ZAKLJUČNO POROČILO O REZULTATIH OPRAVLJENEGA RAZISKOVALNEGA DELA NA PROJEKTU V OKVIRU CILJNEGA RAZISKOVALNEGA PROGRAMA (CRP) »KONKURENČNOST SLOVENIJE 2006 - 2013« I. Predstavitev osnovnih podatkov raziskovalnega projekta 1. Naziv težišča v okviru CRP: 5.8.1. Varnostna vprašanja tehnologij jedrskih in sevalnih objektov 2. Šifra projekta: V2-0553 3. Naslov projekta:_ Razvoj potrebnih znanj za spremljanje, ovrednotenje in nadzor obvladovanja staranja jedrskih objektov 3. Naslov projekta 3.1. Naslov proj ekta v slovenskem j eziku:_ Razvoj potrebnih znanj za spremljanje, ovrednotenje in nadzor obvladovanja staranja jedrskih objektov 3.2 Naslov projekta v angleškem jeziku:_ Development of knowledge, indispensable for evaluation, assessment and surveillance of ageing management in nuclear facilities 4. Ključne besede projekta 4.1. Ključne besede projekta v slovenskem jeziku:_ upravljanje z znanji, obvladovanje staranja, jedrski objekti, jedrska varnost 4.2 Ključne besede projekta v angleškem jeziku:_ Knowledge management, ageing management, nuclear facilities, nuclear dafety Obrazec ARRS-RPROJ-CRP-KS-ZP-2010 Stran 1 od 11 5. Naziv nosilne raziskovalne organizacije: Institut "Jožef Stefan" 5.1. Seznam sodelujočih raziskovalnih organizacij (RO): 6. Sofinancer/sofinancerji : MOP, Uprava za jedrsko varnost Republike Slovenije 7. Šifra ter ime in priimek vodje projekta: 07025 prof. dr. Leon Cizelj Datum: 15.9.2010 Podpis vodje projekta: Podpis in žig izvajalca: prof. dr. Leon Cizelj prof.drJadran Lenarčič direktor Obrazec ARRS-RPROJ-CRP-KS-ZP-2010 Stran 2 od 11 II. Vsebinska struktura zaključnega poročila o rezultatih raziskovalnega projekta v okviru CRP 1. Cilji projekta: 1.1. Ali so bili cilji projekta doseženi? M a) v celoti □ b) delno □ c) ne Če b) in c), je potrebna utemeljitev. _ Cilji projekta so v celoti doseženi. Štejemo, da so preseženi, še posebej na področju upravljanja z znanjem. V času projekta smo namreč pripravili monografijo in dve poglavji v monografijah pri priznanih mednarodnih založbah (več v tč 6 tega poročila).. 1.2. Ali so se cilji projekta med raziskavo spremenili? I | a) da ^ b) ne Če so se, je potrebna utemeljitev:_ Obrazec ARRS-RPROJ-CRP-KS-ZP-2010 Stran 3 od 11 2. Vsebinsko poročilo o realizaciji predloženega programa dela1:_ 1. sklop: Znanja za obvladovanje staranja Pomembnost prehodnih pojavov za utrujanje smo ocenjevali na primeru razslojenega toka v prelivnem vodu tlačnika. Razslojeni tok sodi med najpomembnejše prispevke k utrujanju tlačne meje reaktorskega hladila. Na konkretnih primerih smo s pomočjo realističnih podatkov ocenili pomembnost, potrebno natančnost in pogostost meritev temperatur na zunanji površini prizadetega cevovoda. Pomembnost, potrebno natančnost in potrebno pogostost meritev smo ocenili s pomočjo analitičnih rešitev in numeričnih simulacij z metodo končnih elementov. Podrobni opisi in zaključki so zbrani v treh delovnih poročilih ([COBISS.SI-ID 22545191], [COBISS.SI-ID 22545447], in[COBISS.SI-ID 22545703]), dveh konferenčnih prispevkih ([COBISS.SI-ID 23179047], [COBISS.SI-ID 23660839]) in članku v SCI reviji [COBISS.SI-ID 23572007]. Okrepljeno sodelovanje v mednarodnih projektih s področja staranja jedrskih objektov na kratko opisujemo v nadaljevanju. NULIFE V evropski mreži odličnosti NULIFE (6. Okvirni program EURATOM) so zbrani pomembnejši industrijski in raziskovalni akterji na področju obvladovanja staranja jedrskih objektov. IJS koordinira izmenjavo doktorskih študentov med partnerji, kar sodi med pomembnejše aktivnosti mreže. Neposredno smo sodelovali pri naslednjih izmenjavah: mag. Mitja Uršič iz IJS v IRSN, David Gonzalez iz Materials Performance Centre Univerze v Manchestru v IJS in Stefan Heussner iz Areva v IJS. Posredno pa smo sodelovali pri organizaciji približno 10 izmenjav. Mreža odličnosti NULIFE prerašča v neprofitno združenje, pri čemer z več kot 50 partnerji mreže aktivno sodelujemo. ICONE International Conference on Nuclear Engineering (ICONE) sodi med v industriji najodmevnejše mednarodne konference na področju jedrske tehnike. Soorganizirajo jo ameriško (ASME) in japonsko (JSME) združenje strojnih inženirjev in kitajsko jedrsko združenje (CNS). Pri organizaciji kot kot »track co-chair«, torej so-predsedujoča tematskim sklopom konference že nekaj let sodelujeva L. Cizelj »Structural integrity« in I. Kljenak »Advanced Reactor Designs«. V obdobju tega projekta smo izpeljali konferenci ICONE 17 (Bruselj, julij 2009, več kot 800 udeležencev iz vseh kontinentov) in ICONE 18 (Xi'An, Kitajska, maj 2010, več kot 1000 udeležencev). Trenutno pa so v teku priprave za ICONE 19 (maj 2011, Makuhari, Japonska). Vzporedno s konferenco nastajajo tudi strokovni odbori ASME na področju jedrskega inženirstva, ki jih »track co-chairs« organiziramo in jim tudi sopredsedujemo. 1 Potrebno je napisati vsebinsko raziskovalno poročilo, kjer mora biti na kratko predstavljen program dela z raziskovalno hipotezo in metodološko-teoretičen opis raziskovanja pri njenem preverjanju ali zavračanju vključno s pridobljenimi rezultati projekta. Obrazec ARRS-RPROJ-CRP-KS-ZP-2010 Stran 4 od 11 ENEN Združenje ENEN (European Nuclear Education Network) je združenje, ki evropske univerze in inštitute z jedrskim program povezuje med sabo in z jedrskimi deležniki. Združenje predvsem pospešuje mednarodno sodelovanje pri magistrskem študiju jedrske tehnike. Podeljuje tudi naziv »evropski magister jedrske tehnike«, ki ga ima že več kot 40 diplomantov. V upravnem odboru združenja aktivno deluje L. Cizelj. Med 4. in 6.03.2010 smo v v Ljubljani izpeljali sestanek upravnega odbora in skupščino združenja. Del dogodkov v sklopu skupščine je bila tudi okrogla miza z naslovom »Strategija izobraževanja in usposabljanja za potrebe povečane proizvodnje jedrske energije«, na kateri so sodelovali prof. dr. Joseph Safieh, European Nuclear Engineering Network, Pariz, Francija, dr. Keiko Hanamitsu, International Atomic Energy Agency, Dunaj, Avstrija, dr. FranckWastin, Skupni raziskovalni center Evropske komisije, Bruselj, Belgija, dr. David Gilchrist, Ente Nazionale per l'Energia eLettrica, Rim, Italija, dr. Andrej Stritar, Uprava Republike Slovenije za jedrsko varnost, Ljubljana, Slovenija in dr. Georges Van Goethem, Direktorat za raziskave Evropske komisije, Bruselj, Belgija OECD/NEA Udeležili smo se delavnice »Commendable Practices for the Safe, Long Term Operation of Nuclear Reactors - OECD/NEA Stress Corrosion Cracking and Cable Ageing Project (SCAP)« in srečanja »International symposium on ageing management of the NPP (ISAG2010)« (Tokia, Japonska, maj 2010). Na srečanjih so bili predstavljeni rezultati mednarodnih raziskovalnih projektov, ki jih je na področju staranja opreme in kablov jedrskih elektrarn financirala japonska uprava za jedrsko varnost (NISA), izpeljal pa jih je mednarodni konzorcij pod pokrovitelj stvom OECD/NEA. Organizirali in izpeljali smo mednarodno konferenco Nuclear Energy for New Europe 2009 (Bled, Slovenija, september 2009)z več kot 200 registriranimi udeleženci iz 30 držav. 2. sklop: Varnostna vprašanja Razvijali smo uporabo metod za modeliranje staranja v verjetnostnih varnostnih analizah. Pri tem nas je zanimala predvsem primerjava vključitve modelov staranja v začetne dogodke dreves odpovedi z vključitvijo modelov staranja v najkrajše poti odpovedi, ki so rezultati analize dreves odpovedi. Razvijali smo nadgradnjo modelov staranja v okviru verjetnostnih analiz z mislimi na optimizacije preizkušanja in vzdrževanja. Sodelovali smo z Institute for Energy iz Pettna na Nizozemskem. Delo smo predstavili na mednarodnih konferencah ter ga objavili v njihovih zbornikih in v reviji s SCI faktorjem. Rezultat dela je članek o staranju in verjetnostnih varnostnih analizah v reviji s faktorjem vpliva, ki vključuje razvoj metode za upoštevanje staranja v verjetnostnih analizah (M. Čepin, A. Volkanovski, Consideration of ageing within probabilistic safety assessment models and results, Kerntechnik (1987), vol. 74, no. 3, pp. 140-149, 2009. [COBISS.SI-ID 22601767]. Vključuje tudi način in vpliv vključitve zanesljivosti pasivnih komponent in sistemov v verjetnostne varnostne analize. Proučevali smo vpliv staranja, ki lahko spremeni zanemarljivo majhnost prispevka zanesljivosti pasivnih komponent in sistemov k rezultatom verjetnostnih varnostnih analiz. Najpomembnejša ugotovite glede vključitve pasivnih sistemov je ta, da glede prispevka k frekvenci poškodbe sredice ne prispevajo veliko ali pa skoraj nič, lahko pa imajo pasivni sistemi visoke faktorje povečanja tveganja, kar pomeni, da niso tako zanemarljivi, kot na prvi pogled kaže le merilo tveganja: frekvenca poškodbe sredice._ Obrazec ARRS-RPROJ-CRP-KS-ZP-2010 Stran 5 od 11 Razvijali smo metodo za izboljšano modeliranje varnostnih sistemov, kjer je s kombiniranimi modeli možno modelirati več konfiguracij istih sistemov, več funkcij teh sistemov in več obratovalnih stanj elektrarne. Delo smo podkrepili realnimi analizami za jedrsko elektrarno v Krškem, s katero smo sodelovali pri modifikaciji verjetnostnih varnostnih analiz. Rezultat dela je referat o opisu metode namenjene združitvi obravnavanja načinov delovanja elektrarne (M. Čepin, R. Prosen, Probabilistic safety assessment for other modes than power operation, V: Safety, reliability and risk analysis: theory, methods and applications : proceedings of the European Safety and Reliability Conference, ESREL 2008, and 17th SRA-Europe, Valencia, Spain, September 22-25, 2008, Sebastián Martorell, ur., C. Guedes Soares, ur., Julie Barnett, ur., Boca Raton ... [etc.], CRC Press, 2009, zv. 4, pp. 2883-2889. [COBISS.SI-ID 22036007]. Rezultati kažejo, da so merila tveganja večinoma nižja za stanje obratovanja na nizki moči, za stanje v pripravljenosti in za stanje v vroči zaustavitvi, če jih primerjamo z merili tveganja s stanjem na moči. Poleg tega smo analizirali posebej vpliv človeških akcij v okviru primerjav verjetnostnih varnostnih analiz za različna stanja elektrarne. Rezultati dela so objavljeni v referatu na mednarodni konferenci (M. Čepin, Human reliability analysis within probabilistic safety assessment for other modes than power operation, V: Challenges to PSA during the nuclear renaissance, PSA 2008, International Topical Meeting on Probabilistic Safety Assessment & Analysis September 7 - 11, 2008 Knoxville, Tennessee, TN, [S. l.], American Nuclear Society, 2008, 8 pp. [COBISS.SI-ID 22034727]. Glavna ugotovitev je ta, da je prispevek človeških akcij k tveganju večji za ostala omenjena stanja elektrarne: stanje obratovanja na nizki moči, stanje v pripravljenosti in stanje v vroči zaustavitvi, v primerjavi s stanjem obratovanja na moči. Analizirali smo izboljšano izračunavanje prispevka človeškega faktorja v kompleksnih sistemov k tveganju. Osredotočili smo se na vplive medsebojnih odvisnosti med človeškimi akcijami in na napredovanje negotovosti od determinističnih analiz do verjetnostnih varnostnih analiz. Obravnavanje medsebojne odvisnosti je izjemno subjektivno in njegovo ocenjevanje je povezano z velikimi negotovostmi. Napredovanje negotovosti od determinističnih do verjetnostnih varnostnih analiz smo preverili na izbranih človeških akcijah v zvezi z izbranimi scenariji varnostnih analiz jedrske elektrarne. Del aktivnosti je potekal v sodelovanju z Nuclear Regulatory Commission iz ZDA. Rezultat dela so članki v tuji reviji in v mednarodni reviji s faktorjem vpliva, kjer članki vključujejo opis razvoja in primerjave metod za vključevanje obnašanja človeka v PSA. Opis metode je v članku v tuji reviji (M. Čepin, IJS-HRA - a method for human reliability analysis, Asigurarea Calitatii, vol. 15, no. 57, pp. 21-27, 2009. [COBISS.SI-ID 23174183]. Razvito metodo smo analizirali in pri pregledu rezultatov in napredovanja vplivov podatkov skozi metodo do rezultatov ugotovili, da je pomembnost le majhnega števila človeških akcij velika. Pomembnost velikega števila človeških akcij je majhna, kar pomeni, da se je dobro osredotočiti le na nekaj najpomembnejših. Hkrati je prikazan pomen specifičnih parametrov človeških akcij, kjer se prav tako izkaže, da je le nekaj parametrov, ki po pomembnosti odstopajo. Rezultati dela so v mednarodni reviji s faktorjem vpliva (M. Čepin, Importance of human contribution within the human reliability analysis (IJS-HRA), Journal of Loss Prevention in the Process Industries, vol. 21, no. 3, pp. 268-276, 2008, [COBISS.SI-ID 20884775]._ Obrazec ARRS-RPROJ-CRP-KS-ZP-2010 Stran 6 od 11 Primerjava metod za analizo človeškega faktorja je v objavljenem referatu na mednarodni konferenci (M. Čepin, Risk comparison of methods for dependency determination within human reliability analisys, V: Proceedings : an IAPSAM conference, PSAM 9, International Conference on Probabilistic Safety Assessment & Management, 18-23 May 2008, Hong Kong, China, Tsu-Mu Kao, ur., Enrico Zio, ur., Vincent Ho, ur., Hong Kong, Edge Publication Group Limited, 2008, 8 pp. [COBISS.SI-ID 21796135]. Glavna ugotovitev je v tem, da zaradi velikih subjektivnosti, ki so vključene v metode za analizo zanesljivosti človeka in v medsebojne odvisnosti med človeškimi akcijami, rezultati različnih metod dajejo za enake človeške akcije precej različne vrednosti verjetnosti človeških napak. Med izvajanjem projekta smo dobili še pametne ideje, ki jih je bilo vredno raziskati (to ni bilo čisto predvideno v projektu, pa dodajamo, ker je pomemben prispevek na področju). Raziskovali smo vpliv negotovosti na rezultate verjetnostnih varnostnih analiz. To pomeni proučevati zadevo, ki je izjemno kompleksna. Vpliv negotovosti na rezultate verjetnostnih varnostnih analiz smo prikazali na primerih povezave determinističnih in verjetnostnih varnostnih analiz, za kar je bilo tudi v tujini kar nekaj zanimanja (A. Prošek, M. Čepin, Success criteria time windows of operator actions using RELAP5/MOD3.3 within human reliability analysis, Journal of Loss Prevention in the Process Industries, vol. 21, no. 3, pp. 260-267, 2008. [COBISS.SI-ID 21594151]. ESREL International conference on Safety and Reliability sodi med najbolj industrijsko znanstveno povezane konference s področja varnosti in zanesljivosti. Organizira jo združenje ESRA (European safety and Reliability Association), kjer M. Čepin vodi področje Kvantitativne analize tveganja (Quantitative Risk Analysis). Pri organizaciji konferenc in pri njihovi izpeljavi aktivno sodelujemo pri izbiri referatov in pripravi programa ter pri vodenju sekcij. Primer ESREL 2008: M. Čepin (Koordinator tehničnega področaj - Technical Area Coordinator). Primer ESREL 2009: M. Čepin (Odgovorna oseba tehničnega področja - technical area responsible), A. Volkanovski (član programskega odbora - Technical Programme Committee). Primer ESREL 2010: A. Volkanovski (član programskega odbora - Technical Programme Committee). Obrazec ARRS-RPROJ-CRP-KS-ZP-2010 Stran 7 od 11 3. Izkoriščanje dobljenih rezultatov: 3.1. Kakšen j e potencialni pomen2 rezultatov vašega razi skovalnega proj ekta za: I | a) odkritje novih znanstvenih spoznanj; I I b) izpopolnitev oziroma razširitev metodološkega instrumentarija; 1X1 c) razvoj svoj ega temelj nega razi skovanj a; I I d) razvoj drugih temeljnih znanosti; 1X1 e) razvoj novih tehnologij in drugih razvojnih raziskav. 3.2. Označite s katerimi družbeno-ekonomskimi cilji (po metodologiji OECD-ja) sovpadajo rezultati vašega raziskovalnega projekta: I I a) razvoj kmetijstva, gozdarstva in ribolova - Vključuje RR, ki je v osnovi namenjen razvoju in podpori teh dejavnosti; >3 b) pospeševanje industrijskega razvoja - vključuje RR, ki v osnovi podpira razvoj industrije, vključno s proizvodnjo, gradbeništvom, prodajo na debelo in drobno, restavracijami in hoteli, bančništvom, zavarovalnicami in drugimi gospodarskimi dejavnostmi; >3 c) proizvodnja in racionalna izraba energije - vključuje RR-dejavnosti, ki so v funkciji dobave, proizvodnje, hranjenja in distribucije vseh oblik energije. V to skupino je treba vključiti tudi RR vodnih virov in nuklearne energije; I | d) razvoj infrastrukture - Ta skupina vključuje dve podskupini: • transport in telekomunikacije - Vključen je RR, ki je usmerjen v izboljšavo in povečanje varnosti prometnih sistemov, vključno z varnostjo v prometu; • prostorsko planiranje mest in podeželja - Vključen je RR, ki se nanaša na skupno načrtovanje mest in podeželja, boljše pogoje bivanja in izboljšave v okolju; >3 e) nadzor in skrb za okolje - Vključuje RR, ki je usmerjen v ohranjevanje fizičnega okolja. Zajema onesnaževanje zraka, voda, zemlje in spodnjih slojev, onesnaženje zaradi hrupa, odlaganja trdnih odpadkov in sevanja. Razdeljen je v dve skupini: I | f) zdravstveno varstvo (z izjemo onesnaževanja) - Vključuje RR - programe, ki so usmerjeni v varstvo in izboljšanje človekovega zdravja; I | g) družbeni razvoj in storitve - Vključuje RR, ki se nanaša na družbene in kulturne probleme; >3 h) splošni napredek znanja - Ta skupina zajema RR, ki prispeva k splošnemu napredku znanja in ga ne moremo pripisati določenim ciljem; I | i) obramba - Vključuje RR, ki se v osnovi izvaja v vojaške namene, ne glede na njegovo vsebino, ali na možnost posredne civilne uporabe. Vključuje tudi varstvo (obrambo) pred naravnimi nesrečami. 2 Označite lahko več odgovorov. Obrazec ARRS-RPROJ-CRP-KS-ZP-2010 Stran 8 od 11 3.3. Kateri so neposredni rezultati vašega raziskovalnega projekta glede na zgoraj označen potencialni pomen in razvojne cilje?_ Okrepljena kadrovska struktura Okrepljene mednarodne raziskovalne in poslovne povezave 3.4. Kakšni so lahko dolgoročni rezultati vašega raziskovalnega projekta glede na zgoraj označen potencialni pomen in razvojne cilje?_ Ohranjena in okrepljena odličnost raziskovanja Odlična strokovna podpora industriji in upravnim organom doma in v tujini 3.5. Kje obstaj a verj etnost, da bodo vaša znanstvena spoznanj a deležna zaznavnega odziva? >3 a) v domačih znanstvenih krogih; >3 b) v mednarodnih znanstvenih krogih; >3 c) pri domačih uporabnikih; >3 d) pri mednarodnih uporabnikih. 3.6. Kdo (poleg sofinancerjev) že izraža interes po vaših spoznanjih oziroma rezultatih? Industrijski člani mreže odličnosti NULIFE Člani združenja ENEN 3.7. Število diplomantov, magistrov in doktorjev, ki so zaključili študij z vključenostjo v raziskovalni projekt?_ 1 magisterij 1 diploma 4. Sodelovanje z tujimi partnerji: 4.1. Navedite število in obliko formalnega raziskovalnega sodelovanja s tujimi raziskovalnimi inštitucijami._ Mreža odličnosti NULIFE (Nuclear Plant Life Management, 6. okvirni program EURATOM), polnopravni član mreže Združenje ENEN (European Nuclear Education Network), član mreže, L. Cizelj član upravnega odbora Obrazec ARRS-RPROJ-CRP-KS-ZP-2010 Stran 9 od 11 APSA European Network, Use of PSA for evaluation of ageing effects to the safety of energy facilities, M. Čepin 4.2. Kakšni so rezultati tovrstnega sodelovanja?_ Okrepljena kadrovska struktura Okrepljene mednarodne raziskovalne in poslovne povezave Ohranjena in okrepljena odličnost raziskovanja Odlična strokovna podpora industriji in upravnim organom doma in v tujin 5. Bibliografski rezultati3 : Za vodjo projekta in ostale raziskovalce v projektni skupini priložite bibliografske izpise za obdobje zadnjih treh let iz COBISS-a) oz. za medicinske vede iz Inštituta za biomedicinsko informatiko. Na bibliografskih izpisih označite tista dela, ki so nastala v okviru pričujočega projekta. 3 Bibliografijo raziskovalcev si lahko natisnete sami iz spletne strani:http:/www.izum.si/ Obrazec ARRS-RPROJ-CRP-KS-ZP-2010 Stran 10 od 11 6. Druge reference4 vodje projekta in ostalih raziskovalcev, ki izhajajo iz raziskovalnega projekta:_ Monografija: L. Cizelj, I. Simonovski, Microstructurally Short Cracks in Polycrystalls Described by Crystal Plasticity, Nova Science Publishers, ZDA, ISBN 978-1-61668-811-0 https://www.novapublishers.com/catalog/product_info.php?products_id=14542 Poglavje v knjigi: L. Cizelj, G. Roussel, Reliability of Steam Generator Tubes, in Steam Generator Systems, ISBN 978-953-7619-X-X, Intechweb.org Poglavje v knjigi: M. Čepin, Probabilistic Safety Assessment and Risk-Informed Decision-Making, Nuclear Power", ISBN 978-953-7619-X-X, Sciyo Urejanje posebne številne revije Nuclear Engineering and Design B. Mavko, L. Cizelj, Y. Hassan: posebna številka revije Nuclear Engineering and Design, s 40 izbranimi in razširjenimi prispevki s konference Nuclear Energy for New Europe 2009. Članstvo v urednškem odboru znanstvene revije Reliability Engineering and System Safety (M. Čepin)_ 4 Navedite tudi druge raziskovalne rezultate iz obdobja financiranja vašega projekta, ki niso zajeti v bibliografske izpise, zlasti pa tiste, ki se nanašajo na prenos znanja in tehnologije. Navedite tudi podatke o vseh javnih in drugih predstavitvah projekta in njegovih rezultatov vključno s predstavitvami, ki so bile organizirane izključno za naročnika/naročnike projekta. Obrazec ARRS-RPROJ-CRP-KS-ZP-2010 Stran 11 od 11 IJS Delovno Poročilo IJS Report IJS-DP-10077 Izdaja 1, marec 2009 Revision 1, March 2009 Baza prehodnih pojavov v jedrski elektrarni Krško Data Base of Transients in Nuclear Power Plant Krško B. Zafošnik, L. Cizelj Ljubljana, marec 2009 Institut »Jožef Stefan«, Ljubljana, Slovenija Institut »Jožef Stefan«, Ljubljana, Slovenija Naročnik: Javna agencija za raziskovalno dejavnost Republike Slovenije Ordered by: Tivolska c. 30, Ljubljana Nuklearna elektrarna Krško d.o.o., Vrbina 12, 8270 Krško Izvajalec: Prepared by: Pogodba štev.: Contract Number: Nosilec naloge: Responsible Person: Naslov poročila: Report Title: Institut »Jožef Stefan« 1000 Ljubljana Jamova 39 Slovenija Odsek za reaktorsko tehniko (Reactor Engineering Division) Z2-9488-0106-06 (IJS in ARRS) U1-BL-R4-3/03 (IJS in NEK) dr. Boštjan Zafošnik, univ. dipl. inž. str. Baza prehodnih pojavov v jedrski elektrarni Krško Data Base of Transients in Nuclear Power Plant Krško Avtorji poročila: Authors: Dr. Boštjan Zafošnik, univ.dipl.inž.str. Prof. dr. Leon Cizelj, univ.dipl.inž.str. Štev. delovnega poročila: Report Number: Konto: Account Number: Kopije: Distribution: IJS-DP-10077 Izdaja 1 V2-0375-C > Naročnik (3) > Knjižnica/Library (1x) > Nosilec naloge/Responsible Person (1x) > Avtorji/Authors (1x) > Arhiv OR4/Archive (1x + original) Ljubljana, marec 2009 IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran i Institut »Jožef Stefan«, Ljubljana, Slovenija tZ POVZETEK V poročilu smo zbrali najpomembnejše vire informacij o projektnih in dejanskih prehodnih pojavih reaktorskega hladilnega sistema jedrske elektrarne v Krškem. Mednje sodijo projekt elektrarne z vsemi spremembami, procesni informacijski sistem elektrarne in lokalne meritve temperatur na zunanji površini nekaterih cevovodov. Opravili smo preliminarno analizo celovitosti in uporabnosti dostopnih podatkov o prehodnih pojavih za analize utrujanja komponent ter preliminarno primerjavo med izbranimi izmerjenimi in projektnimi prehodnimi pojavi. Izbrani izmerjeni prehodni pojavi so bili s stališča utrujanja ugodnejši od projektnih. Opredelimo najpogostejše težave pri interpretaciji podatkov, še posebej v primerih, ko o temperaturah hladila sklepamo na podlagi meritev na zunanji površini cevi. Nakazujemo tudi nekatere prijeme, s katerimi bi bilo mogoče manjkajoče podatke rekonstruirati. Poročilo predstavlja del rezultatov projekta »Zasnova metode za spremljanje izrabe komponent jedrskih elektrarn«, ki sta ga sofinancirala Javna agencija za raziskovalno dejavnost Republike Slovenije (pogodba št. 1000-07-219488) in Nuklearna elektrarna Krško d.o.o. (pogodba št. P0G-3408). IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran ii Institut »Jožef Stefan«, Ljubljana, Slovenija ABSTRACT The most relevant sources of information on design and actual transients of the reactor coolant system in Krško nuclear power plant are identified in the report. These include design documentation of the plant including all relevant design changes, plant process information system and local measurements of temperatures at the outer surface pf pipes. A preliminary analysis of consistency and applicability of the available transient data to the fatigue analyses has been performed, followed by a preliminary comparison of selected design and actual transients. Selected actual transients confirmed conservativity of design transients from the fatigue viewpoint. The most probable difficulties with interpretation of transient data in fatigue analyses have been identified with special emphasis on coolant temperatures deduced form the measured temperatures at the tube outside surface. Some approaches facilitating the reconstruction of the missing data are also highlighted. This report contains a part of the results of the project »Conception of a method for monitoring of the usage of nuclear power plant components«, cosponsored by the Slovene research Agency (grant No. 1000-07-219488) and Nuklearna elektrarna Krško d.o.o. (grant No. POG-3408). IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran iii Institut »Jožef Stefan«, Ljubljana, Slovenija KAZALO POVZETEK II ABSTRACT III KAZALO IV SEZNAM SLIK VI SEZNAM TABEL VII 1 UVOD 1 1.1 Namen poročila 1 1.2 Ozadje 1 1.3 Organizacija poročila 1 2 PROJEKTNI PREHODNI POJAVI V JE KRŠKO 2 2.1 Obratovalne obremenitve 2 2.1.1 Normalno obratovanje 2 2.1.2 Moteno obratovanje 2 2.1.3 Zasilno obratovanje 2 2.1.4 Nezgoda 3 2.2 Preizkusi 3 2.3 Projektni prehodni pojavi za primarni krog jedrske elektrarne Krško 3 2.4 Viri informacij o projektnih prehodnih pojavih jedrske elektrarne Krško 3 3 IZMERJENI PREHODNI POJAVI V JE KRŠKO 5 3.1 Globalno merjenje tlaka in temperature reaktorskega hladila 5 3.1.1 Ogrevanje elektrarne 6 3.1.2 Ohlajanje elektrarne 8 3.1.3 Ustavitev reaktorj a s polne moči 10 3.2 Lokalno merjenje temperature reaktorskega hladila 11 3.2.1 Turbulentna penetracija 11 3.2.2 Toplotno razslojeni tokovi 12 3.2.3 Meritve temperatur na zunanji površini stene cevi 13 3.2.4 Osnovne omejitve meritev na zunanji steni cevi 15 3.2.5 Vpliv prestopa toplote iz tekočine na cev 18 3.3 Rekonstrukcija manjkajočih podatkov 18 3.4 Prehodni pojavi, ki so se zgodili v NEK 19 IJS-DP-10077 Izdaja 1 Marec 2009 stran iv File. IJS-DP-10077-R1.doc Institut »Jožef Štefan«, Ljubljana, Slovenija 4 ZAKLJUČKI 20 5 VIRI 21 IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran v Institut »Jožef Stefan«, Ljubljana, Slovenija tZ SEZNAM SLIK Slika 1 Primer izmerjenega poteka temperatur med ogrevanjem elektrarne 6 Slika 2 Primer izmerjenega poteka tlaka v primarnem krogu med ogrevanjem elektrarne 7 Slika 3 Primerjava tlaka v primarnem krogu in tlaka nasičenja v tlačniku 7 Slika 4 Primer izmerjenega poteka temperatur med ohlajanjem elektrarne 8 Slika 5 Primer izmerjenega poteka tlaka v primarnem krogu med ohlajanjem elektrarne 9 Slika 6 Primer izmerjenega poteka temperatur med ustavitvijo reaktorja s polne moči 9 Slika 7 Primer izmerjenega poteka tlaka v primarnem krogu med ustavitvijo reaktorja s polne moči 10 Slika 8 Turbulentna penetracija iz glavnega cevovoda v stanski cevovod [9] 11 Slika 9 Razslojeni tok v horizontalni cevi 12 Slika 10 Značilne razporeditve merilnih elementov na zunanji površini cevi 13 Slika 11 Razporeditev senzorjev pri cevovodu za nadzor toplotnega šoka in stratifikacije cevi [10] 14 Slika 12 Primer izmerjenih temperature na zunanji površini prelivnega voda med zagonom elektrarne [10] 14 Slika 13 Stopničasta sprememba temperature iz 0 na 1 in nazaj na 0: a) enkratna in b) periodična 15 Slika 14 Maksimalna temperatura na zunanji površini kot funkcija debeline stene cevi a in normaliziranega časa trajanja At temperaturne spremembe na notranji površini cevi 16 Slika 15 Zakasnitev Amax med koncem temperaturne spremembe in pojavom maksimalne temperature Tmax na zunanji površini 17 Slika 16 Amplituda temperaturne spremembe na zunanji strani cevi glede na različne debeline cevi a in frekvenco spremembe temperature na notranji strani 17 IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran vi Institut »Jožef Stefan«, Ljubljana, Slovenija tZ SEZNAM TABEL Tabela 1 Projektni prehodni pojavi jedrske elektrarne Krško [13] 4 Tabela 2 Prehodni pojavi, ki so se zgodili v NEK 18 IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran vii Institut »Jožef Stefan«, Ljubljana, Slovenija 1 UVOD 1.1 Namen poročila V poročilu predstavljamo del rezultatov projekta »Zasnova metode za spremljanje izrabe komponent jedrskih elektrarn«, ki sta ga sofinancirala Javna agencija za raziskovalno dejavnost Republike Slovenije (pogodba št. 1000-07-219488) in Nuklearna elektrarna Krško d.o.o. (pogodba št. P0G-3408). Preostali rezultati projekta so predstavljeni v spremljajočih poročilih: • Zasnova metode za spremljanje izrabe komponent jedrskih elektrarn [1] in • Pilotni primeri izračuna faktorja utrujenostne izrabe [2]. 1.2 Ozadje Projektna trajnostna doba jedrskih elektrarn temelji na zbirki predpostavljenih projektnih dogodkov. Vsak izmed projektnih dogodkov v sistemih in komponentah elektrarne povzroči prehodne pojave s spremembami temperatur, tlakov in včasih tudi drugih obratovalnih parametrov. Prehodni pojavi torej povzročajo tudi spremembe napetosti v cevovodih in tlačnih posodah in s tem potencialno prispevajo k njihovemu utrujanju. Za natančno določevanje faktorjev izrabe posameznih komponent je torej natančno poznavanje prehodnih pojavov ključno. Pri tem imamo v mislih tako predpostavljene projektne prehodne pojave kot tudi izmerjene dejanske prehodne pojave. Hkrati je pomembno upoštevati tudi dejstvo, da ločljivost podatkov v projektu in v zapisih izmerjenih prehodnih pojavov praviloma zadoščata za popis večine enostavnejših stanj v sistemih in njihovih komponentah. V primeru nekaterih kompleksnejših pojavov, kot so npr. toplotno razslojeni tokovi, turbulentna penetracija v priključni cevovod s pretežno mirujočo tekočino in toplotni šok ([3], [4], [5], [6], [7], [8], [9]), so za pravilno karakterizacijo dogajanj in s tem obremenitev v cevovodih nujno potrebne podrobnejše lokalne meritve [3], [10]. Zanesljiva interpretacija lokalnih meritev ponavadi zahteva tudi razmeroma zahtevne analize izmerjenih vrednosti, še posebej v primerih, ko na temperaturo tekočine v cevi sklepamo na osnovi meritev temperatur na zunanji površini cevi [11]. Osnovni cilj pričujočega poročila sta identifikacija in preliminarna analiza celovitosti in uporabnosti dostopnih podatkov o prehodnih pojavih za analize utrujanja komponent. Nakazujemo tudi nekatere prijeme, s katerimi bi bilo mogoče manjkajoče podatke rekonstruirati. Pri tem se omejujemo na komponente reaktorskega hladilnega sistema. 1.3 Organizacija poročila V poglavju 2 opisujemo projektne prehodne pojave v reaktorskem hladilnem sistemu jedrske elektrarne Krško. Poglavje 3 predstavlja prehodne pojave, ki so jih v jedrski elektrarni Krško izmerili in so zabeleženi v procesno informacijskem sistemu. Opredelimo najpogostejše težave pri interpretaciji podatkov in nakažemo nekatere prijeme, s katerimi bi bilo mogoče manjkajoče podatke rekonstruirati. Poročilo se konča z zaključki v poglavju 4 in viri v poglavju 5. IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran 1 Institut »Jožef Stefan«, Ljubljana, Slovenija £ 2 PROJEKTNI PREHODNI POJAVI V JE KRŠKO Jedrske elektrarne so po ASME B&PV Code [12] projektirane za projektne, obratovalne in preizkusne obremenitve. Prehodni pojavi s spremembami obremenitev, predvsem temperature in tlaka, so sestavni delo obratovalnih in preizkusnih obremenitev, ki so podrobneje opredeljene v nadaljevanju. Projektne obremenitve so statične in kot takšne na utrujanje nimajo vpliva. 2.1 Obratovalne obremenitve V skladu z ASME B&PV Code [12] obratovalne obremenitve s spremljajočimi prehodnimi pojavi razdelimo v štiri skupine in sicer: • normalno obratovanje, • moteno obratovanje, • zasilno obratovanje in • nezgode. V nadaljevanju podrobneje opišemo vse štiri skupine. Tabela 1 podaja tudi vsa v projektu predvidene obratovalne dogodke skupaj z njihovim projektno predvidenim številom. Kontrola na utrujanje po ASME B&PV Code [12] izrecno zajema normalno in moteno obratovanje. Zasilno obratovanje pa je v kontrolo utrujanja vključeno le posredno in sicer z omejitvijo skupnega števila vseh obremenitvenih ciklov z amplitudo napetosti večjo od amplitude napetosti pri 106 obremenitvenih ciklih (Wohlerjeva krivulja) na največ 25. 2.1.1 Normalno obratovanje Normalno obratovanje zajema vsa stanja pri zagonu, obratovanju v predvidenem območju moči, vročo zaustavitev in zaustavljanje elektrarne, ki ne sodijo v moteno ali zasilno obratovanje ali med nezgode. 2.1 .2 Moteno obratovanje Moteno obratovanje zajema vsa stanja, ki odstopajo od normalnega obratovanja in se lahko zgodijo dovolj pogosto, da jih je elektrarna sposobna vzdržati brez kakršnihkoli poškodb. V moteno obratovanje sodijo predvsem tisti prehodni pojavi, ki so posledica enojne odpovedi opreme ali enojne napake operaterjev. Vzroke za moteno obratovanje je praviloma mogoče odpraviti brez zaustavitve elektrarne. V redkih primerih, ko je zaustavitev potrebna, pa zaradi posledic motenega obratovanja ne bo potrebno odpravljati poškodb na opremi. 2.1.3 Zasilno obratovanje Zasilno obratovanje je odstopanje od normalnega obratovanja, ki ga je mogoče odpraviti z zaustavitvijo elektrarne in zamenjavo oz. popravilom poškodovane opreme. Projektiranje opreme na tovrstne dogodke zagotavlja, da naključne okvare opreme ne bodo povzročile poškodb tlačne meje reaktorskega hladila. Skupno število predvidenih tovrstnih dogodkov v trajnostni dobi elektrarne naj bi povzročilo kvečjemu 25 obremenitvenih ciklov z amplitudo napetosti večjo od amplitude napetosti pri 106 obremenitvenih ciklih (Wohlerjeva krivulja). IJS-DP-10077 Izdaja 1 Marec 2009 stran 2 File. IJS-DP-10077-R1.doc Institut »Jožef Stefan«, Ljubljana, Slovenija 2.1.4 Nezgode Nezgode so kombinacije dogodkov izjemno nizkih verjetnosti, ki bi lahko ogrozile obratovalno sposobnost elektrarne, vodile do trajnih poškodb opreme in v izjemnih primerih vplivale tudi na varnost in zdravje okoliškega prebivalstva. Pri tovrstnih dogodkih je ključni cilj projekta varna ustavitev elektrarne, možnost morebitnega ponovnega zagona pa je prepuščena prihodnjim analizam in odločitvam upravnih organov. 2.2 Preizkusi V skladu z ASME B&PV Code [12] je opredeljenih več vrst preizkusov, ki dokazujejo predvsem celovitost tlačnih mej primarnega in sekundarnega hladilnega kroga ter obratovalno sposobnost turbine. Tabela 1 podaja vse v projektu predvidene prizkuse skupaj z njihovim projektno predvidenim številom. Kontrola na utrujanje po ASME B&PV Code [12] izrecno zajema obremenitve zaradi preizkusov. 2.3 Projektni prehodni pojavi za primarni krog jedrske elektrarne Krško Projektni dogodki oz. prehodni pojavi, ki jih je za 40 letno trajnostno dobo predvidel projekt jedrske elektrarne Krško, so skupaj s projektno predvidenim številom dogodkov zbrani v Tabeli 5.2-1 v [13] (Tabela 1 jih povzema). 2.4 Viri informacij o projektnih prehodnih pojavih jedrske elektrarne Krško Podrobnejši potek projektnih prehodnih pojavov opisujejo tudi dokumenti [13], [14], [15], [16], [17] in v njih citirani dokumenti. Pomembne informacije je mogoče dobiti tudi v projektnih specifikacijah in poročilih. V precejšnji meri so omenjeni v dokumentu [18]. Projektni prehodni pojavi so se v času obratovanja elektrarne nekajkrat spremenili. Kot največja mejnika sprememb omenjamo projektne analize, ki so omogočale obratovanje z začeplj enimi uparjalniki [14] in projektne analize ob zamenjavi uparjalnikov in hkratnem povečanju moči elektrarne [15], [16], [17]. Mogoče je torej pričakovati, da se bodo spreminjali tudi v bodočnosti. Pomembno je poudariti, da zbrani podatki podajajo dobro globalno sliko o predvidenem dogajanju v sistemih jedrske elektrarne. Praviloma pa so bili obratovalni prehodni pojavi in njihovo število v fazi projekta ocenjeni dokaj konzervativno in so opredeljeni do te mere, da je mogoče izpolniti projektne zahteve. Hkrati pa praviloma niso dovolj podrobni za natančno oceno lokalnih razmer v posameznih komponentah. Pogost primer tovrstne situacije je mešanje tekočin v spojih cevi. Že zmerne razlike v temperaturah in pretokih lahko vodijo v spremembe lokalnih napetosti, ki so s stališča utrujanja pomembne. V takšnem primeru lahko kompleksne termo-hidravlične robne pogoje določimo oz. rekonstruiramo s pomočjo računalniških programov za dinamiko tekočin. Začetne in robne pogoje za tovrstne simulacije lahko dobimo iz projektnih opisov prehodnih pojavov, podatkov iz procesnega informacijskega sistema in neposrednih meritev. Sodobna orodja praviloma omogočajo predvsem simulacijo povprečnih hitrosti fluidov in temperatur pri turbulentnih tokovih. V nekaterih primerih je mogoča tudi neposredna simulacija turbulentnih tokov; omejitev so predvsem izjemno dolgi računski časi. IJS-DP-10077 Izdaja 1 Marec 2009 stran 3 File. IJS-DP-10077-R1.doc Institut »Jožef Stefan«, Ljubljana, Slovenija tZ Prehodni pojav Število v projektu predvidenih dogodkov NORMALNO OBRATOVANJE Ogrevanje s 100°F (55.6 K) na uro 200 Ohlajanje s 100°F (55.6 K) na uro 200 Zvezno povečevanje moči s hitrostjo 5% polne moči na minuto 13200 Zvezno zmanjševanje moči s hitrostjo 5% polne moči na minuto 13200 Koračno povečanje moči za 10% polne moči 2000 Koračno zmanjšanje moči za 10% polne moč 2000 Veliko koračno zmanjšanje moči z dušenjem pare skozi turbinski obvod 200 Nihanja temperature in tlaka reaktorskega hladila (± 1.67°C, ± 0.17 MPa) 1.5105 Nihanja temperature in tlaka reaktorskega hladila (± 0.28°C, ± 0.041 MPa) 1.5106 Vbrizgavanje mrzle napajalne vode v uparjalnika v stanju vroče zaustavitve 2000 Obremenjevanje med 0% in 15% celotne moči 500 Razbremenjevanje med 0% in 15% celotne moči 500 Izenačevanje koncentracije borove kisline 26400 Menjava goriva 80 MOTENO OBRATOVANJE Izpad električnega bremena brez takojšnje zaustavitve reaktorja 80 Izpad zunanjega napajanja (z naravno cirkulacijo v reaktorskem hladilnem sistemu) 40 Delna izguba pretoka reaktorskega hladila zaradi izpada ene črpalke 80 Ustavitev reaktorja s polne moči brez ohlajanja 230 z ohlajanjem, brez varnostnega vbrizgavanja 160 z ohlajanjem, z varnostnega vbrizgavanjem 10 Nenamerno zmanjšanje tlaka reaktorskega hladila 20 Padec regulacijske palice 80 Nenamerna vključitev sistema za zasilno hlajenje sredice 60 Potres ob obratovanju (OBE, 20 potresov s po 10 cikli) 200 Prekomeren pretok napajalne vode 30 ZASILNO OBRATOVANJE Mala izlivna nezgoda 5 Mali zlom parovoda 5 Popolni izpad pretoka reaktorskega hladila 5 NEZGODA Velika izlivna nezgoda 1 Zlom glavnega parovoda 1 Zlom glavnega napajalnega cevovoda 1 Blokada rotorja črpalke reaktorskega hladila 1 Izmet regulacijske palice 1 Zlom cevi uparjalnika Potres ob varni ustravitvi (SSE) 1 PREIZKUSI Preizkus turbine 20 Tlačni preizkus primarnega sistema 10 Tlačni preizkus sekundarnega sistema 10 Preizkus netesnosti primarnega sistema 200 Preizkus netesnosti sekundarnega sistema 80 Preizkus netesnosti cevi uparjalnikov 800 Tabela 1 Projektni prehodni pojavi jedrske elektrarne Krško [13] IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran 4 Institut »Jožef Stefan«, Ljubljana, Slovenija 3 IZMERJENI PREHODNI POJAVI V JE KRŠKO 3.1 Globalno merjenje tlaka in temperature reaktorskega hladila V nadaljevanju na kratko opišemo meritve temperature in tlaka, ki jih opravlja originalna instrumentacija elektrarne predvsem v podporo varnemu obratovanju. Rezultate teh meritev zajema in hrani tudi procesni informacijski sistem v jedrski elektrarni Krško. Tovrstni podatki so posredno uporabni tudi pri analizah utrujenosti sistemov in komponent. Tlak reaktorskega hladila v jedrski elektrarni Krško merijo v vroči in hladni veji ter v tlačniku z induktivnimi tlačnimi tipali. Za merjenje temperature reaktorskega hladila uporabljajo uporovne merilne naprave RTD (Resistant Temperature Detectors), ki so nameščene v posebni zaščiti (angl. thermowell), ki ščiti merilno napravo, hkrati pa zmanjšuje možnost puščanja reaktorskega hladila. Merilno območje RTD naprav je med 0 in 400°C. Takšno območje merjenja je potrebno za merjenje temperature pri prehodnih pojavih in za izvajanje postopkov zaganjanja in zaustavitev elektrarne. Glede na posredovane podatke iz NEK, se bomo v nadaljevanju omejili na merjenje temperature hladila v vroči in hladni veji ter v prelivnem vodu in tlačniku. Temperaturo reaktorskega hladila merijo v obeh vročih in hladnih vejah [13]. V obeh vročih vejah reaktorsko hladilo zajamejo na približno polovici dolžine skozi po tri odjemna mesta, nameščena po obodu v razmiku 120° (TE-413 in TE-423). Cevi iz treh odjemnih mest se združijo in vodijo reaktorsko hladilo iz vsake izmed obeh vročih vej posebej skozi merilce temperature [13]. V obeh hladnih vejah hladilo zajamejo za črpalkama (TE-414 in TE-424, [13]). V prelivnem vodu merijo temperaturo hladila približno na polovici dolžine med vročo vejo in tlačnikom s potopljenim termometrom [13]. V tlačniku merijo temperaturo kapljevine (TE-608, v bližini grelcev) in temperaturo pare (TE-607) s potopljenima termometroma [13]. Posredne meritve v vroči in hladni veji zagotavljajo natančne meritve temperature hladila v vseh razmerah, kjer so spremembe temperature razmeroma počasne. Neposredno merjenje temperature (prelivni vod, tlačnik) pa zagotavlja razmeroma natančne meritve tudi v primeru hitrih sprememb v temperaturi hladila. Za zanesljivo oceno porazdelitve temperatur po notranji steni cevi, ki pri ocenah utrujanja predstavlja vhodni podatek, tovrstne meritve zadoščajo le v primeru velikih pretokov, torej v področjih hitrih in turbulentnih tokov. V vseh ostalih primerih je kompleksne termo-hidravlične robne pogoje smiselno določiti s pomočjo računalniških programov za dinamiko tekočin. Začetne in robne pogoje za tovrstne simulacije pa lahko dobimo iz izmerjenih vrednosti. Nekaj podatkov o spremembah temperature in tlaka pri obratovalnih dogodkih v jedrski elektrarni Krško, ki so bili zabeleženi s procesno informacijskim sistemom, prestavljamo v nadaljevanju [19]. IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran 5 Institut »Jožef Stefan«, Ljubljana, Slovenija 3.1. 1 Ogrevanje elektrarne Ogrevanje elektrarne spada med normalne obratovalna stanja elektrarne. Med ogrevanjemje hitrost spremembe temperature reaktorskega hladila omejena na 55.6 °C/h [13]. Iz rezultatov meritev (Slika 1) je razvidno, da je hitrost spremembe temperature reaktorskega hladila manjša od dovoljenih 55.6 °C/h. Poleg tega je razvidno, da ogrevanje ne poteka enakomerno s konstantno hitrostjo, kakor je bilo predvideno v projektu [15]. Krivulje ogrevanja prikazujejo, da se pri času 324 min spremeni temperatura reaktorskega hladila v vroči in hladni veji ter v tlačniku. V tlačniku je hitrost spremembe temperature reaktorskega hladila precej višja (14,7 °C/h), medtem ko je v vroči in hladni veji ~1.5 °C/h. Višja hitrost spremembe temperature reaktorskega hladila v tlačniku je pričakovana in je posledica delovanja grelcev. Podatki o temperaturi so podani do temperature 292°C v vroči in hladni veji primarnega kroga, ki je značilna za vročo zaustavitev reaktorja. -Vroča veja -Tlačnik-grelci -Hladna veja -Tlačnik-para -Prelivni vod Slika 1 Primer izmerjenega poteka temperatur med ogrevanjem elektrarne Primerjava izmerjenih in projektne hitrosti ogrevanja pokaže, da je bilo ogrevanje mnogo bolj počasno, kot je predvideno v projektu. Praviloma to pomeni manj utrujanja in manjši faktor izrabe. Rezultati tudi prikazujejo, da je temperatura v tlačniku nekaj časa nižja od temperature v prelivnem vodu, od časa 805 minut po zagonu elektrarne pa termometer kaže približno enako temperaturo v prelivnem vodu in temperaturo pare v tlačniku. IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran 6 Institut »Jožef Stefan«, Ljubljana, Slovenija Tlak v primarnem krogu, merjen v vroči veji, je po zagonu 2.5 MPa (Slika 2). Ta tlak vzpostavijo drugi sistemi v elektrarni (npr. sistem za odvajanje zaostale toplote). Pri tem tlaku lahko parni mehur v tlačniku nastane šele pri 223.9 °C [20]. Čas [min] Slika 2 Primer izmerjenega poteka tlaka v primarnem krogu med ogrevanjem elektrarne 14 12 10 ra 8 o. .2 6 0 Tlak-meritev Tlak-izra čun 833 933 1033 1133 1233 1333 1433 1533 Čas [min] 4 2 Slika 3 Primerjava tlaka v primarnem krogu in tlaka nasičenja v tlačniku IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran 7 Institut »Jožef Stefan«, Ljubljana, Slovenija Časovni potek tlaka (Slika 2) je skoraj brez večjih oscilacij, ki bi lahko dodatno utrujale komponente in vplivale na faktor izrabe. V tlačniku je reaktorsko hladilo večino časa hkrati v plinati in kapljeviti fazi. Zato lahko na osnovi temperature pare v tlačniku določimo tlak v sistemu (Slika 3). Primerjava med izmerjenim tlakom v vroči veji (Slika 2) in tlakom nasičene vodne pare [20] iz tlačnika ob upoštevanju višinskih razlik in hitrosti hladila kaže dobro ujemanje (Slika 3). 