh has been conside ed, because i can ha e a signi ican in luence on a 2 m can ile e . The mass o he de ice is 39,465 kg and he cen oid in on x- axis (953,5 mm). Finally, he loads gene a ed by eddy cu en s calcula ed in he p e ious chap e a e applied as poin momen s. The load o lexion in he small cylinde is o ally negligible (16 𝑁∙𝑚) compa ed o he es , bu o be on he sa e y side i is joined wi h he loads applied o he la ge cylinde . The o sion loads a e applied on he cen oins o each cylinde . Figu e 24 shows he bounda y condi ions on FILD a) Elemen quali y b) Aspec a io Figu e 23. Elemen me ics o he p e ious mesh S uc u al analysis o FILD 32 Figu e 24. Bounda y condi ions in he s uc u al s a ic model A good p ac ice o check ha he bounda y condi ions a e well applied is o ob ain he eac ions in he ixed suppo . These esul s a e shown in able 5. Table 5. Fo ce and momen s eac ions in he ixed suppo Fx (N) Fy (N) Fz (N) Mx (𝑁∙𝑚) My (𝑁∙𝑚) Mz (𝑁∙𝑚) 0 0 387 2413 369 187 The eac ion o ces on he x and y axes a e ze o and on he z-axis is he weigh o FILD. On he o he hand, he eac ion momen s o o sion (x axis) is equal o he sum o he momen s applied, and he same happens wi h he lexion in he z-axis. The e is also a momen in he y-axis due o he applica ion o he weigh in he cen e o g a i y o FILD. The ob ained alues coincide wi h he heo e ical ones so he nex s ep is o pe o m he s a ic analysis. 4.3.3 S a ic s uc u al analysis In his sec ion, once he mesh and he bounda y condi ions a e explained, he esul s o he s a ic analysis will be displayed. To check he easibili y o he design, he esul s o he equi alen Von-Misses s ess will be compa ed wi h he elas ic limi o he ma e ial (270 MPa). Plas ici y is an undesi able si ua ion because i gene a es a pe manen de o ma ion ha can a ec he s uc u al in eg i y and in addi ion o he measu emen made. Bu he plas ici y o small a eas e y localized is accep ed as long as i does no comp omise he en i e sec ion. Figu e 25 shows he s ess dis ibu ion in FILD. In his igu e, c oss sec ions a e shown because he p edominan e ec is he o sion ha gene a es he same ension on he su ace bu a ies in hickness. Wi h a c oss sec ion i can be seen a ep esen a ion o he s ess a ia ion. The e a e wo con lic ing zones ha a e po en ial s ess concen a o s. The union o cylinde 1 (la ge cylinde ) and cylinde 2 (smalle cylinde ) and he union o cylinde 2 wi h he olle suppo . These zones will be analyzed in de ail and shown in igu e 25 b – c. 33 S uc u al assessmen o he ITER Fas -Ion Loss De ec o a) S ess dis ibu ion in FILD (gene al iew) b) S ess in he s ess concen a o 1 c) S ess in he s ess concen a o 2 Figu e 25. S ess dis ibu ion in FILD The i s conclusion ha is ob ained om his igu e is ha he e is plas i ica ion because he maximum s ess is 288,73 MPa ha occu s in he s ess concen a o 2. In gene al, i can be seen ha cylinde 1, as is logical, ha dly suppo s s ess due o i s g ea e diame e and he e o e g ea e ine ia. Howe e , cylinde 2 (smalle ), is exposed o a s ess a ound 224 MPa on i s su ace. In he s ess concen a o 1 (Figu e 25 – b) he e is no p oblem because he s ess simply a ies be ween he alue o cylinde 1 and cylinde 2 and does no inc ease. In he s ess concen a o 2 (Figu e 25 – c) he same does no happen. Due o he p oximi y o he suppo and a e a can ile e o 2 me e s, he s ess is concen a ed in a localized a ea. This zone will be he one ha limi s he design, al hough i i is in a localized a ea, he only hing ha would happen wild be a small supe icial plas i ica ion in he s ess concen a o and a ha dening by de o ma ion. Ano he in e es ing aspec is o e i y ha he e a e no excessi e de o ma ions. Figu e 26 shows he o al de o ma ions in FILD. S uc u al analysis o FILD 34 a) To al de o ma ion ( o oidal iew) b) To