3.1.2 Ohlajanje elektrarne Slika 4 prikazuje spremembe temperatur pri spremembi moči reaktorja iz 100% na 0%. Temperatura v vroči veji se znižuje iz 325°C na 292°C, ko je reaktor v stanju vroče zaustavite. Po tem se temperaturi v vroči in hladni veji enakomerno znižujeta z največjo hitrostjo ohlajanja 41.1°C/h do temperature hladne zaustavitve. Dovoljena hitrost ohlajanja je 55.6 °C/h. Opazimo lahko spremembo temperature v prelivnem vodu pri času 1262 min. Sklepati je mogoče, da je v tlačniku prišlo do znižanja temperature pare, zaradi česar je prišlo do znižanja tlaka. Zaradi višjega tlaka v preostalem delu sistema je prišlo do vdora hladila iz vroče veje v prelivni vod. Ko so z grelci začeli ogrevati hladilo v tlačniku, se je tlak začel višati in je toplejše hladilo iz tlačnika potisnilo hladnejše hladilo proti vroči veji, s čemer se je višala temperatura v okolici termometra v prelivnem vodu. Primerjava izmerjenih in projektne hitrosti ogrevanja pokaže, da je bilo ohlajanje mnogo bolj počasno, kot je predvideno v projektu. Praviloma to pomeni manj utrujanja in manjši faktor izrabe. Časovni potek tlaka (Slika 5) je skoraj brez večjih oscilacij, ki bi lahko dodatno utrujale komponente in vplivale na faktor izrabe. Slika 4 Primer izmerjenega poteka temperatur med ohlajanjem elektrarne IJS-DP-10077 Izdaja 1 Marec 2009 stran 8 File. IJS-DP-10077-R1.doc Institut »Jožef Stefan«, Ljubljana, Slovenija £ Čas [min] Slika 5 Primer izmerjenega poteka tlaka v primarnem krogu med ohlajanjem elektrarne 35G 34G 330 Tempera 32G 31G 3GG 29G 2SG .1.1. 1 i'..........- r r H ft*«»^!* tura [°C \ ] / / 5G1 Vroča veja Hladna veja Tlačnik-para Prelivni vod 1001 Čas [min] 15G1 2GG1 Slika 6 Primer izmerjenega poteka temperatur med ustavitvijo reaktorja s polne moči IJS-DP-iGGll Izdaja i File. IJS-DP-iGGll-Ri.doc Marec 2009 stran 9 Institut »Jožef Stefan«, Ljubljana, Slovenija 3.1.3 Ustavitev reaktorja s polne moči Slika 6 prikazuje ustavitev reaktorja s polne moči, pri čemer je bila začetna temperatura reaktorskega hladila v vroči veji 325°C. Temperature reaktorskega hladila se spreminjajo v vroči veji, v prelivnem vodu in v tlačniku. Ko je prišlo do ustavitve reaktorja, se je znižala temperatura v vroči veji, hkrati pa sta se znižala tudi temperatura v tlačniku in tlak v sistemu. Opazimo lahko tudi vdor hladila iz vroče veje v prelivni vod, kar je povzročilo nihanje temperature v prelivnem vodu. Z dvigom temperature v tlačniku se je dvignila tudi tlak v sistemu, zaradi česar je hladilo iz prelivnega voda potisnilo v vročo vejo in dvignilo temperaturo v okolici merilca v prelivnem vodu. Če primerjamo dejanski in projektni prehodni pojav lahko vidimo, da je hitrost spremembe temperature v prelivnem vodu 0.04508 °C/s, medtem ko je projektna hitrost spremembe temperature 1.4 °C/s. Primerjava izmerjenih in projektne hitrosti ogrevanja pokaže, da so spremembe počasnejše, kot je predvideno v projektu. Praviloma to pomeni manj utrujanja in manjši faktor izrabe. Časovni potek tlaka (Slika 7) nakazuje padca tlaka na 0 MPa, ko je reaktor še obratoval na polni moči. Do takšnih anomalij prihaja velikokrat zato, ker sistem v tistem trenutku ni zabeležil podatka o tlaku. Na anomalijo pri teh rezultatih je mogoče sklepati tudi s primerjavo med izmerjenimi temperaturami (Slika 6) in spremembami tlaka (Slika 7). Če zanemarimo padce na 0 MPa, so največje spremembe tlaka pri tem prehodnem pojavu nekaj manj kot 10% začetnega. Iz projektnih prehodnih pojavov pa izhaja sprememba, ki je nekaj večja kot 10% začetnega tlaka [15]. 18 16 14 12 £ 10 ra 8 r -----p^i""-1 —™--—«o---------1— 501 1001 Čas [min] 1501 2001 Slika 7 Primer izmerjenega poteka tlaka v primarnem krogu med ustavitvijo reaktorja s polne moči 6 0 IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran 10 Institut »Jožef Stefan«, Ljubljana, Slovenija 3.2 Lokalno merjenje temperature reaktorskega hladila V področjih laminarnih tokov ali skoraj mirujočega hladila lahko zaradi različnih temperatur prihaja do toplotnega razslojevanja. Tovrstni pojavi v originalnem projektu jedrske elektrarne niso bili upoštevani. V zadnjem času pa je znano, da se lahko pojavijo in da lahko imajo razmeroma močan vpliv na napetostno stanje v prizadetih cevovodih, s tem pa tudi na utrujenost materiala cevovoda. V takih okoliščinah je za zanesljivo oceno napetostnega polja potrebno poznati porazdelitev temperatur po notranji površini cevi. Za takšno meritev bi potrebovali večje število potopljenimi termometrov: rezultate meritev z enim samim potopljenim termometrom lahko namreč uporabimo samo kot dopolnilo k ostalim meritvam. Vgradnja več potopljenih merilcev temperature pa je lahko zapletena ali celo onemogočena, saj gre za neposreden poseg v tlačno mejo hladila. Zato podatke o razmerah znotraj cevovoda najpogosteje dobimo posredno z namestitvijo merilnih elementov na zunanji površini cevi. Za zanesljivo interpretacijo rezultatov takih meritev pa je praviloma potrebno izvesti posebne analize. V nadaljevanju povzemamo najpomembnejše procese v hladilu znotraj cevi, osnovne načine merjenja temperatur na zunanji steni cevi in osnovne rezultate analitičnih prijemov, ki so lahko v veliko pomoč pri interpretaciji izmerjenih temperatur. V zahtevnejših primerih je potrebno uporabiti računalniške simulacije s pomočjo orodij za računalniško dinamiko tekočin. Tako dobljene rezultate lahko z analizo pretvorimo v temperaturo na notranji strani cevi. 3.2.1 Turbulentna penetracija Turbulentna penetracija tekočine iz večje cevi v manjšo je pomemben pojav pri spoju dveh cevi, v katerih sta tekočini različnih temperatur in hitrosti (Slika 8). Globine turbulentne penetracije navadno ni mogoče enostavno določiti. Znano je, da se intenzivnost turbulentne penetracije zmanjšuje eksponentno z razdaljo, pri čemer je temperatura tekočine približno konstantna na dolžini nekaj premerov cevovoda, kasneje pa se zmanjšuje [9]. Dolžina turbulentne penetracije je večja pri večjih hitrostih tekočine v večjem cevovodu. Odvisna je tudi od oblike manjšega cevovoda. Za tlačnovodne reaktorje, kakršen je tudi v NEK, je značilna dolžina turbulentne penetracije v stransko vejo z mirujočo tekočino v območju od 15 do 25 notranjih premerov stranske veje. Pri tem lahko turbulentna penetracija med drugim povzroča mešanje tekočin v cevovodih, toplotno razslojenost ali vzdolžno gibanje meje med vročo in hladno tekočino oz. toplotni šok. Turbulentna penetracija Razslojeni tok Puščanje ventila Glavni cevovod Stranski cevovod Slika 8 Turbulentna penetracija iz glavnega cevovoda v stanski cevovod [9] IJS-DP-1GG77 Izdaja 1 File. IJS-DP-1GG77-R1.doc Marec 2009 stran 11 Institut »Jožef Stefan«, Ljubljana, Slovenija 3.2.2 Toplotno razslojeni tokovi Toplotno razslojevanje tokov praviloma nastane kot posledica različnih gostot oz. temperatur medija. Pojav oz. njegove posledice so v prelivnih vodih jedrskih elektrarn opazili konec 80 let prejšnjega stoletja [21], [22]. Vroč medij se bo zaradi nižje gostote zbiral na vrhu posode ali cevovoda, hladen pa spodaj (Slika 9). Pojav je izrazitejši pri neizoliranih komponentah z majhnim pretokom ali celo brez pretoka, kjer so temperaturne razlike lahko tudi več 10 °C [23]. Pojav toplotnega razslojevanja lahko v ravnih delih cevovoda povzroči po prerezu spremenljive toplotne napetosti oz. deformacije. Meja med hladnim in vročim medijem se lahko spreminja. Thqt Upogibanje cevi zaradi toplotnega razsloievania STRATIFICATION LEVEL A STflA I IhlCATlON LEtfEL B STRESS PROFILES (-) -J» > C a H Thct Tcold Napetosti po prerezu cevi zaradi toplotnega razslojevanja Slika 9 Razslojeni tok v horizontalni cevi IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran 12 Institut »Jožef Stefan«, Ljubljana, Slovenija 3.2.3 Meritve temperatur na zunanji površini stene cevi Da bi dobili čimbolj natančno informacijo o dogajanju v notranjosti cevovoda, je potrebno merilne elemente namestiti smiselno tako, da dobimo čim več informacij o dogajanju na zunanjem obodu cevi [3], [10]. Slika 10 prikazuje značilne razporeditve merilcev na zunanji površini cevi. Toplotni šok lahko zaznamo že z dvema merilnima elementoma, ki sta nameščena na zgornji in spodnji površini cevovoda (Slika 10a, Slika 11a). Ta konfiguracija načeloma zadošča tudi za zaznavo toplotnega razslojevanja tekočine. Opredelitev meje med toplotno razslojenima tekočinama praviloma zahteva podrobnejše informacije. V primeru horizontalnega cevovoda ali cevovoda z majhnim nagibom navadno zadošča namestitev nekaj merilnih elementov po polovici oboda cevi (Slika 10b in Slika 11b). c) d) Slika 10 Značilne razporeditve merilnih elementov na zunanji površini cevi Če želimo opredeliti razmere pri turbulentnem mešanju v bližini spojev dveh cevi ali tokovne razmere v navpični cevi, je smiselno merilne elementi namestiti po celem obodu (Slika 10d) [1]. V primerih določevanja temperature tekočine pred in za spojem vroče veje in prelivnega voda v praksi merijo temperaturo na zunanji strani cevovoda kot prikazuje Slika 10c [3]. Do velikih temperaturnih sprememb navadno prihaja v prelivnem vodu, kjer lahko prihaja tudi do toplotnega razslojevanja in toplotnih šokov [10]. Slika 12 prikazuje primer temperatur, izmerjenih na zunanji površini prelivnega voda. IJS-DP-10077 Izdaja 1 Marec 2009 stran 13 File. IJS-DP-10077-R1.doc Institut »Jožef Stefan«, Ljubljana, Slovenija £ Slika 11 Razporeditev senzorjev pri cevovodu za nadzor toplotnega šoka in stratifikacije cevi [10] 251J -, 200- 1SÜ- 50 J 12/06/9L 17: 05: 23 ^Merilno -Merilno ✓Merilno mesto A mesto B mesto C Slika 12 Primer izmerjenih temperature na zunanji površini prelivnega voda med zagonom elektrarne [10] IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran 14 Institut »Jožef Stefan«, Ljubljana, Slovenija 3.2.4 Osnovne omejitve meritev na zunanji steni cevi Iz temperatur, izmerjenih na zunanji površini cevi (Slika 12), je mogoče sklepati tudi na temperature notranje površine cevi, ki jih potrebujemo pri analizah utrujanja [1]. Prevajanje toplote skozi steno cevi namreč povzroči zakasnitve in večinoma tudi zmanjšanje temperaturnih sprememb. Dogajanje v dolgi, na zunanji strani izolirani cevi s predpisano temperaturo na notranji površini lahko popišemo z analitičnimi rešitvami [1]. Predpostavimo, da spremembe temperature na notranji površini cevi sledijo stopničasti funkciji (Slika 13), kjer se temperatura hipoma spremeni od 0 na 1. Ker imamo opravka z linearnim sistemom, lahko rešitve pri drugačnih spremembah temperature enostavno dobimo kar s skaliranjem. Poleg tega stopničasta sprememba temperature povzroča največje temperaturne gradiente in je zato med vsemi mogočimi spremembami temperature tudi najbolj konzervativna. 0 At a) Atp b) Slika 13 Stopničasta sprememba temperature iz 0 na 1 in nazaj na 0: a) enkratna in b) periodična Spremembe temperature na zunanji steni cevovoda pri stopničasti spremembi temperature na notranji steni cevovoda so prikazane na primeru cevi iz primarnega kroga jedrske elektrarne. Debeline cevi v primarnem krogu jedrske elektrarne značilno v področju med 5 in 15% polmera cevi. Iz tega sledi področje razmerij med notranjim in zunanjim polmerom med a = 0.85 in a = 0.95. Rezultati (Slika 14) so v skladu s poglavjem 5.2.2. v [1] predstavljeni za tri značilna razmerja a: 0.85, 0.9 in 0.95. Snovne lastnosti, uporabljene v analizi, so značilne za nerjavna jekla, ki se uporabljajo v jedrski tehnologiji, in zajemajo toplotno prevodnost X- 20 W / m K, gostoto p = 7880 kg / m3, specifično toploto cp = 502 J / kg K, modul elastičnosti E = 206.842 GPa, linearni toplotni razteznostni koeficient a = 1.8710-5 K-1. Čas t0 je izražen z R22 / x, kjer je toplotna difuzivnost x = 5.056 10-6 m2 / s. Za prelivni vod tlačnika z zunanjim radijem R2.= 0,1619 m torej velja t0 = 5184 s. Pri slikah v nadaljevanju bi v primeru prelivnega voda tlačnika odčitali: • Čas 0,005 [t0] kot 25,9 s in • Frekvenco 200 [1/t0] kot 0,039 Hz. 1 1 0 IJS-DP-10077 Izdaja 1 Marec 2009 stran 15 File. IJS-DP-10077-R1.doc 0.000 0.001 0.002 0.003 0.004 0.005 Čas trajanja temperaturne spremembe At [t0] Slika 14 Maksimalna temperatura na zunanji površini kot funkcija debeline stene cevi a in normaliziranega časa trajanja A temperaturne spremembe na notranji površini cevi Temperaturne spremembe na notranji površini cevi, ki jih lahko zaznamo na zunanji površini cevi, so močno odvisne od amplitude temperature in trajanja temperaturne spremembe At, debeline stene cevi in materiala (Slika 14). Rezultati so predstavljeni za enojno stopničasto spremembo temperature iz 0 na 1 za čas At (Slika 13a). Rezultati (Slika 14) so lahko zelo uporabni pri določevanju temperaturne spremembe skozi steno valja in določevanju najmanjše temperaturne spremembe na notranji površini, ki jo še lahko zaznamo z merilno napravo na zunanji površini. Pri meritvah je dostikrat pomembno, da poznamo zakasnitev temperaturne motnje skozi steno cevi do merilne naprave. Za primer spremembe temperature na sliki 5a se največja temperatura pojavi na zunanji strani proti koncu prehodnega pojava na notranji površini (Slika 15). Slika 16 prikazuje največjo temperaturo, ki jo lahko zaznamo na zunanji površini v primeru, da se temperatura na notranji strani spreminja periodično (Slika 13b) z velikostjo amplitude 1 in s frekvenco 1/t0 [1]. Pri nizkih frekvencah se amplituda temperature na zunanji strani cevi približuje amplitudi na notranji strani cevi. Povečevanje frekvence na notranji strani in debeline stene cevi znižujeta amplitudo, ki jo zaznamo na zunanji površini. IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran 16 Institut »Jožef Stefan«, Ljubljana, Slovenija 0.0030 0.0025 0.0020 0.0015 0.0010 0.0005 0.0000 a = 0.95 -i-1-1-1-1-1-1-1-p Sprememba temperature na notranji stani cevi Sprememba temperature na zunanji stani cevi a = 0.9 £ 0.000 0.005 0.010 0.015 0.020 Čas trajanja temperaturne spremembe At [t0] 0.025 Slika 15 Zakasnitev Atmax med koncem temperaturne spremembe in pojavom maksimalne temperature Tmax na zunanji površini Slika 16 Amplituda temperaturne spremembe na zunanji strani cevi glede na različne debeline cevi a in frekvenco spremembe temperature na notranji strani IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran 17 Institut »Jožef Stefan«, Ljubljana, Slovenija 3.2.5 Vpliv prestopa toplote iz tekočine na cev V dosedanji razpravi smo predpostavili, da sta temperatura tekočine in notranje stene cevi enaki. S tem predpostavimo neskončni koeficient prestopa toplote, kar zagotavlja nahjvečje temperaturne gradiente in s tem tudi največje napetosti v cevi in je razumno pri visokih hitrostih tokov, npr. v vroči in hladni veji. Značilne vrednosti koeficienta prestopa toplote tam znašajo tudi več 10 kW/m2K [24]. Za razsloj ene tokove pa so značilni laminarni tokovi z nizkimi hitrostmi in več velikostnih razredov nižji koeficienti prestopa toplote v višini nekaj 10 W/m2K [20]. 3.3 Rekonstrukcija manjkajočih podatkov Določevanje temperaturnih porazdelitev v notranjosti cevovoda je tudi z razmeroma kompleksnimi merskimi rezultati lahko dokaj zapleten proces. Velikokrat lahko za določevanje porazdelitve temperature po obodu in vzdolž notranje površine cevovoda uporabimo numerična orodja, še posebej orodja za modeliranje dinamike tekočin (npr. programski paket CFX). S temi orodji lahko izračunamo porazdelitev temperature v cevovodih (npr. prelivni vod) za primere laminarnih in turbulentnih tokov [5]. Prav tako lahko z orodji za modeliranje dinamike tekočin modeliramo turbulentno penetracijo [8]. Problem pri takšnih modelih je predpisovanje ustreznih robnih in začetnih pogojev (npr. tlak, temperatura in hitrost tekočine). Včasih lahko manjkajoče podatke pomagamo rekonstruirati tudi parametričnimi študijami [5]. Meritve temperatur na zunanji površini cevovoda so pri tem lahko v veliko pomoč. Ko so znane temperaturne porazdelitve na notranji strani, lahko v skladu z veljavnimi standardi (npr. ASME [12]) razmeroma enostavno opredelimo pripadajoče amplitude napetosti in faktorje utrujenostne izrabe [1]. Prehodni pojav Zabeleženi v prvi polovici trajnostne dobe Predvideni v celotni trajnostni dobi NORMALNO OBRATOVANJE Ogrevanje 56 200 Ohlajanje 56 200 MOTENO OBRATOVANJE Izpad električnega bremena brez takojšnje zaustavitve reaktorja 5 40 Izpad zunanjega napajanja 3 40 Delna izguba pretoka reaktorskega hladila 2 80 Ustavitev reaktorja s polne moči brez ohlajanja 73 230 z ohlajanjem, brez varnostnega vbrizgavanja 62 160 z ohlajanjem, z varnostnega vbrizgavanjem 2 10 Nenamerno zmanjšanje tlaka reaktorskega hladila 3 20 Padec regulacijske palice 2 80 PREIZKUSI Tlačni preizkus primarnega sistema 1 20 Tlačni preizkus sekundarnega sistema 1 10 Preizkus netesnosti primarnega sistema 1 10 Preizkus netesnosti primarnega sistema < 56 200 Tabela 2 Prehodni pojavi, ki so se zgodili v NEK IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran 18 Institut »Jožef Štefan«, Ljubljana, Slovenija 3.4 Prehodni pojavi, ki so se zgodili v NEK Prehodne pojave, ki so se zgodili v primarnem krogu jedrske elektrarne Krško v prvi polovici njene projektno predvidene trajnostne dobe 40 let, smo povzeli po [25] (Tabela 2). Iz primerjave med dejanskimi in projektnimi prehodnimi pojavi (Tabela 2) je razvidno, da je število prehodnih pojavov, ki so se zgodili majhno. Iz te primerjave je mogoče sklepati, da je v izrabi komponente še velika rezerva. Za bolj natančen odgovor o izrabi komponent pa je potrebno najprej določiti dejanske obremenitve in nato izračunati faktor izrabe [1]. IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran 19 Institut »Jožef Stefan«, Ljubljana, Slovenija £ 4 ZAKLJUČKI Projektna trajnostna doba jedrskih elektrarn temelji na zbirki predpostavljenih projektnih dogodkov. Vsak izmed projektnih dogodkov v sistemih in komponentah elektrarne povzroči prehodne pojave s spremembami temperatur, tlakov in včasih tudi drugih obratovalnih parametrov. Prehodni pojavi torej povzročajo tudi spremembe napetosti v cevovodih in tlačnih posodah in s tem potencialno prispevajo k njihovemu utrujanju. Za natančno določevanje faktorjev izrabe posameznih komponent je torej ključno natančno poznavanje prehodnih pojavov. Pri tem imamo v mislih tako predpostavljene projektne prehodne pojave kot tudi izmerjene dejanske prehodne pojave. V poročilu smo zbrali najpomembnejše vire informacij o projektnih in dejanskih prehodnih pojavih reaktorskega hladilnega sistema jedrske elektrarne v Krškem. Mednje sodijo projekt elektrarne z vsemi spremembami, procesni informacijski sistem elektrarne in lokalne meritve temperatur na zunanji površini nekaterih cevovodov. Opravili smo preliminarno analizo celovitosti in uporabnosti dostopnih podatkov o prehodnih pojavih za analize utrujanja komponent ter preliminarno primerjavo med izbranimi izmerjenimi in projektnimi prehodnimi pojavi. Izbrani izmerjeni prehodni pojavi so bili s stališča utrujanja ugodnejši od projektnih. Opredelimo najpogostejše težave pri interpretaciji podatkov, še posebej v primerih, ko o temperaturah hladila sklepamo na podlagi meritev na zunanji površini cevi. Nakazujemo tudi nekatere prijeme, s katerimi bi bilo mogoče manjkajoče podatke rekonstruirati. IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran 20 Institut »Jožef Stefan«, Ljubljana, Slovenija £ 5 VIRI [1] Zafošnik, B., Cizelj, L.: Zasnova metode za spremljanje izrabe komponent jedrskih elektrarn, IJS delovno poročilo, IJS-DP-10078, 2009. [2] Zafošnik, B., Cizelj, L.: Pilotni primeri za izračun faktorja utujenostne izrabe, IJS delovno poročilo, IJS-DP-10076, 2009. [3] Bartonicek, J., Schoeckle, F.: Monitoring of unspecified loads as a tool for ageing management, ASME PVP Conference, Seattle, 2000. [4] Pockl, C., Kleinoeder, W.: Developing and Implementation of a Fatigue Monitoring System for the new European Pressurized Water Reactor EPR, International Conference Nuclear energy for New Europe 2008, Portorož, 10. - 13. september 2007. [5] Boros, I., Aszodi, A.: Analysis of thermal stratification in the primary circuit of a VVER-440 reactor with the CFX code, Nucl. Eng. Des., 238, 2008, str. 453-459. [6] Bieniussa, K. W., Reck, H.: Piping specific analysis of stresses due to thermal stratification, Nucl. Eng. Des., 190, 1999, str. 239-249. [7] Ensel, C., Colas, A., Barthez, M.: Stress analysis of a 900 MW pressurizer surge line including stratification effects, Nucl. Eng. Des., 153, 1995, str. 197-203. [8] Frank, T., Adlakha M., Adlakha, C., Lifante, H.-M., Prasser, F. Menter: Simulation of Turbulent and Thermal Mixing in T-Junctions Using URANS and Scale-Resolving Turbulenc Models in ANSYS CFX, XCFD4NRS - Experiments and CFD Codes Application to Nuclear Reactor Safety, OECD/NEA & International Atomic Agency (IAEA) Workshop, 10.-12. September 2008, Grenoble, France, str. 23. [9] Assessment and management of ageing of major nuclear power plant components important to safety, Primary piping in PWRs, IAEA-TECDOC-1361,http://www-pub.iaea.org/MTCD/publications/PDF/te_1361_web.pdf, prenešeno 12. 12. 2008. [10] Kleinoder, W., Golembiewski, H.-J.: Monitoring for fatigue - examples for unexpected component loading, SMiRT 16, Washington DC, August 2001. [11] Zafošnik, B., Cizelj, L.: Safe Fatigue Life of Nuclear Piping exposed to Temperature and Pressure Fluctuations, International Conference Nuclear energy for New Europe 2008, Portorož, 8. - 11. september 2008. [12] ASME Boiler and Pressure Vessel Code, 1986. [13] NEK, Updated Safety Analysis Report, Rev. 14. [14] Westinghouse, Krško 18% Steam Generator Tube Plugging Margin Analysis, , WENX 89/06 (1989). [15] Westinghouse, Design Transients Specification, SSR-NEK-5.1, Revison 3, November 1999, Final IJS-DP-10077 Izdaja 1 Marec 2009 stran 21 File. IJS-DP-10077-R1.doc Institut »Jožef Stefan«, Ljubljana, Slovenija [16] Westinghouse, Balance of Design Transients Specification, SSR-NEK-5.2, Revison 1, November 1999, Final [17] Westinghouse, Hydraulic Forcing Functions, SSR-NEK-5.3, Revison 2, July 1999, Final [18] Westinghouse, Mechanical Review, SSR-NEK-12, Rev. 1. Feb. 2000, Final. [19] Nuklearna elektrarna Krško Thermal Stratification Monitoring, 382-RC-L-ESD-TR-04/06, 2006. [20] Krautov strojniški priročnik, Tehniška založba Slovenije, 1998. [21] US NRC Bulletin No. 88-11: Pressurizer Surge Line Thermal Stratification, Dec. 20, 1988. [22] US NRC Information Notice No. 88-80: Unexpected Piping Movement Attributed To Thermal Stratification, Oct. 7, 1988. [23] Kleinoder, W., Golembiewski, H.-J.: Monitoring for fatigue - examples for unexpected component loading, SMiRT 16, Washington DC, August 2001. [24] KWU NDM5/98/E1214, Stress and Fatigue Analysis for the Primary Nozzles of the Replacement Steam Generators, Rev. A, 1998. [25] Review and Categorization of NPP Krško Transients of Operational Cycles, ESD-TR-08/02, Revison 2, Nuklearna elektrarna Krško, 2008 IJS-DP-10077 Izdaja 1 File. IJS-DP-10077-R1.doc Marec 2009 stran 22 IJS Delovno Poročilo IJS Report IJS-DP-1GG76 Izdaja 1, marec 2GG9 Revision 1, March 2009 Pilotni primeri izračuna faktorja utrujenostne izrabe Pilot cases for the calculation of fatigue usage factor B. Zafošnik, L. Cizelj Ljubljana, marec 2009 Institut »Jožef Stefan«, Ljubljana, Slovenija Institut »Jožef Stefan«, Ljubljana, Slovenija • • Naročnik: Ordered by: Javna agencija za raziskovalno dejavnost Republike Slovenije Tivolska c. 30, Ljubljana Nuklearna elektrarna Krško d.o.o., Vrbina 12, 8270 Krško Izvajalec: Prepared by: Pogodba štev.: Contract Number: Nosilec naloge: Responsible Person: Naslov poročila: Report Title: Institut »Jožef Stefan« 1000 Ljubljana Jamova 39 Slovenija Odsek za reaktorsko tehniko (Reactor Engineering Division) Z2-9488-0106-06 (IJS in ARRS) U1-BL-R4-3/03 (IJS in NEK) dr. Boštjan Zafošnik, univ. dipl. inž. str. Pilotni primeri izračuna faktorja utrujenostne izrabe Pilot cases for the calculation of fatigue usage factor Avtorji poročila: Authors: Dr. Boštjan Zafošnik, univ.dipl.inž.str. Prof. dr. Leon Cizelj, univ.dipl.inž.str. Štev. delovnega poročila: Report Number: Konto: Account Number: Kopije: Distribution: IJS-DP-10076 Izdaja 1 V2-0375-C > Naročnik (3) > Knjižnica/Library (1x) > Nosilec naloge/Responsible Person (1x) > Avtorji/Authors (1x) > Arhiv OR4/Archive (1x + original) Ljubljana, marec 2009 IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran i Institut »Jožef Stefan«, Ljubljana, Slovenija POVZETEK V poročilu demonstriramo uporabo metode za izračun faktorja izrabe v izbranih komponentah na dveh pilotnih primerih: izstopni šobi reaktorske tlačne posode (proti vroči veji) in prelivnem vodu tlačnika. Izbor pilotnih primerov zagotavlja tudi širok spekter obremenitvenih primerov. Z modelom izstopne šobe reaktorske tlačne posode smo ocenili faktor izrabe za projektne in dejanske prehodne pojave v jedrski elektrarni Krško: ogrevanje in ohlajanje elektrarne ter ustavitev reaktorja s polne moči brez ohlajanja. Primerjava izračunanih faktorjev izrabe je pokazala, da je dejanska izraba obravnavanih komponent za obravnavane prehodne pojave manjša od predvidene v projektu. Pokazali smo tudi mogoče vplive toplotnega razslojevanja in termičnega šoka na utrujenostno izrabo prelivnega voda tlačnika. Pri tem smo posebno pozornost posvetili temperaturam, ki bi jih v obravnavanih hipotetičnih prehodnih pojavih prikazovali merilci temperatur na zunanjem obodu prelivnega voda. Poročilo predstavlja del rezultatov projekta »Zasnova metode za spremljanje izrabe komponent jedrskih elektrarn«, ki sta ga sofinancirala Javna agencija za raziskovalno dejavnost Republike Slovenije (pogodba št. 1000-07-219488) in Nuklearna elektrarna Krško d.o.o. (pogodba št. POG-3408). IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran ii Institut »Jožef Štefan«, Ljubljana, Slovenija ABSTRACT The implementation of the method for monitoring the usage of nuclear power plant is demonstrated with two pilot cases: the reactor pressure vessel outlet nozzle and pressurizer surge line. The selection of pilot cases facilitates wide spectra of applied loads. The model of the reactor pressure vessel outlet nozzle was used to estimate the partial fatigue usage factors during the design and actual transients in Krško nuclear power plant: heatup and cooldown and reactor trip from full power without cooldown. Comparison of calculated partial fatigue usage factors confirms the conservativity of plant design. Possible consequences of stratified flows and thermal shocks on the fatigue usage of the pressurizer surge line were also demonstrated. Special attention has been devoted to the simulated output of potential termocouples placed at the outer surface of the surge line. This report contains a part of the results of the project » Conception of a method for monitoring of the usage of nuclear power plant components «, cosponsored by the Slovene Research Agency (grant No. 1000-07-219488) and Nuklearna elektrarna Krško d.o.o. (grant No. POG-3408). IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran iii Institut »Jožef Stefan«, Ljubljana, Slovenija KAZALO POVZETEK II ABSTRACT III KAZALO IV SEZNAM SLIK VI SEZNAM TABEL VIII 1 UVOD 1 1.1 Namen poročila 1 1.2 Ozadje 1 1.3 Organizacija poročila 1 2 MODELIRANJE TEMPERATURNIH IN NAPETOSTNIH SPREMEMB 2 2.1 Numerično modeliranje temperaturnega polja 2 2.1.1 Vpliv števila končnih elementov po debelini cevi 2 2.1.2 Vpliv koeficienta prestopa toplote s hladila na cev 3 2.2 Numerično modeliranje napetostnega polja 5 2.2.1 Linearizacija napetosti 6 3 IZSTOPNA ŠOBE REAKTORSKE TLAČNE POSODE 8 3.1 Geometrija modela 8 3.1.1 Poenostavitve 8 3.2 Snovne lastnosti 8 3.3 Obremenitve 10 3.3.1 Temperaturne obremenitve 10 3.3.2 Tlačne obremenitve 11 3.4 Robni pogoji 12 3.5 Rezultati 13 3.5.1 Ogrevanje in ohlajanje reaktorja 14 3.5.2 Ustavitev reaktorja s polne moči brez ohlajanja 15 • • IJS-DP-10076 Izdaja 1 Marec 2009 stran iv File. IJS-DP-10076-R1.doc Institut »Jožef Štefan«, Ljubljana, Slovenija 4 MODEL PRELIVNEGA VODA TLAČNIKA 18 4.1 Geometrija modela 18 4.1.1 Poenostavitve 18 4.2 Snovne lastnosti 20 4.3 Obremenitve 20 4.3.1 Toplotno razslojeni tok 20 4.3.2 Toplotni šok 20 4.4 Robni pogoji in predpostavke 21 4.4.1 Toplotna analiza 21 4.4.2 Napetostna analiza 22 4.5 Rezultati 22 4.5.1 Toplotno razslojeni tok 22 4.5.2 Toplotni šok 35 5 ZAKLJUČKI 42 6 VIRI 43 IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran v Institut »Jožef Stefan«, Ljubljana, Slovenija • • SEZNAM SLIK Slika 1 Slika 2 Slika 3 Slika Slika Slika Slika Slika 8 Slika Slika Slika Slika Slika Slika Slika Slika Slika Slika Slika Slika Slika Slika Slika Slika Slika Slika Slika Slika Slika Slika Slika Slika 2 3 4 7 9 13 14 15 16 17 17 19 19 21 Primerjava analitične in numerične porazdelitev temperature po debelini stene cevi pri stopničasti spremembi temperature na notranji površini cevi za 20 °C in 8.1 s (trije končni elementi) Primerjava analitične in numerične porazdelitev temperature po debelini stene cevi pri stopničasti spremembi temperature na notranji površini cevi za 20 °C in 12 s (dva končna elementa) Porazdelitev stacionarnih temperatur po preseku cevi glede na višino meje med vročim in hladnim slojem hladila pri h = 50 W/m2K Primer poti za linearizacijo napetosti Prostorski model izstopne šobe z delom reaktorske posode in vroče veje Kinematični robni pogoji v modelu izstopne šobe Največja Trescova ekvivalnentna napetost med projektnim prehodnim pojavom ogrevanja in ohlajanja reaktorja Močno pretirana deformacija izstopne šobe zaradi obremenitve z notranjim tlakom in pripadajoča Trescova ekvivalentna napetost 9 Največja Trescova ekvivalentna napetost med izmerjenim ogrevanjem in ohlajanjem 10 Največja Trescova ekvivalnentna napetost med projektnim prehodnim pojavom ustavitve reaktorja s polne moči brez ohlajanja 11 Največja Trescova ekvivalnentna napetost med izmerjenim prehodnim pojavom ustavitve reaktorja s polne moči brez ohlajevanja Prostorski model prelivnega voda tlačnika Predpostavljena merilna mesta M1 do M4 na prelivnem vodu tlačnika Kinematični robni pogoji modela prelivnega voda tlačnika Porazdelitev temperature pri spremembi lege gladine iz spodnje do zgornje in nazaj do spodnje z vmesnim stacionarnim stanjem v zgornji legi 23 Porazdelitev temperature v notranji (M4-A-N) in zunanji (M4-A-Z) točki pri spremembi lege gladine z vmesnim stacionarnim stanjem 24 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M1 v času do 1000 s 24 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M2 v času do 1000 s 25 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M3 v času do 1000 s 25 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M4 v času trajanja cikla do 1000 s 27 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M1 v času trajanja cikla med 40000 s in 60000 s 27 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M2 v času trajanja cikla med 40000 s in 60000 s 28 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M3 v času trajanja cikla med 40000 s in 60000 s 28 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M4 v času trajanja cikla med 40000 s in 60000 s 29 Največja Trescova ekvivalentna napetost pri enem ciklu z vmesnih stacionarnim stanjem 29 Vpliv tlaka 2,5 MPa na Tresca ekvivalentno napetost v prelivnem vodu 30 Porazdelitev temperature pri spremembi lege gladine iz spodnje do zgornje in nazaj do spodnje brez vmesnega stacionarnega stanja v zgornji legi 31 Porazdelitev temperature v notranji (M4-A-N) in zunanji (M4-A-Z) točki pri spremembi lege gladine (en cikel) brez vmesnega stacionarnega stanja 32 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M1 v času trajanja cikla do 1000 s 32 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M2 v času trajanja cikla do 1000 s 33 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M3 v času trajanja cikla do 1000 s 34 32 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M4 v času trajanja cikla do 1000 s 34 IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran vi Institut »Jožef Stefan«, Ljubljana, Slovenija • • Slika 33 Slika 34 Slika 35 Slika 36 Slika 37 Slika 38 Slika 40 Slika 39 Slika 41 Največja Trescova ekvivalentna napetost pri enem ciklu brez vmesnega stacionarnega stanja 35 Porazdelitev temperature pri spremembi lege gladine v vzdolžni smeri cevovoda z vmesnim stacionarnim stanjem v skrajni vzdolžni legi 36 Porazdelitev temperature v notranji (M2-A-N) in zunanji (M2-A-Z) točki pri potovanju motnje preko tega merilnega mesta z vmesnim stacionarnim stanjem (en cikel) 37 Porazdelitev temperature v notranji (M2-A-N) in zunanji (M2-A-Z) točki pri potovanju motnje preko tega merilnega mesta za čas do 40 s 37 Porazdelitev temperature v notranji (M2-A-N) in zunanji (M2-A-Z) točki pri potovanju motnje preko tega merilnega mesta za čas od 4000 do 7000 s 38 Največja Trescova ekvivalentna napetost pri ciklu z vmesnim stacionarnim stanjem 39 Porazdelitev temperature v notranji in zunanji točki na merilnem mestu M2 pri ciklu spremembe lege gladine hladila brez vmesnega stacionarnega stanja 39 Porazdelitev temperature pri spremembi lege gladine v vzdolžni smeri cevovoda brez vmesnega stacionarnega stanja v skrajni vzdolžni legi 40 Največja Tresca ekvivalentna napetost pri enem ciklu brez vmesnega stacionarnega stanja 41 IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran vii Institut »Jožef Štefan«, Ljubljana, Slovenija SEZNAM TABEL Tabela 1 Največja (rmax) in najmanjša (rmin) temperatura v steni cevi v odvisnosti od koeficienta prestopa toplote in meje med vročim in hladnim slojem (Slika 3) 5 Tabela 2 Primerjava analitičnih in numeričnih ocen Trescove ekvivalentne napetosti pri stopničasti hipni spremembi temperature s časom trajanja 8.1s 5 Tabela 3 Vpliv števila elementov na radialno (o;.), obročno (o^) in vzdolžno (oz) komponento napetosti pri stopničasti spremembi temperature dolžine 8.1s (analitično: o. = 0 MPa, o = 73.85 MPa in oz = 22.16 MPa) 6 Tabela 4 Vpliv števila elementov na radialno (o), obročno (o^) in vzdolžno (oz) komponento napetosti pri stopničasti spremembi temperature dolžine 60s (analitično: o = 0 MPa, o = 44.55 MPa in oz = 13.37 MPa) 6 Tabela 5 Primerjava lineariziranih in neposredno odčitanih Trescovih ekvivalentnih napetosti 6 Tabela 6 Pregled materialov v modelu izstopne šobe 9 Tabela 7 Temperaturni cikel ogrevanja in ohlajanja reaktorja za projektni prehodni pojav 11 Tabela 8 Temperaturni cikel ogrevanja in ohlajanja reaktorja za dejanski prehodni pojav 11 Tabela 9 Temperaturni cikel ustavitve reaktorja s polne moči brez ohlajanja za projektni prehodni pojav 12 Tabela 10Temperaturni cikel ustavitve reaktorja s polne moči brez ohlajanja za dejanski prehodni pojav 12 Tabela 11 Tlačni cikel ogrevanja in ohlajanja reaktorja za projektni prehodni pojav 12 Tabela 12 Tlačni cikel ogrevanja in ohlajanja reaktorja za dejanski prehodni pojav 13 IJS-DP-10076 Izdaja 1 Marec 2009 File. IJS-DP-10076-R1.doc stran viii Institut »Jožef Stefan«, Ljubljana, Slovenija 1 UVOD 1.1 Namen poročila V poročilu predstavljamo del rezultatov projekta »Zasnova metode za spremljanje izrabe komponent jedrskih elektrarn«, ki sta ga sofinancirala Javna agencija za raziskovalno dejavnost Republike Slovenije (pogodba št. 1000-07-219488) in Nuklearna elektrarna Krško d.o.o. (pogodba št. P0G-3408). Preostali rezultati projekta so predstavljeni v spremljajočih poročilih: • Zasnova metode za spremljanje izrabe komponent jedrskih elektrarn [1] in • Baza prehodnih pojavov v Nuklearni elektrarni Krško [2]. 1.2 Ozadje Za podaljševanje obratovalne dobe jedrskih elektrarn je zelo pomembno čimbolj natančno določevanje faktorja izrabe komponent. V ta namen smo zasnovali metodo za spremljanje izrabe komponent jedrskih elektrarn [1] in bazo dejanskih prehodnih pojavov [2]. Uporabo metode za izračun faktorja izrabe v izbranih komponentah v poročilu demonstriramo na dveh pilotnih primerih: izstopni šobi reaktorske tlačne posode (proti vroči veji) in prelivnem vodu tlačnika. Reaktorska tlačna posoda, vroča veja in prelivni vod tlačnika so del tlačne meje reaktorskega hladila v tlačnovodni jedrski elektrarni (varnostni razred 1). Skrbi za dobro projektiranje tlačne meje reaktorskega hladila med obratovanjem elektrarne sledi skrb za njeno varnost in strukturno celovitost. Izbor pilotnih primerov zagotavlja tudi širok spekter obremenitvenih primerov: za prelivni vod tlačnika je znano, da je lahko obremenjen tudi s toplotnim razslojevanje in toplotnimi šoki [3], [4], [5], [6]. 1.3 Organizacija poročila V poglavju 2 je opisano modeliranje temperaturnega in napetostnega polja z metodo končnih elementov, s poudarkom na diskretizaciji modela po debelini stene cevi. V poglavju 3 je predstavljen model spoja izstopne šobe reaktorske tlačne posode ter izračun faktorja izrabe za dejanske prehodne pojave, dobljene iz NEK. V poglavju 4 je na modelu prelivnega voda tlačnika prikazan potencialni vpliv toplotnega razslojevanja in toplotnega šoka na spremembe temperature na hipotetičnih merilnih mestih na zunanjem obodu cevovoda in na delni faktor izrabe. Poročilo se konča z zaključki v poglavju 5 in napisanimi viri v poglavju 6. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 1 Institut »Jožef Štefan«, Ljubljana, Slovenija 2 MODELIRANJE TEMPERATURNIH IN NAPETOSTNIH SPREMEMB V tem poglavju opišemo najpomembnejše vplive, ki jih je potrebno upoštevati pri modeliranju temperaturnih in napetostnih polj zaradi sprememb temperature in tlaka na notranji strani votle valjaste geometrije. Vse numerične rešitve, opisane v tem poročilu, so dobljene z metodo končnih elementov in računalniškim programom ABAQUS [7]. 2.1 Numerično modeliranje temperaturnega polja 2.1.1 Vpliv števila končnih elementov po debelini cevi Natančnost numerične ocene nestacionarne porazdelitve temperatur skozi steno cevi je odvisna predvsem od števila končnih elementov po debelini stene. Numerično natančnost najlaže ocenimo tako, da numerične rezultate primerjamo z analitičnimi rešitvami [1]. Kot primer si oglejmo cev z značilnostmi prelivnega voda (notranji polmer R1 = 128,6 mm, zunanji polmer R2 = 161,9 mm). Potrebujemo še snovne lastnosti, značeilne za austenitno nerjavno jeklo: toplotna prevodnost materiala A = 20 W/mK, gostota p = 7850 kg/m3 in specifična toplota cp = 502 J/kg K. Na notranji površini stene cevi smo predpostavili hipno stopničasto spremembo temperature za 20°C, ki traja 8.1 sek. Nato opazujemo temperaturno porazdelitev skozi steno cevi (Slika 1). Izkaže se, da trije parabolični končni elementi vzdolž debeline cevi zadoščajo za najmanj 5% natančnost numerične rešitve. O o ca 13 ro i— CD Ci E (D 20 15 10 5 Čas trajanja spremembe na notranjem robu t = 8.1 s Št. elementov po debelini = 3 Analitično določen potek T Numerično določen potek T 0 0.13 0.135 0.14 0.145 0.15 0.155 0.16 Polmer cevi [m] Slika 1 Primerjava analitične in numerične porazdelitev temperature po debelini stene cevi pri stopničasti spremembi temperature na notranji površini cevi za 20 °C in 8.1 s (trije končni elementi) IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 2 Institut »Jožef Štefan«, Ljubljana, Slovenija c C 0 Čas trajanja spremembe na notranjem robu t = 12 s Št. elementov po debelini = 2 Numerično določen potek T Analitično določen potek T 0.13 0.135 0.14 0.145 0.15 0.155 0.16 Slika 2 Primerjava analitične in numerične porazdelitve temperature po debelini stene cevi pri stopničasti spremembi temperature na notranji površini cevi za 20 °C in 12 s (dva končna elementa) Slika 2 prikazuje primerjavo med numerično in analitično porazdelitvijo temperature vzdolž debeline stene cevi pri motnji, ki traja 12 s in z uporabo dveh paraboličnih končnih elementov po debelini valjaste cevi. Tudi tokrat je razlika med numerično in analitično oceno največ 5%. Zaključimo lahko, da lahko z dvema končnima elementoma z zadostno natančnostjo ujamemo posledice stopničastih motenj dolžine 12 s, s tremi končnimi elementi pa 8 s. 2.1.2 Vpliv koeficienta prestopa toplote s hladila na cev V dosedanji razpravi smo predpostavili, da sta temperatura tekočine in notranje stene cevi enaki. S tem predpostavimo neskončni koeficient prestopa toplote, kar zagotavlja največje temperaturne gradiente in s tem tudi največje napetosti v cevi in je razumno pri visokih hitrostih tokov, npr. v vroči in hladni veji. Značilne vrednosti koeficienta prestopa toplote tam znašajo tudi več 10 kW/m2K [8]. Za razslojene tokove pa so značilni laminarni tokovi z nizkimi hitrostmi in več velikostnih razredov nižji koeficienti prestopa toplote v višini nekaj 10 Pričakujemo, da bo vpliv izbire koeficienta prestopa toplote največji pri modeliranju razslojenih tokov. Tudi tokrat uporabimo cev z značilnostmi prelivnega voda (poglavje 2.1.1). Za vroče hladilo predpostavimo temperaturo Th = 223°C in T = 96 °C za hladno hladilo. Ti dve temperaturi sta značilni za prelivni vod tlačnika med ogrevanjem reaktorja [2]. Koeficiente prestopa toplote izberemo kot h = 50, 500 in 1000 W/m2K. To so značilne vrednosti, ki se lahko pojavijo v prelivnem vodu med obratovanjem jedrske elektrarne in so odvisne predvsem od hitrosti hladila. Zanima pa nas stacionarna porazdelitev temperatur po preseku cevi zaradi razslojenega toka z različnimi višinami meje med obema slojema. Uporabimo ravninski model (Slika 3), v katerem spreminjamo višino meje med slojema hladila: cev napolnjena z vročim hladilom, meja med toplim in hladnim slojem na polovici W/m2K [9]. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 3 • • Institut »Jožef Štefan«, Ljubljana, Slovenija notranjega premera cevi in meja med toplim in hladnim slojem na osmini notranjega premera cevi. Koeficient prestopa toplote smo postavili na h = 50 W/m2K. r +3.