al de o ma ion ( adial iew) Figu e 26. To al de o ma ion in FILD The o al de o ma ion gene a ed especially by he o sion o que and he own weigh eaches a peak o 18,12 mm. Because his s a e is inadmissible, i is necessa y o change he cu en design o ob ain a esul in which s esses and de o ma ions a e adequa e, wi hou he concep ual design being subs an ially modi ied. Be o e modi ying he design, i is impo an o e i y he mesh used in he p e ious case. To do his, a sensi i i y analysis o he mesh is pe o med, a ying he numbe o elemen s and checking he alue o he maximum equi alen Von-Misses s ess (Figu e 27). Figu e 27. Sensi i i y analysis o he mesh. 35 S uc u al assessmen o he ITER Fas -Ion Loss De ec o This analysis has been done by a ying he numbe o elemen s be ween app oxima ely 30000 elemen s and 230000. In his g aph, i can be obse ed, as expec ed, an inc ease in he maximum s ess as he numbe o elemen s inc eases and inally he con e gence a ound a alue o 288,7 MPa. This is why he mesh used o he p e ious analysis is alid and will be used o he ollowing ones. In addi ion, o comple e his analysis he a ia ion o he s ess along he hickness has been s udied in he a ea whe e i is maximum, a he beginning o he ounding o he s ess concen a o . By a ying he size o he mesh, i is in ended o alida e he esul along he hickness. This is impo an because a e y high s ess on he su ace may be accep able i plas i ica ion does no occu in he en i e sec ion. This analysis has been ca ied ou aking in o accoun he las h ee meshes o he sensi i i y analysis, when he maximum s ess alue has al eady s abilized. The da a o he meshes a e he ollowing: • Mesh 1: 233100 elemen s / 1134358 nodes. • Mesh 2: 173204 elemen s / 861634 nodes. • Mesh 3: 142272 elemen s / 718220 nodes. Figu e 28 shows he s ess-leng h (along he hickness) cu es o he p e iously desc ibed meshes. Figu e 28. Equi alen s ess s leng h in hickness. Compa a i e be ween se e al meshes. In his igu e i can be seen ha he esul s a e e y simila o he di e en meshes so i can be concluded ha he mesh used p e iously no only calcula es co ec ly he maximum equi alen s ess, bu also he s esses along he hickness. In addi ion, an impo an ac ha can be ex ac ed om his g aph is ha only he i s 0.5 mm (app oxima ely) o he hickness (8 mm) a e plas i ied in said egion. S uc u al analysis o FILD 36 Once hese checks a e made, he nex s ep is o make changes in he design op imally so ha he s esses a e below he elas ic limi and ge less de o ma ions. To make hese necessa y changes in an op imal way, an ANSYS ool called esponse su ace has been used. This ool is capable o s a ing om one o se e al inpu pa ame e s, es ablishing se e al design poin s, adjus ing one o se e al ou pu a iables by means o a cu e o su ace. T ansla ing his idea o he FILD model, he ou pu a iable is clea , he maximum equi alen s ess. To selec he inpu pa ame e s, a iables ha inc ease he ine ia o he cylinde 2 ha e been used as c i e ia. The e o e, he a iables selec ed o pe o m he pa ame ic analysis a e he ou e adius and he hickness o he cylinde 2. These a iables ha e been assigned a ange wi hin which he ool no mally o e s 10 design poin s. In his case o be e cap u e he esponse has been modi ied o 20 design poin s and he a iables oscilla ing in he ollowing ange: • La ge adius: Be ween 25 mm (concep ual design) and 35 mm. • Thickness: Be ween 8 mm (concep ual design) and 15 mm. The esul is a 3D su ace whe e he x-axis is he la ges adius, he y-axis he hickness and he z-axis he maximum equi alen s ess (Figu e 29). Figu e 29. Equi alen s ess maximum esponse su ace e sus la ge adius and hickness. A consequence o obse ing he p e ious igu e is ha he inc ease in he g ea e adius dec eases mo e he maximum equi alen s ess han he