Î30Ç*«« Y +2.230e-Q2 +2-230c+02 I +2.230®+-02 Y +2,230c+02 t- +2.2306+02 Y +2.230e+02 l +2.23CW+03 l +2.2306+02 +2.230c*02 L +2.2306+02 Y +2.2306+02 L +2.2306+02 Primer 1 r +2.0376+02 Y +1.9636+02 Y + l-8ft*í+02 + I.81&6+02 , + 1 7426+02 I + 1.6696+02 Y + l~595e+02 Y +i «16+02 + 1.448e*û2 I +1.3016+02 . +1.2276+02 L +t.1536+02 Primer 2 r +2.2l0c+02 Y +2.1826 +02 l +2.1266+02 Y Y +2.0706+02 Y +2 0420+02 l +2.0146*02 Y + 1.9B5e»02 I +1.9576*02 Y +1.929e+02 + I.901C-02 L +1.8736+02 Th - temperatura vročega fluida Tc - temperatura hladnega fluida h = 50 W/m2K Primer 3 Tc = 96°C Slika 3 Porazdelitev stacionarnih temperatur po preseku cevi glede na višino meje med vročim in hladnim slojem hladila pri h = 50 W/m2K IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 4 Institut »Jožef Štefan«, Ljubljana, Slovenija V primeru, da je koeficient prestopa toplote enak h = 500 W/m2K h oz. h = 1000 W/m2K, so najvišje (Tmax) in najnižje (Tmin) temperature, ki se pojavijo v steni cevi prikazane v Tabeli 1. Iz rezultatov je razvidno, da imata koeficient prestopa toplote in položaj meje med vročim in hladnim slojem hladila velik vpliv na velikost in porazdelitev temperature po preseku cevi. Pri manjši vrednosti koeficienta prestopa toplote so tudi temperaturni gradienti v steni cevi manjši, kar ugodno vpliva na napetostno stanje v cevi. Koef. prestopa toplote [W/m2K] Primer 1 Primer 2 Primer 3 500 Tmax = 223 C Tmax = 222,5 C Tmin = 96,5 C Tmax = 223 C Tmin = 138 °C 1000 Tmax = 223 C Tmax = 222,9 C Tmin = 96,1 °C Tmax = 223 C Tmin = 122,9 C Tabela 1 Najvišja (Tmax) in najnižja (Tmin) temperatura v steni cevi v odvisnosti od koeficienta prestopa toplote in meje med vročim in hladnim slojem (Slika 3) 2.2 Numerično modeliranje napetostnega polja V poglavju 2.1 smo ugotovili, da lahko spremembe temperature zadovoljivo opišemo s tremi elementi, če sprememba temperature traja najmanj 8 s. Tabela 2 primerja numerične in analitične vrednosti Trescove ekvivalentne napetosti na notranji površini stene cevi , ki jih povzroči stopničasta sprememba temperature velikosti 20°C v trajanju 8.1s. Število končnih elementov 0T [MPa] numerično 0T [MPa] analitično Odstopanje [%] 3 66.22 73.85 -10.33 4 69.92 73.85 -5.32 5 71.61 73.85 -3.03 Tabela 2 Primerjava analitičnih in numeričnih ocen Trescove ekvivalentne napetosti pri stopničasti hipni spremembi temperature s časom trajanja 8.1s V primeru, da traja stopničasta sprememba temperature za 20°C na notranji površini 60s, je za tri elemente po debelini stene cevi razlika med numerično in analitično ocenjeno napetostjo -4.05%, kar je primerljivo s pričakovano natančnostjo metode končnih elementov. Največji vpliv na natančnost izračuna Trescove ekvivalentne napetosti ima radialna komponenta napetosti, ki je najbolj občutljiva na kvaliteto mreže in čas trajanja prehodnega pojava. Tabela 3 prikazuje rezultate za čas trajanja prehodnega pojava 8.1s in odstopanje od analitično izračunanih vrednosti za radialno (or), obročno (o^) in vzdolžno (oz) napetost. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 5 Institut »Jožef Štefan«, Ljubljana, Slovenija • • Število končnih elementov Gr [MPa] G [MPa] g, [MPa] MKE [MPa] A [%] MKE [MPa] A [%%] MKE [MPa] A [%%] 3 4.13 - 70.33 -4.77 18.59 -16.08 4 2.04 - 71.44 20.32 -3.26 -8.29 5 1.19 - 72.13 21.01 -2.33 -5.18 Tabela 3 Vpliv števila elementov na radialno (or), obročno (o) in vzdolžno (oz) komponento napetosti pri stopničasti spremembi temperature dolžine 8.1s (analitično: or = 0 MPa, O) = 73.85 MPa in oz = 22.16 MPa) Pri dolžini stopničaste spremembe 60 s pa je odstopanje že pri treh končnih elementih v velikostnem razredu 1% (Tabela 4). Gr [MPa] Gf [MPa] g, [MPa] MKE [MPa] A [%%] MKE [MPa] A [%%] MKE [MPa] A [%%] 2.21 - 44.95 0.89 13.71 2.55 Tabela 4 Vpliv števila elementov na radialno (or), obročno (o) in vzdolžno (oz) komponento napetosti pri stopničasti spremembi temperature dolžine 60s (analitično: or = 0 MPa, O) = 44.55 MPa in oz = 13.37 MPa) 2.2.1 Linearizacija napetosti Glede na navodila standarda ASME se glavne napetosti iz rezultatov MKE računajo z upoštevanjem komponent napetosti, ki se dobijo z linearizacijo napetosti [10]. Pri linearizaciji pa nastopi nevarnost doseganja netočnih rezultatov, na kar vpliva izbira poti, po kateri lineariziramo in število segmentov na katere razdelimo pot. Določanje poti je predvsem zahtevno pri spojih šob in cevovoda ali reaktorske posode. Število GpT [MPa] - 7 točk-linearizacija GpT [MPa] direktno Odstopanje [%] elementov GpT [MPa] - 31 točk-linearizacija iz rezultatov 3 52.45 51.28 -2.24 51.76 -0.92 4 53.58 52.29 -2.42 52.99 -1.32 Tabela 5 Primerjava lineariziranih in neposredno odčitanih Trescovih ekvivalentnih napetosti IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 6 Institut »Jožef Stefan«, Ljubljana, Slovenija Pot za linearizacijo Slika 4 Primer poti za linearizacijo napetosti Analiza na modelu cevi (Slika 4) s programskim paketom Abaqus [7] je pokazala, da je razlika med Trescovo ekvivalentno napetostjo določeno na osnovi linearizacije in direktno odčitano Trescovo ekvivalentno napetostjo na notranji površini stene cevi praktično zanemarljiva. V takem primeru je za določevanje faktorja izrabe smiselno rezultate numerične analize uporabiti neposredno (Tabela 5) in se postopku linearizacije napetosti izogniti. IJS-DP-10076 Izdaja 1 Marec 2009 stran 7 File. IJS-DP-10076-R1.doc Institut »Jožef Štefan«, Ljubljana, Slovenija 3 IZSTOPNA ŠOBE REAKTORSKE TLAČNE POSODE V tem poglavju predstavimo izračun delnega faktorja izrabe za projektne in dejanske prehodne pojave a) ogrevanje in ohlajanje reaktorja in b) ustavitve reaktorja s polne moči brez ohlajanja. 3.1 Geometrija modela Vsi modeli geometrije posode in izstopne šobe so izdelani po delavniških risbah serije E-19273. 3.1.1 Poenostavitve Modeliranje z metodo končnih elementov zahteva določeno poenostavljanje geometrije in mej materialov. 1. Zanemarjanje drobnih geometrijskih detajlov. Modeliranje velikih kosov opreme, kakršna je tlačna posoda reaktorja, s pomočjo končnih elementov praviloma zahteva določene poenostavitve oz. zanemarjanje nekaterih detajlov. Predvsem pri tem mislimo na detajle, kot so npr. predori za instrumentacijo sredice, ki ne vplivajo bistveno na odziv celotne posode. V primeru potrebe pa lahko pozneje iz rezultatov velikega modela dobimo robne pogoje za mikro analizo posameznega detajla. 2. Spoji materialov. Spoj dveh materialov je praviloma izveden z varjenjem. Za celovito analizo razmer v varjenih spojih (kot npr. spoj posode in vstopne šobe) je potrebno natančno poznati postopek izdelave. Potem je mogoče oceniti zaostale napetosti in kolikor toliko natančno geometrijo spoja. Takih informacij nimamo. Po drugi strani pa je za zvare značilno, da so meje med različnimi materiali in s tem snovnimi lastnostmi v njih in njihovi bližini zabrisane. Ostra meja med snovnimi lastnostmi pa sama po sebi povzroči lokalne koncentracije napetosti, kar je konzervativno. Zato je zvar modeliran kot idealen spoj dveh materialov. 3. Oplata posode. Oplati posode ni potrebno pripisati nosilnosti, kadar analiziramo odpornost posode na ciklične obremenitve (ASMe III NB 3122.3), če je debelina oplate 10% ali manj celotne debeline komponente. Pri izdelavi prostorskega modela (Slika 5) smo se držali smernic glede uporabe končnih elementov, ki so opisane v [1]. V modelu smo uporabili 6824 paraboličnih končnih elementov. Po debelini posamezne komponente smo uporabili najmanj tri končne elemente. Gostota mreže je primerna glede na spremembe hitrosti temperature v obravnavanih prehodnih pojavih. 3.2 Snovne lastnosti Posamezni deli tlačne posode in cevovoda vroče veje so izdelani iz različnih materialov (Tabela 6). Snovne lastnosti, ki jih potrebujemo pri analizi so: - modul elastičnosti E [MPa] - linearna temperaturna razteznost a [1/K] - toplotna prevodnost A [W/mK] in - specifična toplota Cp [J/kg K] Snovske lastnosti so definirane za posamezne skupine materialov, kot so npr. ogljikovo jeklo, nerjavno jeklo, itd., v ASME B&PV Code, Section III. (Apendix I) [10] in so temperaturno odvisne. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 8 Institut »Jožef Štefan«, Ljubljana, Slovenija • • Slika 5 Prostorski model izstopne šobe z delom reaktorske posode in vroče veje Del komponente Vrsta materiala Oznaka Referenca Telo posode Nizko legirano jeklo (Mn-1/2 Mo-1/2 Ni) SA 533 Gr B, Class I [10] Šoba posode Ogljikovo jeklo (3/4 Ni-1/2 Mo- 1/3 Cr- V) SA 508, Class II [10] Zaključek šobe (safe end) Avstenitno nerjavno jeklo (16 Cr-12 Ni - 2 Mo) SA 182 Gr F 316 [10] Cevovod vroče veje Avstenitno nerjavno jeklo (16 Cr-8 Ni) SA-351 Gr CF8A [10] Tabela 6 Pregled materialov v modelu izstopne šobe Moduli elastičnosti s temperaturo padajo približno linearno, pri čemer ima nerjavno jeklo pri sobni temperaturi nekaj nižji modul elastičnosti kot ogljikova in nizko legirana jekla. Približno pri obratovalni temperaturi razlika postane zanemarljiva in se pri 400°C praktično izgubi. Razlika v elastičnih modulih je pomembna zato, ker povzroča lokalne napetosti v bližini spoja materialov. Linearna temperaturna razteznost s temperaturo narašča pri vseh štirih vrstah materialov. Nerjavno jeklo se pod vplivom toplote širi najbolj. Razlike v linearni temperaturni razteznosti, podobno kot pri modulih elastičnosti, povzročajo lokalne napetosti v bližini spojev različnih materialov. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 9 Institut »Jožef Štefan«, Ljubljana, Slovenija Toplotna prevodnost skupaj s specifično toploto določa hitrost prodiranja toplote v telo. Nerjavno jeklo ima nižjo toplotno prevodnost kot konstrukcijski jekli za telo posode in šobo posode, medtem ko je razlika njihovih specifičnih toplot pri obratovalni temperaturi povsem zanemarljiva. Upoštevanje temperaturne odvisnosti snovskih lastnosti povzroči nelinearnost problema temperaturnega polja, kar podraži numerično reševanje. Neupoštevanje temperaturnih odvisnosti snovskih lastnosti po drugi strani bistveno oteži analizo napetosti na spojih različnih materialov. Zato smo se odločili za modeliranje temperaturno odvisnih snovskih lastnosti. 3.3 Obremenitve Opazujemo samo obremenitve, ki se s časom spreminjajo in kot take povzročajo ciklične spremembe napetosti v obravnavanih komponentah. Take obremenitve povzročajo tlačni in temperaturni prehodni pojavi reaktorskega hladila. Prehodni pojavi v reaktorskem hladilu na stene primarnega kroga vplivajo neposredno, kar pomeni, da povzročajo napetosti, ki so popisane v [1]. Poleg tega je posledica temperaturnih prehodnih pojavov raztezanje oz. krčenje primarnega kroga, kar povzroča dodatne obremenitve cevovodov in s tem tudi šob. Poseben problem je realistično modeliranje drsenja podpor reaktorske posode v radialni smeri. V pričujoči analizi smo upore proti drsenju podpor zanemarili. V poročilu obravnavamo samo neposredne efekte prehodnih pojavov. Vpliv različnega raztezanja vroče in hladne veje, ki bi preko vroče veje lahko povzročalo dodatne obremenitve šobe, smo zanemarili. Obravnavali smo dva tlačno temperaturna prehodna pojava reaktorskega hladila, za katere smo dobili podatke iz NEK [2]: 1. ogrevanje in ohlajanje reaktorja 2. ustavitev reaktorja s polne moči brez ohlajanja. 3.3.1 Temperaturne obremenitve Na osnovi standarda ASME smo ocenili, da lahko temperaturne (pod)cikle, manjše od 11.7°C, zanemarimo. Pri tem smo upoštevali snovne lastnosti za zaključke šob, ki imajo od obravnavanih materialov najnižje mehanske lastnosti (Sm = 114,5 MPa in Sa (pri 106 ciklih) = 86 MPa) [11]. Temperaturne obremenitve za prehodni pojav ogrevanja in ohlajanja reaktorja so zbrane v tabeli 7 (projekt) in v tabeli 8 (izmerjeno). Pri tem so podatki pri ogrevanju reaktorja, ki smo jih dobili iz NEK, zabeleženi in upoštevani le do temperature 292 °C [1], ko je toplotna moč reaktorje enaka nič. Glede na projektne podatke ogrevanje reaktorja s stanja vroče ugasnitve do polne moči časovno poteka s približno enako hitrostjo spremembo temperature kot ohlajanje s temperature pri polni moči reaktorja do stanja vroče ugasnitve, smo hitrost segrevanja pri dejanskem prehodnem pojavu določili na osnovi znane hitrosti ohlajanja s polne moči [2]. Pri zasilni ustavitvi reaktorja s polne moči brez ohlajanja so razpoložljivi podatki, ki smo jih dobili iz NEK takšni, da ne prikazujejo celotnega cikla. Zato smo manjkajoče podatke predpostavili. Iz rezultatov meritve temperature je razvidno, da je bil reaktor v vroči ugasnitvi več kot 20 ur. Ogrevanje na polno moč poteka mnogo počasneje, kot je bila sprememba IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 10 Institut »Jožef Štefan«, Ljubljana, Slovenija temperature pri ustavitvi reaktorja s polne moči brez ohlajanja. Hitrost ogrevanja v praksi poteka s hitrostjo približno 5°C/h. Zato smo to vrednost upoštevali tudi v naši analizi. Čas, ko je bil reaktor v vroči ustavitvi pa smo aproksimirali s časom, pri katerem v obravnavanih pogojih temperatura v komponenti doseže stacionarno stanje (pribl. 11,1 ure oz. 40000 s). Čas [h] J[°C] 0 49 4,4 292 5,3 292 5,5 321,5 17,2 321,5 17,5 292 18,0 292 22,4 49 Tabela 7 Temperaturni cikel ogrevanja in ohlajanja reaktorja za projektni prehodni pojav Čas [h] J[°C] 0 44 5,5 84 16,7 96 28,3 290 34 290 34,6 325 45.7 325 48,3 290 51,4 282 55,3 141 66,2 44 Tabela 8 Temperaturni cikel ogrevanja in ohlajanja reaktorja za dejanski prehodni pojav 3.3.2 Tlačne obremenitve Na osnovi standarda ASME smo ocenili, da lahko tlačne (pod)cikle, manjše od 3,96 MPa, zanemarimo. Tlačne spremembe v obravnavanih komponentah pri ogrevanju in ohlajanju reaktorja, ki smo jih upoštevali v analizi, prikazujeta tabeli 11 in 12. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 11 Institut »Jožef Štefan«, Ljubljana, Slovenija Iz tabele 12 izhaja, da smo pri času 51,1 ure upoštevali tudi spremembo tlaka v sistemu, ki je bila manjša od 3,96 MPa in torej po ASME zanemarljiva. To smo naredili zato, ker se je v času 50. ure pojavila največja Trescova ekvivalentna napetost in smo s tem natančnejše simulirali dogajanje v komponenti. Čas [s] T[°C] 0 321,5 25 290,5 75 287,4 40075 287,4 64458 321,5 Tabela 9 Temperaturni cikel ustavitve reaktorja s polne moči brez ohlajanja za projektni prehodni pojav Čas [s] T[°C] 0 325 720 288 1920 292 41920 292 65680 325 Tabela 10 Temperaturni cikel ustavitve reaktorja s polne moči brez ohlajanja za dejanski prehodni pojav Čas [h] p [MPa] 0 3,32 2,3 3,32 4,4 16,08 18,0 16,08 19,1 3,32 22,4 3,32 Tabela 11 Tlačni cikel ogrevanja in ohlajanja reaktorja za projektni prehodni pojav Pri ustavitvi reaktorja s polne moči brez ohlajanja so vse tlačne spremembe manjše od 3.96 MPa. Zato smo v analizi upoštevali stacionarni tlak 16,08 MPa za projektni prehodni pojav in 15,81 MPa za dejanski prehodni pojav, s čemer smo zagotovili konservativnost rezultatov. 3.4 Robni pogoji V analizi smo obravnavali izsek iz reaktorske posode z izstopno šobo in del cevovoda vroče veje. Upoštevali smo takšne robne pogoje, s katerimi simuliramo vpliv okoliških komponent na obravnavan model. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 12 Institut »Jožef Stefan«, Ljubljana, Slovenija • • Čas [h] p [MPa] 0 2,5 20,0 2,83 28,9 13,97 30,6 16,39 32,1 15,77 34,6 15,77 51,1 15,6 54,5 2,5 66,2 2,5 Tabela 12 Tlačni cikel ogrevanja in ohlajanja reaktorja za dejanski prehodni pojav Z cela zg. ploskev Z1 = konst Konstanten pomik točk prereza cevi v vzdolžni (Z2) smeri Izhodišča lokalnih koord. sistemov: 01 - na srednjici posode, v višini središča šobe 02 - v središču prereza cevi vroče veje cela ploskev: t = 0 R^J01 cela ploskev: t = 0 ti cela sp. ploskev Z1 = konst Slika 6 Kinematični robni pogoji v modelu izstopne šobe 3.5 Rezultati Kot rezultate analize predstavljamo največje Trescove ekvivalentne napetosti med obremenitvenimi cikli , ki so definirani v 3.3.1 in 3.3.2. Vrednosti predstavljajo vsoto termičnih in tlačnih napetosti . Na osnovi Trescove ekvivalentne napetosti izračunamo amplitudo nihanja napetosti Sa in nato delni faktor izrabe. Pri tem smo izračunali faktor izrabe, tako za projektne prehodne pojave, kot za dejanske prehodne pojave. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 13 Institut »Jožef Stefan«, Ljubljana, Slovenija 3.5.1 Ogrevanje in ohlajanje reaktorja V projektnem prehodnem pojavu se največja Trescova ekvivalentna napetost 360,4 MPa pojavi v času 17,5 ur (ohlajanje reaktorja) na notranji površini izstopne šobe (Slika 7), ko je dosežena temperatura 292°C. Po 18 h urah se v sistemu začne zmanjševati tlak, kar zmanjšuje napetosti kljub temu, da je gradient temperature velik. Dopustna napetost za ciklično obremenjeno šobo znaša 3Sm = 552,3 MPa [10], kar pomeni, da je šoba obremenjena v dopustnih mejah. s, Tresca (Avg: 75%) +3,6D4e+02 +3.312e+02 +3.021e+02 +2.729e+02 +2.438e+02 +2.146e+02 + 1.854e+02 +1.563e+02 +1.271e+02 +9.797e+01 +6.881e+01 +3.965e+01 + 1.049e+01 Y Slika 7 Največja Trescova ekvivalnentna napetost med projektnim prehodnim pojavom ogrevanja in ohlajanja reaktorja Amplituda nihanja napetosti Sa = 180,2 MPa se izračuna kot polovica Trescove ekvivalentne napetosti [1]. Na osnovi Sa določimo dopustno število obremenitev N = 34153 iz ustrezne Wohlerjeve krivulje (krivulja za materiale z natezno trdnostjo manjšo od 551,6 MPa [10]). Delni faktor izrabe za eno ponovitev prehodnega pojava je tako u1 = 2,93-10-5 oz. u56 =1,64^ 103 za 56 ponovitev prehodnega pojava, kolikor se jih je glede na dostavljene podatke zgodilo do sedaj v NEK [2]. V času 17,5 ure je bil reaktor v fazi ohlajanja. Razlog za največje napetosti pri zniževanju temperature je razviden iz slike 9, ki prikazuje močno pretirano deformacijo izstopne šobe in Trescovo ekvivalentno napetost izstopne šobe zaradi obremenitve s tlakom 16,08 MPa in brez toplotnih obremenitev. Primerjava napetosti (slika 7 in slika 8) pokaže, da imajo napetosti zaradi tlačne obremenitve večji vpliv na največje napetosti v šobi kot temperaturne spremembe za obravnavane prehodne pojave. Pri analizi izmerjenega prehodnega pojava se največja Trescova ekvivalentna napetost 338,3 MPa pojavi v času 50 ur (ohlajanje reaktorja) na notranji površini šobe (Slika 9). V tem času se IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 14 Institut »Jožef Stefan«, Ljubljana, Slovenija v sistemu že delno znižuje tlak, kar znižuje napetosti. Ker se v tem času znižuje tudi temperatura, ki povečuje napetosti, je v času 50 ur dosežena najbolj neugodna kombinacija vpliva tlaka in temperature. Dopustna napetost za ciklično obremenjeno šobo znaša 3Sm = 552,3 MPa [10], kar pomeni, daje šoba obremenjena v dopustnih mejah. S, Tresca (Avg: 75%) +3.140e+02 +2.864S+02 * +2.627C+02 — - +2.3706+02 +2.113e+02 +1.8576+02 + 1.600e+02 +1.343e+02 + 1.0876+02 + 8.3006+01 + 5.7336+01 +3.1666+01 +5.995e+00 «J Slika 8 Močno pretirana deformacija izstopne šobe zaradi obremenitve z notranjim tlakom in pripadajoča Trescova ekvivalentna napetost Amplituda nihanja napetosti Sa = 169,2 MPa se izračuna kot polovica Trescove ekvivalentne napetosti [1]. Na osnovi Sa določimo dopustno število obremenitev N = 40765 iz ustrezne Wohlerjeve krivulje (krivulja za materiale z natezno trdnostjo manjšo od 551,6 MPa). Delni faktor izrabe za eno ponovitev prehodnega pojava je tako u1 = 2,45^ 10-5. Ob nekoliko nerealni predpostavki, da so bila vsa dosedanja ogrevanja in ohlajanja reaktorja enaki obravnavanemu, bi faktor izrabe za 56 ponovitev prehodnega pojava, kolikor se jih je glede na dostavljene podatke zgodilo do sedaj v NEK, znašal u56 =1,37^ 10-3. Primerjava rezultatov pokaže, da ima izmerjeni prehodni pojav manjši vpliv na utrujanje obravnavanih komponent kot projektni, kar kaže v tem primeru na konzervativnost projektiranja elektrarne. 3.5.2 Ustavitev reaktorja s polne moči brez ohlajanja Prii analizi projektne ustavitve reaktorja s polne moči brez ohlajevanja se največja Trescova ekvivalentna napetost 381,2 MPa pojavi v času 25 s (ohlajanje reaktorja) na notranji površini izstopne šobe (Slika 10), ko je dosežena temperatura 290,5°C. V nadaljevanju se sicer temperatura še znižuje do 287,4 °C, vendar je hitrost zniževanja temperature mnogo manjša in zato ne vpliva na povečanje napetosti. Dopustna napetost za ciklično obremenjeno šobo znaša 3Sm = 552,3 MPa [10], kar pomeni, da je šoba obremenjena v dopustnih mejah. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 15 Institut »Jožef Stefan«, Ljubljana, Slovenija • • S, Tresca (Avg: 75%) B+3.383e+Q2 +3.106e+02 +2.830e+02 +2.553e+02 +2.276e+Q2 +2.000e+Q2 + 1.723e+C2 +l,447e+02 + 1.17Qe+02 E+8.936e+01 +6.171e+01 +3.40Se+01 +6.396e+00 Slika 9 Največja Trescova ekvivalentna napetost med izmerjenim ogrevanjem in ohlajanjem Amplituda nihanja napetosti Sa = 190,6 MPa se izračuna kot polovica Trescove ekvivalentne napetosti [1]. Na osnovi Sa določimo dopustno število obremenitev N = 29194 iz ustrezne Wohlerjeve krivulje (krivulja za materiale z natezno trdnostjo manjšo od 551,6 MPa). Delni faktor izrabe za eno poonvitev prehodnega pojava je tako u1 = 3,43^ 10-5 oz. u73 =2,5-10-3 za 73 ponovitev prehodnih pojavov, kolikor se jih je glede na dostavljene podatke zgodilo do sedaj v NEK. Analiza izmerjenega prehodnega pojava pokaže največjo Trescovo ekvivalentno napetost 354,9 MPa pojavi v času 720 s (ohlajanje reaktorja) na notranji površini izstopne šobe (Slika 11), ko je dosežena temperatura 288 °C. Dopustna napetost za ciklično obremenjeno šobo znaša 3Sm = 552,3 MPa [10], kar pomeni, da je šoba obremenjena v dopustnih mejah- Amplituda nihanja napetosti Sa = 181,2 MPa se izračuna kot polovica Tresca ekvivalentne napetosti [1]. Na osnovi Sa določimo dopustno število obremenitev N = 33629 iz ustrezne Wohlerjeve krivulje (krivulja za materiale z natezno trdnostjo manjšo od 551,6 MPa). Delni faktor izrabe za eno ponovitev prehodnega pojava je tako u1 = 2,97^ 10-5. Ob nekoliko nerealni predpostavki, da so bila vsa dosedanja ogrevanja in ohlajanja reaktorja enaki obravnavanemu, bi faktor izrabe za 73 prehodnih pojavov, kolikor se jih je glede na dostavljene podatke zgodilo do sedaj v NEK, znašal u73 =2,1710-3. Primerjava rezultatov pokaže, da ima obravnavani izmerjeni prehodni pojav ustavitve reaktorja s polne moči brez ohlajevanja manjši vpliv na utrujanje obravnavanih komponent kot projektni, kar kaže v tem primeru na konzervativnost projektiranja elektrarne. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 16 Institut »Jožef Stefan«, Ljubljana, Slovenija • • s, Tresca (Avg: 75%) r +3.812e+02 - +3.505e+02 - +3.198e+02 - +2.890e+02 - +2.583e+02 - +2.276e+C2 - +1.969e+02 - +1.661S+02 - +1.3546+02 - +1.0476+02 - +7.396e+01 H- +4.324e+01 +1.2Sla+Cl v xJ- Slika 10 Največja Trescova ekvivalnentna napetost med projektnim prehodnim pojavom ustavitve reaktorja s polne moči brez ohlajanja s, Tresca (Avg: 75%) r2ï5 r +3.549e+02 1— - +3.260e+02 „j - +2,971e+02 - +2.662e+02 - +2.393e+02 - +2.104e+02 - + 1.615e+02 - +l,526e+02 - +1.237e+02 - +9,4786+01 - +6.588e+01 +3.697e+01 +8.063e+00 x z- Slika 11 Največja Trescova ekvivalnentna napetost med izmerjenim prehodnim pojavom ustavitve reaktorja s polne moči brez ohlajevanja IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 17 Institut »Jožef Štefan«, Ljubljana, Slovenija 4 MODEL PRELIVNEGA VODA TLAČNIKA V tem poglavju predstavimo izračun temperatur, napetosti in delnih faktorjev izrabe v prelivnem vodu tlačnika med dvema hipotetičnima prehodnima pojavoma toplotnega razslojevanja hladila in potovanja toplotnega šoka po prelivnem vodu. Pri tem opazujemo tudi časovne poteke temperatur na hipotetično zamišljenih položajih temperaturnih tipal na zunanji površini prelivnega voda. 4.1 Geometrija modela Vsi modeli geometrije prelivnega voda in šobe med prelivnim vodom in vročo vejo so izdelani po risbah C-318-601 in 1209E72. 4.1.1 Poenostavitve Modeliranje z metodo končnih elementov zahteva določeno poenostavljanje geometrije in mej materialov. 1. Zanemarjanje drobnih geometrijskih detajlov. Podobno kot v primeru izstopne šobe reaktorske tlačne posodein smo tudi v modelu prelivnega voda tlačnika zanemarili nekatere detajle. Predvsem pri tem mislimo na detajle, kot so npr. a) predori za merjenje temperature v prelivnem vodu s potopljenim termometrom, b) obešala za prelivni vod , ki ne vplivajo bistveno na odziv celotnega sistema v predstavljenih analizah. V primeru potrebe pa lahko pozneje iz rezultatov modela dobimo robne pogoje za mikro analizo posameznega detajla. 2. Modeliran del cevi vroče veje v okolici spoja s prelivnim vodom, ki služi predvsem kot podpora prelivnemu vodu, saj je praktično gledano prelivni vod dvostransko trdno pritrjen cevovod. 3. Spoji materialov. Spoj dveh materialov je praviloma izveden z varjenjem. Za celovito analizo razmer v varjenih spojih (kot npr. spoj šobe in prelivnega voda) je potrebno natančno poznati postopek izdelave. Potem je mogoče oceniti zaostale napetosti in kolikor toliko natančno geometrijo spoja. Takih informacij nimamo. Po drugi strani pa je za zvare značilno, da so meje med različnimi materiali in s tem snovnimi lastnostmi v njih in njihovi bližini zabrisane. Zato je zvar modeliran kot idealen spoj prelivnega voda in šobe. Pri izdelavi prostorskega modela smo se držali smernic glede uporabe končnih elementov, ki so opisane v [1]. Prostorski model prelivnega voda je modeliran v celotni dolžini od spoja s šobo pri vroči veji do reducirke pred vstopno šobo tlačnika. Gostota mreže je primerna glede na hitrost spremembe temperatur. Temperaturno porazdelitev smo določili z modelom, v katerem smo uporabili 34049 paraboličnih končnih elementov za simulacijo prenosa toplote. Za trdnostno analizo pa smo model diskretizirali z enako mrežo, pri čemer smo uporabili končne elemente, ki omogočajo izračun napetostno-deformacijskega polja. V obeh analizah smo po debelini uporabili tri končne elemente, s čemer lahko glede na uporabljene vhodne podatke z zadostno natančnostjo modeliramo temperaturna in napetostno deformacijska polja. V prelivnem vodu tlačnika smo predpostavili štiri hipotetična merilna mesta za merjenje temperatur na zunanji površini cevi (M1 do M4 na sliki 13). Izračunane časovne poteke IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 18 Institut »Jožef Stefan«, Ljubljana, Slovenija • • temperatur smo v nadaljevanju poleg v v petih točkah (A do E) na zunanji površini cevovoda prikazali tudi v pripadajočih petih točkah na notranji površini cevovoda. Slika 12 Prostorski model prelivnega voda tlačnika z Slika 13 Predpostavljena merilna mesta M1 do M4 na prelivnem vodu tlačnika IJS-DP-10076 Izdaja 1 Marec 2009 stran 19 File. IJS-DP-10076-R1.doc Institut »Jožef Stefan«, Ljubljana, Slovenija 4.2 Snovne lastnosti Cevovod in šoba prelivnega voda sta izdelani iz materiala SA376 Type 316, za katerega so snovske lastnosti definirane v ASME B&PV Code, Section III. (Apendix I) [10] in so temperaturno odvisne. Snovne lastnosti, ki jih potrebujemo pri analizi so: - modul elastičnosti E [MPa] - linearna temperaturna razteznost a [1/K] - toplotna prevodnost A [W/mK] in - specifična toplota cp [J/kg K] - koeficient prestopa toplote h [W/m2K] 4.3 Obremenitve Izbrane obremenitve so hipotetične in so namenjene demonstraciji možnosti, ki jih zasnovana metoda ponuja pri analizi odziva prelivnega voda na toplotne šoke in toplotno razslojene tokove s spremenljivo mejo med toplim in hladnim slojem. Obremenitve so izbrane z ozirom na zmogljivosti sistemov v jedrski elektrarni Krško [2] tako, da se po naši oceni lahko pojavijo tudi v praksi. Namen tega dela analize torej ni podati prispevka prehodnega pojava k utrujenosti komponente, ampak demonstracija možnosti zasnovane metode. Kot temperaturi hladnega in toplega sloja hladila privzamemo največjo temperaturno razliko med hladilom v vroči veji in v tlačniku med ogrevanja in ohlajanja reaktorja: Tc = 96 °C in Th = 223 °C [2]. Upoštevamo tudi tlak p = 2,5 MPa [2]. 4.3.1 Toplotno razslojeni tok Toplo hladilo je v tlačniku, hladno v vroči veji. Med njima je idealna vodoravna meja. Na začetku analize predpostavimo mejo med obema hladiloma blizu spodnje površine cevovoda na mestu, kjer se začne drugo koleno (Slika 13), gledano iz smeri vroče veje proti tlačniku. Na začetku prehodnega pojava predpostavimo, da je toplotno polje v stacionarnem stanju. Mejo med hladiloma nato v prehodnem pojavu dvigamo in spuščamo. V prvem primeru v najvišji točki počakamo na stacionarno stanje, nato gladino z enako hitrostjo spustimo v izhodišče. V drugem primeru gladina nemudoma zapusti najvišjo točko in se z enako hitrostjo vrne v izhodišče. Hitrost dviganja in spuščanja gladine smo ocenili na 2,57 mm/s. Ocena upošteva značilno hitrost potovanja hladila po prelivnem vodu, pri katerem se razslojeni tekočini ne pomešata in znaša v literaturi okoli 50 mm/s [6]. Koeficient prestopa toplote pri taki hitrosti ocenimo na h = 50 W/m2K. 4.3.2 Toplotni šok Toplo hladilo je v tlačniku, hladno v vroči veji. Med njima je idealna meja, ki je pravokotna glede na os prelivnega voda tlačnika. Meja med hladnim in vročim hladilom potujena razdalji 2,1 m po prelivnem vodu tlačnika s hitrostjo 0,4 m/s, ki smo jo ocenili na osnovi moči grelcev v tlačniku [12]. Pri takšni hitrosti hladila sledi koeficient prestopa toplote h = 2100 W/m2K. Pred začetkom premikanja meje predpostavimo, da je toplotno polje v stacionarnem stanju. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 20 Institut »Jožef Stefan«, Ljubljana, Slovenija Analizirali smo dve značilni gibanji meje med hladiloma. V prvem primeru prepotuje 2,1 m s hitrostjo 0,4 m/s. V novem položaju meja miruje vse dotlej, da se ponovno vzpostavi stacionarno stanje. Nato se z enako hitrostjo vrne v izhodišče. V drugem primeru prepotuje 2,1 m s hitrostjo 0,4 m/s in se nato nemudoma obrne in z enako hitrostjo vrne v izhodišče. Izhodiščni položaj meje med hladiloma je od merilnega mesta M2 dovolj oddaljen v smeri proti vroči veji, da merilno mesto ob začetku prehodnega pojava ne zazna vpliva različnih temperatur hladil. 4.4 Robni pogoji in predpostavke V analizi smo obravnavali prelivni vod tlačnika od spoja s šobo na vroči veji do reducirke pri vstopni šobi v tlačnik. Upoštevali smo takšne robne pogoje, s katerimi simuliramo vpliv okoliških komponent na obravnavan model. 4.4.1 Toplotna analiza Glavni predpostavki pri toplotni analizi sta: - zunanje površine primarnega kroga so popolnoma izolirane. Pri ohlajanju sistema zato vso toploto odvedemo iz stene s pomočjo reaktorskega hladila, kar zagotavlja največje temperaturne gradiente in s tem konzervativnost analize. - v prelivnem vodu upoštevamo prestop toplote s hladila na trdnino in obratno preko koeficienta prestopa toplote h. Kot je že bilo poudarjeno, je porazdelitev temperature po preseku cevi zelo odvisna od koeficienta prestopa toplote s tekočine na trdnino. Pri višjem koeficientu prestopa toplote (višje hitrosti tekočine) se temperatura trdnine hitreje izenači s temperaturo tekočine. Nižji koeficienti prestopa toplote torej praviloma pomenijo nižje razlike temperatur v trdnini in posledično tudi nižje napetosti. Snovske lastnosti z izjemo koeficienta prestopa toplote so modelirane kot temperaturno odvisne veličine, zato je analiza temperaturnega polja nelinearna. Konstanten pomik točk prereza cevi Y smeri Slika 14 Kinematični robni pogoji modela prelivnega voda tlačnika IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 21 Institut »Jožef Stefan«, Ljubljana, Slovenija 4.4.2 Napetostna analiza Robne pogoje pri napetostni analizi predstavljajo časovno odvisna temperaturna polja. Slika 14 prikazuje kinematične robne pogoje. Premike vroče veje zaradi toplotnega raztezanja smo v analizi zanemarili. V primeru toplotnega razslojevanja se lahko v šobi med vročo vejo in prelivnim vodom med prehodnim pojavom spreminjajo smeri glavnih napetosti. To v skladu s pravili kontrole na utrujanje po ASME B&PV Code zahteva posebno obravnavo, ki pa jo na tem mestu nismo izvedli, ker so ocenjeni delni faktorji izrabe le hipotetični. 4.5 Rezultati V analizi smo obravnavali dva značilna primera, ki se lahko pojavita v prelivnem vodu: 1. toplotno razslojeni tok in 2. toplotni šok. 4.5.1 Toplotno razslojeni tok Kot rezultat analize predstavljamo: 1. časovno odvisno porazdelitev temperature na notranji in zunanji steni cevovoda na mestih, kjer smo predpostavili merilce temperature po zunanjem obodu cevovoda (Slika 13). 2. največjo vrednost Trescove ekvivalentne napetosti in faktor izrabe. 3. Obravnavali smo dva primera: 1. gladina se dvigne iz spodnje lege v zgornjo lego in tam obstane dokler se ne vzpostavi stacionarno stanje. Po tem se gladina vrne nazaj v izhodiščno lego. 2. gladina se dvigne iz spodnje lege v zgornjo lego in takoj nazaj v izhodiščno lego. Za spremembo gladine iz spodnje lege v zgornjo lego cevovoda, kjer stoji toliko časa, da se vzpostavi stacionarno stanje in šele po tem vrne v izhodiščno lego, prikazuje slika 16 temperaturne porazdelitve v vmesnih stanjih. V primeru, da se gladina dvigne od spodnjega do zgornjega roba cevovoda in tam obstane dokler se ne vzpostavi stacionarno stanje (Slika 15) in se šele nato vrne v izhodiščno lego, se temperatura za cel cikel na merilnem mestu M4-A spreminja kot prikazuje slika 16. Zaradi lažje predstavitve rezultatov bomo prikazali porazdelitev temperature za čas: - od 0 do 1000 s, ko se je gladina dvigovala iz začetne lege na tem intervalu in - od 40000 do 60000 s, kar zajema čas preden je v zgornji legi doseženo stacionarno stanje in čas ko se je gladina spustila v izhodiščno lego Slika 17 prikazuje spremembo temperature na merilnem mestu M1. Iz rezultatov na sliki 17 je razvidno, da je po celem obodu in skozi debelino stene cevi dosežena konstantna temperatura 223°C in da obravnavana sprememba gladine med vročim in hladnim fluidom ne vpliva na temperaturne spremembe na tem mestu. Slika 18 prikazuje spremembo temperature na merilnem mestu M2. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 22 Institut »Jožef Stefan«, Ljubljana, Slovenija • • NTll +2.230e+02 +2.124e+02 + 2.018e+02 + 1.913e+02 +1.807e+02 +1.701e+02 +1.595e+02 +1.489e+02 +1.383e+02 t-1.278e+02 +1.172e+02 +1.066e+02 l- +9.600e+01 Spodnja lega gladine NTll +2.2306+02 +2.1246+02 +2.0186+02 +1,9136+02 +1.8076+02 +1.70le+02 +1.5956+02 ■ +1.4896+02 ■ +1.383e+02 + 1.2786+02 +1.1726+02 + 1.0666+02 +9.600e+01 Zgornja lega gladine v stacionarnem stanju NTll _ r +2.2306+02 F - +2.124e+02 - +2.01Be+02 - +1.913e+02 - +1.807e+02 - +1.701e+02 - +1.595a+02 - +1.489e+02 - +1.383e+02 — - +1.278e+02 - +l,172e+02 - +l,066e+Q2 a L +9.600e+01 Spodnja lega gladine Slika 15 Porazdelitev temperature pri spremembi lege gladine iz spodnje do zgornje in nazaj do spodnje z vmesnim stacionarnim stanjem v zgornji legi IJS-DP-10076 Izdaja 1 Marec 2009 stran 23 File. IJS-DP-10076-R1.doc Institut »Jožef Stefan«, Ljubljana, Slovenija • • Čas [s] M4-A-N M4-A-Z Slika 16 Porazdelitev temperature v notranji (M4-A-N) in zunanji (M4-A-Z) točki pri spremembi lege gladine z vmesnim stacionarnim stanjem Slika 17 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M1 v času do 1000 s IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 24 Institut »Jožef Stefan«, Ljubljana, Slovenija • • Čas [s] M2-A-N M2-A-Z M2-B-N M2-B-Z M2-C-N M2-C-Z M2-D-N M2-D-Z M2-E-N M2-E-Z Slika 18 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M2 v času do 1000 s Čas [s] M3-A-N M3-A-Z M3-B-N M3-B-Z M3-C-N M3-C-Z M3-D-N M3-D-Z M3-E-N M3-E-Z Slika 19 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M3 v času do 1000 s IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 25 Institut »Jožef Stefan«, Ljubljana, Slovenija Iz rezultatov na sliki 18 je razvidno, da so razlike med notranjimi in zunanjimi temperaturami pri dvigovanju gladine večje v zgornjem delu cevovoda, kjer so tudi največji temperaturni gradienti. Iz diagrama je tudi razvidno, da se je začela temperatura na merilnem mestu M2-A-N spreminjati najkasneje. Temperaturne spremembe v točkah na zunanji površini so bolj gladke, kot na notranji strani. Temperature na zunanji strani so po nižanju temperature v cevovodu po višini višje kakor na notranji strani, kar je posledica vpliva koeficienta prestopa, koeficienta prevoda toplote in omočenosti z vročo in hladno vodo (poglavje 2.1.2). Slika 19 prikazuje spremembo temperature na merilnem mestu M3. V primerjavi z rezultati na sliki 18 se pri dvigu gladine temperatura na mestu M3-A-N začne spreminjati prej kot na mestu M2-A-N, saj je mesto M3-A-N nižje po višini kot M2-A-N (Slika 14), zaradi česar do tega mesta prej pride hladen fluid. Pri nižjih merilnih merilnih mestih (M3-D in M3-E) spremembe temperature praktično ni zaznati. Slika 20 prikazuje spremembo temperature na merilnem mestu M4. Rezultati kažejo podobno spreminjanje temperature kot pri merilnem mestu M3. Slika 17 prikazuje spremembo temperature na merilnem mestu M1 v času med 40000 in 60000 s. Rezultati na sliki 21 kažejo, da je skozi debelino dosežena konstantna temperatura 223°C, kar pomeni, da sprememba gladine med vročim in hladnim hladilom za obravnavani primer ne vpliva na temperaturne spremembe na tem mestu. Slika 22 prikazuje spremembo temperature na merilnem mestu M2 v času med 40000 s in 60000 s. Iz rezultatov na sliki 22 je razvidno, da je po gibanju gladine navzdol za merilno mesto M2 temperatura na zunanjih točkah D in E višja od notranje temperature, medtem, ko je v točkah A do C temperatura na notranji strani višja. Do tega pride zaradi interakcije temperatur pri prestopu toplote s tekočine na trdnino in pri prevodu skozi po steni cevi. Slika 23 prikazuje spremembo temperature na merilnem mestu M3 v času med 40000 s in 60000 s. Iz rezultatov na sliki 23 je razvidno, da je hitrost spreminjanja temperature manjša kot na merilnem mestu M2. Slika 24 prikazuje spremembo temperature na merilnem mestu M4 v času med 40000 s in 60000 s. Primerjava rezultatov z merilnim mestom M2 in M3 pokaže, da je tukaj hitrost spreminjanja temperature najmanjša, ko se gladina na začetku drugega kolena spušča iz zgornje površine proti spodnji površini. Slika 25 prikazuje največjo Trescovo ekvivalentno napetost med spremembo gladine od spodnje lege do zgornje lege in nazaj. Največja napetost se pojavi v začetnem oz. končnem stacionarnem stanju, torej, ko je gladina v spodnji legi. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 26 Institut »Jožef Stefan«, Ljubljana, Slovenija • • Čas [s] M4-A-N M4-A-Z M4-B-N M4-B-Z M4-C-N M4-C-Z M4-D-N M4-D-Z M4-E-N M4-E-Z Slika 20 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M4 v času trajanja cikla do 1000 s Slika 21 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M1 v času trajanja cikla med 40000 s in 60000 s IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 27 Institut »Jožef Stefan«, Ljubljana, Slovenija • • 230 210 190 O O K 170 150 130 110 90 40000 45000 50000 Čas [s] 55000 60000 - M2-A-N M2-A-Z M2-B-N M2-B-Z M2-C-N M2-C-Z M2-D-N M2-D-Z M2-E-N M2-E-Z Slika 22 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M2 v času trajanja cikla med 40000 s in 60000 s Čas [s] M3-A-N M3-A-Z M3-B-N M3-B-Z M3-C-N M3-C-Z M3-D-N M3-D-Z M3-E-N M3-E-Z Slika 23 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M3 v času trajanja cikla med 40000 s in 60000 s IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 28 Institut »Jožef Stefan«, Ljubljana, Slovenija • • Čas [s] M4-A-N M4-A-Z M4-B-N M4-B-Z M4-C-N M4-C-Z M4-D-N M4-D-Z M4-E-N M4-E-Z Slika 24 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M4 v času trajanja cikla med 40000 s in 60000 s s, Tresca (Avg; 75%) r +1.423e+02 - + 1.305e+02 - +1.187e+02 - +1.069e+02 - +9.515e+01 - +8.337e+01 - 47.15Be+01 - +5.9B0a+01 - +4.B02e+01 - +3.624e+01 - +2.446e+01 - +1.267e+01 L +8.920e-01 z X Slika 25 Največja Trescova ekvivalentna napetost pri enem ciklu z vmesnih stacionarnim stanjem IJS-DP-10076 Izdaja 1 Marec 2009 stran 29 File. IJS-DP-10076-R1.doc Institut »Jožef Stefan«, Ljubljana, Slovenija Amplituda nihanja napetosti Sa = 71,2 MPa se izračuna kot polovica Tresca ekvivalentne napetosti [1]. Na osnovi Sa določimo dopustno število obremenitev N = 3,18^ 108 iz ustrezne Wohlerjeve krivulje (krivulja za avstenitne materiale z Sa < 198,6 MPa). Delni faktor izrabe za eno ponovitev prehodnega pojava je tako u1 = 3,15^ 10-9. Pri analizi spoja izstopne šobe iz reaktorske posode smo ugotovili, da ima tlak večji vpliv na napetosti kot temperaturne spremembe. V prelivnem vodu povzroča tlak 2,5 MPa največjo Trescovo ekvivalentno napetost v velikosti 15,7 MPa, kar je mnogo manj kot jo povzroča toplotno razslojevanje. Zato je v primeru prelivnega voda potrebno posebno pozornost posvetiti temperaturnim obremenitvam. S, Tresca (Avg; 75%) • • Y Slika 26 Vpliv tlaka 2,5 MPa na Tresca ekvivalentno napetost v prelivnem vodu V primeru, da se gladina dvigne od spodnje površine do zgornje površine cevovoda in nato takoj nazaj v izhodiščno lego, prikazuje slika 27 porazdelitev temperature v vmesnih stanjih. Iz rezultatov na sliki 27 je razvidno, da je sprememba temperature na zunanji površini mnogo manj izrazita, kot je v primeru, če gladina v zgornji legi stoji toliko časa, da se vzpostavi stacionarno stanje (Slika 15). V primeru, da se gladina dvigne od spodnjega robu do zgornjega robu cevovoda in takoj nazaj v izhodiščno lego, se temperatura za cel cikel na merilnem mestu M4-A spreminja kot prikazuje slika 27. Slika 29 prikazuje spremembo temperature na merilnem mestu M1. Iz rezultatov na sliki 28 je razvidno, da je po celem obodu in skozi debelino dosežena konstantna temperatura 223°C in da obravnavana sprememba gladine med vročim in hladnim fluidom ne vpliva na temperaturne spremembe na tem mestu. IJS-DP-10076 Izdaja 1 Marec 2009 stran 30 File. IJS-DP-10076-R1.doc Institut »Jožef Stefan«, Ljubljana, Slovenija Slika 30 prikazuje spremembo temperature na merilnem mestu M2. • • ■ +2.230e+02 +2 124e+02 ■ +2.018e+02 ■ +1.1136+02 +1 807e+02 ■ + 1.701e+G2 +l.S95e+02 ■ + 1.489e+02 + 1.383e+02 ■ + 1.278e+02 +1172e+02 ■ + 1.066e+02 . - ^ 600'' ■ 'J: Spodnja lega gladine NTll r +2,2305+02 - +2.1246+02 - +2.0185 + 02 - + 1,9135 + 02 - + 1.807e + 02 - +1.7015 + 02 - + 1.S9S5 + 02 - + 1.4895 + 02 _ - +1.3835 + 02 - + 1,2785+02 - + 1.172e + 02 - +1.0665 + 02 L +9,600e+01 Zgornja lega gladine brez stacionarnega stanja wni r +2,2328+02 — - +2.126S+02 - +2.0205 + 02 - +1,9145+02 - +1.808e + 02 - +1.7025 + 02 - +1.S96S+02 - +1.4905 + 02 - +1.3845 + 02 - +1,2785+02 - +1.1725 + 02 — - +1.0665 + 02 — L +9,6005+01 Spodnja lega gladine Slika 27 Porazdelitev temperature pri spremembi lege gladine iz spodnje do zgornje in nazaj do spodnje brez vmesnega stacionarnega stanja v zgornji legi IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 31 Institut »Jožef Stefan«, Ljubljana, Slovenija • • 210 190 170 O a- 150 k 130 110 90 porazdelitev v točki na notranji strani porazdelitev v točki na zunanji strani 2000 4000 6000 Čas [s] 8000 10000 M4-A-N M4-A-Z 0 Slika 28 Porazdelitev temperature v notranji (M4-A-N) in zunanji (M4-A-Z) točki pri spremembi lege gladine (en cikel) brez vmesnega stacionarnega stanja Slika 29 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M1 v času trajanja cikla do 1000 s IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 32 Institut »Jožef Stefan«, Ljubljana, Slovenija • • 230 210 190 170 O K 150 130 110 90 M2-A-N M2-A-Z M2-B-N M2-B-Z M2-C-N M2-C-Z M2-D-N M2-D-Z M2-E-N M2-E-Z 200 400 600 800 1000 Cas [s] 0 Slika 30 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M2 v času trajanja cikla do 1000 s Iz rezultatov na sliki 30 je razviden čas trajanja spremembe temperature na notranji strani cevovoda, pri čemer je na merilnih mestih D in E sprememba temperature najmanj izrazita. Iz rezultatov je tudi razvidno, da se je sprememba na merilnem mestu A začela najkasneje in se je tudi najhitreje končala, kar je skladno z gibanjem gladine. Spremembe v točkah na zunanji površini so gladke in ne pokažejo na način spremembe gibanja gladine v cevovodu. Slika 31 prikazuje spremembo temperature na merilnem mestu M3. V primerjavi z rezultati na sliki 30 traja temperaturna sprememba na notranji strani dlje časa, vendar tudi tukaj te spremembe na zunanji strani ni zaznati. Slika 32 prikazuje spremembo temperature na merilnem mestu M4.Temperaturna sprememba na notranji strani je na merilnem mestu M4 trajala najdlje, pri čemer so spremembe na notranji strani praktično opazne samo za točke A in B. Na zunanji strani sprememb temperature na način, kot se spreminja na notranji strani, ni mogoče opaziti. Slika 33 prikazuje največjo Tresca ekvivalentno napetost med spremembo gladine od spodnje lege do zgornje lege in nazaj brez vmesnega stacionarnega stanja. Največja napetost se pojavi v začetnem oz. končnem stacionarnem stanju, torej, ko je gladina v spodnji legi. Rezultat je enak kot v primeru z vmesnim stacionarnim stanjem, kar pomeni, da v obravnavanem primeru hitrost spremembe gladine iz zgornjega v spodnje stanje nima vpliva na največjo napetost. Amplituda nihanja napetosti Sa = 71,2 MPa se izračuna kot polovica Trescove ekvivalentne napetosti [1]. Na osnovi Sa določimo dopustno število obremenitev N = 3,18^ 108 iz ustrezne Wohlerjeve krivulje (krivulja za avstenitne materiale z Sa < 198,6 MPa). Delni faktor izrabe za eno ponovitev prehodnega pojava je tako u = 3,15^ 10-9. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 33 Institut »Jožef Stefan«, Ljubljana, Slovenija • • 210 190 170 O £- 150 K 130 110 90 M3-A-N M3-A-Z M3-B-N M3-B-Z M3-C-N M3-C-Z M3-D-N M3-D-Z M3-E-N M3-E-Z 200 400 600 Čas [s] 800 1000 Slika 31 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M3 v času trajanja cikla do 1000 s 210 190 170 O £- 150 K 130 110 90 M4-A-N M4-A-Z M4-B-N M4-B-Z M4-C-N M4-C-Z M4-D-N M4-D-Z M4-E-N M4-E-Z 200 400 600 Čas [s] 800 1000 Slika 32 Porazdelitev temperature v notranjih in zunanjih točkah na merilnem mestu M4 v času trajanja cikla do 1000 s 0 0 IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 34 Institut »Jožef Stefan«, Ljubljana, Slovenija • • s. Tresca (Avg: 75%) 1- + 1.423e+02 - +1.305e+02 - +1.187e+02 - +1.0706+02 - +9.517e+01 - +8.3386+01 - +7.1606+01 - +S. 9816+01 - +4.803e+01 - +3.625e+01 - +2.446e+01 H- + 1.2686+01 ■L +8.9236-01 Slika 33 Največja Trescova ekvivalentna napetost pri enem ciklu brez vmesnega stacionarnega stanja 4.5.2 Toplotni šok Kot rezultat analize predstavljamo: 1. časovno odvisno porazdelitev temperature na notranji in zunanji steni cevovoda na mestu M2, kjer smo hipotetično predpostavili merilec temperature po zunanjem obodu cevovoda (Slika 13). 2. največjo vrednost Trescove ekvivalentne napetosti in faktor izrabe. Obravnavali smo dva primera: 1. meja med vročim in hladnim hladilom se v končni legi ustavi in stoji, dokler ni vzpostavljeno stacionarno stanje in nato potuje nazaj v izhodiščno lego. 2. meja med vročim in hladnim hladilom se po zaustavitvi v vmesni legi giba takoj nazaj v izhodiščno lego. Za spremembo lege meje med vročim in hladnim hladilom iz začetne lege v skrajno lego vzdolž cevovoda, kjer meja stoji toliko časa, da se vzpostavi stacionarno stanje in se šele po tem vrne v izhodiščno lego, prikazuje slika 34 temperaturne porazdelitve v izbranih stanjih. Ker se vertikalna meja giba, vsa merilna mesta po obodu cevovoda kažejo enako temperaturo (Slika 35). Zato bomo v nadaljevanju prikazovali rezultate le za točko A merilnega mesta M2. Zaradi lažje predstavitve rezultatov bomo prikazali porazdelitev temperature za čas: - od 0 do 40 s, ko se je meja gibala preko merilnega mesta M2 in - od 4000 do 7000 s, kar zajema čas preden je gladina dosegla stacionarno stanje v skrajni vzdolžni legi, in čas po tem, ko se je meja gibala nazaj v izhodiščno mesto. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 35 Institut »Jožef Stefan«, Ljubljana, Slovenija • • - +2.2336+02 - +2,125e+02 - +2,0l7e+02 +1.909e+02 - + l.Ô02e+02 - +l,6$4e+02 - + l,SB6c+02 - + 1.478C+02 - +1.371C+02 +i.263e+02 + 1,1556+02 + 1.0476+02 - +9.3946+01 Začetna lega meje - +2.2306+02 - +2,124e+Q2 - +2.01Be+02 + 1.9l3e+02 - +1.ÔO7C+02 - +1.70le+02 - + l,S9Se+02 - + l,4ft9c+02 - +l,3»3e+02 + 1.278e+02 + M 776+02 +1.0666+07 - +9.6006+01 - +2.2336+02 - +2,125e+02 - +2,0l7e+02 +1.909e+02 - + l.Ô02e+02 - +l,6$4e+02 - + l,SB6c+02 - +l,478e+02 - + 1.3716+02 + 1.263e+Q2 + 1,1556+02 + 1.0476+02 - +9.3946+01 Skrajna lega meje v vzdolžni smeri v stacionarnem stanju Končna lega meje po zaključku cikla Slika 34 Porazdelitev temperature pri spremembi lege gladine v vzdolžni smeri cevovoda z vmesnim stacionarnim stanjem v skrajni vzdolžni legi IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 36 Institut »Jožef Stefan«, Ljubljana, Slovenija • • 230 210 190 O O K 170 150 130 110 90 / # „ _ porazdelitev v _ točki na zunanji """ strani porazdelitev v ✓ točki na notranji / strani V stacionarno , stanje / V, • . C < 2000 4000 6000 Čas [s] 8000 M2-A-N M2-A-Z M2-B-N M2-B-Z M2-C-N M2-C-Z M2-D-N M2-D-Z M2-E-N M2-E-Z Slika 35 Porazdelitev temperature v notranji (M2-A-N) in zunanji (M2-A-Z) točki pri potovanju motnje preko tega merilnega mesta z vmesnim stacionarnim stanjem (en cikel) 230 210 190 170 O p . K 150 130 110 90 M2-A-N M2-A-Z 10 15 20 25 Čas [s] 30 35 40 Slika 36 Porazdelitev temperature v notranji (M2-A-N) in zunanji (M2-A-Z) točki pri potovanju motnje preko tega merilnega mesta za čas do 40 s 0 0 5 IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 37 Institut »Jožef Stefan«, Ljubljana, Slovenija Iz rezultatov na sliki 36 je razvidna velika razlika med temperaturo na notranji strani in temperaturo na zunanji strani, kar pomeni, da se je gladina gibala tako hitro, da zunaj ni mogoče zaznati te spremembe, ko je gladina dosegla skrajno sprednjo točko po času 5,25 s. Slika 37 prikazuje spremembo temperature na merilnem mestu M2 za čas od 4000 do 7000 s. 230 210 190 170 O O ° K 150 130 110 90 M2-A-N M2-A-Z 4000 4500 5000 5500 Čas [s] 6000 6500 7000 Slika 37 Porazdelitev temperature v notranji (M2-A-N) in zunanji (M2-A-Z) točki pri potovanju motnje preko tega merilnega mesta za čas od 4000 do 7000 s Iz rezultatov na sliki 37 je razvidno hitro naraščanje temperature namerilnem mestu M2 zaradi velike hitrosti gibanja meje in kasnejše počasno spremembo do stacionarnega stanja. Slika 38 prikazuje največjo Trescovo ekvivalentno napetost med spremembo meje v vzdolžni smeri iz začetnega stanja naprej do skrajne lege v vzdolžni smeri in nazaj v izhodiščno lego z vmesnim stacionarnim stanjem v skrajni vzdolžni legi (Slika 34). Največja napetost se pojavi v času 38,81 s po začetku gibanja gladine, kar pomeni, da v času, ko je meja med vročim in hladnim hladilom že bila v skrajni vzdolžni legi. Amplituda nihanja napetosti Sa = 159,7 MPa se izračuna kot polovica Tresca ekvivalentne napetosti [1]. Na osnovi Sa določimo dopustno število obremenitev N = 2,02^ 106 iz ustrezne Wohlerjeve krivulje (krivulja za avstenitne materiale z Sa < 198,6 MPa). Delni faktor izrabe za eno ponovitev prehodnega pojava je tako u1 = 4,95^ 10-7. Za gibanje vertikalne meje med vročim in hladnim hladilom tako, da ni vmesnega stacionarnega stanja, prikazuje temperaturne porazdelitve po obodu cevovoda v skrajnih legah slika 39. Slika 39 prikazuje spremembo temperature na merilnem mestu M2, ko se meja med vročim in hladnim hladilom giba v vzdolžni smeri proti skrajni legi in nazaj v izhodišče. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 38 Institut »Jožef Stefan«, Ljubljana, Slovenija • • Slika 38 Največja Trescova ekvivalentna napetost pri ciklu z vmesnim stacionarnim stanjem Čas [s] Slika 39 Porazdelitev temperature v notranji in zunanji točki na merilnem mestu M2 pri ciklu spremembe lege gladine hladila brez vmesnega stacionarnega stanja IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 39 Institut »Jožef Stefan«, Ljubljana, Slovenija Začetna lega meje • • - +2,2336+02 - +2.125e+02 - +2.01?e+02 + 1,9096+02 + 1.802O 02 - +1.6Me+02 + 1.586e+02 - + 1,4786+02 - +1.3718+02 + 1.263e+02 + 1,1556+02 - +1.0470+02 * +9.394e+0l Porazdelitev temperature za skrajno lego meje v vzdolžni smeri brez stacionarnega stanja * +2,2336+02 - +2.1258+02 - +2.01?e+02 + 1,9096+02 - +1.8026+02 + 1.694e+02 +1.586e+02 - +1,4786+02 - +1,3718+02 + 1.263e+02 + 1,1556+02 - +1.0470+02 - +9.394e+0l Končna lega meje po zaključku cikla Slika 40 Porazdelitev temperature pri spremembi lege gladine v vzdolžni smeri cevovoda brez vmesnega stacionarnega stanja v skrajni vzdolžni legi IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 40 Institut »Jožef Stefan«, Ljubljana, Slovenija Iz rezultatov na sliki 40 je razvidno, da se je gladina gibala v času približno 10 s nazaj proti izhodiščni legi. Potek temperature na zunanji strani kaže na to, da merilec ne bi mogel zaznati takšne spremembe temperature v cevovodu, saj temperatura pada zelo počasi. Slika 41 prikazuje največjo Trescovo ekvivalentno napetost med spremembo meje med vročim in hladnim hladilom v vzdolžni smeri naprej in nazaj brez vmesnega stacionarnega stanja. Največja napetost se pojavi v času 5,25 s po začetku gibanja meje, kar pomeni, da v času, ko je meja dosegla skrajno vzdolžno lego. Slika 41 Največja Tresca ekvivalentna napetost pri enem ciklu brez vmesnega stacionarnega stanja Amplituda nihanja napetosti Sa = 107,3 MPa se izračuna kot polovica Tresca ekvivalentne napetosti [1]. Na osnovi Sa določimo dopustno število obremenitev N = 9,14T06 iz ustrezne Wohlerjeve krivulje (krivulja za avstenitne materiale z Sa < 198,6 MPa). Delni faktor izrabe za eno ponovitev prehodnega pojava je tako u = 1,09T0-7. Primerjava rezultatov z vmesnim stacionarnim stanjem in brez njega pokaže, da slednje bolj ugodno vpliva na napetosti, saj v tem primeru toplota ni imela dovolj časa za prestop na trdnino, s čemer bi temperaturno obremenjevala cevovod. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 41 Institut »Jožef Štefan«, Ljubljana, Slovenija 5 ZAKLJUČKI V poročilu demonstriramo uporabo metode za izračun faktorja izrabe v izbranih komponentah na dveh pilotnih primerih: izstopni šobi reaktorske tlačne posode (proti vroči veji) in prelivnem vodu tlačnika. Izbor pilotnih primerov zagotavlja tudi širok spekter obremenitvenih primerov: za prelivni vod tlačnika je namreč znano, da je lahko obremenjen tudi s toplotnim razslojevanje in toplotnimi šoki. Z modelom izstopne šobe reaktorske tlačne posode smo ocenili faktor izrabe za projektne in dejanske prehodne pojave v jedrski elektrarni Krško: ogrevanje in ohlajanje elektrarne ter ustavitev reaktorja s polne moči brez ohlajanja. Primerjava izračunanih faktorjev izrabe je pokazala, da je dejanska izraba obravnavanih komponent za obravnavane prehodne pojave manjša od predvidene v projektu. To spoznanje je lahko pomembno tudi s stališča morebitnega podaljševanja obratovalne dobe elektrarne. Seveda pa bi bilo za dokončno odločitev potrebno ovrednotiti vse projektne in dejanske prehodne pojave. Pokazali smo tudi mogoče vplive toplotnega razslojevanja in termičnega šoka na utrujenostno izrabo prelivnega voda tlačnika. Pri tem smo posebno pozornost posvetili temperaturam, ki bi jih v obravnavanih hipotetičnih prehodnih pojavih prikazovali merilci temperatur na zunanjem obodu prelivnega voda. Model prelivnega voda tlačnika je zastavljen tako, da lahko rezultate tovrstnih meritev v prihodnosti s pridom uporabi. IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 42 Institut »Jožef Stefan«, Ljubljana, Slovenija 6 VIRI [1] Zafošnik, B., Cizelj, L.: Zasnova metode za spremljanje izrabe komponent jedrskih elektrarn, IJS delovno poročilo, IJS-DP-10078, 2008. [2] Zafošnik, B., Cizelj, L.: Baza prehodnih pojavov v Nuklearni elektrarni Krško, IJS delovno poročilo, IJS-DP-10077, 2008 [3] Kleinoder, W., Golembiewski, H.-J.: Monitoring for fatigue - examples for unexpected component loading, SMiRT 16, Washington DC, August 2001. [4] Bartonicek, J., Schoeckle, F.: Monitoring of unspecified loads as a tool for ageing management, ASME PVP Conference, Seattle, 2000. [5] Boros, I., Aszodi, A.: Analysis of thermal stratification in the primary circuit of a VVER-440 reactor with the CFX code, Nucl. Eng. Des., 238, 2008, str. 453-459. [6] Jong, C. J., Young, H. C. Seok, K. C.: Numerical Analysis of Unsteady Conjugate Heat Transfer and Thermal Stress for a Curved Piping System Subjected to Thermal Stratification, J. Press. Vess. Tech., 125, 2003, str. 467-474. [7] ABAQUS 6.6-1, 2006. [8] KWU NDM5/98/E1214, Stress and Fatigue AnalyReplacement Steam Generators, Rev. A, 1998. [9] Krautov strojniški priročnik, Tehniška založba Slovenije, 1998. [10] ASME Boiler and Pressure Vessel Code, 1986. [11] Krško modernization - UPR, Mechanical Review, SSR-NEK-12, Revison 1, February 2000, Final. [12] USAR (varnostna poročila NEK). IJS-DP-10076 Izdaja 1 File. IJS-DP-10076-R1.doc Marec 2009 stran 43 IJS Delovno Poročilo IJS Report IJS-DP-10078 Izdaja 1, marec 2009 Revision 1, March 2009 Zasnova metode za spremljanje izrabe komponent jedrskih elektrarn Design of a method for monitoring the usage of nuclear power plant components B. Zafošnik, L. Cizelj Ljubljana, marec 2009 Institut »Jožef Stefan«, Ljubljana, Slovenija Institut »Jožef Stefan«, Ljubljana, Slovenija tZ Naročnik: Javna agencija za raziskovalno dejavnost Republike Slovenije Ordered by: Tivolska c. 30, Ljubljana Nuklearna elektrarna Krško d.o.o., Vrbina 12, 8270 Krško Izvajalec: Prepared by: Pogodba štev.: Contract Number: Nosilec naloge: Responsible Person: Naslov poročila: Report Title: Institut »Jožef Stefan« 1000 Ljubljana Jamova 39 Slovenija Odsek za reaktorsko tehniko (Reactor Engineering Division) Z2-9488-0106-06 (IJS in ARRS) U1-BL-R4-3/03 (IJS in NEK) dr. Boštjan Zafošnik, univ. dipl. inž. str. Zasnova metode za spremljanje izrabe komponent jedrskih elektrarn Design of a method for monitoring the usage of nuclear power plant components Avtorji poročila: Authors: Dr. Boštjan Zafošnik, univ.dipl.inž.str. Prof. dr. Leon Cizelj, univ.dipl.inž.str. Štev. delovnega poročila: Report Number: Konto: Account Number: Kopije: Distribution: IJS-DP-10078 Izdaja 1 V2-0375-C > Naročnik (3) > Knjižnica/Library (1x) > Nosilec naloge/Responsible Person (1x) > Avtorji/Authors (1x) > Arhiv OR4/Archive (1x + original) Ljubljana, marec 2009 IJS-DP-10078 Izdaja 1 File. IJS-DP-10078-R1.doc Marec 2009 stran ii Institut »Jožef Stefan«, Ljubljana, Slovenija POVZETEK V poročilu smo zasnovali metodo za spremljanje izrabe komponent jedrskih elektrarn. Za zanesljivo oceno dejanske izrabe komponent poleg projektnih in dejansko izmerjenih podatkov o obratovalnih dogodkih in prehodnih pojavih potrebujemo še primerne računske modele. V poročilu nakazujemo ključne vire podatkov, ki jih lahko v ta namen uporabimo. To so projektna dokumentacija, procesni informacijski sistem, neposredne meritve, simulacije s programi za računalniško dinamiko tekočin in tuje izkušnje. Dostopnost in podrobnost podatkov pa seveda bistveno vplivata na natančnost ocene izrabe. Zasnovano metodo označujeta primerno uravnotežena dostopnost podatkov in kompleksnost uporabljenih računskih modelov. Nakazujemo tudi nekatere možne poti za rekonstrukcijo manjkajočih podatkov. Metoda je zasnovana v skladu s standardom ASME, po katerem je projektirana in grajena jedrska elektrarna v Krškem. Zato omogoča tudi primerjave z originalnimi projekti. Metoda je namenjena predvsem podpori pri načrtovanju zamenjave komponent in preventivnega vzdrževanja jedrskih elektrarn. Zelo uporabna bi lahko bila tudi pri neodvisni presoji projektnih izračunov, tudi tistih v podporo podaljšanju obratovalnega dovoljenja. Zasnova pa omogoča tudi morebitno dodelavo in razširitev za izvajanje projektnih izračunov v prihodnosti. Poročilo predstavlja del rezultatov projekta »Zasnova metode za spremljanje izrabe komponent jedrskih elektrarn«, ki sta ga sofinancirala Javna agencija za raziskovalno dejavnost Republike Slovenije (pogodba št. 1000-07-219488) in Nuklearna elektrarna Krško d.o.o. (pogodba št. POG-3408). IJS-DP-10078 Izdaja 1 Marec 2009 stran iii File. IJS-DP-10078-R1.doc Institut »Jožef Stefan«, Ljubljana, Slovenija ABSTRACT Design of a method for monitoring of the usage of nuclear power plant components is detailed in the report. Design and operational data are needed in addition to the appropriate computational models to arrive at a reliable estimate of the component usage. The crucial sources of the data needed in monitoring the usage are identified. These include design documentation, process information system, direct measurements, simulations with computational fluid dynamics software and relevant experience from third parties. The availability and accuracy of data are key factors affecting the accuracy of the estimated usage. The proposed method is characterized by balanced availability of data and complexity of the computational models utilized. Some possible approaches to reconstruct the missing data are indicated. The method is consistent with the ASME Code, which was utilized during the design of the Krško nuclear power plant. It therefore enables comparisons with the original design. The method is intended to be used primarily as tool supporting the component replacement schedule and preventive maintenance of nuclear power plants. Another possible use is the independent verification of design analyses supporting the plant life extension. Finally, a possibility of future upgrades toward a tool for design analyses is also assumed in the design. This report contains a part of the results of the project »Conception of a method for monitoring of the usage of nuclear power plant components«, cosponsored by the Slovene research Agency (grant No. 1000-07-219488) and Nuklearna elektrarna Krško d.o.o. (grant No. POG-3408). IJS-DP-10078 Izdaja 1 Marec 2009 stran iv File. IJS-DP-10078-R1.doc Institut »Jožef Stefan«, Ljubljana, Slovenija KAZALO fi POVZETEK III ABSTRACT IV KAZALO V SEZNAM SLIK VII SEZNAM TABEL VIII 1 UVOD 1 1.1 Namen poročila 1 1.2 Ozadje 1 1.3 Organizacija poročila 2 2 UTRUJANJE KOVINSKIH MATERIALOV 3 2.1 Opis utrujanja 3 2.2 Osnovne metode projektiranja 3 2.2.1 Napetostna metoda 3 2.2.2 Deformacijska metoda 5 2.3 Utrujanje in ASME B&PV Code 5 2.3.1 Ključne predpostavke 5 2.3.2 Upoštevane obremenitve 7 2.3.3 Toplotno razslojeni tokovi 8 2.3.4 Varnostna klasifikacija komponent 8 3 VIRI PODATKOV O OBREMENITVENIH CIKLIH 9 3.1 Originalni projekt 9 3.2 Spremembe originalnega projekta 9 3.3 Procesni informacijski sistem 9 3.4 Neposredne meritve 10 3.5 Simulacije s programi za računalniško dinamiko tekočin 10 IJS-DP-10078 Izdaja 1 File. IJS-DP-10078-R1.doc Marec 2009 stran v Institut »Jožef Štefan«, Ljubljana, Slovenija 4 OCENA UTRUJENOSTNE IZRABE 12 4.1 Obremenitveni cikli 12 4.1.1 Definicija 12 4.1.2 Wohlerjeva krivulja 12 4.2 Skupni faktor izrabe 13 4.3 Delni faktorji izrabe 13 4.3.1 Napetosti 13 4.3.2 Glavne napetosti 13 4.3.3 Največje strižne napetosti - Trescova ekvivalentna napetost 14 4.3.4 Amplituda nihanja napetosti 14 4.3.5 Delni faktor izrabe 15 5 OCENA CIKLIČNIH NAPETOSTI 16 5.1 Osnovne enačbe 16 5.2 Analitično reševanje 16 5.2.1 Omejitve in predpostavke 16 5.2.2 Napetosti zaradi temperaturnih sprememb 17 5.2.3 Napetosti zaradi notranjega tlaka 22 5.3 Numerično reševanje 23 5.3.1 Metoda končnih elementov 23 5.3.2 Osnovne omejitve, predpostavke in značilna uporaba modelov 23 6 ZAKLJUČKI 25 7 VIRI 26 IJS-DP-10078 Izdaja 1 File. IJS-DP-10078-R1.doc Marec 2009 stran vi iS Institut »Jožef Stefan«, Ljubljana, Slovenija SEZNAM SLIK Slika 1 Sinusna ciklična obremenitev 4 Slika 2 Potek določitve faktorja izrabe 6 Slika 3 Razslojeni tok v horizontalni cevi 7 Slika 4 Meritev temperature po obodu cevi v odvisnosti od lege cevovoda [8] 10 Slika 5 Simulacija vrtinčnega mešanja tekočin z različnima temperaturama [20] 11 Slika 6 Določitev dopustnega števila ciklov obremenitve glede na izračunano amplitudo nihanja napetosti Sa 12 Slika 7 Stopničaste spremembe temperature iz 0 na 1 in nazaj na 0 20 Slika 8 Vpliv frekvence f stopničaste spremembe temperature na notranji površini stene cevi na amplitudo nihanja napetosti Sa 21 Slika 9 Vpliv brezdimenzijskega polmera R1/R2 na brezdimenzijsko amplitudo napetosti Sa 23 IJS-DP-10078 Izdaja 1 File. IJS-DP-10078-R1.doc Marec 2009 stran vii Institut »Jožef Štefan«, Ljubljana, Slovenija SEZNAM TABEL Tabela 1 Vpliv stopničaste spremembe (Slika 7a) na amplitudo nihanja napetosti Sa za različne debeline stene cevi 21 IJS-DP-10078 Izdaja 1 File. IJS-DP-10078-R1.doc Marec 2009 stran viii Institut »Jožef Stefan«, Ljubljana, Slovenija 1 UVOD tZ 1.1 Namen poročila V poročilu predstavljamo del rezultatov projekta »Zasnova metode za spremljanje izrabe komponent jedrskih elektrarn«, ki sta ga sofinancirala Javna agencija za raziskovalno dejavnost Republike Slovenije (pogodba št. 1000-07-219488) in Nuklearna elektrarna Krško d.o.o. (pogodba št. POG-3408). Preostali rezultati projekta so predstavljeni v spremljajočih poročilih: • Baza prehodnih pojavov v Nuklearni elektrarni Krško [1] in • Pilotni primeri izračuna faktorja utrujenostne izrabe [2]. 1.2 Ozadje Med gradnjo NE Krško in vse do uveljavitve ZVISJV [3] 1.10.2002 je bila v Sloveniji v primeru odsotnosti domačih predpisov uzakonjena uporaba predpisov države, ki je jedrsko elektrarno dobavila. Zato je jedrska elektrarna Krško projektirana v skladu s predpisi in prakso v ZDA (ASME Boiler and Pressure Vessel Code, [4], v nadaljevanju ASME B&PV Code) za trajnostno dobo 40 let. Predvidena trajnostna doba jedrske elektrarne Krško (in podobnih jedrskih elektrarne v ZDA) temelji na ekonomskih razmislekih in je bila opredeljena na 40 let [5]. Opredelitev trajnostne dobe je vplivala na zasnovo in projekte elektrarn. V projektnih predpisih (ASME B&PV Code [4]) je s stališča trajnostne dobe elektrarne velika pozornost posvečena odpornosti na utrujanje. Projekti predvidevajo vnaprej določen nabor hipotetičnih obratovalnih dogodkov in prehodnih pojavov. Za 40 letnemu obratovanju prilagojeno število obratovalnih dogodkov s predpisano varnostno rezervo tudi dokažejo ustrezno odpornost na utrujanje. Obratovalno osebje elektrarne nato izrabo komponent enostavno oceni kar s štetjem obratovalnih dogodkov in prehodnih pojavov, ki ga primerja s projektno predvidenim številom. Izkušnje z obratovanjem in vzdrževanjem jedrskih elektrarn ter seveda tudi napredek znanosti v zadnjih desetletjih jasno kažejo na možnost podaljšanja trajnostne dobe. Ključni element pri podaljšanju obratovalnega dovoljenja v ZDA predstavlja obvladovanje staranja pasivnih in za varnost pomembnih sistemov, struktur in komponent, ki je opredeljeno v 10 CFr 54 [6]. Med pomembnejše aktivnosti pri obvladovanju staranja pasivnih komponent (npr. cevovodi in tlačne posode) sodi tudi ponovna analiza odpornosti na utrujanje. Tukaj si lahko obratovalno osebje elektrarne v veliki meri pomaga z izmerjenimi parametri obratovalnih dogodkov in prehodnih pojavov. Praviloma so spremembe tlakov, temperatur in pretokov manjše, kot je bilo konzervativno ocenjeno v projektu. Zato je tudi njihov vpliv na trajnostno dobo dostikrat manjši. Za zanesljivo oceno dejanske izrabe komponent poleg projektnih in dejansko izmerjenih podatkov o obratovalnih dogodkih in prehodnih pojavih potrebujemo še računske modele, s katerimi ocenimo prispevke posameznega prehodnega pojava k skupni izrabi komponent. Skupku medsebojno uravnoteženih podatkov in računskih modelov v literaturi navadno pravijo metoda ali sistem za spremljanje izrabe komponent. IJS-DP-10078 Izdaja 1 File. IJS-DP-10078-R1.doc Marec 2009 stran 1 Institut »Jožef Stefan«, Ljubljana, Slovenija V literaturi najdemo različne metode oziroma sisteme za spremljanje izrabe komponent jedrskih objektov (npr. [7] in [8]). Eden izmed zelo pomembnih korakov pri spremljanju izrabe komponent je določitev temperaturnega in napetostnega odziva v komponentah. Pogosto je uporabljena tehnika Greenovih funkcij [9], [10] ki je v splošnem omejena na analize linearnih odzivov [11]. Zelo pogosto za določevanje temperaturnih in napetostnih odzivov uporabljajo tudi metodo končnih elementov [7], [10], [12], [13], [14]. Metoda je zelo splošna in uporabna tudi v zelo kompleksnih situacijah. Je pa za uporabo potrebno imeti ustrezno usposobljeno osebje ter programsko in strojno opremo. Zasnova tovrstne metode s primerno uravnoteženo natančnostjo in kompleksnostjo je osnovni cilj projekta, o katerem poročamo v tem poročilu. Metoda je namenjena predvsem podpori pri načrtovanju zamenjave komponent in preventivnega vzdrževanja jedrskih elektrarn. Zelo uporabna bi lahko bila tudi pri neodvisni presoji projektnih izračunov. Zasnova pa omogoča tudi morebitno dodelavo in razširitev za izvajanje projektnih izračunov v prihodnosti. 1.3 Organizacija poročila V poglavju 2 opisujemo fenomen utrujanja, ki je splošnem posledica spreminjajočih se obremenitev. Osnovne informacije o virih podatkov o obremenitvenih ciklih, ki so potrebni za določanje izrabe komponent, predstavljamo v poglavju 3. Postopek za določitev izrabe komponente na osnovi delnih in skupnega faktorja izrabe opisujemo v poglavju 4. V poglavju 5 so zbrane osnovne enačbe za napetosti, ki so pomembne za določitev izrabe komponente, z izbranimi analitičnimi in numeričnimi rešitvami. Sledijo zaključki v poglavju 6 in viri v poglavju 7. IJS-DP-10078 Izdaja 1 Marec 2009 stran 2 File. IJS-DP-10078-R1.doc Institut »Jožef Stefan«, Ljubljana, Slovenija 2 UTRUJANJE KOVINSKIH MATERIALOV V tem poglavju na kratko orišemo pomembnost spreminjajočih se obremenitev za projektiranje komponent na utrujanje. 2.1 Opis utrujanja Kovinske mehanske komponente, ki so obremenjene s spreminjajočimi se obremenitvami, lahko odpovedo pri napetostih, ki so bistveno nižje od natezne trdnosti. Odpoved je tudi pri žilavih materialih posledica nastanka in napredovanja kvazi krhkih utrujenostnih razpok. Pred nastankom razpok pa je mogoče opaziti značilne spremembe v mikrostrukturi. Takšen pojav imenujemo utrujanje. V literaturi je bil prvič omenjen že v letu 1838 [15]. Utrujanje praviloma povzročajo spreminjajoče se toplotne ali mehanske obremenitve. Tem se bomo posvetili v pričujočem poročilu. V nekaterih primerih se lahko utrujanje pojavi v kombinaciji z drugimi degradacijskimi procesi. Spreminjajoča se obremenitev pri visokih temperaturah lahko povroči utrujenostno lezenje (angl. creep fatigue), v prisotnosti agresivnega medija pa korozijsko utrujanje (angl. corrosion fatigue, environmentally assissted fatigue). Značilne faze razvoja utrujenostnih poškod v splošnem zajemajo: - mikrostukturne spremembe v materialu, - nastanek mikroskopskih razpok, - rast in združevanje mikroskopskih razpok, ki oblikujejo t. i. vodilne makrorazpoke, - stabilna rast vodilnih makrorazpok in končno - strukturna nestabilnost oz. lom komponente Celotno trajnostno dobo komponente lahko torej delimo v čas oz. obremenitvene cikle pred nastankom utrujenostnih razpok in čas oz. število ciklov stabilne rasti razpok. V pričujočem poročilu se omejujemo na čas do nastanka utrujenostnih razpok. 2.2 Osnovne metode projektiranja V literaturi pogosto naletimo na dve značilni vrsti mehanskega in toplotnega utrujanja z značilnima pripadajočima metodama za oceno trajnostne dobe komponente pred nastankom razpok [15], [5]: • visoko ciklično utrujanje - napetostna (a - N) metoda in • nizko ciklično utrujanje - deformacijska (s - N) metoda. ASME B&PV Code uporablja pristop, ki je nekoliko bliže (a - N) metodi. Zato se (a - N) metodi v nadaljevanju posvečamo nekoliko podrobneje. 2.2.1 Napetostna metoda Napetostna metoda (a - N) je najstarejša metoda projektiranja na utrujanje. Temelji na Wohlerjevi krivulji dinamične trdnosti gradiva (Slika 6). Wohlerjeva krivulja povezuje amplitudo napetosti a z največjim številom ciklov N, ki še zagotavlja nepoškodovanost komponente. Uporabljamo jo predvsem pri visokocikličnem utrujanju, ko je komponenta praviloma izpostavljena visokemu številu ciklov z razmeroma nizko amplitudo napetosti. Gonilna sila visoko cikličnega utrujanja so praviloma ciklične napetosti. IJS-DP-10078 Izdaja 1 Marec 2009 stran 3 File. IJS-DP-10078-R1.doc Institut »Jožef Stefan«, Ljubljana, Slovenija tZ Slika 1 prikazuje predpostavljeno sinusno ciklično spreminjanje napetosti v odvisnosti od števila ciklov. + o ■M CD cd Za 02 > 03, ki predstavljajo glavne napetosti. 4.3.3 Največje strižne napetosti - Trescova ekvivalentna napetost Napetostni tenzorje v praksi navadno primerjamo s podatki o materialih, ki so bili izmerjeni v razmerah enoosnih obremenitev. V ta namen uvedemo ekvivalentno napetost, ki je nekakšna skalarna mera velikosti napetostnega tenzorja. V inženirski praksi uporabljamo več definicij ekvivalentne napetosti; možnosti je namreč neskončno mnogo. Inženirske definicije praviloma temeljijo na fizikalno smiselnih podmenah. ASME B&PV Code [4] uporablja Trescovo ekvivalentno napetost, ki temelji na predpostavki, da nastopi porušitev materiala zaradi delovanja največje strižne napetosti w [15]. Trescova ekvivalentna napetost sodi med najkonzervativnejše ekvivalentne napetosti v inženirski praksi. Izračunamo jo kot: = 2^max = maX(jG1 — G |G2 — G |G3 — G11) . (11) GTr p " " max kjer predstavljajo o1, o2 in o3 glavne napetosti. 4.3.4 Amplituda nihanja napetosti Določitev velikosti amplitude nihanja napetosti Sa, s pomočjo katere se določi dovoljeno število ciklov obremenitve, se izvaja po naslednjem postopku: 1. določitev glavnih napetosti za obremenitveni cikel v odvisnosti od časa 01 (t), 02 (t) in 03 (t), 2. določitev absolutne vrednosti razlik glavnih napetosti med potekom cikla S12(t) = (t) -a2(t)| S23 (t) = \ d t . (30) V dolgem valju z notranjim polmerom R1 in zunanjim polmerom R2, kjer je temperaturna porazdelitev T(r) znana in odvisna le od polmera r, znašajo radialna, obročna in osna komponenta termičnih napetosti [24]: a E 1 Gr = G = 1 — v r a E 1 1—v r2 aE 1 —v -J T (r )r d r — J T (r jr di 1 a a a y "2 2 1 r —J T (r )r d r + J T (r ) d r — T (r) 1 a a a y J T (r )7 d r — T ( j^+aE (( — TR (ooj) 1 — a „ (31) kjer predstavlja a linearni temperaturni razteznostni koeficient, E modul elastičnosti, r je brezdimenzijski polmer skladno z izrazom (24). Tref je temperatura, pri kateri je oz = 0. V izrazu (31) je bilo upoštevano A _ _ _ _ J (( (r ) —Tr (o j j r d r = R22 J T (r ) r d r (32) Gz = IJS-DP-10078 Izdaja 1 File. IJS-DP-10078-R1.doc Marec 2009 stran 19 Institut »Jožef Štefan«, Ljubljana, Slovenija •* V primeru cevi proste na obeh koncih je potrebno k az dodati a iZ d (A Tref ): g° = a E\Ta - Trf = a E J T (r) 2n r d; a_ n (1 - a2) (ref - Tr («>)) (33) Povprečna temperatura v steni cevi je definirana kot: _ 2 i____ Ta =--2 J T (r) r d r . 1 - a J (34) Spremembe temperature na notranji površini cevi torej povzročajo spremembe temperature in s tem napetosti skozi debelino stene cevi. Najbolj konservativna oblika temperaturne spremembe na notranji površini cevi je stopničasta sprememba (Slika 7), ki predstavlja ovojnico vsem drugim oblikam temperaturnih sprememb (linearna, sinusna,...). 1 0 At 1 0 Atp a) enotna stopnica b) periodična sprememba Slika 7 Stopničaste spremembe temperature iz 0 na 1 in nazaj na 0 Vpliv stopničaste spremembe temperature na amplitudo nihanja napetosti je prikazan na primeru cevi iz primarnega kroga jedrske elektrarne. Debeline cevi značilno znašajo 5-15% polmera cevi. Iz tega sledi razmerje med notranjim in zunanjim polmerom a = 0.85 in a = 0.95. Rezultati so predstavljeni za tri značilna razmerja a: 0.85, 0.9 in 0.95. Materialni parametri, uporabljeni v analizi so značilni za avstenitna nerjavna jekla, ki se uporabljajo v jedrski tehniki: toplotna prevodnost A = 20 W/mK, gostota p = 7880 kg/m3, specifična toplota cp = 502 J/kgK, modul elastičnosti E = 206842 MPa, linearni toplotni razteznostni koeficient a = 1.8710-5 K-1. Čas t0 je v skladu z enačbo (24) izražen z R22 / x, kjer je vrednost toplotne difuzivnosti x = 5.056 10-6 m2/s. Za prelivni vod tlačnika z zunanjim radijem R2.= 0,1619 m torej velja t0 = 5184 s. Spreminjajoča se napetost je za enojno stopničasto spremembo (Slika 7a) neodvisna od časa trajanja At, ker se največja razlika napetosti pojavi v času t = 0 na notranji površini stene cevi, ko pride do spremembe temperature (npr. iz 0 na 1 - Slika 7a). Analiziran je bil vpliv debeline stene cevi pri enojni stopničasti spremembi temperature na amplitudo nihanja napetosti. Iz IJS-DP-10078 Izdaja 1 File. IJS-DP-10078-R1.doc Marec 2009 stran 20 Institut »Jožef Stefan«, Ljubljana, Slovenija tZ rezultatov (Tabela 1) je mogoče razbrati, da se največja Sa pojavi za debele cevi. Iz rezultatov je prav tako mogoče razbrati, da debeline stene cevi v območju 5-15% polmera cevi nimajo pomembnega vpliva na Sa. Ri / R2 Sa [MPa] 0.85 2.74565 0.9 2.74515 0.95 2.74465 Tabela 1 Vpliv stopničaste spremembe (Slika 7a) na amplitudo nihanja napetosti Sa za različne debeline stene cevi Pri periodični spremembi temperature (Slika 7b) na notranji površini cevi pa povečanje debeline stene cevi povzroča manjšo napetost Sa (Slika 8). Višje frekvence povzročajo manjše povprečne temperature v steni cevi, kar vodi k nižjim napetostim in posledično k nižjim Sa. Slika 8 prikazuje frekvence v brezdimenzijskem času. Pri njihovi interpretaciji je potrebno upoštevati vrednost to, ki je odvisna od konfiguracije cevovoda. Za prelivni vod tlačnika velja to = 5184 s. Frekvenca 100 [1/ to] torej znaša pribl. 0,02 Hz. rt Ph tO 2^ 1 - RL v r2 j (35) Obročna komponenta napetost v cevi, obremenjeni z notranjim tlakompN, znaša: R1 22 ° = pN n2 n2 R2 - R R2 1 + "t v r j (36) Če sta oba konca valja togo vpeta (sz = 0), nastane hkrati v osni smeri napetost: R2 0z = 2vpn P2 = konst. (37) R2 - R1 Kadar pa je valj na obeh konceh zaprt, notranji tlak v osni smeri povzroči napetost: R2 0z = PN P2 '2 = konst. (38) R2 - R1 V izrazih (35) do (38) je R12 notranji oz. zunanji polmer cevi, r je polmer cevi na katerem računamo napetost (R1 < r < R2) in v Poissonovo število. Obročna napetost (izraz (36)) ima maksimum pri r = R1. Pri tem pogoju lahko z limitnim procesom R2/R1 ^ 1, torej za tankostenske cevi, dobimo t. i. kotlovsko enačbo, ki je osnova za dimenzioniranje valjastih lupin po ASME III [4]. Napetost v obročni smeri v tankostenski cevi dobimo kot [21]: R 0,= PN• (39) R2 - R1 Napetost v osni smeri je približno polovico manjša (R2/R1 ^ 1): R12 R1 1 °z = pNR[-R R~+R - 2 (40) V votlem valju oz. cevi obremenjeni z notranjim tlakom največja napetost nastane v obročni smeri. V primeru, ko je cev obremenjena z notranjim tlakom pN, je največja razlika napetosti odvisna od obročne in radialne komponente napetosti. Vpliv debeline stene cevi na amplitudo nihanja napetosti Sa pokaže, da se le-ta povečuje, ko se debelina stene cevi zmanjšuje (Slika 9). IJS-DP-10078 Izdaja 1 File. IJS-DP-10078-R1.doc Marec 2009 stran 22 Institut »Jožef Stefan«, Ljubljana, Slovenija fi z sa a CO C CO 'i? CO -C "¡3 CO -a 3 CO 16 14 12 10 0.75 0.80 0.85 0.90 0.95 Brezdimenzijski polmer cevi (R / R2) [- Slika 9 Vpliv brezdimenzijskega polmera Ri/R2 na brezdimenzijsko amplitudo napetosti Sa 5.3 Numerično reševanje Kadar ne znamo matematičnega modela rešiti analitično, ga rešujemo numerično. Pri numeričnem reševanju se trudimo čimbolj natančno rešiti nalogo pri danih vrednostih podatkov. Numerične metode so zelo močno orodje za reševanje matematičnih modelov, ki izhajajo iz inženirske prakse. Eno od takšnih orodij je metoda končnih elementov (MKE), ki omogoča reševanje zelo širokega spektra linearnih in nelinearnih inženirskih problemov. 5.3.1 Metoda končnih elementov Metoda končnih elementov je dosegla izreden razvoj, omogoča široko področje uporabe in je praktično nepogrešljiva metoda za reševanje praktičnih primerov v jedrski stroki. Najbolj splošen tip končnih elementov, ki je na razpolago za trdnostne analize, je družina tridimenzionalnih končnih elementov, saj so vse strukture, ki so predmet numeričnih analiz, v svoji izvirni obliki tridimenzionalne. Numerične modele pa lahko tudi poenostavimo in sicer v odvisnosti od oblik obravnavanih komponent, pričakovane natančnosti izračunov in predlogov standardov. Tako lahko poleg tridimenzionalnih volumskih elementov uporabimo še linijske (npr. nosilci, cevi), dvodimenzionalne (npr. plošče) in tridimenzionalne lupinske elemente. 5.3.2 Osnovne omejitve, predpostavke in značilna uporaba modelov V standardu ASME [4] ni navodil za uporabo MKE pri projektiranju komponent. Nekaj smernic pa lahko najdemo v literaturi MKE [5]. Tako je navedeno, da bi se naj glavne napetosti in ekvivalentne napetosti, ki jih potrebujemo za izračun amplitude nihanja napetosti, računale na osnovi linearizacije napetosti. Pri tem pa je potrebno razvrstiti izračunane napetosti v eno ali več skupin: glavna membranska napetost Pm, lokalna membranska napetost PL, glavna 8 6 IJS-DP-10078 Izdaja 1 File. IJS-DP-10078-R1.doc Marec 2009 stran 23 Institut »Jožef Stefan«, Ljubljana, Slovenija upogibna napetost A, napetost zaradi ekspanzije Pe, sekundarna napetost Q, najvišja napetost F. Razdelitev napetosti po kategorijah ni enolična, kljub pojasnjevanju v tabeli NB-3217-1 [4]. Poleg tega pa računalniški programi za analizo po MKE praviloma izračunajo napetosti v obliki celotnih napetostnih tenzorjev in jih ne razdelijo v prej naštete kategorije, kar je omenjeno tudi v opombi pri sliki NB-3222-1 [4]. Dodatna težava lahko nastopi pri izbiri poti za linearizacijo in izbiri števila točk [2], predvsem na mestih diskuntinuitet komponent, kjer lahko slabo izbrana pot za linearizacijo vodi k napačnim rezultatom. Zaradi tega smo intenziteto napetosti določili direktno iz rezultatov analize kot polovico napetosti po Tresca kriteriju, saj so v njej zajete vse uporabljene obremenitve in diskontinuitete komponent in materiala. Pri uporabi prostorskih modelov, diskretiziranih z volumskimi elementi in pri uporabi dvodimenzionalnih elementov morajo biti izpolnjeni trije bistveni pogoji: 1. zagotovljena mora biti dovolj gosta mreža na vseh mestih, kjer se pričakuje velike temperaturne oz. napetostne gradiente. 2. razmerje robov osnovnega gradnika (končni element v obliki prizme pri prostorskih modelih in pravokotnika pri ravninskih modelih) mora ostati v predpisanih mejah [25], sicer lahko pričakujemo numerične nestabilnosti in s tem povezane netočnosti pri rezultatih. Glede na priporočila [5] se naj ne bi uporabljali nepravokotni elementi. 3. končni model mora imeti čim manj elementov, tako, da računski časi niso predolgi. Optimalno mrežo oziroma število končnih elementov vzdolž debeline stene komponente določimo na osnovi primerjave rezultatov analitične rešitve enačb (poglavje 5.2) in numeričnih rezultatov. Numerični model je potrebno verificirati z rezultati dobljenimi po standardu ASME. Predvsem je to pomembno na mestih diskuntinuitet. V ta namen so lahko v pomoč tudi analize v literaturi, npr. [26]. Pri analizah utrujanja lahko kombiniramo različne tipe elementov, s čemer lahko dobimo manjše računske modele ob ne bistveno zmanjšanji natančnosti rezultatov. Tako lahko npr. za problem toplotnega razslojevanja [27] uporabimo kombinacijo tridimenzionalnih volumskih elementov (področje spreminjajočih se temperatur po prerezu) in linijskih elementov (področje konstantnih temperatur po prerezu). Glavni rezultat linijskih modelov so pomiki, katerih vrednosti so podane v vozliščih. Reakcijske sile in momenti ustrezajo predpisanim robnim pogojem. Iz rezultatov lahko uporabimo notranje sile in momente, s katerimi lahko s postopki po ASME izvršimo kontrolo napetosti v obravnavanih prerezih ali pa izračunavamo komponente tenzorja napetosti glede na podane obremenitve. Dvodimenzionalne elemente lahko uporabimo za določevanje možnih temperaturnih sprememb na notranji strani cevi, če poznamo meritve temperature na zunanjem robu cevi. Tako določene temperaturne spremembe na notranji strani lahko potem uporabimo v analizi za določitev izrabe komponent. Tako lahko glede na vhodne podatke potrebne za utrujenostne analize z MKE v linijskih modelih uporabimo podatke dobljene na osnovi meritev iz procesno informacijskega sistema, v ravninskih modelih podatke dobljene na osnovi lokalnih meritev po obodu cevi, v prostorskih modelih pa lahko poleg omenjenih podatkov uporabimo še podatke dobljene na osnovi simulacij s programi za modeliranje dinamike tekočin. IJS-DP-10078 Izdaja 1 Marec 2009 stran 24 File. IJS-DP-10078-R1.doc Institut »Jožef Stefan«, Ljubljana, Slovenija tZ 6 ZAKLJUČKI Med pomembnejše aktivnosti pri obvladovanju staranja pasivnih komponent (npr. cevovodi in tlačne posode) v jedrskih elektrarnah sodi tudi sprotno spremljanje utrujenostne izrabe komponent. Pri tem si lahko obratovalno osebje elektrarne v veliki meri pomaga z izmerjenimi parametri obratovalnih dogodkov in prehodnih pojavov. Praviloma so spremembe tlakov, temperatur in pretokov manjše, kot je bilo konzervativno ocenjeno v projektu. Zato je tudi njihov vpliv na trajnostno dobo dostikrat manjši. Za zanesljivo oceno dejanske izrabe komponent poleg projektnih in dejansko izmerjenih podatkov o obratovalnih dogodkih in prehodnih pojavih potrebujemo še računske modele, s katerimi lahko ocenimo prispevke posameznega prehodnega pojava k skupni izrabi komponent. Ključni viri podatkov v ta namen so projektna dokumentacija, procesni informacijski sitem, neposredne meritve, simulacije s programi za računalniško dinamiko tekočin in tuje izkušnje. Dostopnost in podrobnost podatkov seveda bistveno vplivata na natančnost ocene izrabe. V poročilu smo zasnovali metodo za spremljanje izrabe komponent jedrskih elektrarn, ki jo označujeta primerno uravnotežena dostopnost podatkov in kompleksnost uporabljenih računskih modelov. Nakazujemo tudi nekatere možne poti za rekonstrukcijo manjkajočih podatkov. Metoda je zasnovana v skladu s standardom ASME, po katerem je projektirana in grajena jedrska elektrarna v Krškem. Zato omogoča tudi primerjave z originalnimi projekti. Metoda je namenjena predvsem podpori pri načrtovanju zamenjave komponent in preventivnega vzdrževanja jedrskih elektrarn. Zelo uporabna bi lahko bila tudi pri neodvisni presoji projektnih izračunov. Zasnova pa omogoča tudi morebitno dodelavo in razširitev za izvajanje projektnih izračunov v prihodnosti. IJS-DP-10078 Izdaja 1 File. IJS-DP-10078-R1.doc Marec 2009 stran 25 Institut »Jožef Stefan«, Ljubljana, Slovenija 7 VIRI [1] Zafošnik, B., Cizelj, L.: Baza prehodnih pojavov v jedrski elektrarni Krško, IJS delovno poročilo, IJS-DP-10077, 2009. [2] Zafošnik, B., Cizelj, L.: Pilotni primeri izračuna faktorja utrujenostne izrabe, IJS delovno poročilo, IJS-DP-10076, 2009. [3] Zakon o varstvu pred ionizirajočimi sevanji in jedrski varnosti (ZVISJV-UPB2), Ur.l. RS 102/04, 12360. [4] ASME Boiler and Pressure Vessel Code, 1986. [5] Rao, K. R.: Companion Guide to the ASME Boiler & pressure Vessel Code, Volume 1, ASME PRESS, New York, 2002. [6] 10 CFR 54 - Requirements For Renewal Of Operating Licenses For Nuclear Power Plants (Revised as of January 1, 2006; http://www.gpoaccess.gov/cfr/retrieve.html). [7] Mukhopadhyay, N. K., Dutta, B. K., Swami Prasad, P., Kuswaha, H. S., Kakodkar, A.: Implementation of finite element based fatigue monitoring system at Heavy water Plant Kota, Nucl. Eng. Des., 187, 1999, str. 153-163. [8] Kleinoder, W., Golembiewski, H.-J.: Monitoring for fatigue - examples for unexpected component loading, SMiRT 16, Washington DC, August 2001. [9] Sakai, K., Hojo, K., Kato A., Umehara, R.: On-line fatigue-monitoring system for nuclear power plant, Nucl. Eng. Des., 153, 1994, str. 19-25. [10] Maekawa, O., Kanazawa, Y., Takahashi, Y., Tani, M.: Operating data monitoring and fatigue evaluation systems and findings for boiling water reactors in Japan, Nucl. Eng. Des., 153, 1995, str. 135-143. [11] Botto, D., Zucca, S. Gola, M.M.: A methodology for on-line calculation of temperature and thermal stress under non-linear boundary conditions, Int. J. Press. Vess. Pip., 80, 2003, str. 21-29. [12] Samal, M. K., Dutta, B. K., Guin, S., Kushawa, H. S.: A finite element program for online life assessment of critical plant components, Eng. Fail. Analy., 16, 2009, str. 85111. [13] Duda, P., Taler, J., Roos E.: Inverse method for temperature and stress monitoring in complex-shaped bodies, Nucl. Eng. Des., 227(3), 2004, str. 331-347. [14] Bartonicek, J., Schoeckle, F.: Monitoring of unspecified loads as a tool for ageing management, ASME PVP Conference, Seattle, 2000. [15] Suresh, S.: Fatigue of Materials, second edition, Cambridge University press, 2004. [16] Vojvodič - Tuma, J.: Mehanske lastnosti kovin, Fakulteta za gradbeništvo in geodezijo, Univerza v Ljubljani, 2002. IJS-DP-10078 Izdaja 1 Marec 2009 stran 26 File. IJS-DP-10078-R1.doc Institut »Jožef Stefan«, Ljubljana, Slovenija tZ [17] US NRC Bulletin No. 88-11: Pressurizer Surge Line Thermal Stratification, Dec. 20, 1988. [18] US NRC Information Notice No. 88-80: Unexpected Piping Movement Attributed To Thermal Stratification, Oct. 7, 1988. [19] ANS N-18.2: Nuclear Safety Criteria for the Design of Stationary Pressurized Water Reactor Plants, 1973. [20] Frank, T., Adlakha M., Adlakha, C., Lifante, H.