inc ease o hickness. So, he mos decisi e is o inc ease he adius. Ano he aspec ha can be isually ex ac ed is ha many o he di e en con igu a ions a e below he elas ic limi (270 MPa). So, he goal now is o ge as li le as possible o modi y he concep ual design so as no o exceed he elas ic limi . Fi s , he op ion o modi y he hickness is ejec ed, since i has li le in luence. Second, modi y he adius by in e pola ions o he p e ious cu e o ob ain an op imal esul . These in e pola ions a e made wi h ANSYS, which, like a 3D cu e, can show a cu e wi h he only in luence o he g ea e adius. In his cu e maximum s ess – g ea e adius; he op imal poin is sough . As a esul o hese in e pola ions i is ob ained ha a adius o 30 mm can p o ide a good beha io inc easing his dimension only 5 mm. The expec ed esul is only an in e pola ion, so o be su e ha he beha io is as expec ed is necessa y o pe o m 37 S uc u al assessmen o he ITER Fas -Ion Loss De ec o he s a ic analysis wi h hese condi ions. The esul s o he equi alen Von-Misses s ess a e shown in Figu e 30. Figu e 30. S ess dis ibu ion in FILD (P oposed design) As can be seen in he p e ious igu e, he maximum s ess has dec eased o below 200 MPa wi h only an inc ease o 5 mm adius. No only he maximum s ess in he s ess concen a o has dec eased, bu in he cylinde 2 he s esses a e in a ange be ween 100 and 150 MPa (app oxima ely). This esul is good o s uc u al in eg i y because wi h a p oposed change o 16,7% in he adius o cylinde 2, he maximum s ess has been educed by 32,7%, lea ing i o ally ou o isk o en e ing he plas ic zone. To comple e he compa ison be ween he concep ual and p oposed design, Figu e 31 shows he o al de o ma ion esul s in FILD bo h in o oidal iew (Figu e 31 – a) and in adial iew (Figu e 31 – b). a) To al de o ma ion ( o oidal iew) b) To al de o ma ion ( adial iew) Figu e 31. To al de o ma ion in FILD (P oposed design) S uc u al analysis o FILD 38 The esul s o he o al de o ma ions a e also a o able. Wi h his change, he maximum de o ma ion has been educed by almos 50%. A de o ma ion o 1 cm is o ally accep able and no mal in his ype o de ices. In ac , in he p elimina y design o he Uppe Launche (PBS 52.U#. P) simila de o ma ions a e ob ained [21]. 4.4 Halo cu en loads analysis In his sec ion he s a ic analysis o FILD will be ca ied ou o ensu e he s uc u al in eg i y agains o he loads gene a ed by Halo cu en s. Then, he di e en aspec s o he model (meshing, bounda y condi ions) will be discussed be o e commen ing on he esul s. Be o e going in o de ail explaining he mesh and he bounda y condi ions, i is necessa y o explain an impo an de ail o his load case. The loads calcula ed in chap e 3 o Halo cu en s, a dis ibu ed load o a alue o 14,4 kN/m, a e so la ge ha hey gene a e s esses ha indica e ha he de ice is no capable o suppo ing his load (app oxima ely 9000 MPa). Gi en his esul , making changes in he design, as in he p e ious sec ion, does no p o ide any subs an ial ad an age ha causes he s esses o app oach he elas ic limi . The e o e, he solu ion p oposed is o ake in o accoun he ixed pa o ein o ce he sys em, so ha when FILD is de o med, he e is a con ac ha helps esis s esses. This con ac will be made h ough a ing on he body o FILD. Figu e 32 shows he geome y o he ixed pa and he con ac ing. a) FILD CAD model gene al iew 39 S uc u al assessmen o he ITER Fas -Ion Loss De ec o b) C oss sec ion in he medium plane. Uni s in mm. Figu e 32. FILD CAD model (wi h ixed pa ) This change in he model b ings wi h i se e al consequences, among which is he exis ence o a con ac ha makes he p oblem non-linea and modeling he union o he mo able and ixed pa . This is explained in he bounda y condi ions, bu be o e i is impo an o desc ibe he mesh. 4.4.1 Mesh Including he