-M., Prasser, F. Menter: Simulation of Turbulent and Thermal Mixing in T-Junctions Using URANS and Scale-Resolving Turbulenc Models in ANSYS CFX, XCFD4NRS - Experiments and CFD Codes Application to Nuclear Reactor Safety, OECD/NEA & International Atomic Agency (IAEA) Workshop, 10.-12. September 2008, Grenoble, France, str. 23. [21] Alujevič, A.: Elasto-plastomehanika, Univerza v Mariboru, Tehniška fakulteta 1991. [22] Ozi§ik, M. N.: Heat conduction, John Wiley & Sons, inc., New York, 1993 [23] Myers, G. E.: Analytical Methods in Conduction Heat Transfer, McGraw-Hill, New York, 1971. [24] Timoshenko, S., Goodier J. N.: Theory of elasticity, Kogakusha Company LtD, Tokyo, 1951. [25] ABAQUS 6.6-1, 2006. [26] WENX 98/01 -Rev. 2: Structural Analysis of Reactor Coolant Loop for the KRŠKO Nuclear Power Plant, Volume 1, Piping Analysis of the Reactor Coolant Loop, SSR-NEK-11.5: revison 2, May 2000, Final. [27] Boros, I., Aszodi, A.: Analysis of thermal stratification in the primary circuit of a VVER-440 reactor with the CFX code, Nucl. Eng. Des., 238, 2008, str. 453-459. IJS-DP-10078 Izdaja 1 File. IJS-DP-10078-R1.doc Marec 2009 stran 27 International Conference Nuclear Energy for New Europe 2009 Bled / Slovenia / September 14-17 Fatigue relevance of stratified flows in pipes: a parametric study Leon Cizelj, Igor Simonovski Jožef Stefan Institute, Reactor Engineering Division Jamova 39, 1000 Ljubljana, Slovenia Leon.Cizelj@ijs.si, Igor.Simonovski@ijs.si ABSTRACT Stratified flows may form in pipelines under certain conditions and could lead to increased fatigue loading that was only marginally accounted for during the design phase of the second generation of nuclear power plants. Extension of operational license would require explicit account for fatigue loads imposed by stratified flows. This further requires rather complex state-of-the-art computational technology combined with measurements of the temperatures at the outside surfaces of pipes, which comprise pressure boundary of the reactor coolant. A parametric study using detailed finite element analysis has been performed to quantify the possible range of fatigue loads and fatigue usage factors. The example taken was a typical pressurized water reactor pressurizer surge line containing stratified flow of cold and hot water. The investigated parameters include the film coefficients governing the heat transfer from fluid to the pipe wall and the velocity of the interface between then cold and hot water. Results of the paper include the expected ranges of fatigue loading and usage given the range of investigated parameters. It is shown that the estimation of the film coefficients is essential to arrive at reliable fatigue estimate. Additionally, predictions of readings provided by hypothetical thermocouples at the pipe outer surface are provided. 1 INTRODUCTION Stratified flows that may form in pipelines under certain conditions could lead to increased fatigue loading that was only marginally accounted for during the design phase of the second generation of nuclear power plants [1, 2] designed in accordance to the ASME Boiler and Pressure Vessel Code [3]. Extension of operational license would in most countries require explicit account for fatigue loads imposed by stratified flows. This further requires rather complex state-of-the-art computational technology combined with measurements of the temperatures at the outside surfaces of pipes, which comprise pressure boundary of the reactor coolant [4, 5]. There is a wide consensus that within the reactor coolant systems of the pressurized water reactors (PWR) the stratified flows are most likely to occur in surge lines. The rather slow flows caused by the pressure controlling activities of the pressurizer could result in the stratified flow of cold and hot water. The typically reported velocity of such flows is in the order of cm/s [6]. The typical temperature difference between the hot and cold water is reported to be in the range of 120-150 °C. Such temperature differences are believed to be the cause of rather significant thermal stresses resulting in accelerated fatigue usage and in some cases also in observed fatigue damage [6-9]. 611.1 611.2 An impressive body of open literature already exists. Some recent contributions include, among others, an attempt to simulate stratified flows using the computational fluid mechanics tools [6], proposal [9] to update the fatigue analysis procedures in the ASME Boiler and Pressure Vessel Code [3] and example of surge line fatigue analysis [7]. The published fatigue analyses are however to a large extent based on assumption that the temperatures at the pipe surface are known. In practice however, we may be aware of the temperatures and velocities of stratified fluids. Then, the temperature of the pipe surface would depend on the heat transfer or film coefficient. The intention of this paper is to investigate the consequences of different assumptions on the heat transfer coefficient and the velocity of the fluid-fluid interface on the thermal stress ranges and therefore also on fatigue usage of the pipe. A typical 12 inch pressurized water reactor pressurizer surge line made of austenitic stainless steel has been chosen as the numerical example. 2 MODEL The finite element model is reported in detail in [10, 11] together with some best estimate assessments of the fatigue loading. The model (Figure 1) contains 39049 finite elements with parabolic interpolation. Element types DC3D20 and C3D20 have been used for thermal and stress analyses using the ABAQUS/standard finite element code [12], respectively. The goal of this paper is to give a range of possible fatigue loads. The data on the pipe loads and results may therefore differ significantly from those reported in [10, 11]. The density of the finite element mesh has been evaluated against closed form solutions outlined in [13] and has been found sufficient for the range of loads considered here. The temperature dependent material properties defined in [3] were consistently used. 2.1 Thermal analysis In the first step, a transient heat transfer analysis has been performed. The temperature of the cold fluid entering the pressurizer surge line from the reactor coolant system was assumed at 96°C. The hot fluid entering the pressurizer surge line from the pressurizer was Figure 1: Outline and the finite element mesh of the surge line Proceedings of the International Conference Nuclear Energy for New Europe, Bled, Slovenia, Sept. 14-17, 2009 611.3 assumed at 223°C. The temperature difference between both fluids of 127°C is consistent with data published elsewhere [6-9]. The assumed transient started from a steady state with already developed stratification: the interface between both fluids has been assumed at the lower surface of the surge line close to the nozzle attached to the primary piping (Figure 2, up). The interface was then assumed to move in the vertical direction with the velocity consistent with the typical capacity of the pressurizer sprays. After reaching the top of the pipe (Figure 2, down), the interface started to travel back down with the same velocity. Lower position of the fluid-fluid interface NTH - 2 2 ■■<>■ 1/ ■ +2.12« + 02 ■ + 2.ûlBe + 02 ■ +1.913C K>2 ■ 41.807e+02 ■ + 1.701e + 02 - + 1.5954 + D2 ■ + 1.409e+ 02 ■ + lL3ä3e + 02 . + 1.278S + D2 ■ +1.172C + 02 - + 1.066C + 02 +9.60M + 01 Upper position of the fluid-fluid interface Figure 2: Lower and upper positions of fluid-fluid interface with respective steady state temperature distributions (°C, film coefficient of 50 W/m K) Figure 3: Assumed locations of thermocouples mounted on the outside pipe surface The interface between the fluids was modelled as a horizontal plane with a step change in fluid temperatures in the vertical direction. The film coefficient was assumed constant for both cold and hot fluids with estimated value of 50 W/m2K, which was deemed consistent Proceedings of the International Conference Nuclear Energy for New Europe, Bled, Slovenia, Sept. 14-17, 2009 611.4 with the observed fluid velocities in the order of mm/s [10, 11]. In addition, film coefficients of 100, 500, 1.000 and 100.000 W/m2K have been analyzed in the sensitivity analysis. Outer pipe surface was assumed perfectly insulated in all analyzed cases. The vertical velocity of the interface was estimated at 2 mm/s [10, 11]. In addition, values of 5, 10, 50 and 100 mm/s have been analyzed in the sensitivity analysis. The main results were transient temperature fields in the pipe. Additionally, temperature histories were recorded at inner and outer pipe surface at hypothetical positions of fatigue monitoring system thermocouples as indicated in Figure 3. 2.2 Stress analysis The temperature fields were used to assess the transient stress fields in the second step. In addition, a constant internal pressure of 2,5 MPa was assumed. 2.3 Fatigue analysis The fatigue analysis followed the ASME Boiler and Pressure Vessel rules [3]. The transient principal stresses 01 > 02 > 03 were used to define the stress amplitude: = 0,5 • [max (( (t))- min ((j (t))], (1) with: S^ (t) =0(t) — O 2 (t)| S 23 (t) = |o2 (t) O) (2) S31 (t) = O3 (t) — 01(t)|. The value of the stress amplitude Sa is then compared with the fatigue properties defined in [3] to obtain the allowable number of load cycles. It is useful to note here that for Sa below 93 MPa, 1011 or more of the loading cycles are considered acceptable, given a typical stainless steel used to manufacture the surge line. In other words, load cycles exceeding Sa of 93 MPa should be considered as fatigue relevant. 3 RESULTS The simulated temperature fields are in the first step investigated through the readings of potential thermocouples (for assumed locations see Figure 3). Figure 4 depicts two examples detected at location M3-C. The cold water enters the surge line and pushes the interface between cold and hot water from the lower towards the upper surface of the pipe. When the tops surface is reached, the interface starts the downward motion with the same velocity. As a consequence, the temperature at the pipe inside surface starts to decrease at about 30 s and decreases until about 200 s (dotted lines). Then the downward motion of the interface is noted and the temperatures of the inside surface start to increase. The temperature difference is, as expected, governed by the film coefficient. Different steady state temperatures at the beginning an the end of the transient are attributed to rather low film coefficients giving rise to the competition between heat conduction within the pipe wall and heat transfer from the water to the pipe. This is to some extent illustrated by the temperature field in Figure 6 indicating notable circumferential heat fluxes at the pipe inner surface. The outside surface temperature readings (bold lines, Figure 4) clearly show delays and significantly underestimate the temperature transients at the pipe inner surface. While larger film coefficient clearly improves the sensitivity of the outside surface thermocouple, Figure 5 shows that faster movement of the fluid interface would tend to decrease both the maximum Proceedings of the International Conference Nuclear Energy for New Europe, Bled, Slovenia, Sept. 14-17, 2009 611.5 temperature difference experienced by any material point of the pipe and the indication given by a potential thermocouple. We may also argue that the thermocouples may be able to detect the vertical motion of the stratification interface with velocities in the order of mm/s and are at the same time rather insensitive to motions with velocities exceeding some cm/s. It is therefore clear that a reliable interpretation of the thermocouple signals requires a significant amount of reverse engineering. Readings of potential thermocouple position M3-C Time [s] Figure 4: Example readings of potential thermocouple at position M3-C (Figure 3) with inside surface temperatures A snapshot of a Tresca stress field is shown in Figure 7 and indicates rather high local variations. The results obtained as maxima of eq. (1) applied to the entire transient stress field are summarized in Table 1. It is shown that the velocity of the fluid interface (assuming fixed film coefficient value!) has negligible influence on the resulting stress amplitudes and that the increasing film coefficient increases the stress amplitude. Assuming that fatigue relevance requires stress amplitudes exceeding 93 MPa, it may be concluded that the transient studied is marginally fatigue relevant. It shall be noted here that it is only theoretically possible to decouple film coefficient and fluid velocities: it is well known that increasing fluid velocities increase the film coefficient. A detailed computational fluid dynamic study on the fluid to pipe wall heat transfer would certainly contribute to the more refined assessment of the fatigue relevance. Table 1: Maximum stress amplitude Sa in the model [MPa] Velocity of the fluid interface [mm/s] Film Coefficient [W/m2K] 50 100 500 1.000 100.000 2 68,6 84,4 105,1 114,1 228,9 100 68,7 84,5 105,4 Proceedings of the International Conference Nuclear Energy for New Europe, Bled, Slovenia, Sept. 14-17, 2009 611.6 Film coefficient = 100 W/m2 K 25 ^ 20 ct2 > ct3 were used to define the stress amplitude, Eqn. (3): = 0.5 .[max(\ (t))-min(Sy. (t))] With S. (t) defined in set of Eqn. (4) Sj2(t) = |oj(t) -02(t)| S23(t) = |ct2 (t) -CT3(t) S3j(t) = \o3(t) -Oj(t)|. The value of the stress amplitude Sa is then compared with the fatigue properties defined in [3] to obtain the allowable number of load cycles. It is useful to note here that for Sa below 93 MPa, 10jj or more of the loading cycles are considered acceptable, given a typical stainless steel used to manufacture the surge line. In other words, only load cycles exceeding Sa of 93 MPa should be considered as fatigue relevant. RESULTS The simulated temperature fields are in the first step investigated through the readings of potential thermocouples (for assumed locations see Fig. 4). As a second step, simulated Tresca stress fields are evaluated regarding values of maximum stress amplitudes results during the whole model simulation. Horizontal interface between fluids Figure 5 depicts two examples of temperature histories detected at location M3-C, for DT=127K. The cold water enters the surge line and pushes the interface between cold and hot water from the lower towards the upper surface of the pipe. When the top surface is reached, the interface starts the downward motion with the same velocity. Readings of potential thermocouple position M3-C, DT=127K 200 - u e- 190 - 160 -150 - .... .____ ..... ..... ...... — Outsi de, 50 W /m2K, 2 mm/s ■ ---Inside, 50 W/m2K, 2 mm/s -Outside, 500 W/m2K, 2 mm/s ---Inside, 500 W/m2K, 2 mm/s 0 50 100 150 200 250 300 350 400 450 500 Time [s] Figure 5. READINGS OF POTENCIAL THERMOCOUPLE AT POSITION M3-C (Fig. 4) WITH INSIDE SURFACE TEMPERATURES. DT=127K. As a consequence, the temperature at the pipe inside surface starts to decrease at about 30 s and decreases until about 200 s (dotted lines). Then the downward motion of the interface is noted and the temperatures of the inside surface start to increase. The temperature difference is, as expected, governed by the film coefficient. Different steady state temperatures at the beginning and the end of the transient are attributed to rather low film coefficients giving rise to the competition between heat conduction within the pipe wall and heat transfer from the water to the pipe. This is to some extent illustrated by the temperature field in Fig. 6 indicating notable circumferential heat fluxes at the pipe inner surface. The outside surface temperature readings (bold lines, Fig. 5) clearly show delays and significantly underestimate the temperature transients at the pipe inner surface. While larger film coefficient clearly improves the sensitivity of the outside surface thermocouple, Fig. 7 shows that faster movement of the fluid interface would tend to decrease both the maximum temperature difference experienced by any material point of the pipe and the indication given by a potential thermocouple. We may also argue that the thermocouples may be able to detect the vertical motion of the stratification interface with velocities in the order of mm/s and are at the same time rather insensitive to motions with velocities exceeding some cm/s. It is therefore clear that a reliable interpretation of the thermocouple signals requires a significant amount of reverse engineering. Temperatures [ C] HI +2.2306+02 ■ +2.105e+02 +1,980e+02 B +1.855e+02 t— +1,730e+02 — +1,605e+02 +14806+02 — +1.3556+02 +1 230e+02 +1.1056+02 _ +9.801e+01 +8.550e+01 +7.300e+01 Figure 6: RADIAL TEMPERATURE DISTRIBUTION IN THE MIDDLE OF ASSUMED TRANSIENT (°C) A snapshot of a Tresca stress field is shown in Fig. 8 and indicates rather high local variations. The results obtained as maxima of Eqn. (3) applied to the entire transient stress field are summarized in Tab. 1, for both temperature differences between hot and cold water. It is shown that the velocity of the fluid interface (assuming fixed film coefficient value!) has negligible influence on the resulting stress amplitudes and that the increasing film coefficient increases the stress amplitude. Assuming that fatigue relevance requires stress amplitudes exceeding 93 MPa, it may be concluded that the transient studied is only marginally fatigue relevant for film coefficient values below approximately 100 W/m2K. 220 210 180 170 140 4 Copyright © 2010 by ASME Film coefficient = 100 W/m2 K 30 g 25 u I ¡w 20 ■S 3 15 i- A S 10 ■8 * 5 i 0 Whole mode DT= 127K Measurement points (outside) DT=127K -o- Whole model DT= 150K Measurement points (outside) DT=150K 0 20 80 100 40 60 Velocity of the fluid interface [mm/s] Figure 7. MAXIMAL TEMPERATURE DIFFERENCE IN THE MODEL: CALCULATED AND INDICATED BY POTENCIAL THERMOCOUPLE. S. Tresca [MPa] (Avg: 50%) +1 9116+02 m +1.753e+02 ■ +1.5956+02 +1.4366+02 +1.2786+02 +1 120e+02 +9.S17e+01 +8.Q35e+01 +6.452e+01 +4.8706+01 _ +3.288e+01 +1.706e+01 ■ +1.2366+00 V Z X Figure 8. TRESCA STRESS DISTRIBUTION IN THE MIDDLE OF ASSUMED TRANSIENT (MPa) Table 1. MAXIMUM STRESS AMPLITUDE Sa [MPa] Temperature difference between hot and cold water [K] Fluid interface velocity [mm/s] Film Coefficient [W/m2K] 50 100 500 1000 2000 100000 127 2 68.6 84.4 105.1 114.1 135.6 228.9 100 68.7 84.5 105.4 114.1 135.6 150 2 72.7 90.8 114.1 134.9 159.6 265.8 100 72.8 90.9 114.4 Vertical interface between fluids Figure 9 depicts two examples detected at location M3-C, for DT=150K. The cold water enters the surge line and pushes the interface between cold and hot water from the left position towards the right position of the pipe (Fig. 3). When the right position is reached, the interface starts the motion in the opposite direction with the same velocity. As a consequence, the temperature at the pipe inside surface starts to decrease at about 5 s and decreases until about 2000 s (dotted lines, Fig. 9), followed by the temperature at the pipe outside surface (bold lines, Fig. 9). It takes around 3000s to achieve the steady state and initiate the motion of the interface between fluids in the opposite direction. At 5000s in the time line for higher film coefficient and 6500s for lower value of film coefficient. Then the temperatures of the inside surface start to increase again, followed by the outside surface temperatures. The temperature difference in time is, as expected, governed by the film coefficient. This is to some extent illustrated by the temperature field in Fig. 10 indicating notable axial heat fluxes at the pipe inner surface. Figure 10 shows the temperature distribution in the middle of the assumed transient (°C) in an axial section of the pipe. The outside surface temperatures readings (bold lines, Fig. 9) clearly show some delays with the inner surface temperatures readings. Figure 9 indicates that larger film coefficient clearly improves the sensitivity of the outside surface thermocouple. Readings of potential thermocouple position M3-C, DT=150K 230 210 . 190 [ 170 150 130 110 90 70 -Outside, 1000 W/m2K, 200 mm/s ■ - - Inside, 1000 W/m2K, 200 mm/s -Outside, 4000 W/m2K, 200 mm/s ■ - - Inside, 4000 W/m2K, 200 mm/s 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Time [s] Figure 9. EXAMPLE READINGS OF POTENTIAL THERMOCOUPLE AT POSITION M3-C (SEE FIG. 3) WITH INSIDE SURFACE TEMPERATURES. The rather scarce mesh density may give rise to overestimated temperature differences with higher values of film coefficients (e.g., over approximately 1000 W/m2 K) [13]. This is considered conservative with respect to the fatigue loading and is not further pursued in this paper. Use of more detailed mesh is however recommended for the future analyses. The resulting stress amplitudes obtained as maxima of Eqn. (3) applied to the entire transient stress field are summarized in Tab. 2. It is shown that the velocity of the fluid interface (assuming fixed film coefficient value!) has negligible influence on the resulting stress amplitudes and that the increasing film coefficient increases the stress amplitude. Assuming that fatigue relevance requires stress amplitudes 5 Copyright © 2010 by ASME exceeding 93 MPa, it may be concluded that the transient studied is fatigue relevant. It shall be noted here that it is only theoretically possible to decouple film coefficient and fluid velocities; it is well known that increasing fluid velocities increase the film coefficient. A detailed computational fluid dynamic study on the fluid to pipe wall heat transfer would certainly contribute to the more refined assessment of the fatigue relevance. Temperatures [°C] +2.2306+02 ■ +2.105e+02 ■ +1,980e+02 +1.855e+02 — +1,730e+02 +1.605e+02 +1.4806+02 +1.3556+02 +1 23ÜS+02 j—r +1.1056+02 _ +9.800e+01 +8.S50e+01 ■ +7.300e+01 Figure 10. AXIAL TEMPERATURE DISTRIBUTION IN THE MIDDLE OF ASSUMED TRANSIENT (°C) Table 2. MAXIMUM STRESS AMPLITUDE Sa [MPa] direction and, in the second case the interface is a vertical plane with a step change in fluid temperatures in the horizontal direction. In both cases, it has been shown that the velocity of the fluid interface, assuming fixed film coefficient value, has negligible influence on the resulting stress amplitudes and that the increasing film coefficient increases the stress amplitude. It shall be noted here that it is only theoretically possible to decouple film coefficient and fluid velocities; it is well known that increasing fluid velocities increase the film coefficient. Results in the first case with horizontal interface between fluids indicated marginal fatigue relevance for films coefficients below only approximately 100 W/m2K. As well, it has been shown that the potential thermocouples on the outside pipe surface may be able to detect the vertical motion of the stratification interface with velocities in the order of mm/s and are at the same time rather insensitive to motions with velocities exceeding some cm/s. It is therefore clear that a reliable interpretation of the thermocouple signals requires a significant amount of reverse engineering. Results in the second case with vertical interface between fluids indicated fatigue relevance of the analyzed transient. The potential of the thermocouples on the outside pipe surface to accurately capture the transient inside of the pipe is substantial on this case. A detailed computational fluid dynamic study on the fluid to pipe wall heat transfer and more detailed finite element mesh in the analyses involving film coefficients over 1000 W/m2K could contribute to the more refined assessment of the fatigue relevance in the future. Temperature difference between hot and cold water [K] Fluid interface velocity [mm/s] Film Coeffic [W/m2K] ient 1000 2000 4000 127 200 96.5 129.1 159.8 400 96.7 129.9 160.6 800 97.2 130.0 160.3 150 200 112.6 152.0 187.4 400 113.1 151.8 187.0 800 113.45 152.6 187.6 CONCLUSIONS A parametric study using detailed finite element analysis has been performed to quantify the possible range of fatigue loads. The example taken was a typical pressurized water reactor pressurizer surge line containing stratified flow of cold and hot water. The investigated parameters include the film coefficients governing the heat transfer from fluid to the pipe wall and the velocity of the interface between cold and hot water. Two cases for the fluid-fluid interface have been modeled. In first case, the interface has been modeled as a horizontal plane with a step change in fluid temperatures in the vertical ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support from Slovenian research agency (grants Z2-9488(B), V2-0553 (C) and P2-0026 (C)), Krško Nuclear Power Plant (grant Z2-9488(B)) and Slovene Nuclear Safety Administration (grant V2-0553 (C)). The authors are also indebted to Mr. Oriol Costa Garrido, who helped immensely in running the simulations and compiling the results. REFERENCES [1] Pressurizer surge line thermal stratification. Bulletin 8811: U.S. Nuclear Regulatory Commission; 20.12.1988. [2] Unexpected piping movement attributed to thermal stratification. Information notice 88-80: U.S. Nuclear Regulatory Commission; 7.10.1988. [3] ASME. Boiler and pressure vessel code. III Rules for construction of nuclear power plant components: ASME; 1989. [4] Bartonicek J, Zaiss W, Hienstorfer W, Kocklemann H, Schockle F. Monitoring systems and determination of 6 Copyright © 2010 by ASME actual fatigue usage. Nucl Eng Des. 1995;153(2-3):127-133. [5] Pöckl C, Kleinöder W. Developing and implementing of a fatigue monitoring system for the new European pressurized water reactor EPR. In: Jenčič I, Lenošek M, editors. International conference Nuclear energy for new Europe. Portorož, Slovenia: Nuclear Society of Slovenia; 2007. [6] Boros I, Aszodi A. Analysis of thermal stratification in the primary circuit of a VVER-440 reactor with the CFX code. Nucl Eng Des. 2008;238(3):453-459. [7] Jhung MJ, Choi YH. Surge line stress due to thermal stratification. Nuclear Engineering and Technology. 2008;40(3):239-250. [8] Kim KC, Lim JH, Yoon JK. Thermal fatigue estimation due to thermal stratification in the RCS branch line using one-way FSI scheme. Journal of Mechanical Science and Technology. 2008;22(11):2218-2227. [9] Kweon HD, Kim JS, Lee KY. Fatigue design of nuclear class 1 piping considering thermal stratification. Nucl Eng Des. 2008;238(6):1265-1274. [10] Zafošnik B, Cizelj L. Data base of transients in nuclear power plant Krško (in Slovene). "Jožef Stefan" Institute; 2009. [11] Zafošnik B, Cizelj L. Design of a method for monitoring the usage of nuclear power plant components (in Slovene). "Jožef Stefan" Institute; 2009. [12] ABAQUS. ABAQUS User's Manual 6.6-1. Providence, RI, USA: Dassault Systèmes Simulia Corp; 2006. [13] Zafošnik B, Cizelj L. Safe fatigue life of nuclear piping exposed to temperature and pressure fluctuations. In: Rožman S, Žagar T, Žefran B, editors. International conference Nuclear energy for new Europe. Portorož, Slovenia: Nuclear Society of Slovenia; 2008. 7 Copyright © 2010 by ASME ARTICLE IN PRESS Nuclear Engineering and Design xxx (2010) xxx-xxx Contents lists available at ScienceDirect Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes Fatigue relevance of stratified flows in pipes: A parametric study Leon Cizelj *, Igor Simonovski Jozef Stefan Institute, Reactor Engineering Division, Jamova Cesta 39, SI-1000 Ljubljana, Slovenia ARTICLE INFO Article history: Received 25 January 2010 Received in revised form 19 March 2010 Accepted 24 March 2010 Available online xxx ABSTRACT Stratified flows may form in pipelines under certain conditions and could lead to increased fatigue loading that was only marginally accounted for during the design phase of the second generation of nuclear power plants designed in accordance with the ASME Boiler and Pressure Vessel Code. Extension of operational license would require explicit account for fatigue loads imposed by stratified flows. This typically involves rather complex state-of-the-art computational technology, which may in some cases be combined with measurements of the temperatures at the outside surfaces of pipes, which comprise pressure boundary of the reactor coolant. A parametric study using detailed finite element analysis of the entire span of the pipe has been performed to quantify the possible range of fatigue loads and fatigue usage factors. The example taken was a typical pressurized water reactor pressurizer surge line containing stratified flow of cold and hot water. The investigated parameters include the film coefficients governing the heat transfer from the both fluids to the pipe wall and the velocity of the interface between then cold and hot water. The main results include the expected ranges of fatigue loading and usage factors given the range of investigated parameters. It is clearly shown that the choice of the film coefficients is essential to arrive at reliable fatigue estimate. Additionally, predictions of readings provided by hypothetical thermocouples at the pipe outer surface are provided. Some of their limitations are identified and discussed. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Stratified flows that may form in pipelines under certain conditions could lead to increased fatigue loading that was only marginally accounted for during the design phase of the second generation of nuclear power plants (USNRC, 1988a,b) designed in accordance with the ASME Boiler and Pressure Vessel Code (ASME, 1989). Extension of operational license would in most countries require explicit account for fatigue loads imposed by stratified flows. This typically involves rather complex state-of-the-art computational technology, which may in some cases be combined with measurements of the temperatures at the outside surfaces of pipes, which comprise pressure boundary of the reactor coolant (Bartonicek et al., 1995; Pöckl and Kleinöder, 2007). There is a wide consensus that within the reactor coolant systems of the pressurized water reactors (PWR) the stratified flows are most likely to occur in pressurizer surge lines. The rather slow flows caused by the pressure controlling activities of the pressurizer could result in the stratified flow of cold and hot water. The typically * Corresponding author. Tel.: +386 1 5885 215; fax: +386 1 5885 377. E-mail addresses: Leon.Cizelj@ijs.si (L. Cizelj), lgor.Simonovski@ijs.si (I. Simonovski). 0029-5493/$ - see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2010.03.030 reported velocity of such flows is in the order of cm/s (Boros and Aszodi, 2008). The typical temperature difference between the hot and cold water is reported to be in the range of 120-150 °C. Such temperature differences are believed to be the cause of rather significant thermal stresses resulting in accelerated fatigue usage and in some cases also in observed fatigue damage (Boros and Aszodi, 2008; Jhung and Choi, 2008; Kim et al., 2008; Kweon et al., 2008). The possible safety consequences of the material ageing are studied elsewhere (e.g., Cepin and Volkanovski, 2009; Leskovar and Uršič, 2009; Prošek and Mavko, 1999). An impressive body of open literature already exists. Some recent contributions include, among others, an attempt to simulate stratified flows using the computational fluid mechanics tools (Boros and Aszodi, 2008; Strubelj et al., 2010), proposal (Kweon et al., 2008) to update the fatigue analysis procedures in the ASME Boiler and Pressure Vessel Code (ASME, 1989) and example of surge line fatigue analysis (Jhung and Choi, 2008). In typical practical situations, the histories of the temperatures and velocities of stratified fluids inside the pipe, and, possibly, the temperatures at selected points along the outside pipe surface, may be known. The published fatigue analyses are to a large extent based on the assumption equating the temperatures at the pipe surface with the temperatures of the fluid. The conservativity of such approach is widely accepted, especially while dealing with rather large fluid velocities causing rather large transfer of heat between Please cite this article in press as: Cizelj, L., Simonovski, I., Fatigue relevance of stratified flows in pipes: A parametric study. Nucl. Eng. Des. (2010), doi:10.1016/j.nucengdes.2010.03.030 ■BBBMarticle in press 2 L. Cizelj, I. Simonovski / Nuclear Engineering and Design xxx (2010) xxx-xxx Nomenclature A area (of heat transfer) Cp specific heat capacity h film coefficient k thermal conductivity q heat flux Sa stress amplitude Sij difference between principal stresses oi and oj t time T temperature Tf temperature of the fluid far from the surface Tp temperature of the pipe surface Greek symbols P density oi, a2 > a3 were used to define the stress amplitude: Sa = 0.5 [max(Sj(t) - min(Sy(t))J with: Sl2(t) = S23(t) = S3I(t) = ffl(t) - 02(t) 02(t) - 0-3(t) 03(t) - ^l(t) (1) (2) The value of the stress amplitude Sa is then compared with the fatigue properties defined in ASME (1989) to obtain the allowable number of load cycles. For the purpose of this paper it is sufficient to note that for Sa below 93 MPa, 1011 or more of the loading cycles are considered acceptable, given a typical stainless steel used to manufacture the surge line. In other words, load cycles exceeding Sa of93 MPa should be considered as fatigue relevant. 3. Results 3.1. Temperatures The simulated temperature fields are in the first step investigated through the readings of potential thermocouples. Fig. 4 depicts two examples detected at location M3-C (see Fig. 3) for Fig. 4. Example readings of potential thermocouple at position M3-C (see Fig. 3) with inside surface temperatures. 30 E ë a 10 E -0-Whole model AT=150K a\ ■a Whole mode AT=127K —Measurement points (outside) AT=150K a Measurement points (outside) AT=127K li\ A\ --— 0 10 20 30 40 50 60 70 80 90 100 Velocity of the fluid interface [mm/s] Fig. 5. Maximal calculated temperature differences in the model compared to the maximal indication of all thermocouples (h = 100 W/m2 K). two different values of the film coefficient. Please note that in the assumed thermal cycle the cold water enters the surge line and pushes the interface between cold and hot water from the lower towards the upper surface of the pipe. When the top surface is reached, the interface starts the downward motion with the same velocity. As a consequence, the temperature at the pipe inside surface starts to decrease at about 30 s and decreases until about 200 s. Then the downward motion of the interface is noted and the temperatures of the inside surface start to increase. The temperature difference between the temperatures at the wetted inside and monitored outside surface is, as expected, strongly related to the film coefficient. Different steady state temperatures at the beginning and the end of the transients with film coefficients of 50 and 500 W/m2 K are also attributed to rather low film coefficients giving rise to the competition between heat conduction within the pipe wall and heat transfer from the water to the pipe. This is to some extent illustrated by the temperature field in Fig. 6, which clearly shows notable circumferential heat fluxes at the pipe inner surface. The outside surface temperature readings (Fig. 4) clearly show delays in the temperature changes. Also, the temperature histories measured at the outside surface are shown to significantly underestimate the temperature transients at the pipe inner surface. Larger film coefficient clearly improves the relative sensitivity of the outside surface thermocouple. Faster movement of the fluid interface tends to decrease both the maximum temperature difference experienced by any material 3 Please cite this article in press as: Cizelj, L., Simonovski, I., Fatigue relevance of stratified flows in pipes: A parametric study. Nucl. Eng. Des. (2010), doi:10.1016/j.nucengdes.2010.03.030 ■BBBMarticle in press 4 L. Cizelj, I. Simonovski / Nuclear Engineering and Design xxx (2010) xxx-xxx Table 1 Maximum stress amplitude Sa in the model [MPa]. Temperature difference between hot and cold water [K] Velocity of the fluid interface [mm/s] Film coefficient [W/m2 K] 50 100 500 1.000 2.000 100.000 127 2 68.6 84.4 105.1 114.1 135.6 228.9 100 68.7 84.5 105.4 114.1 135.6 150 2 72.7 90.8 114.1 134.9 159.6 265.8 100 72.8 90.9 114.4 Fig. 6. Example of the temperature distribution through a pipe wall in the middle of the assumed transient (°C). point of the pipe and the indication given by a potential thermocouple (Fig. 5). It is also clearly shown that the thermocouples may be able to detect the vertical motion of the stratification interface of fluids with temperature differences of 127 or 150 K with velocities in the order of mm/s and are at the same time rather insensitive to motions with velocities exceeding some cm/s (Fig. 5). It is therefore clear that a reliable interpretation of the thermocouple signals requires a significant amount of reverse engineering. 3.2. Stress amplitudes A snapshot of a Tresca stress field is shown in Fig. 7 and indicates rather high local variations. The stress amplitudes (Eq. (1)) were therefore obtained for the entire transient stress field in the analyzed pipe. The maximal values are summarized in Table 1. The velocity of the fluid interface (assuming fixed film coefficient value!) is shown to have only minor influence on the Please cite this article in press as: Cizelj, L., Simonovski, I., Fatigue relevance of stratified flows in pipes: A parametric study. Nucl. Eng. Des. (2010), doi:10.1016/j.nucengdes.2010.03.030 gaBBIM ARTICLE IN PRESS L. Cizelj, I. Simonovski / Nuclear Engineering and Design xxx (2010) xxx-xxx 5 resulting stress amplitudes. As expected, increasing the film coefficient would increase the thermal gradients and therefore also increases the stress amplitude. It is also clearly shown that the conservativity of the traditional conservative approach with very large film coefficient might in certain cases overestimate the stress amplitudes by a factor of two or even more. Assuming that fatigue relevance requires stress amplitudes exceeding 93 MPa, it maybe concluded that the transient studied is marginally fatigue relevant. It shall be noted here that it is only theoretically possible to decouple film coefficient and fluid velocities: it is namely well known that increasing fluid velocities increases the film coefficient. A detailed computational fluid dynamic study on the fluid to pipe wall heat transfer would certainly contribute to the more refined assessment of the fatigue relevance in the future. 4. Conclusions A parametric study using detailed finite element analysis has been performed to quantify the possible range of fatigue loads and fatigue usage factors. The example taken was a typical pressurized water reactor pressurizer surge line containing stratified flow of cold and hot water. The investigated parameters include the film coefficients governing the heat transfer from fluid to the pipe wall and the velocity of the interface between then cold and hot water. It has been shown that the increasing film coefficient increases the stress amplitude and that the velocity of the fluid interface (assuming fixed film coefficient value) has only minor influence on the resulting stress amplitudes. The results also indicated marginal fatigue relevance of the investigated transient. It shall be noted here that it is only theoretically possible to decouple film coefficient and fluid velocities: it is well known that increasing fluid velocities increase the film coefficient. A detailed computational fluid dynamic study on the fluid to pipe wall heat transfer would certainly contribute to the more refined and reliable assessment of the fatigue relevance. For the transient studied, the potential thermocouples on the outside pipe surface may be able to detect the vertical motion of the stratification interface with velocities in the order of mm/s and are at the same time rather insensitive to the motions with velocities exceeding some cm/s. It is therefore clear that a reliable interpretation of the thermocouple signals requires a significant amount of reverse engineering. Acknowledgements The authors gratefully acknowledge the financial support from Slovenian research agency (grants Z2-9488(B), V2-0553 (C) and P2-0026 (C)), Krško Nuclear Power Plant (grant Z2-9488(B)) and Slovene Nuclear Safety Administration (grant V2-0553 (C)). References ABAQUS, 2006. ABAQUS User's Manual 6.6-1. Dassault Systèmes Simulia Corp, Providence, RI, USA. ASME, 1989. 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Fatigue design of nuclear class 1 piping considering thermal stratification. Nuclear Engineering and Design 238 (6), 1265-1274. Leskovar, M, Uršic, M., 2009. Estimation of ex-vessel steam explosion pressure loads. Nuclear Engineering and Design 239 (11), 2444-2458. Myers, G.E., 1971. Analytical Methods in Conduction Heat Transfer. McGraw-Hill, New York. Pockl, C., Kleinoder, W., 2007. Developing and implementing of a fatigue monitoring system for the new European pressurized water reactor EPR. In: Jenciš, I., Lenošek, M., International Conference Nuclear Energy for New Europe. Nuclear Society of Slovenia, Portorozš, Slovenia. Prošek, A., Mavko, B., 1999. Evaluating code uncertainty. I. Using the CSAU method for uncertainty analysis of a two-loop PWR SBLOCA. Nuclear Technology 126, 170-185. Strubelj, L., Ézsol, G., et al., 2010. Direct contact condensation induced transition from stratified to slug flow. Nuclear Engineering and Design 240 (2), 266-274. USNRC, 1988a. Pressurizer surge line thermal stratification. Bulletin 88-11. U.S. Nuclear Regulatory Commission. USNRC, 1988b. Unexpected piping movement attributed to thermal stratification. Information notice 88-80. U.S. Nuclear Regulatory Commission. Zafosnik, B., Cizelj, L., 2008. Safe fatigue life of nuclear piping exposed to temperature and pressure fluctuations. In: Rozman, S., /Žagar, T., Zefran, B. International Conference Nuclear energy for New Europe. Nuclear Society of Slovenia, Portorož, Slovenia. Zafosnik, B., Cizelj, L., 2009a. Data base of transients in nuclear power plant Krško (in Slovene). "Jozef Stefan" Institute. Zafosnik, B., Cizelj, L., 2009b. Design of a method for monitoring the usage of nuclear power plant components (in Slovene). "Jozef Stefan" Institute. Please cite this article in press as: Cizelj, L., Simonovski, I., Fatigue relevance of stratified flows in pipes: A parametric study. Nucl. Eng. Des. (2010), doi:10.1016/j.nucengdes.2010.03.030 Safety, Reliability and Risk Analysis: Theory, Methods and Applications - Martorell et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-48513-5 Probabilistic safety assessment for other modes than power operation Marko Cepin "Jožef Stefan'' Institute, Jamova cesta 39, SI-1000 Ljubljana, Slovenia Rudolf Prosen Nuclear Power Plant Krško, Vrbina 12, SI- 8270 Krško, Slovenia ABSTRACT: Probabilistic safety assessment is a standardized method for assessment and improvement of nuclear power plant safety. The paper presents the probabilistic safety assessment of 4 modes of operation of the nuclear power plant: 1) normal power operation, 2) plant startup, 3) hot standby and 4) hot shutdown. The modeling features are presented and the differences between the models are highlighted with the emphasis on comparison between hot standby and normal power operation. The results are shown and the findings are discussed. The considered probabilistic safety assessment model includes internal and external events, but the comparison is made considering internal events only. The considered probabilistic safety assessment model is a model of a nuclear power plant with pressurized water reactor, with two loops and with more than 20 years of successful plant operation. The results of probabilistic safety assessment for other modes than plant normal power operation show certain differences in risk measures for each considered mode. In spite of the fact that the time duration of plant being in other modes is short comparing to the power operation, some conservatism in modeling and consequently in the results is reduced, which lead to our higher confidence in better models and results. 