ixed pa in he model means ha he mesh is made o his pa . The meshing philosophy is he same as in he p e ious sec ion, using hexahed al elemen s. On he o he hand, he s a egy is di e en , mainly due o he exis ence o a non-linea con ac p oblem. I he mesh was a e y impo an aspec in he analysis o he p e ious sec ion (linea ), in a non-linea p oblem i is much mo e, no only o cap u ing he esul p ope ly, bu also o he con e gence o a solu ion. In addi ion, compu ing ime is inc eased by he use o i e a i e me hods. Fo hese easons, he meshing s a egy has been he ollowing: • Use a la ge mesh size on he ixed pa . The esul s in his pa a e no he main objec o s udy, so knowing exac ly he s ess dis ibu ion in his elemen would inc ease he compu a ional cos . • Re ine he mesh size in he s ess concen a o 2. I is known ha he mos con lic i e a ea is he s ess concen a o ; he e o e, a ine mesh has been used in his place o co ec ly cap u e he maximum s ess. • A medium mesh size o he es o he body o FILD. To speed up he calcula ion ime, wi hou gi ing up a good esul . Figu e 33 shows he ype o mesh used in his model (61933 elemen s). Figu e 33. Mesh in Halo cu en model. S uc u al analysis o FILD 46 Figu e 42. Sensi i i y analysis o he mesh F om 50000 o 80000 elemen s app oxima ely, he e is a clea con e gence in which he s ess luc ua es a ound 1 MPa. The con e gence is ob ained o a smalle numbe o elemen s (wi h espec o he mesh o eddy cu en s model) hanks o he op imiza ion o he mesh, wi h a e y e ined mesh in he s ess concen a o , medium size in he body o FILD and la ge size in he ixed pa . Wi h his esul i is concluded ha he mesh used in he las s a ic analysis is alid because i is wi hin he con e gence ange, al hough i a sligh ly hicke mesh is used i could dec ease he calcula ion ime and ob ain a eliable esul . In o de o con inue wi h he design and ha he de ice can esis he loads, he p ocedu e ou lined in he design o FILD in he case o eddy cu en loads is ollowed. In his case he only pa ame e o s udy is he ou e adius, keeping he hickness ixed since i adds weigh and does no in luence as much as he adius. Main aining he same idea as in he con ac ing analysis, he ollowing s udy is based on s udying he s uc u al beha io o he sys em agains changes in he ex e nal adius. A hick mesh will be used o cap u e he beha io , and hen a he op imum poin i is e ined o ob ain a alid esul . The a ia ion ange is be ween a adius o 25 mm (concep ual design) and 40 mm (maximum modi ica ion conside ed o no subs an ially change he concep ual design). Figu e 43 shows he esul s o his analysis. 47 S uc u al assessmen o he ITER Fas -Ion Loss De ec o Figu e 43. Equi alen s ess maximum e sus la ge adius The in luence o he adius on he s esses ha occu is comple ely clea since i inc eases he ine ia o he weakes sec ion. The dec ease in he maximum s ess be ween he concep ual design and he maximum adius alue conside ed is app oxima ely 30 %. Howe e , e en o a adius o 40 mm he s esses ha a e expec ed a e s ill excessi e, a ound 320 MPa, bu wi h a hick mesh, which when e ined (en e ing he con e gence zone) will be expec ed o be mo e s esses. Fo hese easons, he ou e adius is se a 40 mm o ad ance he design, bu no comple e i , because i is necessa y o educe mo e he s ess. To know exac ly whe e he s esses occu and wi h wha alue a s a ic analysis is made wi h a su icien ly ine mesh o be in he con e gence zone (Figu e 44). Figu e 44. S ess dis ibu ion in FILD (40 mm la ge adius) S uc u al analysis o FILD 48 Figu e 44 shows a simila dis ibu ion o s esses wi h espec o he one ob ained p e iously in he concep ual design, wi h he di e ence o a lowe s ess peak (375 MPa). I should be no ed ha he s ess in he con ac as well as in he base o he suppo o he ixed pa has inc eased i s in luence, bu in no case i exceeds he s esses ha occu in he s ess concen a o 2 (only place whe e plas i ica ion exis s). Al hough he s ess peak occu s in a e y speci ic a ea, and no he en i e sec ion is plas i ied, i is con enien o educe he s ess in his a ea o con lic . Fo i , and because in gene al he s esses ha appea on he body o FILD a e e y accep able, he in luence o pa ame e s ha educe he s ess in a localized way will be s udied. These pa ame e s a e he ollowing: • S ess concen a o adius: This pa ame e is one o he mos in luen ial in he s ess ha is eached in a s ess concen a o and s ill emains a a low alue (7,5 mm) which can be inc eased o a maximum conside ed amoun o 15 mm and obse e he s uc u al beha io . • Thickness: The hickness o he a ea be ween he s ess concen a o and he con ac o he wo pa s can in luence ha he e is a g ea e concen a ion o s esses in he cu a u e. In o de o be e dis ibu e he s esses in his a ea, he inc ease in hickness om 8 mm o 15 mm will be s udied. This s udy is ca ied ou by means o he esponse su ace o he maximum s ess (z-axis) in on o hese wo pa ame e s (Figu e 45). Figu e 45. Equi alen s ess maximum esponse su ace e sus s ess concen a o adius and hickness. The i s consequence o his s udy is ha i can be de e mined ha he adius o he s ess concen a o in luences mo e han he hickness o educe he s ess. Ano he consequence is ha a la ge pa o he su ace is below he 270 MPa limi . Any poin ha could p o ide a maximum s ess alue o less han 270 MPa could be ob ained, bu because wi h li le a ia ion o he wo pa ame e s he esul is much imp o ed, he maximum alue (15 mm) has been chosen o hese a iables (a ound 220 MPa o maximum equi alen s ess). Figu e 46 shows he s ess dis ibu ion o his con igu a ion. 49 S uc u al assessmen o he ITER Fas -Ion Loss De ec o Figu e 46. S ess dis ibu ion in he p oposed inal design The simula ion shows a peak s ess o 221 MPa which is signi ican ly below he c i ical 3Sm alue o 270 MPa. I can be obse ed how he s ess is dis ibu ed mo e in he con ac and in he suppo o he ixed pa . Finally, a alid model has been ob ained ha suppo s he loads applied wi h a wide ma gin o sa e y o a oid plas i ica ion. Bu he e is one inal aspec o keep in mind: The sepa a ion be ween he con ac ing and he ixed pa is 1 mm, while he own weigh o FILD, in his las con igu a ion gene a es a lexion o app oxima ely 2 mm (Figu e 47) which would cause a pe manen con ac which is no allowed because i exis s ela i e mo emen in acuum o change om he measu emen posi ion o a pa king posi ion (i is allowed in case o loads o Halo cu en s). Figu e 47. De o ma ion gene a ed by own weigh To sol e his p oblem, i is p oposed o ex end he diame e o he ixed pa o a alue g ea e han 2 mm, so ha FILD’s own weigh does no cause pe manen con ac . Inc easing he diame e leads o an inc ease in he s esses since he e is a longe ime when he loads a e only suppo ed by FILD, he e o e a con igu a ion is p oposed so ha he e is a sepa a ion o 4 mm. S uc u al analysis o FILD 50 Figu e 48. S ess dis ibu ion in p oposed inal design (Gap 4 mm) In he p e ious igu e i can be seen he dis ibu ion o s esses in his con igu a ion. The peak s ess ha occu s in he ol age concen a o 2 is 277 MPa, so he e is a small plas i ica ion in a e y small and supe icial a ea. Fo mo e de ail in Figu e 49 he mos a ec ed a ea is shown. a) De ail 1 o he plas i ied zone b) De ail 2 o he plas i ied zone Figu e 49. De ails o he plas i ied zone Taking in o accoun he low plas i ica ion alue (Figu e 48), he small plas ic a ea (Figu e 49 – a) and he li le pene a ion in he hickness (Figu e 49 – b), i can be concluded ha he only phenomenon ha can occu is a small pe manen de o ma ion a he su ace le el, which will also gene a e a ha dening by de o ma ion a oiding successi e pe manen de o ma ions. Fo hese easons, a alid design is conside ed s uc u ally and unc ionally since i a oids he pe manen con ac gene a ed by he own weigh . Finally, he de o ma ions ha occu in his model a e shown in igu e 50 below. 