1 INTRODUCTION Probabilistic safety assessment (PSA) is a standardized method for assessment and improvement of nuclear power plant safety, which is widely applied (Cepin & Mavko 2002, Cepin 2005). Normally, it is performed for plant power operation, although it can be used for other plant modes (Kiper 2002). Consideration of the plant shutdown is in practice usually a separate issue and a probabilistic safety assessment of a nuclear power plant at shutdown states is therefore separated from analyses of plant power operation. The objective of the paper is to show how can probabilistic safety assessment model for normal power operation be used for development of probabilistic safety assessment models for other modes of plant operation such as start-up, hot standby and hot shutdown. The paper presents the probabilistic safety assessment of 4 modes of operation of the nuclear power plant: 1) power operation, 2) plant startup, 3) hot standby and 4) hot shutdown. The modeling features are presented and the differences between the models are highlighted. The procedure for preparation of new models is described. The results are shown and the findings are discussed. 2 METHOD The procedure for development of PSA models for selected plant states is developed (section 2.1). The method for integration of the results of specific models is defined to assess the overall risk (section 2.2). 2.1 Procedure The respective probabilistic safety assessment documents and the computerized probabilistic safety assessment model are both analyzed. For each of the selected plant states: - plant operation in plant startup (mode 2), - plant operation in hot standby (mode 3) and - plant operation in hot shutdown (mode 4), its respective PSA model was prepared based on the PSA model for normal plant operation. Initiating events and their frequencies are reviewed and changed, if needed for a specific mode of operation. E.g. the frequencies of Loss of Coolant Accidents are lower for plant in hot shutdown than for plant in normal operation and are changed to lower frequencies in the PSA model for plant operation in hot shutdown. 2883 Table 1. Link between PSA models and plant parameters. Name and description Definition of plant of PSA model Basic PSA model Basic PSA model is assumed to be representative Changed PSA model: POSlC-preliminary Changed PSA model: POS2A-preliminary Changed PSA model: POS3A-preliminary The functional events and the branches of the event tree are reviewed and changed, if needed for a specific mode of operation. E.g. functional event: reactor trip is not needed and it is deleted from the respective event trees in the PSA model for plant operation in hot shutdown. The fault trees linked to the respective functional events of the event trees are reviewed and changed if needed for a specific mode of operation. Those potential changes include: - the change of logic of the fault tree (e.g. a branch or a gate is removed, if it is not needed in the model), - change of basic events of the fault tree (e.g. basic event is deleted, if it is not needed in the model), - changes of parameters of the basic events (e.g. change of failure probability of certain equipment or change of human error probability, if it is needed in the model). Definition of plant operating states (POS) is selected similarly as in document NUREG/CR-6144, which defines 15 plant operating states (POS1, POS2,... POS15). Some of the sub-states are defined in addition for certain states, which in more details represent the connection between specific operational mode and the operating state: e.g. POS1A, POS1B, POS1C, POS2A, POS2B, POS3A, POS3B, POS15A, POS15B, POS15C. There is no exact mach between definition of specific POS and definition of specific operational mode. Definition of plant operational modes is written in technical specifications (6 modes) of the plant safety analysis report. Comments about description of the main plant parameters Plant operation at full power Plant operation at reduced power Plant operation at reducing power Increasing power Cool-down with Steam Generators, core is sub-critical Reactor coolant system heat up with steam generators AFW and RHR are in operation, plant cooling is assured by AFW, core is sub-critical POS13 Reactor coolant system heat up The following assumptions are stated for determining the plant conditions for analyzed PSA models, which are summarized in Table 1: - For normal steady state operation of NPP, the existing PSA for normal operation applies. - For power operation at reduced power in mode 1 and not in a steady state operation, PSA fornormal operation is assumed to be representative. As the power level is lower than the nominal, the initial decay heat after reactor trip is lower. Operators have more time for respond to transients, so their respective human error probabilities are the same as for power operation or lower. Initiating event frequency for loss of main feedwater could be slightly higher. - For power operation at reduced power in mode 2, a slightly changed PSA model named POS1C-preliminary is developed. - For hot standby, a slightly changed PSA model named POS2A-preliminary is developed. - For hot shutdown, a slightly changed PSA model named POS3A-preliminary is developed. Normally, the plant conditions are in certain operating state not identical for both possibilities: if the plant goes in the direction of shutting it down or if the plant goes in the direction of starting it up. 2.2 Method for assessing the overall risk The results of probabilistic safety assessment of specific modes can be used to assess the overall risk of the plant. The method is simple and it bases on determining the mean value of the considered results of considered modes of operation taking into account operation Plant mode Plant state steady state full power operation Not steady state operation Not steady state operation Hot standby Hot shutdown MODE 1 MODE 1 MODE 2 MODE 3 MODE 4 POS1C POS15A POS2A POS14 POS3A 2884 the time duration of each of considered modes. The expression for determining the overall risk is the following: R = , RiTi Ei=i Ti (1) where R = overall risk measure (either core damage frequency on the plant or event tree or sequence level, or the system unavailability at the system or subsystem level); R, = risk measure of i—th mode of operation; T, = the time duration for the plant being in i—th mode of operation; I = the number of considered modes of operation. 3 MODELS The considered probabilistic safety assessment model includes internal and external events. It is a model of a nuclear power plant with pressurized water reactor, with two loops and with more than 20 years of successful plant operation. The probabilistic safety assessment model for normal operation is a detailed model consisting of thousands of basic events and gates, hundredths of system and subsystem fault trees and tenths of event trees. The model integrates the internal and external events, but only the portion for internal events is selected for comparison purposes in this paper. 3.1 PSA model for Mode 2 - Plant operation at reducing power Plant operating state POS1C covers the following plant conditions, which apply to Mode 2 (less than 5% of nominal plant power): - Turbine is shutdown. - Main feedwater pumps are shutdown, feedwater system is not needed, but it may serve as a backup for auxiliary feedwater system operation, if it fails. - Motor driven pumps of auxiliary feedwater system are running. - The power is between 0 and 5% of nominal power. The key similarities between POS1C, which is represented by POS1C-preliminary model, and power operation are the following: - RCS temperatures and pressures are essentially the same. - The secondary side temperatures and pressures are essentially the same. - The same types of initiating events are applicable. The key differences between POS1C, which is represented by POS1C-preliminary model, and power operation are the following: - The plant is not operating in a stable steady state. - The reactor power level is significantly decreased. - The decay heat is lower. - Plant transients are developing slower than at full power. - The control rods are nearly fully inserted into the core. - Engineered safety features actuation system and reactor trip system setpoints and interlocks may be changed or may be blocked. 3.2 PSA model for Mode 3 - Hot standby Plant operating state POS2A covers the following plant conditions, which apply to hot standby (Mode 3): - Turbine is shutdown. - Main feedwater pumps are shutdown, feedwater system is not needed, but it may serve as a backup for auxiliary feedwater system operation, if it fails. - Motor driven pumps of auxiliary feedwater system are running. The key similarities between POS2A, which is represented by POS2A-preliminary model, and power operation are the following: - RCS temperatures and pressures are essentially the same. - The secondary side temperatures and pressures are essentially the same. The key differences between POS2A, which is represented by POS2A-preliminary model, and power operation are the following: - The decay heat is lower in hot standby than in power operation. - All control rods and shutdown rods are fully inserted into the core. - Initiating event anticipated transient without scram—ATWS is not needed. - As the power conversion system is shutdown, the respective initiating events are not applicable (transients with main feedwater, transients without main feedwater, large steam/feedline break). - Initiating event frequencies for loss of coolant accidents (LOCA), steam generator tube rupture (SGTR) are significantly lower. - Human error probabilities are lower in general due to slower transients and due to more time to respond. Table 2 shows the selected 6 changes from out of more than 50 changes applicable forthe internal events for hot standby PSA model versus normal operation PSA model. i 2885 Table 2. Changes for hot standby PSA model versus normal operation PSA model. Affected issue in NEK PSA model Description of the change Justification for the change Medium loss of coolant accident, event tree, sequence no. 8 Medium loss of coolant accident, event tree, functional event: reactor trip 1 Basic event HFE-OP1-751, probability parameter Parameter, frequency initiating event small loss of coolant accident Event tree steam line break Fault tree auxiliary feedwater system Sequence no. 8 is deleted Functional event: reactor trip 1 is deleted probability parameter OP1-751 is changed to 1,3E-3 frequency changed from 2,7E-3/ry to 1,62E-3/ry Event tree steam line break is deleted Basic events BE-11020, BE-11000, BE-11044 are deleted Medium loss of coolant accident, event tree, consequence: anticipated transient without scram is not applicable, because the control rods are fully inserted Human error probability HFE-OP1-751 is for a factor of 8.1E-2 smaller due to longer time for action initiating event frequency is significantly lower in hot standby As the power conversion system is shutdown, the respective initiating event is not applicable AFW is already running (motor driven pumps) 3.3 PSA model for Mode 4 - Hot shutdown Plant operating state POS3A covers the following plant conditions, which apply to hot shutdown (Mode 4): - Turbine is shutdown. - Main feedwater pumps are shutdown, feedwater system is not needed, but it may serve as a backup for auxiliary feedwater system operation, if it fails. - Motor driven pumps of auxiliary feedwater system are running. - Reactor coolant temperature is decreasing. The key differences between POS3A, which is represented by POS3A-preliminary model, and power operation are the following: - The decay heat is lower in hot shutdown than in power operation. - All control rods and shutdown rods are fully inserted into the core. - Initiating event anticipated transient without scram - ATWS is not needed. - As the power conversion system is shutdown, the respective initiating events are not applicable (transients with main feedwater, transients without main feedwater, large steam/feedline break). - Initiating event frequencies for loss of coolant accidents (LOCA) are significantly lower. - Initiating event steam generator tube rupture (SGTR) is not needed in hot shutdown. - Human error probabilities are lower in general due to slower transients and due to more time to respond. - Reactor coolant temperature is decreasing. - Component cooling water system (CCW), service water system (ESW) and instrument air system (IA) logic are limited to branches connected to operating systems (e.g. AFW). 4 ANALYSIS AND RESULTS The results of probabilistic safety assessment include: - lists of minimal cut sets for all and for individual event trees and sequences, - lists of minimal cut sets for fault trees of safety systems, subsystems and support systems, - core damage frequency, - risk measures for components and human failure events and for their groups at all levels of analyses from fault tree analysis to sequence analysis and all event trees analysis. Figure 1 shows part of the results of the probabilistic safety assessment for normal operation: contribution to core damage frequency for all defined initiating events, which represent the internal events probabilistic safety assessment. Table 3 shows descriptions of initiating events presented on Figure 1. The results of the PSA model for internal initiating events for hot standby shows that the number of gates and basic events in the fault trees and event trees is notably lower, which is expected due to the fact that some event trees and some event tree sequences have been deleted, some fault tree branches and some events have been removed. The core damage frequency decreases for 30% and distribution of contributions from initiating events changes slightly, which is presented on Figure 2. 2886 CDF Contribution by Initiating Events ISL 0,6' AWS 1,1 SGR1 1,2% VE 1,2% SLB SLO 4,4% 5,3% LDC ,4% INA 0,0% LLO 0,1% J . ^AV TRO - TRA 11,2% SBO LSP TRA TRO CCW ESW MLO SLO SLB VEF SGR AWS ISL LDC LLO INA Figure 1. Contribution to core damage frequency for internal events for normal operation. Figure 3 shows the fractional contribution of selected human failure events for normal operation and for hot standby. The figure shows that the fractional contribution for selected human failure events is lower in hot standby and for some it is higher in hot standby. Fractional contribution (FC) is calculated based on expression: FCi = R - R(Qi = 0) R (2) where R = risk measure, which can be either core damage frequency on the plant or event tree or sequence level, or the system unavailability on the system or subsystem level; Qi = unavailability of component i; FCi = fractional contribution of component i. The events for which fractional contribution is lower at hot standby are connected with establishing power to instrumentation, if the normal power supply fails. Figure 4 shows the fractional contribution of selected groups of components for normal operation and for hot standby. Table 4 shows the definitions ofthe groups ofevents shown on Figure 4. Table 3. Initiating events. INITIATING EVENT IE ANTICIPATED TRANSIENT WITHOUT AWS SCRAM INTERFACING SYSTEMS LOCA ISL LARGE LOCA LLO LOSS OF 125V DC VITAL BUS LDC LOSS OF COMPONENT COOLING CCW WATER SYSTEM LOSS OF ESSENTIAL SERVICE WATER ESW SYSTEM LOSS OF INSTRUMENT AIR INA LOSS OF OFFSITE POWER LSP MEDIUM LOCA MLO SMALL LOCA SLO STATION BLACKOUT SBO STEAM GENERATOR TUBE RUPTURE SGR STEAM LINE BREAK SLB TRANSIENT WITH MFW AVAILABLE TRA TRANSIENT WITH MFW UNAVAILABLE TRO VESSEL FAILURE VEF CDF Contribution by Initiating Events IEV-SGR 1,3% IEV-VEF IEV-ESW 1,7% A 1,5% l\ °,1/° IEV-ISL 0,0% IEV-L 0,8 IEV-S □ IEV-SBO ■ IEV-CCW □ IEV-LSP □ IEV-TRA ■ IEV-MLO □ IEV-SLO ■ IEV-LLO □ IEV-VEF ■ IEV-ESW ■ IEV-SGR □ IEV-LDC □ IEV-ISL Figure 2. Contribution to core damage frequency for internal events for hot standby. The fractional contribution for a group named human-errors, which comprise all human failure events, is lower in hot standby. All human error probabilities of all human failure events have either remained the same or have been reduced due to larger amount of time for operators. The fractional contribution of auxiliary feedwater pumps is higher in hot standby in spite of the fact 2887 Table 4. Definition of groups of events. I □ FC hot standby □ FC normal I JIlU HE-01 HE-02 HE-03 HE-04 HE-05 HE-09 HE-10 selected human failure events Figure 3. Fractional contribution of selected human failure events. I □ FC hot standby □ FC normal I DIESEL-GEN HUMAN- AFW-PUMPS HUMAN-E-INI HUMAN-E-ERRORS PRE-INI selected groups of components BASIC EVENT GROUP NAME BASIC EVENT GROUP DESCRIPTION DIESEL-GEN All basic events corresponding to diesel generators HUMAN-ERRORS All basic events corresponding to human failure events AFW-PUMPS All basic events corresponding to auxiliary feedwater pumps HUMAN-E-INI All basic events corresponding to initiator human failure events HUMAN-E-PRE-INI All basic events corresponding to pre-initiator human failure events Figure 5. Core damage frequency comparison for the selected plant states. is relatively lower than the contribution of removal of other items that are not connected to auxiliary feedwater. Figure 5 shows the preliminary core damage frequency comparison for the selected plant states. 5 CONCLUSIONS U,UUE+UU Figure 4. Fractional contribution of selected groups of components. that all changes related to auxiliary feedwater system were only connected with removal of respective basic events (e.g. removalofpump fails to start, asthepumps are already running) and removal of branches of the fault trees (e.g. contribution of test and maintenance activities). The reason for this lays in a fact that the contribution of removed part connected with auxiliary feedwater The results of probabilistic safety assessment for other modes than plant power operation show certain differences in risk measures for each considered mode. Although, the time duration of plant being in other modes is short comparing to the power operation, some conservatism in modeling and consequently in the results is reduced, which lead to our higher confidence in better models and results. In addition, the results contribute to the overall goal to complete the probabilistic safety assessment of different plant operating states with the same concept as it is used for the normal operation. This will give a 2888 comparison to shutdown PSA, which was performed for the plant under investigation well ago. REFERENCES Cepin M. & B. Mavko. 2002. A Dynamic Fault Tree. Reliability Engineering and System Safety 75 (1): 83-91. Cepin M. 2005. Analysis of Truncation Limit in Probabilistic Safety Assessment. Reliability Engineering and System Safety 87 (3): 395-403. Cepin, M. & Prosen, R. 2006. Update of human reliability analysis fornuclearpowerplant. In Glumac, Bogdan(ed.), Lengar, Igor (ed.), International Conference Nuclear Energy for New Europe, Portorož, 2006. Proceedings. Nuclear Society of Slovenia. Kiper K.L. 2002. Insights from an All-Modes PSA at Seabrook Station. International Topical Meeting on Probabilistic Safety Assessment. Detroit 2002. Proceedings. 429-434. ANS. NUREG/CR-6144, Evaluation of Potential Severe Accident During Low Power and Shutdown Operations at Surry, Unit 1, NRC, 1995. 2889 Risk Comparison of Methods for Dependency Determination within Human Reliability Analysis Marko Čepin Institut Jožef Stefan, Ljubljana, Slovenia Abstract: Dependency between human failure events is an issue, which include subjectivity in the models and consequently in the results of human reliability analysis and thus in probabilistic safety assessment. Many methods connected with human reliability analysis were developed in the last decades, which mostly include determination of dependency between human failure events: e.g. Standardized Plant Analysis Risk HRA - SPAR-H and Institute Jožef Stefan - Human Reliability Analysis - IJS-HRA. A comparison of dependency as it is applied within the selected methods is performed on an example probabilistic safety assessment model of a selected nuclear power plant. Pre-initiators and post-initiators are considered. It is investigated how the contribution of consideration of dependency of pre-initiators and dependency of post-initiators and dependency of both impacts the human error probabilities, which are then used within probabilistic safety assessment. The results of comparison show that selection of the method for determining dependency between human failure events may largely impact the results of human reliability analysis and consequently the probabilistic safety assessment. The subjectivity can be reduced by development of more detailed guidelines for human reliability analysis with many detailed practical examples for all steps of the process of evaluation of human performance. Keywords: Probabilistic Safety Assessment, Human Reliability, Dependency, Human Error Probability. 1. INTRODUCTION Dependency between Human Failure Events (HFE) is an issue, which include subjectivity in the models and consequently in the results of Human Reliability Analysis (HRA) and thus in Probabilistic Safety Assessment (PSA). The human reliability analysis is a systematic framework, which includes the process of evaluation of human performance and associated impacts on structures, systems and components for a complex facility. 1.1. Objectives The objective of the paper is to show that subjectivism can largely impact the results of human reliability analysis and consequently the results and applications of probabilistic safety assessment in a Nuclear Power Plant (NPP). The objective is to identify the key features, which may decrease the subjectivity of human reliability analysis. In this sense, two human reliability analysis methods are compared with emphasis on the comparison of dependency consideration: Institute Jožef Stefan -Human Reliability Analysis (IJS-HRA) [1, 2, 3, 4] and Standardized Plant Analysis Risk HRA (SPAR-H) [5]. They are selected from a large set of existing methods, because they are relatively new. 1.2. Overview of Current Developments A number of developed methods for assessment of human reliability were published in last decades in addition to the mentioned two methods. Those include: Technique for Human Error Rate Prediction -THERP [6], Systematic Human Action Reliability Procedure - SHARP [7], Accident Sequence Evaluation Program - ASEP [8], A Technique for Human Event Analysis - ATHEANA [9, 10], Cognitive Reliability and Error Analysis Method - CREAM [11], Human Cognitive Reliability - HCR [12], Electric Power research Institute HRA - EPRI HRA [13], Commission Errors Search and Assessment - CESA [14]. In addition, good practices about HRA were published [15]. 2. COMPARISON OF IJS-HRA AND SPAR-H 2.1. IJS-HRA The human reliability analysis (IJS-HRA) is a method for evaluation of human failure events in sense to determine the reliability of the respective human actions [1, 2, 3, 4]. Human action is a specific action required by human operator. If it is not performed or it is not performed in time and correctly, it is referred to as a human failure event. Figure 1 shows the schematic representation of the IJS-HRA method. The main inputs for IJS-HRA method include (left part of the Figure 1): - Probabilistic Safety Assessment (PSA) model, which is interconnected with the human reliability analysis, - plant information, which is the source of information which supports the evaluation and - state-of-the-art in the respective field: standards, guides, good features of existing methods and good practice. The method is developed including consideration about dependencies between human failure events [1, 4, 6]. The success criteria for human failure events include information about their time window, i.e. information about the time, in which operators have to perform the action. This information about the available time comes from safety analyses, where scenarios about operating safety systems are evaluated. This is the reason for appearance of text box of safety analysis on Figure 1 and its connection with text box: evaluation. Results of the human reliability analysis are inserted into the probabilistic safety assessment, which is shown by upper feedback on the Figure 1. Figure 1 shows that identification of HFE distinguishes pre-initiator events (i.e. pre-initiators), initiator events (i.e. initiators) and post-initiator events (i.e. post-initiators). Pre-initiators are the events that may cause the equipment to be unavailable before the initiating event has occurred. Initiators are the events that may contribute to the occurrence of initiating events. Post-initiators are the events, which are connected with human actions to prevent accident or mitigate its consequences after initiating event has occurred. Evaluation of HFE including evaluation of dependencies integrates assessment of human error probabilities (HEP) with plant information, operator interview, simulator experience and plant data base. Figure 1: Scheme of IJS-HRA method Inputs Process of HRA Development, Evaluation and Application A->■<-► The five levels of dependency are determined in the same way as they are considered in THERP: Zero Dependency (ZD), Low dependency (LD), Moderate dependency (MD), High dependency (HD), Complete dependency (CD) [2]. Human error probability (HEP) of dependent HFE A and B is determined according to equation: PXD(PB|PA)=PA*(1+K-PB)/(K+1); where: K=0, 1, 6, 19, oo, for dependency levels ZD, LD, MD, HD, CD, where X=Z, L, M, H, C, respectively [6]. Figure 2: IJS-HRA Dependency - Pre-Initiator HFE PRE- SYSTEM PERSON ACTION PROCEDURE TIMING ACTION CONDITION NO . DEPENDENCY INITIATOR DESCRIPTION SIMILARITY LEVEL CALIBRATION PRE-INITIATOR ALIGNMENT SEQUENTIAL ¿10MIN Ï10MIN SIMILAR NOT SIMILAR SIMILAR JOINED P>1E-5 NOT SIMILAR NOT SIMILAR NOT SIMILAR NOT SIMILAR 01 CD 02 HD 03 CHANGE 04 MD 05 CHANGE 06 LD 07 CHANGE 08 HD 09 CHANGE 10 MD 11 CHANGE 12 LD 13 CHANGE 14 ZD 15 CHANGE 16 CD 17 HD 18 CHANGE 19 MD 20 CHANGE 21 LD 22 CHANGE 23 ZD 24 CHANGE 25 ZD 26 CHANGE 27 ZD 28 CHANGE Figure 3: IJS-HRA Dependency - Post-Initiator HFE POST- CUE TIME CREW STRESS COMPLEXITY CONDITION NO . DEPENDENCY INITIATOR BETWEEN LEVEL COMMON <30MIN , 25MIN DIFFERENT MODERATE HIGH SAME Ï30MIN MODERATE LOW DIFFERENT COMPLEX SIMPLE COMPLEX SIMPLE SIMPLE COMPLEX SIMPLE - 01 CD JOINED P^1E-5 02 hD JOINED P<1E-5 03 CHANGE - 04 HD 05 CHANGE - 06 HD - 07 CHANGE - 08 MD - 09 CHANGE - 10 MD - 11 CHANGE - 12 LD - 13 CHANGE - 14 HD 15 CHANGE - 16 HD 17 CHANGE - 18 MD 19 CHANGE 20 MD 21 CHANGE 22 LD 23 CHANGE - 24 ZD 25 CHANGE Figure 2 for pre-initiators and Figure 3 for post-initiators show that the dependency evaluation code is identified (e.g. LD12) based on the parameters, which are connected with their representative human failure events. Dependency evaluation code consists of first two characters identifying the level of dependency (e.g. ZD, LD, MD, HD, CD). The next numbers in the code represents the scenario number of the corresponding scenario from dependency method presented in its respective figure and identify parameters that are important for determining the level of dependency: e.g. cue, time between, crew, stress, complexity, location, system, action description, procedure, timing, person, action similarity [1, 4]. E.g. for 2 dependent post-initiators, a dependency level LD is determined on Figure 3 (LD12), which shows: different cue, 5-30 min between the events, low stress, simple action and no change of probability needed as joined HEP>1E-5. Additionally, an algorithm based on geometry average is used for pre-initiators for calculation of HEP [1, 4], which determines the same HEP for similar actions on both trains and prevents that associated HEP of HFE on one train and HEP of HFE on another train would differ significantly, if both HFE represent similar actions. 2.2. SPAR-H Standardized Plant Analysis Risk HRA (SPAR-H) is a method for estimating the human error probabilities (HEP) associated with operator actions and decisions in nuclear power plants [5]. Table 1 shows how dependency between HFE is determined within SPAR-H. Five levels of dependency are determined, similarly to THERP and IJS-HRA. The parameters for determining the level of dependency differ from THERP and from IJS-HRA. Table 1: SPAR-H Dependency [5] Condition Number Crew (same or different) Time (close in time or not close in time) Location (same or different) Cues (additional or no additional) Dependency 1 S C S NA COMPLETE When considering 2 A COMPLETE recovery in a series: 3 D NA HIGH e.g., 2nd, 3rd, or 4th 4 A HIGH checker: 5 NC S NA HIGH if this error is the 3rd error in the sequence, then the dependency is at least moderate; if this error is the 4th error in the sequence, then the dependency is at least high. 6 A MODERATE 7 D NA MODERATE 8 A LOW 9 D C S NA MODERATE 10 A MODERATE 11 D NA MODERATE 12 A MODERATE 13 NC S NA LOW 14 A LOW 15 D NA LOW 16 A LOW 17 ZERO SPAR-H dependency table is applicable to both: pre-initiators and post-initiators. 3. ANALYSIS AND RESULTS 3.1. Qualitative Comparison Table 2 shows a theoretical comparison of both dependency methods in sense to compare the dependency determined by IJS-HRA method and by SPAR-H method. Table 3 is the subset of Table 2. Table 3 focuses only to those scenarios (specific scenario suit specific set of parameters), which suit real HFE considered in the specific HRA (practical comparison of both dependency methods based on specific PSA model). Both tables show, that for specific HFE, their respective HEP may be evaluated as a different value, if it is determined with one or the other method. More dependencies in columns at SPAR-H means that among all HFE, for which a certain dependency level was determined by IJS-HRA, application of SPAR-H required certain dependency level for some HFE and certain dependency level for some other HFE. Table 2: Comparison o Pre-Initiators Post-Initiators IJS-HRA SPAR-H IJS-HRA SPAR-H CD1 CD1, HD3 CD1 CD1, HD3, HD5, MD7, MD9, MD11, LD13, LD15 HD2 CD2, HD4 HD2 CD2, HD4, MD10, MD12 MD4 HD5, MD7 HD4 CD2, HD4, MD6, LD8, MD10, MD12, LD14, LD16 LD6 MD6, LD8 HD6 CD2, HD4, MD6, LD8, MD10, MD12, LD14, LD16 HD8 CD1, HD3 MD8 CD2, HD4, MD6, LD8, MD10, MD12, LD14, LD16 MD10 CD2, HD4 MD10 CD2, HD4, MD6, LD8, MD10, MD12, LD14, LD16 LD12 HD5, MD7 LD12 CD2, HD4, MD6, LD8, MD10, MD12, LD14, LD16 ZD14 MD6, LD8 HD14 MD6, LD8 CD16 CD1, CD2, HD3, HD4 HD16 MD6, LD8 HD17 HD5, MD7 MD18 MD6, LD8 MD19 MD6, LD8 MD20 MD6, LD8 LD21 CD1, CD2, HD3, HD4 LD22 MD6, LD8 ZD23 HD5, MD6, MD7, LD8 ZD24 LD14, LD16 ZD25 MD9, MD10, MD11, MD12, LD13, LD14, LD15, LD16 ZD27 CD1, CD2, HD3, HD4, HD5, MD6, MD7, LD8, MD9, MD10, MD11, MD12, LD13, LD14, LD15, LD16 dependency levels - theory CD 3 £ & -a to ^ o S o •S3 SC o S co K TO i_( cd CD £ ^ Table 3: Comparison of dependency levels - practice for dependencies of the specific PSA model Pre-Initiators Post-Initiators IJS-HRA SPAR-H IJS-HRA SPAR-H LD12+calculation [1,4] HD5 CD1 CD1 HD17+calculation [1,4] HD5 HD2 CD2, MD12 Example row-> MD8 HD4, LD8 MD18 LD8 MD20 LD8 LD12 LD8 MD-3th-in-sequence LD22 MD6, LD8 MD-3th-in-sequence, HD-4th-in-sequence ZD24 LD14, LD16 MD-3th-in-sequence, HD-4th-in-sequence In the example row in Table 3: among 13 post-initiators, for which the dependency level LD22 was determined by IJS-HRA, for 6 of them low dependency LD8 is determined by SPAR-H, for one of them moderate dependency MD6 is determined and for others moderate dependency MD (for 3 of them: MD-3th-in-sequence) and high dependency HD (for 3 of them: HD-4th-in-sequence) is determined due to SPAR-H rule (see the right column of table 1: for more events in a sequence, it is possible that the dependency level is required to be increased from the initially determined one). 3.2. Quantitative Comparison PSA model, which was used for the evaluation purposes, includes 64 HFE, which HEP are changed if HRA dependency method changes. Table 4 shows a selected part of those HFE with identified dependency levels and calculated the respective HEP for both methods IJS-HRA and SPAR-H. The terms CALC and IND marked at pre-initiators represent the calculation of final HEP as the geometry average between the independent value of HEP for action at one train and the respective dependent HEP assessed as low dependency (LD12) for similar action at the other train. Table 4: Selected HFE with quanti fied HEP (for IJS-HRA and for SPAR-H) BASIC EVENT ID DEPENDENCY LEVEL IJS-HRA FINAL HEP IJS-HRA DEPENDENCY LEVEL SPAR-H FINAL HEP SPAR-H PRE INI 01 CALC, IND, LD12 1,91E-03 HD5 5,00E-01 PRE_INI_02 CALC, IND, LD12 1,91E-03 HD5 5,00E-01 POST INI 34 ZD24 4,52E-03 LD16 5,43E-02 POST INI 42 MD8 1,71E-01 LD8 8,08E-02 POST INI 53 ZD24 1,58E-02 LD14 6,50E-02 POST INI 63 LD22 5,07E-02 HD-4th-in-seq 5,00E-01 POST_INI_66 HD2 5,16E-01 MD12 1,70E-01 POST INI 69 ZD24 1,04E-03 LD14 5,10E-02 POST_INI_79 ZD24 1,96E-04 MD-3th-in-seq 1,43E-01 Table 5 shows the results of importance factors, i.e. Risk Increase Factor (RIF) and Risk Decrease Factor (RDF) of selected HFE, which are calculated based on analysis runs with PSA model evaluated based on IJS-HRA dependency and same PSA model evaluated based on SPAR-H dependency considered. Selected HFE in the table are those with RDF>1,05 and RIF>2, according to criteria for identification of risk significant events. The differences between identification of importance factors in PSA model evaluated using IJS-HRA and in PSA model evaluated using SPAR-H are significant. Table 5 shows that identification of important HFE shows only one HFE, which is identified as important in both analyses (POST_INI_04, which deals with operator establishing Auxiliary Feedwater Pumps). Table 5: Results PSA MODEL BASED ON HEP OF HFE DETERMINED BY IJS-HRA HFE RDF HFE RIF POST_INI_42 1,13E+00 POST_INI_04 2,26E+02 POST_INI_63 1,09E+00 POST_IM_12 7,46E+01 POST_INI_88 1,09E+00 POST_INI_100 4,49E+01 POST_INI_95 3,66E+01 INI_01 2,34E+01 INI_02 2,34E+01 POST_INI_102 2,23E+01 POST_INI_02 1,75E+01 POST_INI_34 6,73E+00 POST_INI_35 3,19E+00 POST_INI_69 2,68E+00 POST_INI_63 2,62E+00 POST_INI_60 2,01E+00 of HFE PSA MODEL BASED ON HEP OF HFE DETERMINED BY SPAR-H HFE RDF HFE RIF PRE_INI_06 1,01E+01 POST_INI_53 5,76E+00 PRE_INI_05 8,18E+00 POST_INI_04 5,63E+00 POST_INI_102 2,07E+00 POST_INI_53 1,55E+00 PRE_INI_09 1,51E+00 PRE_INI_10 1,51E+00 PRE_INI_04 1,40E+00 PRE_INI_01 1,40E+00 PRE_INI_02 1,38E+00 PRE_INI_03 1,38E+00 POST_INI_79 1,06E+00 Figure 4: Comparison of Fractional Contribution of HFE 1,00E+00 1,00E-01 c o | 1,00E-02 c o * 1,00E-03 c O fc 1,00E-04 1,00E-05 • IJS-HRA FC ■ SPAR-H FC ■ ■ ■ ■■ ■■ ■■ ♦ ♦ ........ ■ ■ ■ ■ * «». ■ ■ ■ ■ ■■ ■ ■■ ■ ■ ■ ■ ■ ■ - ■ ■ _ _ ♦♦♦ ■■ ■ ■ ■ ■ ■ ■ ■ ♦♦♦♦♦♦ ■ Figure 5: Comparison of Risk Increase Factor of HFE ► IJS-HRA RIF ■ SPAR-H RIF ♦♦•It >ttiti< \/ /\/ A/ - y A/ A/ A/ A/ A/ A/ A/ - y A/ 1,05, RTF,>2, there are two human failure events with RDF,> 1.05 and 12 human failure events with RTF, >2. No event exists, which would not be identified by RTF or RDF lists and would appear at fractional contribution of more than 1% to the overall result, so fractional contribution does not reveal any additional human failure events. Events HFE_048 (i.e. operator is aligning high pressure recirculation) and HFE_028 (example event described in Section 4) are candidates for HEP reduction, as the HEP reduction would decrease risk. For both events an independent verification or other means may be added to the procedure, which may result in justification of lower human error probability of recovery. For the event HFE_048 many subtasks are modelled, each is considered little conservatively as omission of steps represents a generic HEP from human reliability database. And, no favourable performance shaping factors are considered for omissions, although the procedure steps exists and are well written, operators are well trained and experienced and low stress is assessed. The modelling should be reviewed in details and the links of tasks to appropriate human error probabilities should be checked. Fig. 4. Importance factors for individual human failure events (example PSA model). 12 human failure events (including example event) with RIF,>2 are candidates for simulator training (Fig. 4), because their occurrence may significantly increase the risk. 5.2. Results of example event Results show that risk contribution of the example event (manual actuation of auxiliary feedwater in case of transients: HFE_028) to the plant risk is significant (Fig. 4). The event is contributing to the core damage frequency for approximately 10%, which ranks it to the 2nd place among the most important risk contributors. The event is the most important among the events ranked by RIF and has a high RIF, which means the simulator training on this event should be performed. The event is 2nd among the events ranked by RDF, but has a low RDF, so improvement of procedures is possible but it may not significantly reduce the risk connected with the event. M. (Cepin / Journal of Loss Prevention in the Process Industries 21 (2008) 268-276 275 5.3. Results connected with importance of parameters Fig. 5 shows importance factors for parameters from human reliability database (part of database is in Table 1). Each parameter contributes to one or more human failure events depending on the nature of the parameter. It can be more universal, which means that it contributes to several (or even more tenths) human failure events. Or, it can be more specific, which means that it may contribute to few or to only one human failure event. According to the importance criteria for the risk important components: RDF,>1.05, RIF,>2, there are three parameters with RDF,->1.05 and 8 parameters with RIF,>2. Those three parameters with RDF, >1.05 (PAR_58, PAR_15, PAR_14) contribute to many human failure events: PAR_58 contributes to 50 HFE, PAR_15 contributes to 73 HFE and PAR_14 contributes to 40 HFE. Those identified parameters are candidates for human reliability database improvement. Namely, from history of simulator training it is needed to specify more specific human tasks for the human reliability database and increase their number from only 17 to more. At the same Fig. 5. Importance factors for HRA parameters (example PSA model). time the human error probabilities of those added tasks should be estimated and the human reliability database is updated with plant specific information. 5.4. Implications of the results The analysis of importance of parameters from human reliability database showed that only 13 parameters from human reliability database, which consists of 66 generic parameters, are actually modeled in the HRA. Eight of those 13 parameters are identified as important parameters. As each of those parameters relates to a relatively large number of human failure events, which may differ significantly one from another by the nature of the tasks, it is recommended to make new specific parameters, which will replace the generic ones. A larger number of more specific parameters in the human reliability database will allow evaluation of the human failure events and their respective tasks in more detailed manner using more convenient and specific human error probabilities obtained from the experience of simulator training. The replacement of human failure events, which are modeled in PSA with their respective human error probability (one HFE is represented with one basic event with its respective human error probability), with human error fault trees, which contain several basic events with their respective parameters from human reliability database, causes the difference in results due to truncation (Cepin, 2005b). Truncation is a term, which means that contribution of contributors to risk is neglected, if the contribution to risk is lower than the specified limit (i.e. truncation limit). This replacement means that more events with lower probabilities are consisting the model. At the same truncation limit, larger portion of the risk results may be cut off. This may cause more difficulties for direct comparison of the effects of replacement. A selection of lower truncation limit reduces the difference. 6. Conclusions The IJS-HRA is a method for evaluation of human failure events in sense to determine the reliability of the respective human actions. This method: • integrates features of several methods known from the field of HRA, • includes some specific features: O inclusion of parameters from plant specific full scope simulator: timing of human actions under investigation in the real scenarios, O experience of simulator training for adjustment of generic human error probabilities in the first phase (this is done) and parameters from simulator training for determining plant specific human error probabilities in the second phase (this is planned) and • includes the newest recommendations and good practice in the field. 276 M. (Cepin / Journal of Loss Prevention in the Process Industries 21 (2008) 268-276 The method is applicable for HRA of complex facilities including nuclear power plants. The method can be used as an on-line tool for sensitivity analysis within PSA with a wide number of options for evaluation of the model and its physical and conceptual parts. These evaluations from different points of view gives new knowledge about the observed plant, which may be used for the improvement of HRA and thus plant safety. The results of importance analysis show that only few human failure events dominate in the HRA. The results show that only few parameters from human reliability database contribute significantly to the risk. Identification of dominating human failure events and identification of the significant parameters are a valuable input for determining the priorities of simulator training. Future work includes the more detailed analysis of simulator experience, which will result in more detailed and plant specific human reliability database. Acknowledgements The Slovenian Research Agency supported this research (partly research program P2-0026, partly research projects J2-6556 and V2-0376 supported together with Slovenian Nuclear Safety Administration). References ASME RA-S-2002. (2002). Standard for probabilistic risk assessment for nuclear power plant applications. The American Society ofMechanical Engineers. Cepin, M. (2002). Optimization of safety equipment outages improves safety. Reliability Engineering and System Safety, 77, 71-80. Cepin, M. (2005a). Human reliability analysis—Methods and applications, problems and solutions. Internal Report, IJS. Cepin, M. (2005b). Analysis of truncation limit in probabilistic safety assessment. Reliability Engineering and System Safety, 87(3), 395-403. Cepin, M. & He, X. (2006). Development of a method for consideration of dependence between human failure events. ESREL2006. Cepin, M., & Mavko, B. (1997). 