51 S uc u al assessmen o he ITER Fas -Ion Loss De ec o Figu e 50. De o ma ion in p oposed inal design (Gap 4 mm) The de o ma ions ha occu a e la ge in gene al, wi h a peak o abou 3 cm. Bu conside ing he alue o he loads o which FILD is exposed and ha i is a can ile e o 2 m, hese de o ma ions a e conside ed admissible. 53 5 CONCLUSIONS 5.1 Conclusions S a ing om he objec i e o his mas e hesis, he s uc u al design o FILD agains he loads gene a ed by elec omagne ic dis up ions in ITER, he ollowing conclusions a e ob ained: • A design capable o suppo ing he loads gene a ed by Halo cu en s has been p oposed modi ying he concep ual design as li le as possible. This design esis , in addi ion, he case o loading by eddy cu en s, less se e e, since he inal design p oposed o Halo cu en s, includes he p oposed design o he case o Eddy cu en s. • A design is p oposed no only wi h good s uc u al in eg i y, bu also unc ional. The pe manen con ac in acuum is no allowed, so aking in o accoun ha he concep ual design o FILD de lec s 15 mm and in he inal design 2 mm by he own weigh , has been sol ed inc easing he slack be ween he mo able and ixed pa . • Models ha e been gene a ed o calcula e induced elec omo i e o ce, induced in ensi y and applied momen s in de ices such as FILD. In addi ion, hese models ha e been mo ed o ano he FILD cu en ly being designed o he okamak JT 60-SA (Japan). • Th oughou he de elopmen o his p ojec , knowledge o he gene al ope a ion o ITER, i s componen s, diagnos ic sys ems and, in pa icula FILD has been acqui ed. Ano he objec i e ul illed is o unde s and he loads ha ac on in e nal componen s o de elop he necessa y models. • The expansion o knowledge o he ANSYS ool, so impo an in he ield o mechanical enginee ing and design, as well as he de elopmen o a simula ion ool ha can be adap ed o u u e design easily. 5.2 Fu u e wo ks ITER includes many es ic ions and he design p ocess is e y complex. Cu en ly he design is in concep ual phase so he es ima es made a e alid, bu i is necessa y o co obo a e hem wi h o he me hods. F om his p esen ed model, se e al lines o wo k a e opened: • Check he es ima ion o elec omagne ic loads due o dis up ion e en s by ob aining a 3D map o o ces (in an Equa o ial Po Plug) and in e pola ing he model in his egion. This map can be ob ained om a p e ious solu ion o a dedica ed elec omagne ic analysis ca ied ou by o he g oups, o by ca ying ou he s udy i sel in he egion o in e es . • Deepen he knowledge o Halo cu en s. The e a e con lic ing opinions abou he exis ence o Halo cu en s in his ype o de ices, one o he wo s load case. In addi ion, mo e de ailed s udies can be ca ied ou on he e ac ion sys em and i i is able o p e en Halo cu en s om en e ing FILD. • Weigh op imiza ion. The weigh o he se o he ixed and mo able pa is a ound 167 kg. I is an imp o able weigh o a can ile e o 2 m so an impo an aspec o in es iga e in he u u e is o ealize a ligh ened design ha p ope ly suppo s he loads. • Check he design in o he loads cases. The p oposed design co ec ly suppo s elec omagne ic loads, bu he same canno be said abou o he cases o loads, such as seismic. So, o ca y ou an analysis o he p oposed design in on o an ea hquake, o mo emen s o he Vacuum Vessel du ing a VDE would be an in e es ing wo k. 55 REFERENCES [1] Wo ld Ene gy Council, "Wo ld Ene gy Scena ios 2016," 2016. [2] U.S. Ene gy In o ma ion Adminis a ion, "In e na ional Ene gy Ou look 2017," 2017. [3] J. 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