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Some insights from recent applications of HRA methods in PSA effort and plant operation feedback in Czech Republic. Reliability Engineering & System Safety, 83(2), 169-177. Kennedy, G. A. L., Siemieniuch, C. E., Sinclair, M. A., Kirwan, B. A., & Gibson, W. H. (2007). Proposal for a sustainable framework process for the generation, validation, and application of human reliability assessment within the engineering design lifecycle. Reliability Engineering & System Safety, 92(6), 755-770. Khan, F., Amyotte, P. R., & DiMattia, D. G. (2006). HEPI: A new tool for human error probability calculation for offshore operation. Safety Science, 44(4), 313-334. Mosleh, A., & Chang, Y. H. (2004). Model-based human reliability analysis: Prospects and requirements. Reliability Engineering & System Safety, 83, 241-253. NUREG-1624. (1999). Technical basis and implementation guidelines for a technique for human event analysis (ATHEANA). US NRC. NUREG-1792. (2005). 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Volkanovski Consideration of ageing within probabilistic safety assessment models and results Ageing is a process, where the properties of systems and processes may degrade through the time and age. The objective of the paper is to analyze the possibilities of introduction of ageing directly into the probabilistic safety assessment. Theoretical models of ageing and examples of their application are investigated, which show, how the current models can be upgraded in sense to directly include the effects of ageing into the models of probabilistic safety assessment. This paper shows that consideration of ageing is theoretically a straightforward issue, which can be dealt with in several ways, which are demonstrated in the paper. The most important problem is the lack of data about the effects of ageing, which would suit to the detailed models of ageing. The results, which are obtained, do not show significantly different results compared to the initial models without direct consideration of ageing. The majority of risk measures change slightly or notably, but no major break through has been found. Contribution of ageing may be smaller then contribution of changes due to other parameters. Berücksichtigung der Alterung in Modellen und Ergebnissen der probabilistischen Sicherheitsanalyse. Alterung ist ein Prozess, bei dem die Eigenschaften der Systeme und Prozesse sich im Laufe der Zeit verschlechtern. Ziel dieses Papiers ist die Analyse der Möglichkeiten, Alterung direkt in probabilistischen Sicherheitsanalysen (PSA) zu berücksichtigen. Theoretische Alterungsmodelle und Beispiele ihrer Anwendung werden dahingehend untersucht, wie die gegenwärtigen Modelle erweitert werden können, um direkt die Alterungseffekte in die PSA-Modelle einzufügen. Das Papier zeigt, dass die Betrachtung der Alterung auf verschiedene Weise behandelt werden kann, wie hier näher ausgeführt wird. Das größte Problem ist aber die ungenügende Datenbasis über Alterungseffekte, die sich für eine detaillierte Modellierung der Alterung eignet Die erzielten Ergebnisse zeigen keine signifikant unterschiedlichen Ergebnisse im Vergleich mit dem ursprünglichen Modell ohne direkte Betrachtung der Alterung. Die Mehrzahl der Risikomaße ändern sich wenig oder auch deutlich, aber ein großer Durchbruch wurde nicht gefunden. Eventuell sind die Beiträge aufgrund der Alterung kleiner als die Beiträge aufgrund von Änderungen anderer Parameter. 1 Introduction Ageing is a process, where the properties of systems and processes may degrade through the time and age. A large number of ongoing activities connected with evaluation of ageing can be generally divided to those, which study the properties of materials and their degradation [1, 2], to those, which in- vestigate the mathematical models of ageing [3-5], to those, which assess the degradation and ageing effects of actual equipment [6-9] and to those, which include a part or most of these. 1.1 State-of-the-art Several studies include the effects of the ageing of the specific nuclear power plant (NPP) components, systems and structures [10-14] including the reactor pressure vessel and primary coolant system [15,16]. The application of the two parametric Weibull distribution and Bayesian models for ageing modelling was proposed [17, 18] including the statistical approach for estimation of age of the degraded system [19]. The implication of maintenance, test strategies and working conditions on ageing of the components was analysed [20, 21] including the optimization of maintenance activities accounting the ageing of the components [22, 23]. The approaches for managing the effects of ageing in the NPP and inclusion of passive components ageing into probabilistic safety assessment (PSA) were proposed [24, 25]. Activities connected with probabilistic safety assessment of NPP include: collected and evaluated data for age-related degradation of US NPP [26], modelling ageing of passive systems, structures and components (SSC) by incorporating a flow accelerated corrosion model into PSA [27], a procedure for transformation of PSA to age-depended evaluation [28], a quantification of the ageing induced risk using PSA and component ageing models [29, 30], a derivation of the linear ageing model and extension to nonlinear and depended ageing phenomena [31], ageing-related failure analysis of the nuclear power plant operational data [32, 33] and the impact of the component ageing on the selected support systems reliability and NPP safety [34]. The application of the methods is more theoretical than practical due to lack of real data for the support of the parameters in mathematical formulations. 1.2 Objectives Probabilistic safety assessment is a standardized tool for assessment of safety of nuclear power plants [35-38]. The guidelines are developed and the risk criteria are established [39-41]. Existence of guidelines and criteria enable that the results of probabilistic safety assessment are more and more included in the risk-informed decision-making, which is proven with an increasing number of its applications [42-44]. The issues connected with degradation and ageing are currently included in the models through the constant failure rate approach. The first objective of the paper is to investigate, if the ageing effects can be considered in probabilistic safety assessment in more details, as it is currently done. The second ob- KERIMTECHMK 74 (2009) 3 © Carl Hanser Verlag, München 1 KT_kt-110021 - 9.3.09/stm media kothen M. Cepin and A. Volkanovski: Consideration of ageing within probabilistic safety assessment models and results jective is to examine the options for direct and separate inclusion of ageing in probabilistic safety assessment to compare the effectiveness of the models and the applicability of the results. The work is focused to existing nuclear power plants with light water reactors. 2 Methods Many mathematical methods for consideration of ageing exist. Usually, they include mathematical formulations of parameters, for which it is very difficult to get appropriate data, which could make the methods widely applicable for practical purposes. Selected methods for consideration of ageing are presented in the following sections, which seem the most suitable for their use for upgrading the existing probabilistic safety assessment models. 2.1 Basic methods for modelling of ageing The linear method, the exponential method and the Weibull method are presented [28]. 2.1.1 Linear method This method represents the failure rate of equipment with a function, where the failure rate is changed with age of equipment from constant failure rate before the threshold age to linear increasing failure rate after the threshold age [28]. Threshold can be incorporated in the mathematical formulation to represent the beginning of ageing at some nonzero age. The basic mathematical formulation of the method is presented in the equation below. X (w) = X V w wo (1) Xo ... initial constant failure rate a ... linear ageing rate w0 ... threshold age after which the failure rate increases 2.1.2 Exponential method This method represents the failure rate of equipment with a function, where the failure rate is changed with age of equipment from constant failure rate before the threshold age to exponentially increasing failure rate after the threshold age [28]. The basic mathematical formulation of the method is presented in the equation below. X ( w ) = X o X ( w ) = X o V w w o ( 2) Xo ... initial constant failure rate c ... exponential scale parameter w0 ... threshold age after which the failure rate increases 2.1.3 Weibull method This method represents the failure rate of equipment with a function, where the failure rate is changed with age of equipment from constant failure rate before the threshold age to the Weibull increasing failure rate after the threshold age [28]. The basic mathematical formulation of the method is presented in the equation below. X (w) = X o V w w o ( 3) No direct ageing considered Basic Event BEI (no direct ageing consideration,ageing is considered within constant failure rate) f lexers 7T 7T Pbei ~ f( para meters known from probabilistic safety assessment -PSA} Pi = Pno_aping^i Basic Event BEI (ageing consideration) -u— Pbei ^parameters known from PSA; parameters from selected ageing method) Pi = Pno_3ginflJ + Pnninn J Fig. 1. Schematic modelling for consideration of ageing Xo ... initial constant failure rate b ... Weibull shape parameter w0 ... threshold age after which the failure rate increases 2.2 Basic methods for consideration of ageing in probabilistic safety assessment Two main options exist when the basic methods for consideration of ageing in probabilistic safety assessment are considered. The first option, which is known as stepwise constant failure rates, includes modification of probabilistic safety assessment models in sense that the ageing contribution is added to the initial models, which consequently causes also the modified results, when evaluation is performed [28]. The failure rates are determined as constant in determined time intervals, but as the time intervals go on, the failure rates increase, if the ageing contribution to the failure rates increase [33]. The second option includes modification of the resulted minimal cut sets in sense that the ageing contribution is added to the resulted minimal cut sets [28, 29]. 2.2.1 Method of stepwise constant failure rates The standpoint for the development of this method lays in a fact that a detailed probabilistic safety assessment of a nuclear power plant exist, which does not directly include consideration of ageing in its probabilistic models. In this sense, it seemed that the extension of the existing probabilistic safety assessment models with addition of ageing as an independent contribution would be the easiest solution. The deficiency of such approach would be the fact that contribution of ageing may not be independent from existing contribution. Fig. 1 shows the difference in modelling, if ageing is considered as independent contribution or not. Stepwise constant failure rate method assumes the constant failure rates or constant failure probabilities of equipment in the determined time intervals Ageing considered 1 Kerntechmk 74 (2009) 3 KT_kt-110021 - 9.3.09/stm media kothen M. Cepin and A. Volkanovski: Consideration of ageing within probabilistic safety assessment models and results {tt, i,+1}, and hence this failure rates or failure probabilities are determined as their average through the time of the time interval. The failure rates or failure probabilities change through the selected time intervals according to the selected method for evaluation of failure rates or failure probabilities due to ageing. At each selected time interval the average failure rates or failure probabilities are calculated for the equipment under investigation and the evaluation of the probabilistic safety assessment is performed. An advantage of this method is that it can be used in standard probabilistic safety assessment by standard tools for performing probabilistic safety assessment. Figure 2 shows the basic principle of method. Update of probabilistic safety assessment model for consideration of ageing is done in two directions: • addition of components to the models and • changes made to existing models, changes of the probabilistic data. The focus of the activities can be placed to the most important components or to all components, alternatively. The risk criteria for determining the most important equipment can follow the suggested guidelines [40]. The risk criteria for selection of equipment, for which a consideration about the neighbouring passive components is performed, are presented in Table 1. In the current probabilistic safety assessment it is possible that: • the failures of certain structures or passive components or other equipment are not considered, because their failure probability is negligibly low, or • the failures of certain passive components are indirectly considered within the existing models and data connected with the corresponding active components. w[yr] Fig. 2. Method of stepwise constant failure rates Table 1. Risk criteria for determining important equipment In other words, probabilistic safety assessment models generally does not directly include passive components, which may be susceptible to the ageing issues more than active and tested components. Therefore the models may be updated with inclusion of the passive components. The method for selection of passive components may consider the importance results of existing probabilistic safety assessment. The equipment with higher risk importance factors may be investigated in sense if the consideration of additional passive components improves the model. Frequencies of initiating events such as large, medium or small loss of coolant accident, steam generator turbine rupture and steam line break depends on the history of experience with the pipes. The frequencies of failures of newer pipelines may be lower than the frequencies of older ones. Method of stepwise constant initiating event frequency can be used considering linear increase of initiating event frequency. 2.2.2 Method of prioritization of ageing from results of probabilistic safety assessment The method of assessment of ageing from results of probabilistic safety assessment is presented in reference [28], while the data are analysed also in reference [33]. The mathematical formulation bases on the database about components ageing rates: TIRGALEX database [33], which is presented in Table 2. The mathematical formulation of the method is the following. The change of the failure rate Ak; of component i due to the ageing is given with expression: Ak = %i- Xi0 (4) X,o ... failure rate of equipment i (no ageing considered) Xi... failure rate of equipment i with ageing considered Ak ... the increase of failure rate of equipment i due to ageing Risk importance measures Criteria RAW - Risk Achievement Worth > 2 RRW - Risk Reduction Worth system level component level >1.05 > 1.005 FV-Fussell - Vesely Importance system level component level >0.05 >0.005 Table 2. TIRGALEX data base for ageing rates of equipment [per hour per year] Component Ageing rate AC bus 1.0E-09/h/y Air operated valve 4.0E-07/h/y Battery 3.0E-07/h/y Check valve 4.0E-09/h/y Circuit breaker 2.0E-08/h/y DC bus 1.0E-09/h/y Diesel generator 3.6E-06/h/y Motor driven pump 2.0E-07/h/y Motor operated valve 3.6E-06/h/y Relay 3.0E-07/h/y Safety/relief valve 7.0E-07/h/y Transformer 2.0E-09/h/y Turbine driven pump 3.0E-06/h/y Solenoid operated valve 6.7E-07/h/y 10 Kerntechnik 74 (2009) 3 KT_kt-110021 - 9.3.09/stm media kothen M. Cepin and A. Volkanovski: Consideration of ageing within probabilistic safety assessment models and results The change of the component unavailability Ag, with consideration of the ageing is given as: Aqi = qi- qio ( 5) A qt = - a i ( L i - T! ) Ti + - a ! Tf ( 6) L '=r A. 10 ( 7) a Taylor expansion approach was utilized to express A CDF as a function of the Ag,: qio ... unavailability of equipment i (no ageing considered) qt... unavailability of equipment i with ageing considered A qi... the increase of unavailability of equipment i due to ageing For a linear ageing failure rate, the average unavailability increase [29] due to the ageing for tested equipment is : A CDF = siA H + S jA qi A qi + S S jkA qi A qiA qk + ■ i i>J i >j> k + s 12 ■■„ Agi Aq2 ■■■Aqn ( 9) a, ... ageing rate of equipment i Ti... test interval of equipment i T,... replacement (overhaul) interval of equipment i The overhaul or replacement interval L is the interval at which the component is replaced with a new one and the age of the component is restored effectively to a value of zero. The surveillance interval T is interval at which the component surveillance is performed, in order to assure operational status with minimal repair being performed. The component is basically in the same condition after the test as before the test. The replacement interval of equipment i(L,) is obtained [29] as: A CDF... change in core damage frequency Si ... standard Taylor expansion coefficients, importance of equipment i A qi... change of the component/system unavailability The Taylor expansion coefficients are obtained as multi order derivates of the CDF and are termed as a core damage frequency sensitivity coefficients or core damage frequency importance coefficients. If only the first order Taylor coefficients are accounted, the upper equation can be simplified as : A CDF = Y, S i A qi ( 10) The importance coefficients 5, of equipment i is obtained from the Fussel-Vesely importance measure for specific component. FVt = CDF - CDF ( qi = 0) CDF S FVi* CDF CDF - CDF (qt = 0) ( 11) ( 12) If there is no surveillance tests expected on the component between replacements, then T is set equal to L. In the case when the mean time to failure of the component is larger than the facility lifetime and there is no surveillance test expected the formula for the unavailability increase [29] with is : A qi = ^ Oi % (8) t0 ... facility lifetime To calculate the core damage frequency change A CDF as a function of the component and structure ageing changes Ag„ CDF... core damage frequency CDF (qi = 0) ... core damage frequency when unavailability of equipment i is set to zero FVi... Fussel-Vesely importance measures for equipment i qi... unavailability of equipment i It is important to know that the relative error for such expression can be very large, if the values CDF and CDF (qt = 0) are close to each other [37]. 3 Analysis and results of selected examples Table 3. Data for parameters of containment spray system considering ageing contribution Identification b w0 BE-PAR-01 1 5y BE-PAR-02 (CCF) 1,3 7y BE-PAR-03 3 4y BE-PAR-04 1 6y BE-PAR-05 4 5y BE-PAR-06 1,3 7y BE-PAR-07 (T&M) 1 2y BE-PAR-08 0,7 4y BE-PAR-09 4 5y BE-PAR-10 0,2 5y BE-PAR-11 17 10y wo ... threshold age b ... Weibull shape parameter 3.1 Ageing consideration for existing containment spray system The containment spray system is selected as an example. Table 3 shows data for 11 parameters of the containment spray system considering ageing contribution. Parameters of ageing connected with of common cause failures are the same as the parameters of ageing connected with the respective basic events modelling respective primary failures. Figure 3 shows calculated basic event unavailabilities due to ageing, which Ë a,00E-03---------- £ EL 3.C0E-03 --n • 2,006-03-.!? 1.OTE-03-- s 0,00E+00 -#—BE-PAR-01 «-ËE-PAR-02 (OOF) BE-PAR-03 ■ BE-PAR-04 BE-PAR-05 *—BE-PAR-06 -1—BE-PAR-07 (TSMJ -EE-PAR-OS -BE-PAR-09 BE-PAR-10 BE-PAR-11 9 10 11 12 13 14 15 w (years) Fig. 3. Basic event unavailability due to ageing kermechmk 74 (2009) 3 KT_kt-110021 - 9.3.09/stm media kothen M. Cepin and A. Volkanovski: Consideration of ageing within probabilistic safety assessment models and results Fig. 4. System unavailability due to ageing v. (years) Fig. 5. Fussel-Vesely Importance due to ageing Fig. 6. Risk Decrease Factor due to ageing ' (years) Fig. 7. Risk Increase Factor due to ageing depend on timely independent unavailability and ageing parameters, such as Weibull parameter b and threshold age. Unavailability of basic events connected to test and maintenance is constant through the age. Figure 4 shows the system unavailability due to ageing, which is obtained through the fault tree evaluations specified for time intervals of 1 year. Results show the increase of system unavailability of one order of magnitude for the considered period of 15 years. Figure 5 shows Fussel-Vesely importance measure for the selected basic events of the fault tree representing selected components of the system. Results show that some equipment can be non-important, if no ageing is considered, and very important if ageing is considered and vice versa. Figure 6 shows the risk decrease factor due to ageing. Figure 7 shows the risk increase factor due to ageing. Results show that risk factors may considerably vary depending on ageing. 3.2 Ageing consideration for passive components in containment spray system The fault tree of containment spray system has been changed. Basic events representing the piping failures were added to their respective places with small piping failure probability assessed based on piping length, number of elbows and number of welds (QpipingO ~ Qpiping0_pipeienght + Qpiping0_no_elbow + Qpipingo_no_weids = 1E-6). Factor of ageing is assessed as linear function A:piping(w) = Ka*w and Ka = 8,76e-6/year is assumed and 15 years of operating time is considered. The results show that system unavailability slightly changed from 5,059E-4 to 5,092E-4, which can be assumed as neglected. The risk measures connected with piping give no indication of piping importance, except of the risk increase factor (RIFpiping = 26), when ageing is 15 years. Experience shows that the most important issue for consideration of piping is that the models of piping are performed on train bases or on appropriate segments basis. If all piping of one system is simplified and considered as one component, the model is not suitable and as such not needed. 3.3 Ageing consideration in complete probabilistic safety assessment Complete probabilistic safety assessment of a nuclear power plant is selected as another example. The probabilistic safety assessment model is a detailed model with thousandths of gates, thousandths of basic events, hundredths of fault trees and 16 event trees with 16 initiating events. 3.3.1 Adding passive components Systems and subsystems, which models are changed with added basic events about piping failure probability are the following: auxiliary feedwater system motor driven pump 1, pump 2, turbine driven pump, chemical volume and control system, component cooling system train A, train B, instrument air train A, train B, residual heat removal train A, train B, safety injection to cold leg 1, cold leg 2, safety injection pump 1, pump 2, containment spray injection pump 1, pump 2, service water system train A and train B. 10 Kerntechnik 74 (2009) 3 KT_kt-110021 - 9.3.09/stm media kothen M. Cepin and A. Volkanovski: Consideration of ageing within probabilistic safety assessment models and results 3, OSE-05 3.00E-05 2.95E-05 2.90E-05 2,35g-05 2,605-05 2.75E-05 2.70E-05 2.9SÊ-05 ' 2,8 JE-05 3.07E-04 ■ 2,6SE-05 2,19E-04 2,81 E-0S 1,316-D4 ' 8.76E-0S _ 5.00E-04 4.50E-04 4.00E-04 M 3.50E-04 I 3.00E-04 I 2.50E-04 J 2.00E-04 fi g 1.50E-04 J 1.00E-04 » 5.00E-05 « 0.00E+00 □ CDF —Qi no ageing 1S 25 35 (years) Fig. 8. Sensitivity of core damage frequency due to changes of the piping failure probabilities due to ageing Added basic events about piping failure probability do not change the core damage frequency and do not impact significantly other probabilistic safety assessment results (Qpiping_i_0 = 1E-6). If the ageing of piping is considered, the core damage frequency changes negligibly from 2,81E-5/ry to 2,88E-5/ry: Qpiping_i_0 = 1,31E-4 for the period between 10 and 20 years of plant operation; Apiping(w) = Ka*w is assumed; Ka = 8,76e-6/year; 15 years of ageing is assumed as the average for the period between 10 and 20 years of plant operation. The risk increase factor of the parameter piping becomes significant (RIFpiping = 1,74E+4). Significant RIFpiping means that the core damage frequency and thus risk may increase significantly with the increase of piping failure probability. Fig. 8 shows sensitivity of core damage frequency due to changes of the piping failure probabilities due to ageing. 3.3.2 Changing existing models - initiating events only Initiating events frequencies were changed for two groups of initiating events. The first group includes initiating events: large loss of coolant accident, medium loss of coolant accident, small loss of coolant accident, steam line break and steam generator tube rupture. The second group includes initiating events: interfacing system loss of coolant accident, loss of essential service water, loss of component cooling water and loss of instrument air. For the initiating events from the first group, the initiating events frequency is changed ac- cording to linear method of consideration of ageing. For the initiating events from the second group, only the assessed part of the initiating event frequency due to piping is changed according to linear method of consideration of ageing. For the initiating events from the second group, this means that the impact of ageing is negligible, because a small increase of small part of the initiating event frequency may be lower than the round up. The resulted core damage frequency increases with increasing initiating event frequencies depending on the percentage contribution of respective initiating events to the core damage frequency. Table 4 shows sensitivity of core damage frequency due to changes of the initiating events frequency due to ageing. Results show that the core damage frequency increases for less than 8 percents, because the contribution of selected basic events to the initial core damage frequency (without consideration of ageing) is approximately only 21 %. 3.3.3 Adding passive components and changing existing models Both separate considerations from previous sections are joined together and the results are obtained. Results on Figure 9 show that core damage frequency changes up to 14%. Results show that importance measures change more than |iz^JCOF [/ry] -»—increase of CDF | 3.20E-Û5.. 2.60E-05 13,38% y - 9,255/" ■ ■■ 4,98%/ / 3,07E-05 3.20E-05 >¿5E-05 B .. 2.81E-05 y 0,00'¡y 15,00% 14,00% 12,00% 10,00% 8,00% 6,00% 4,00% 2,00% 0.00% no ageing 15 /ears 25 years 35 years Fig. 9. Sensitivity of core damage frequency due to ageing Table 4. Sensitivity of core damage frequency due to changes of the initiating events frequency due to ageing f IE0 fiE(15y) fiE(25y) fm(35y) Large LOCA 5,00E-06/ry 5,50E-06/ry 6,05E-06/ry 6,66E-06/ry Medium LOCA 1,38E-03/ry 1,52E-03/ry 1,67E-03/ry 1,84E-03/ry Small LOCA 2,70E-03/ry 2,97E-03/ry 3,27E-03/ry 3,59E-03/ry SLB 1,30E-02/ry 1,43E-02/ry 1,57E-02/ry 1,73E-02/ry SGTR 1,82E-03/ry 2,00E-03/ry 2,20E-03/ry 2,42E-03/ry CDF 2,81E-05/ry 2,88E-05/ry 2,94E-05/ry 3,02E-05/ry IE frequency increases for K i. e. for 10 % per ten years. LOCA ... Loss of Coolant Accident; SLB... Steam Line Break SGTR ... Steam Generator Tube Rupture; CDF... Core Damage Frequency 10 Kerntechnik 74 (2009) 3 KT_kt-110021 - 9.3.09/stm media kothen M. Cepin and A. Volkanovski: Consideration of ageing within probabilistic safety assessment models and results 1,15E-01 -- 1.10E-01------ « 1.05E-01 0 fl- 1,OOE-O1 £ 1 9,50E-02 = 9.0QE-Q2 8.50E-02 8.00E-02 CD no ageing 10-20 years 20-30 years Fig. 10. Fussel-Vesely importance measure for selected basic events core damage frequency (Fussel-Vesely importance measure may change for more than 30 %). Figure 10 shows Fussel-Ve-sely importance measure for selected four important components. The contribution of ageing of tenths of percents of the core damage frequency is smaller than the experienced change of the core damage frequency due to modifications of probabilistic safety assessment model due to plant modifications and due to procedure changes. 3.4 Results of prioritization of ageing from results of probabilistic safety assessment Results of prioritization of ageing from results of probabilistic safety assessment are presented in Table 5 and Table 6. Results include change of core damage frequency due to ageing for different test intervals (T) and replacement intervals (L), given in months, for a selected probabilistic safety assessment model. Table 7 shows the summary of results from Table 5 4 Problems connected with inclusion of ageing in probabilistic safety assessment 30-40 years Experience shows that the contribution of ageing into the probabilistic safety assessment is a difficult issue at the current stage of developed models and availability of data. Some facts still prevent inclusion of ageing into the probabilistic safety assessment: • It is very difficult to distinguish between failures due to other reasons and failures due to ageing. • Ageing components are mostly made of many subcomponents and possibly the problems with subcomponents may cause failures of components. It is difficult to distinguish ageing of component parts and ageing of the components themselves. • Conservatism of models and analyses in probabilistic safety assessment may be much larger as the contribution of ageing itself. • Uncertainty of data is large in probabilistic safety assessment. The uncertainty of the results with inclusion of ageing may be larger. • Consideration of ageing may require significant efforts and largely more complex models, and the effects to the results may not justify the invested efforts. and Table 6, which show larger increase of CDF at larger test intervals and at larger replacement intervals. Table 5 and Table 6 contain only 10 components, which are the largest contributors to the change of core damage frequency due to ageing. The increases of core damage frequency are relatively large and it is questionable how those large increases of core damage frequency are comparable to changes due to other parameter changes. Table 5. Results of consideration of ageing Basic event q¡ FVi ai s T = 1m, L = 18 m A q¡ A CDF¡ BE01 (CCF DG) 2.81E-05 3.05E-03 4.11E-10/h2 1.09E-03/ry 9.41E-04 1.02E-06/ry BE02 (ECCS valve) 1.20E-05 7.81E-04 4.11E-10/h2 6.51E-04/ry 9.41E-04 6.12E-07/ry BE03 (ECCS valve) 2.40E-06 1.56E-04 4.11E-10/h2 6.50E-04/ry 9.41E-04 6.12E-07/ry BE04 (DC bus) 2.40E-05 8.83E-03 3.43E-11/h2 3.68E-03/ry 7.84E-05 2.88E-07/ry BE05 (ECCS valve) 2.40E-06 3.73E-05 4.11E-10/h2 1.55E-04/ry 9.41E-04 1.46E-07/ry BE06 (ECCS valve) 1.20E-05 1.86E-04 4.11E-10/h2 1.55E-04/ry 9.41E-04 1.46E-07/ry BE07 (ECCS valve) 2.40E-06 3.13E-05 4.11E-10/h2 1.30E-04/ry 9.41E-04 1.23E-07/ry BE08 (ECCS valve) 1.45E-03 1.89E-02 4.11E-10/h2 1.30E-04/ry 9.41E-04 1.23E-07/ry BE09 (ECCS valve) 2.96E-05 2.83E-04 4.11E-10/h2 9.56E-05/ry 9.41E-04 9.00E-08/ry BE10 (PCS valve) 1.45E-03 1.29E-02 4.11E-10/h2 8.90E-05/ry 9.41E-04 8.37E-08/ry 10 Kerntechnik 74 (2009) 3 KT_kt-110021 - 9.3.09/stm media kothen M. Cepin and A. Volkanovski: Consideration of ageing within probabilistic safety assessment models and results Table 6. Results of consideration of ageing (continued) Basic event T =18m, L = 18 m T = 1 m, L = 72 m T = 6 m, L = 72 m T = 72 m, L = 72 m A qt A CDFi A qt A CDFi A qt A CDFi A qt A CDFi BE01 1.15E-02 1.25E-05/ry 3.82E-03 4.14E-06/ry 1.28E-01 1.39E-04/ry 1.84E-01 2.00E-04/ry BE02 1.15E-02 7.49E-06/ry 3.82E-03 2.48E-06/ry 1.28E-01 8.32E-05/ry 1.84E-01 1.20E-04/ry BE03 1.15E-02 7.48E-06/ry 3.82E-03 2.48E-06/ry 1.28E-01 8.31E-05/ry 1.84E-01 1.20E-04/ry BE04 9.59E-04 3.53E-06/ry 3.18E-04 1.17E-06/ry 1.07E-02 3.92E-05/ry 1.53E-02 5.64E-05/ry BE05 1.15E-02 1.79E-06/ry 3.82E-03 5.93E-07/ry 1.28E-01 1.99E-05/ry 1.84E-01 2.86E-05/ry BE06 1.15E-02 1.78E-06/ry 3.82E-03 5.92E-07/ry 1.28E-01 1.98E-05/ry 1.84E-01 2.85E-05/ry BE07 1.15E-02 1.50E-06/ry 3.82E-03 4.98E-07/ry 1.28E-01 1.67E-05/ry 1.84E-01 2.40E-05/ry BE08 1.15E-02 1.50E-06/ry 3.82E-03 4.98E-07/ry 1.28E-01 1.67E-05/ry 1.84E-01 2.40E-05/ry BE09 1.15E-02 1.10E-06/ry 3.82E-03 3.65E-07/ry 1.28E-01 1.22E-05/ry 1.84E-01 1.76E-05/ry BE10 1.15E-02 1.02E-06/ry 3.82E-03 3.40E-07/ry 1.28E-01 1.14E-05/ry 1.84E-01 1.64E-05/ry Table 7. Summary of results due to consideration of ageing T PS_TTIL A CDF T = 1 m L = 18 m 4.58E-06/ry T = 18 m L = 18 m 5.60E-05/ry T = 1 m L = 72 m 1.86E-05/ry T = 6 m L = 72 m 6.22E-04/ry T = 72 m L = 72 m 8.96E-04/ry • One can always argue that the consideration of ageing has already been included in the existing models with assumed constant failure rates, because the constant failure rates are determined as the average values, where all failure history is taken into account, no matter if the failures are in the beginning or at the end of the component life time. • Consideration of ageing does not consider changes of human reliability, which is an important issue in probabilistic safety assessments contributing to the core damage frequency in the order of tenths of percents. Neglecting the changes of human reliability due to simulator experience and due to operators experience about the plant itself may be a larger portion than the contribution of ageing. Fig. 11 shows an example of history of core damage frequency for a selected probabilistic safety assessment model. Figure shows that the relative decrease of core damage frequency due to updates of the model according to the plant modifications and procedure changes is much larger then the relative increase of core damage frequency due to ageing. Those findings about consideration of ageing in probabilistic safety assessment: • may change when considering new nuclear power plant designs, when passive components and systems may be in a larger extent a contributor to safety. As new plants are expected to be safer, which means that lower failure probabilities will be reached, the failure probabilities of the passive components may not be negligible compared to other equipment; 1.0E-04 -I-1-1-1-1-1-1-1---i--- 1996 1989 2000 2000 2001 2002 2003 2004 2006 year of issue ofPSAmodel Fig. 11. The history of CDF for a selected PSA model due to changes (plant modifications and procedure changes ') • may not be completely applicable for other than current designs of current light water reactors. Namely, consideration of piping in CANDU (CANada Deuterium Uranium) reactors may be somehow more important than consideration of piping in LWR due to the design features of CANDU reactors, which may impact the results. 5 Conclusions The paper presents theoretical models of ageing and practical examples, which show, how the current models can be upgraded in sense to directly include the effects of ageing into the models of probabilistic safety assessment. The most important problem is the lack of data about the effects of ageing, which would suit to the well developed and detailed models of ageing. Evaluation of ageing within the probabilistic safety assessment is difficult mostly due to two the most important facts: • it is difficult to distinguish equipment random failures and equipment failures, which causes are connected with degradation due to ageing, • it is difficult to define the basic elements of the evaluation, which are the components themselves, as they are mostly made of several parts or subcomponents, which may de- 10 Kerntechnik 74 (2009) 3 KT_kt-110021 - 9.3.09/stm media kothen M. Cepin and A. Volkanovski: Consideration of ageing within probabilistic safety assessment models and results grade through time and age differently one from another and which can be partly exchanged or renewed or inspected. One may argue that ageing is already included in the existing models. It only isn't separated from other causes of components and systems faults. 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Cepin and A. Volkanovski: Consideration of ageing within probabilistic safety assessment models and results clear Power Plants According to their Safety Significance", Rev. 1, 2006 40 Electric Power Research Institute (EPRI): "PSA Applications Guide", TR-105396,1995 41 Cepin, M: "The Risk Criteria for Assessment of Temporary Changes in a Nuclear Power Plant", Risk Analysis, 2007, vol. 27, no. 4, p. 991-998 42 Cepin, M.; Mavko, R: "Probabilistic Safety Assessment Improves Surveillance Requirements in Technical Specifications", Reliability Engineering and Systems Safety, 1997, Vol. 56, p. 69-77 43 Cepin, M.: "Optimization of Safety Equipment Outages Improves Safety", Reliability Engineering and System Safety, 2002, Vol. 77, p.71-80 44 Cepin, M.; Martorell, S.: "Evaluation of Allowed Outage Time Considering a Set of Plant Configurations", Reliability Engineering and System Safety, 2002, Vol. 78, No. 3, p. 259-266 The authors of this contribution Assist. Prof. Dr. Marko Cepin, Reactor Engineering Division, "Jozef Stefan" Institute, Jamova 39, 1000, Ljubljana, Slovenia, E-Mail: marko.cepin@ijs.si; M. Sc. Andrija Volkanovski, Reactor Engineering Division, "Jozef Stefan" Institute, Jamova 39, 1000, Ljubljana, Slovenia, E-Mail: andrija.volkanovski@ijs.si; You will find the article and additional material by entering the document number KT110021 on our website at www.nuclear-engineering-journal.com 10 Kerntechnik 74 (2009) 3 ARTICLE IN PRESS Available online at www.sciencedirect.com ScienceDirect Journal of Loss Prevention in the Process Industries ■ (■■■■) Ill-Ill Journal of Loss Prevention in the process industries www.elsevier.com/locate/jlp Success criteria time windows of operator actions using RELAP5/MOD3.3 within human reliability analysis Andrej Prosek*, Marko Cepin Jozef Stefan Institute, Ljubljana, Slovenia Received 30 March 2007; received in revised form 21 June 2007; accepted 22 June 2007 Abstract Human reliability analysis (HRA) contributes to assessment and to reduction of the impact of human operators to the risk of technologies and processes. The objective of this paper is to integrate realistic deterministic safety analysis and probabilistic safety assessment to show how deterministic safety analysis impacts the HRA, which is integrated into the probabilistic safety assessment. The RELAP5/MOD3.3 computer code is used for realistic safety analysis. Parametric safety analysis studies give time parameters for human actions as an input for selected HRA. Calculated human error probabilities are inserted into probabilistic safety assessment and the results are obtained, where the focus goes to the most important risk contributors. The method and the results are shown on selected HRA method through two selected representative human actions. Results show that realistic safety analysis represents an important standpoint for assessment of human error probabilities within HRA. © 2007 Elsevier Ltd. All rights reserved. Keywords: Human reliability analysis; Success criteria; Probabilistic safety assessment; Deterministic safety analysis 1. Introduction Nuclear safety is assessed and improved through the probabilistic safety assessment, which integrates (ASME RA-S-2002, 2002): • Probabilistic models of components (Jordan Cizelj, Mavko, & Kljenak, 2001), logic models of safety systems and reliability analysis of operator actions, • Scenarios and sequences of safety system actuations and operator actions (Cepin, 2005b), and • Accident physical models (Leskovar & Mavko, 2006). The experience with the results shows that human contribution to undesired events is still significant in spite of the automation of systems and processes. The importance of human contribution causes that the many methods are developed and many activities are performed in the field of human reliability analysis (HRA). This is not true Corresponding author. Tel.: +386 1 5885450; fax: +386 1 5885377. E-mail addresses: andrej.prosek@ijs.si (A. Prosek), marko.cepin@ijs.si (M. Cepin). 0950-4230/$-see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jlp.2007.06.010 only in the nuclear industry (Cepin, 2005a, 2007; Grobbe-laar, Julius, & Rahn, 2005; Kennedy, Siemieniuch, Sinclair, Kirwan, & Gibson, 2007; NUREG/CR-1278, 1983; NUR-EG/CR-6883, 2005; Reer, Dang, & Hirschberg, 2004), but also in other fields such as in the chemical industry (Khan, Amyotte, & DiMattia, 2006) and in the air and space industry (Harris et al., 2005) for example. The objective of this paper is to show how the probability of operator to perform an error depends on parameters obtained from safety analysis and what this means for the safety of the nuclear power plant. Namely, the parameters of safety analysis direct the amount of time in which operator has to perform its action and this amount of time is one of important parameters, which direct the human error probability (HEP), i.e. probability of operator to perform an error. Smaller human error probabilities may cause smaller risk and thus improved safety. IJS-HRA (Institute Jozef Stefan—human reliability analysis) serves as the example method (Cepin, 2005a; Cepin, 2007) for quantification of human error probabilities of specific human actions. The probabilistic safety Please cite this article as: Prosek, A., & Cepin, M. Success criteria time windows of operator actions using RELAP5/MOD3.3 within human reliability analysis. Journal of Loss Prevention in the Process Industries (2007), doi:10.1016/j.jlp.2007.06.010 ARTICLE IN PRESS A. Prosek, M. Cepin / Journal of Loss Prevention in the Process Industries l (llll) Ill-Ill assessment model of a specific nuclear power plant serves as an example model, which shows how quantified human error probabilities relate to assessment of risk and thus safety. Probabilistic safety assessment is evaluated to assess and compare the measures of safety of the plant in two cases: if recovery is considered or not for each operator action separately. The decision, if recovery is considered or not, depends on the amount of additional time, which operators have to perform the required action (i.e. additional available time for action). The additional available time for action is determined from inputs from experience of training of operators on the plant simulator and from deterministic safety analysis. Section 2 gives basic information about the IJS-HRA method, which is integrated with probabilistic safety assessment and with deterministic safety analysis. Section 3 focuses on determining the time parameters, which are important for HRA and which are obtained with deterministic safety analysis. Examples are selected, which demonstrate how the calculations were performed and what the results show. Section 4 shows the results of probabilistic safety assessment with emphasis on selected examples from HRA. Section 5 gives the conclusions and implications of the work. 2. HRA within probabilistic safety assessment The operator actions are mostly only backup for the automatic actuations of the safety systems, which mitigate the accident if undesired initiating event occurs. IJS-HRA integrates some features of existing methods and some new features such as contribution of the simulator experience in order to consider the newest requirements and recommendations in the field and in order to be integrated in a modern computerized probabilistic safety assessment (Cepin, 2005a; Cepin & He, 2006; NUREG-1792, 2005). More information about the method is written in another article of this journal issue (Cepin, 2007). Only the feature important for the contents of this paper is mentioned here: quantification of HEP is performed with consideration or without consideration of recovery. If additional available time for action is larger than determined time interval, e.g. 10min, than recovery as independent mode of verification is considered. If additional available time for action is shorter than determined time interval, recovery is not considered. Additional available time for action (Ta) is defined as the difference between the time window of the action (Tw) and the actual time needed for performing the action (Tp), which is assessed based on real simulator scenarios: T a — T w T P- plant is put into a scenario that leads to a safe state and not to an accident state. The actual time needed for performing the action is the realistic time in which operators perform the action and it can be obtained from the simulator experience. The specified time windows are important for HRA due to the following reason. The HEP of certain operator action is lower if operators have more time available. In the control room of a nuclear power plant there is a team of operators, which is supervised by a shift supervisor. If operators have 10 or more minutes of additional time for action, it can be expected that colleagues or shift supervisor can observe and correct a possible error of their colleague. IJS-HRA method assumes that if the difference between the time window, in which the action has to be performed, and the actual time needed for performing the action is 10min or more, a recovery can be modeled for the investigated action. If additional available time for action is shorter than determined time interval, recovery is not considered. Consideration of recovery causes lower HEP and may cause a different impact of human error to the overall probabilistic safety assessment results. Determination of the time window, in which operators have to perform the action, is obtained from deterministic safety analysis. Fig. 1 shows integration of probabilistic safety assessment and deterministic safety assessment for improvement of HRA. Full arrows represent dependencies between the items, which are important for understanding this methodology. Dotted arrows on the figure represent dependencies between the items, which are not important for this methodology, but exist as part of processes of specific deterministic and probabilistic safety analysis in a nuclear power plant. The time window of the human action actually represents the success criteria for the action. It represents the time interval in which operators have to perform the action in order that the plant is put in a safer state, i.e. the Fig. 1. Integration of probabilistic safety assessment and deterministic safety assessment for improvement of human reliability analysis. Please cite this article as: Prosek, A., & Cepin, M. Success criteria time windows of operator actions using RELAP5/MOD3.3 within human reliability analysis. Journal of Loss Prevention in the Process Industries (2007), doi:10.1016/j.jlp.2007.06.010 2 ARTICLE IN PRESS 2 A. Prosek, M. Cepin / Journal of Loss Prevention in the Process Industries l (llll) Ill-Ill 3. Determining the time window success criteria Best-estimate deterministic safety analyses based on their plant specific model serve for determination of the amount of time in which operator has to perform its action (i.e. time window) in order that the safety parameters are not exceeded. Parametric calculations are performed, where the time window is varied and plant response is simulated in order that the safety parameters are not exceeded, and the longest time window for operator actions is obtained, which results in safe conditions of the plant through the complete simulation time. Deterministic safety analysis represents the time simulation of the most important plant parameters in selected circumstances. Such simulation may include response of the plant to the undesired initiating event, e.g. break of smaller or larger pipe of the most important plant system, e.g. loss of electric power supply, which cause actuation of safety systems to prevent an accident or at least to mitigate its consequences. The simulations of plant behavior after selected undesired initiating events may include a variety of options. Selected safety systems may be assumed operable or inoperable or they may be assumed inoperable for a selected period of time and then be assumed operable. If the most important plant parameters stay all the time within their acceptable limits, the plant is avoiding accident. If the limits are exceeded, the accident conditions are simulated. The main objective of these deterministic safety analyses is to show that the plant can be maintained in safe conditions even after a variety of undesired initiating events. Namely, several safety systems are in place to prevent severe accidents in such cases. The idea of the IJS-HRA method is to use those deterministic safety analyses to perform sensitivity studies of human actions, which are supplement to safety systems actuations. Sensitivity studies include variations of timing of human action. The objective of those sensitivity studies is to determine the latest time, when operators have to perform the needed action in order that the main plant parameters are not exceeded their limits, i.e. in order that the plant is kept in safe conditions and thus avoiding accident. The definition of accident state in the case of nuclear power plant probabilistic safety assessment is connected with the temperature of the reactor core. It is assumed if the temperature in the reactor core exceeds 923 K for more than 30 min or if temperature of the core exceeds 1348 K, the core damage may occur, which may lead to accident state. The cladding temperature of the hot rod in the core at the hottest vertical location is assumed as the maximum temperature in the core. Deterministic safety analyses are performed with complex computer codes. The modular accident analysis program (MAAP) has been used in the past in probabilistic safety assessment, where conservative approach was the accepted solution. Wherever, due to lack of information, the models were incomplete, the worst case was examined and considered. Realistic deterministic safety analyses have been required recently (ASME RA-S-2002, 2002; Han, Lim, & Yang, 2007) for risk-informed applications. So, the realistic i.e. best-estimate RELAP5/MOD3.3 computer code (USNRC, 2001) was used for safety analysis. The RELAP5 computer code has been extensively used in the past for safety analyses (Mavko, Stritar & Prosek, 1993, Prosek & Mavko, 1999). The input model described in reference (Prosek, Parzer, & Krajnc, 2004) was used for calculations. The new contribution of this study is an evaluation how deterministic safety analysis influences the success criteria time windows, which consequently direct the HEP. The procedure and the results are shown for two selected examples of human actions. 3.1. Example for manual actuation of auxiliary feedwater (AFW) at loss-of-coolant accident The first example event is a human action: establishing AFW in case of small or medium loss-of-coolant accident, i.e. break of the pipe connected to the reactor coolant system. In the case of small or medium loss-of-coolant accident in a nuclear power plant, and if high pressure safety injection (SI) fails, one of the means to cool the reactor is through the functioning of the AFW, which is automatically put into operation. If the pumps would not start automatically, operators should intervene. Success criterion requires operation of one of three pumps to maintain the flow by which the reactor coolant system is depressurized. The time window is defined based on safety analysis. Safety analyses were performed for various sizes of equivalent diameter breaks from 1.91 to 7.62 cm (0.75-3 in) and for various cases considering the time of actuation of AFW system. The comparison of the results shows that the latest time that the safety parameters (i.e. rod cladding temperature) are not exceeded is to actuate AFW system is 30min. Technical details of determining this time from performed safety analyses are presented below. Without high pressure SI into the reactor coolant system and the AFW injection into the secondary side there is no additional cooling of the core until the reactor coolant system pressure is depressurized below accumulator injection setpoint at 4.9 MPa. As can be seen from Fig. 2(a) the 5.08 cm (2 in) and larger breaks depressurize (through the break) in any case below accumulator injection setpoint pressure after some time and the AFW is not needed for depressurization. However, AFW is needed for subsequent depressurization for 2.54 cm (1 in) equivalent diameter break and smaller. The reason that 2.54cm break and smaller cannot depressurize the reactor coolant system is that cooling through the break is not sufficient. Therefore, additional cooling is needed provided by AFW system and Please cite this article as: Prosek, A., & Cepin, M. Success criteria time windows of operator actions using RELAP5/MOD3.3 within human reliability analysis. Journal of Loss Prevention in the Process Industries (2007), doi:10.1016/j.jlp.2007.06.010 ARTICLE IN PRESS A. Prosek, M. Cepin / Journal of Loss Prevention in the Process Industries l (llll) Ill-Ill Fig. 2. Calculated trends during loss-of-coolant accident: (a) pressurizer pressure, and (b) rod cladding temperature. 2 Table 1 Operator actions delays for scenarios with 2.54 cm break Case Operator action Auxiliary feedwater start Secondary relief valve full delay opening delay A Action not performed Action not performed B 0 min Action not performed C 20 min 20 min D 25 min 25 min E 30 min 15 min secondary relief valve, while cooling by high pressure SI is not available by assumption. As core heatup is earlier for 2.54 cm break than for 1.91cm break the time window to start AFW was determined for 2.54 cm break. Five different scenarios were analyzed as shown in Table 1. The parameter for indicating depressurization is pressurizer pressure and the parameter for indicating core heatup is rod cladding temperature. The analysis showed (see Fig. 2) that without any AFW (case A) the rod cladding temperature exceeds the criterion 1348 K when core damage may occur. Case B shows that even no delay in the AFW start could not prevent the core heatup. The analysis showed that when the secondary relief valve is operated automatically, it is opened around 25% of the time what is not sufficient to remove all decay heat from the reactor coolant system, resulting in core heatup. This means that another operator action is needed in combination with AFW start—manual full opening of secondary relief valve (cases C, D and E). In the case C, the reactor coolant system is depressurized in time and the core heatup above the core damage criterion is prevented. In the case D, the reactor coolant system is depressurized, but the rod cladding temperature exceeded the criterion. Finally, case E showed that AFW could be delayed 30 min, if secondary relief valve opening delay on AFW start is 15 min. The experience of operators with plant simulator shows that the actual time for performing the event is 1-10 min. So, additional time for performing the event is 20-29 min (i.e. success criteria time minus actual time for performing the event), which gives enough time for possible recovery action. Low stress is assumed, very good labeling of controls is observed, diagnosis and action are assumed as very simple, which gives performance shaping factor 0.1 for commission errors. 3.2. Example for manual actuation of AFW at transient The second example event is a human action: establishing AFW in case of transients. This is the same human action as in the previous case, except that it occurs in different circumstances, which means that different plant parameters may require different scenarios of safety systems. The success criterion says that capacity of one train of AFW is adequate to remove decay heat, to prevent overpressurization of reactor coolant system, and to prevent uncovering of the core resulting in core heatup. Safety analyses were performed for various cases considering the time of actuation of AFW system. The comparison of the results shows that the latest time that the safety parameters (i.e. rod cladding temperature) are not exceeded is to actuate AFW system is 40 min. Technical details of determining this time from performed safety analyses are presented below. The pressurizer pressure shows when the reactor coolant system is overpressurized. The core heatup can be prevented by maintaining sufficient reactor coolant system mass inventory and thereby core level, while the core heatup is indicated by rod cladding temperature. Fig. 3 shows all the relevant parameters: pressurizer pressure, reactor coolant system mass inventory, core collapsed liquid level, and rod cladding temperature. At zero time transient loss of main feedwater was started, followed by reactor trip and SI signal generation starting engineered safety features. At the time when one AFW pump was started to inject into the secondary side, cooling of the secondary side caused the pressurizer pressure to drop below the pressurizer relief valve closure setpoint and then below the maximum pressure capacity of high Please cite this article as: Prosek, A., & Cepin, M. Success criteria time windows of operator actions using RELAP5/MOD3.3 within human reliability analysis. Journal of Loss Prevention in the Process Industries (2007), doi:10.1016/j.jlp.2007.06.010 ARTICLE IN PRESS 2 A. Prosek, M. Cepin / Journal of Loss Prevention in the Process Industries l (llll) Ill-Ill Fig. 3. Calculated trends during transient: (a) pressurizer pressure, (b) reactor coolant system mass inventory, (c) core collapsed liquid level, and (d) rod cladding temperature. pressure safety injection SI pump (see Fig. 3(a)). There is no overpressurization of the reactor coolant system as the pressurizer pressure remains below 18.95 MPa. The closure of the pressurizer relief valve and coolant injection into reactor coolant system resulted in increasing reactor coolant mass inventory as shown in Fig. 3(b) thus recovering the core level shown in Fig. 3(c) and quenching the core as shown in Fig. 3(d). From Fig. 3 it can be seen that the core uncovery depends mainly on the delay of one AFW pump start. Unavailability of AFW injection leads to core uncovery. This means that reactor coolant system mass inventory depletion is mostly function of mass released through the pressurizer relief valves. Realistic modeling of the pressurizer relief valve guarantees realistic calculation of the reactor coolant system mass inventory. The parametric analysis shows that the core uncovers with AFW pump start delayed for 35 min or greater. The case with AFW pump start delayed for 40 min cause small core heatup and with delay of 50 min the core temperature is still below criterion 1348 K for core damage, while in the case with delay of 60 min this value is exceeded. Based on Fig. 3 and considering uncertainties in calculating the rod cladding temperature (Prosek & Mavko, 1999) the time window of 40 min was determined. The actual time for starting the AFW is 1-10 min. So, additional time for performing the event is 30-39 min (i.e. success criteria time minus actual time for performing the event), which gives enough time for possible recovery action. 4. Probabilistic safety assessment results 4.1. Model description The probabilistic safety assessment model of a nuclear power plant is named as HRA_IH_1 and is used for quantification. The characteristics of the model HRA_IH_1 show that it is a large and detailed model, which includes: 4748 gates, 1810 basic events, 16 initiating events and main event trees, 738 fault trees, which include 125 human failure fault trees, 57 parameters (failure rate), 418 parameters (probability), which include 55 parameters connected with HEP (those 55 parameters are obtained from 18 different basic HEP parameters, which are expanded to 55 parameters considering different performance shaping factors for basic HEP parameters), 18 groups for parameters of human errors, 117 groups for human error basic events. Table 2 shows HRA time parameters for selected human actions, which are needed for decision if recovery is considered or no, when quantification of HEP is made. Please cite this article as: Prosek, A., & Cepin, M. Success criteria time windows of operator actions using RELAP5/MOD3.3 within human reliability analysis. Journal of Loss Prevention in the Process Industries (2007), doi:10.1016/j.jlp.2007.06.010 ARTICLE IN PRESS 2 A. Prosek, M. Cepin / Journal of Loss Prevention in the Process Industries l (llll) Ill-Ill Table 2 Parameters for selected human errors Human error Tw (min) Tp (min) Ta = Tw-Tp (min) Manual actuation of auxiliary feedwater at transient 40 1-10 30-39 Manual actuation of auxiliary feedwater at loss-of-coolant accident 30 1-10 20-29 Table 3 Probabilistic safety assessment results Human error Basic human error Fractional Core damage frequency Main minimal cut set and its probability contribution contribution Manual actuation of auxiliary 2.31E-4 6.93E-02 2.487E-5 (Ry-1) 4 7.136E-7 (Ry-1) feedwater at transient Manual actuation of auxiliary 2.31E-4 N/A 2.487E-5 (Ry-1) - - feedwater at loss-of-coolant accident 4.2. Base case results The results of the probabilistic safety assessment include many parameters. Only selected results are mentioned below for the analysis with the following features: • consideration of internal initiating events, • third order approximation, • truncation of 2.7E-11 and Ry_1, • recovery is considered for both selected human actions, because additional available time for action (i.e. the difference between the time in which operators have to perform the action in order that it meets the success criteria and the actual time needed for performing the action) is more than determined time interval, e.g. 10 min. The results include: • Core damage frequency: 2.487E-5 Ry_1. • No minimal cut set, which includes event manual actuation of AFW during loss-of-coolant accident. Minimal cut set is a combination of basic events (i.e. component failures, human errors), which may cause undesired state of the system, e.g. accident state. This means that manual actuation of AFW at loss-of-coolant accident is not a safety significant event as it is not involved in any combination of undesired events. • Minimal cut set no. 4 (ranked by contribution to core damage frequency) contributes to core damage frequency by 7.136E-7 Ry_1 and it is the most contributing minimal cut set of those, which include event manual actuation of AFW in case of transients. This means that manual actuation of AFW at transients is a very safety significant event. • Risk importance factors (i.e. fractional contribution of considered human errors) are provided in Table 3. It is shown that Manual Actuation of AFW at Transient contributes significantly to the core damage frequency, which is observed by high fractional contribution. The manual actuation of AFW in case of loss-of-coolant accident is not listed in the list of minimal cut sets so risk importance factor cannot be calculated (the event is of no safety significance). 4.3. Sensitivity results of selected examples Sensitivity analysis is performed for each of selected example actions for a case if recovery would not be considered in quantification of HEP, i.e. if additional available time for action would be less than determined time interval. Table 4 shows the results for selected human errors without consideration of recovery. Results show that consideration of recovery impacts significantly the HEP. This is observed through the comparison of basic human error probabilities in Table 3 (recovery is considered) and Table 4 (recovery is not considered). The change of HEP can significantly impact the core damage frequency and thus the plant risk, if the affected human error is an important contributor to risk, as it is the case with manual actuation of AFW in case of transients. For the important human error it is necessary to determine additional time for action accurately as this may have significant impact to the assessment of risk. If the conservative analysis would be used instead of the best-estimate analysis, the time window for both actions would be around 15 min, which would not be enough for consideration of recovery. The comparison of results in Tables 3 and 4 shows that selection of best estimate versus conservative analysis leads to significant change in risk Please cite this article as: Prosek, A., & Cepin, M. Success criteria time windows of operator actions using RELAP5/MOD3.3 within human reliability analysis. Journal of Loss Prevention in the Process Industries (2007), doi:10.1016/j.jlp.2007.06.010 ARTICLE IN PRESS 2 A. Prosek, M. Cepin / Journal of Loss Prevention in the Process Industries l (llll) Ill-Ill Table 4 Results for cases if recovery is not considered at specific human error Human error Basic human error Fractional Core damage frequency Main minimal cut set and its probability contribution contribution Manual actuation of auxiliary 2.85E-3 4.80E-01 4.448E-5 (Ry-1) 1 8.810E-6 (Ry-1) feedwater at transient Manual actuation of auxiliary 2.85E-3 7.71E-04 2.494E-5 (Ry-1) 7875 8.424E-11 (Ry-1) feedwater at loss-of-coolant accident results. For manual actuation of AFW in case of loss-of-coolant accident, the change is insignificant, which was expected as the event is not risk important, so its changes does not cause significant changes in the results. For manual actuation of AFW in case of transients, this change is significant, as it nearly doubles the core damage frequency and thus the level of risk. 5. Conclusions The integration of deterministic safety analysis and probabilistic safety assessment is presented in the field of HRA. Safety analyses served for determination of time parameters, which are inputs for HRA within the probabilistic safety assessment. The propagation of impact of safety analysis through the human reliability to the probabilistic safety assessment is demonstrated. The analysis and results are presented on selected practical examples, which represent typical situations. Sensitivity studies of safety analysis for scenarios connected with each of selected human errors were performed. The timing of operator intervention was studied using realistic code and the results of safety analysis were examined in sense how late after the required human intervention the operator performs its action that the safety criteria are not exceeded, i.e. the temperature of the reactor core does not exceed the determined limit. This gives available time for operator to act. The less the time available, the more probable the human error of respective action, which is the implication of the HRA that was performed. The results of HRA and the probabilistic safety assessment results are presented, with focus on the parameters that are connected with impacts of HRA. The results show that consideration of recovery impacts significantly the HEP. The change of HEP can significantly impact the core damage frequency, if the affected human error is an important contributor to risk, as it is the case with one of two example actions. For the important human error it is necessary to determine additional time for action accurately as this may have significant impact to the assessment of risk. In addition, the results implies that best-estimate deterministic safety analysis removes the unnecessary conservatism compared to conservative deterministic safety analysis and consequently reduce the risk, which is true also for the risk contribution of human actions. Acknowledgment The Slovenian Research Agency supported this research (partly research program P2-0026, partly research project V2-0376 supported together with Slovenian Nuclear Safety Administration and partly research project J2-6542). References ASME RA-S-2002. (2002). Standard for probabilistic risk assessment for nuclear power plant applications. The American Society of Mechanical Engineers. Cepin, M. (2005a). Human reliability analysis—methods and applications, problems and solutions. Internal Report, IJS. Cepin, M. (2005b). Analysis of truncation limit in probabilistic safety assessment. Reliability Engineering & System Safety, 87(3), 395-403. Cepin, M. (2007). Importance of human contribution within the human reliability analysis (IJS-HRA). Journal of Loss Prevention in the Process Industries. doi:10.1016/j.jlp.2007.04.012. Cepin, M., & He, X. (2006). Development of a method for consideration of dependence between human failure events. ESREL2006. Grobbelaar, J. F., Julius, J. A., & Rahn, F. (2005). Analysis of dependent human failure events using the EPRI HRA calculator. PSA05. Proceedings. Han, S. J., Lim, H. G., & Yang, J. E. (2007). An estimation of an operator's action time by using the MARS code in a small break LOCA without a HPSI for a PWR. Nuclear Engineering and Design, 237, 749-760. Harris, D., Stanton, N. A., Marshall, A., Young, M. S., Demagalski, J., & Salmon, P. (2005). Using SHERPA to predict design-induced error on the flight deck. Aerospace Science and Technology, 9(6), 525-532. Jordan Cizelj, R., Mavko, B., & Kljenak, I. (2001). Component reliability assessment using quantitative and qualitative data. Reliability Engineering & System Safety, 71, 81-95. Kennedy, G. A. L., Siemieniuch, C. E., Sinclair, M. A., Kirwan, B. A., & Gibson, W. H. (2007). Proposal for a sustainable framework process for the generation, validation, and application of human reliability assessment within the engineering design lifecycle. Reliability Engineering & System Safety, 92(6), 755-770. Khan, F., Amyotte, P. R., & DiMattia, D. G. (2006). HEPI: A new tool for human error probability calculation for offshore operation. Safety Science, 44(4), 313-334. Mavko, B., Stritar, A., & Prosek, A. (1993). Application of code scaling, applicability and uncertainty methodology to large break LOCA analysis of two-loop PWR. Nuclear Engineering and Design, 143, 95-109. Leskovar, M., & Mavko, B. (2006). Simulation of the Phebus FPT1 severe accident experiment with the MELCOR computer code. Journal of Mechanical Engineering, 52(3), 142-160. Please cite this article as: Prosek, A., & Cepin, M. Success criteria time windows of operator actions using RELAP5/MOD3.3 within human reliability analysis. Journal of Loss Prevention in the Process Industries (2007), doi:10.1016/j.jlp.2007.06.010 ARTICLE IN PRESS 2 A. Prosek, M. Cepin / Journal of Loss Prevention in the Process Industries l (llll) Ill-Ill NUREG/CR-1278. (1983). Handbook for human reliability analysis with emphasis on nuclear power plants application. US NRC. NUREG/CR-6883. (2005). The SPAR-H human reliability analysis method. US NRC. NUREG-1792. (2005). Good practices for implementing human reliability analysis (HRA). US NRC. Prosek, A., & Mavko, B. (1999). Evaluating code uncertainty—I: Using the CSAU method for uncertainty analysis of a two-loop PWR SBLOCA. Nuclear Technology, 126, 186-195. Prosiek, A., Parzer, I., & Krajnc, B. (2004). Simulation of hypothetical small-break loss-of-coolant accident in modernized nuclear power plant. Electrotechnical Review, 71(4), 199-204. Reer, B., Dang, V. N., & Hirschberg, S. (2004). The CESA method and its applications in a plant-specific pilot study on errors of commission. Reliability Engineering & System Safety, 83, 187-205. USNRC. (2001). RELAP5/MOD3.3 code manual Vols. 1-8. Rockville, MA, Idaho Falls, ID: Information Systems Laboratories, Inc., (prepared for USNRC). Please cite this article as: Prosek, A., & Cepin, M. Success criteria time windows of operator actions using RELAP5/MOD3.3 within human reliability analysis. Journal of Loss Prevention in the Process Industries (2007), doi:10.1016/j.jlp.2007.06.010 ASÍGURAREA CALITÁTII - QUALITY ASSURANCE lanuarie - Martie 2009 Volumul XV Numárul 57 ASIGURAREA CALITAJII - QUALITY ASSURANCE CUPRINS - CONTENTS □ FDI in Multivariate Process with Naive Bayesian Network in the Space of Discriminant Factors Teodor Tiplica, Sylvain Verron, Abdessamad Kobi □ Extending Health Considerations in Generation/Transmission Power System to Include Uncertainty Using Fuzzy Data R A.K. Verma, A. Srividya, M.V. Bhatkar □ Modern Procedures Evaluating MEMS Reliability Marius Bazu, Cätälin Tibeicä, Lucian Gäläteanu, Virgil Emil Ilian □ IJS-HRA - A Method for Human Reliability Analysis Marko Cepin □ How the Paradigm of Management Control enables managers to find new directions in Quality Management Jos van Iwaarden, Ton van der Wiele © © ® ® ® All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, photocopied, recorded or other wise, without written permission from the editor. When authors submit their papers for publication, they agree that the copyright for their article be transferred to the Romanian Society for Quality Assurance (SRAC), if and only if the articles are accepted for publication. The copyright covers the exclusive rights to reproduce and distribute the article, including reprints and translations. Permission for other use. 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The publisher disclaims all liability in connection with the use of information contained in this publication. -200- ASÍGURAREA CALITÁTII - QUALITY ASSURANCE lanuarie - Martie 2009 Volumul XV Numárul 57 IJS-HRA - A Method for Human Reliability Analysis Marko CEPIN „Jožef Stefan" Institute, Ljubljana, Slovenia Abstract The Human Reliability Analysis (HRA) is a systematic framework, which includes the process of evaluation of human performance and associated impacts on structures, systems and components for a complex facility. The objective of the paper is to present the IJS-HRA method and the results of an example study. IJS-HRA is a method, which is a method for evaluation of the human error probabilities of human actions within the probabilistic safety assessment of the nuclear power plants. It is developed based on integration of several important features of previously developed methods. The resulted human error probabilities, which are calculated with application of the method, are used in the example probabilistic safety assessment. A part of the obtained results are presented, which show that the contribution of human factor is still an important contributor to risk in spite of a wide automation, which took place in recent decades. In addition, the most important human failure events are identified, which are candidates for simulator training, which will consequently reduce their human error probability and contribute to improved safety. Keywords: Human Reliability Analysis, Risk, Safety, Nuclear. 1. INTRODUCTION The experience with the results of probabilistic safety assessment (PSA) and with the contributions of human failure events (HFE) in the models and in the results show that human contribution to the undesired events is still significant in spite of the automation of systems and processes. The Human Reliability Analysis (HRA) is a systematic framework, which includes the process of evaluation of human performance and associated impacts on structures, systems and components for a complex facility. 1.1. Review of Methods in the Field of Human Reliability Analysis The contribution of human factor to safety of complex facilities is large in spite of intensive automation of systems and processes. The field was investigated intensively in the last decades, which is specially the case for nuclear power plants (Reer, Dang & Hirschberg, 2004, Grobbelaar, Julius & Rahn, 2005, Kennedy, Sie-mieniuch, Sinclair, Kirwan & Gibson, 2007). Probabilistic safety assessment applications are source of many interactions with human reliability analysis (Cepin & Mavko, 1997, ASME-RA-S-2002, Cepin, 2002, Cepin & Mavko, 2002, Holy, 2004, Mosleh & Chang, 2004, Cepin, 2005b). Many methods connected with human reliability analysis were developed in this period, including Technique for Human Error Rate Prediction (THERP, NUREG/CR-1278, 1983), Systematic Human Action Reliability Procedure (SHARP, 1984), Accident Sequence Evaluation Program (ASEP, NUREG/CR-4772, 1987), A Technique for Human Event Analysis (ATHEANA, NUREG-1624, 1999, Forester et al., 2004), Cognitive Reliability and Error Analysis Method (CREAM, Hollnagel, 1988), Human Cognitive Reliability (HCR, Spurgin, 1990), Standardized Plant Analysis Risk HRA (SPAR-H, NUREG/CR-6883, 2005) and many others. 1.2. Objective The objective is to present the IJS-HRA method, which is a method for evaluation of the human error probabilities of human actions within the probabilistic * Correspondence to Assoc. Prof. dr. Marko Cepin, e-mail: marko.cepin@ijs.si. -21- ASÍGURAREA CALITÁTII - QUALITY ASSURANCE lanuarie - Martie 2009 Volumul XV Numárul 57 safety assessment of the nuclear power plants. The method integrates specific features of existing methods and specific new features. It includes consideration of dependencies, which is one of the most important features of human reliability analysis. 2. HUMAN RELIABILITY ANALYSIS -METHOD DESCRIPTION Figure 1 shows the scheme of the method. The main inputs for the human reliability analysis are identified (PSA model, plant information, HRA state-of-the-art), which represent the standpoint for development of the method. The method for evaluation of human failure events is developed including consideration about dependencies between human failure events. Figure 1 shows that identification of human failure events distinguishes pre-initiator events (i.e. pre-initia-tors), initiator events (i.e. initiators) and post-initiator events (i.e. post-initiators). Pre-initiators are the events that may cause the equipment to be unavailable before the initiating event has occurred. Initiators are the events that may contribute to the occurrence of initiating events. Post-initiators are the events, which are connected with human actions to prevent accident or mitigate its consequences after initiating event has occurred. Evaluation of human failure events including evaluation of dependencies integrates assessment of human error probabilities with operator interview, simulator experience and plant data base. Information on time windows of human failure events is obtained from safety analysis. The information needed for the human reliability analysis come from three main sources, which are the following: □ Information about the plant: information from safety analysis report (information from safety system descriptions), information from plant procedures: e.g. general operating procedures, system operating procedures, abnormal operating procedures, emergency operating procedures, operating surveillance procedure. □ PSA model including fault trees and event trees and the supporting information. □ Standards, requirements, guidelines and good practice for PSA with emphasis on issues, which are applicable for HRA (e.g. ASME standard on PSA: ASME RA-S-2002), and standards, requirements, guidelines and good practice for HRA itself: e.g. HRA methods: e.g. THERP (NUREG/ CR-1278, 1983), ASEP (NUREG/CR-4772, 1987), SHARP (SHARP, 1984), ATHEANA Figure 1. IJS-HRA - A Human Reliability Analysis Method -22- ASÍGURAREA CALITÁTII - QUALITY ASSURANCE lanuarie - Martie 2009 Volumul XV Numárul 57 (NUREG-1624, 1999), CREAM (Hollnagel, 1988), SPAR-H (NUREG/CR-6883, 2005), good practices for implementation of HRA (NUREG-1792, 2005). The method for analysis of human failure events is developed including consideration about dependencies between human failure events, which are in the PSA model treated as independent. The method for update of human failure events is a method, which include features of several HRA methods, such as THERP (NUREG/CR-1278, 1983), ASEP (NUREG/CR-4772, 1987), ATHEANA (NUREG-1624, 1999), SPAR-H (NUREG/CR-6883, 2005) and features such as dependency method and inclusion of simulator experience. The method consists of the following steps, which are described in the subsequent subsections: 1. Statements on objectives, definition of the work, scope of the analysis 2. Identification of human failure events 3. Task analysis of human failure events 4. Evaluation of human failure events 5. Consideration of dependencies between human failure events 6. Interpretation of results, inclusion of HRA to PSA The success criteria for human failure events include information about their time window, i.e. information about the time, in which operators have to perform the action. This information about the available time comes from safety analyses, where scenarios about operating safety systems are evaluated. This is the reason for appearance of text box of safety analysis on Figure 1 and its connection with text box on HRA method. 2.1. Statements on objectives, definition of the work, scope of the analysis Information on objectives, definition of the work and the scope of the analysis is related with performance of the probabilistic safety assessment of the nuclear power plant. It is important to emphasise that two terms are widely used in human reliability analysis: human action and human failure event. Human action is a term describing an event or a process, which is performed by the plant operators. Human failure event is a term, which can describe the same event or process from its negative side in sense what can go wrong in order that the human action is not performed or it is not performed correctly. 2.2. Identification of human failure events HFE identification, which distinguishes pre-initiator events (i.e. pre-initiators), initiator events (i.e. initia- tors) and post-initiator events (i.e. post-initiators), results in identification of a number of pre-initiators, a number of initiators and a number of post-initiators. Pre-initiators are the events that may cause the equipment to be unavailable before the initiating event has occurred. Initiators are the events that may contribute to the occurrence of initiating events. Post-initiators are the events, which are connected with human actions to prevent accident or mitigate its consequences after initiating event has occurred. Pre-initiators are identified with help of the analysis of systems and their relations with operator intervention, with the analysis of sequence of events in the event trees and with consideration of references on good practice on HRA. Initiators are identified with help of the documents on plant history and with checking the events that may initiate initiating events. The links of fault trees that are linked to the initiating events in the event trees are checked. Post initiators are identified with help of operator interview, with analysis of event trees and their respective scenarios in a team of operator and PSA HRA analyst. 2.3. Task analysis of human failure events Task analysis of human failure events includes: □ collection of information about human failure event, which includes review of plant documents (e.g. safety analysis report, plant procedures), plant databases, PSA (with emphasis on all its parts that are connected with HRA), □ preparation and analysis of talk-through with plant operators, which identify information about tasks, about the time needed for performing human actions, about performance shaping factors connected with their respective human failure events, □ identification of the tasks, which compose the respective human failure event, □ identification and analysis of diagnosis activities, □ identification and analysis of action tasks including omission and commission. 2.4. Evaluation of human failure events Evaluation of human failure events includes: □ measurement of time needed for performing human actions, which is performed through real simulator scenarios, □ assessment of simulator experience with human actions that are included in human failure events, -23- ASiGURAREA CALITÄTii - QUALITY ASSURANCE lanuarie - Martie 2009 Volumul XV Numarul 57 □ preparation of failure model table, which (based on cue table and subtask analysis table) identifies failures and specifies their general evaluation procedure: i.e. consideration or no consideration of recovery. If additional available time for action is determined as one value, e.g. 10 minutes or more, than recovery as independent mode of verification may be considered in such case. Additional available time for action is defined as the difference between the time window of the action (obtained from success criteria for the action: the time in which operators have to perform the action), i.e. the time in which action has to be performed in order that it meets the success criteria, and the actual time needed for performing the action, □ preparation of data table, which connect failures with data base about human error probabilities (HRA data base), □ preparation of quantification table, which contains failure probabilities of tasks within human failure event and overall failure probability of respective human failure event. The quantifica- tion table includes the performance shaping factors, which impact the human error probabilities regarding the specific parameters and conditions of the specific action. A specific performance shaping factor equals to one in nominal conditions. In conditions that are worse than nominal, it changes to 2 or to 5 or to 10 according to specific circumstances of the human failure event under investigation. In conditions that are better than nominal, it changes to 0.5 or to 0.2 or to 0.1 according to specific circumstances of the human failure event under investigation. Each human error probability depends on several performance factors. The product of specific performance shaping factors gives the overall performance shaping factor of the investigated human error. Figure 2 shows an example of calculation of human failure event i.e. operator action, which consists of diagnosis phase and two actions. The diagnosis phase consists of basic diagnosis phase and its recovery phase. Both actions consist of basic action phase and its Figure 2. HRA Event Tree for Calculation of HEP -24- ASiGURAREA CALITÄTii - QUALITY ASSURANCE lanuarie - Martie 2009 Volumul XV Numarul 57 recovery phase. The right branch of each node represents failure probability of the respective phase, while left branch represent its complement. All failure probabilities: failure probability of diagnosis phase, failure probability of diagnosis recovery, failure probability of basic action 1, failure probability of action 1 recovery, failure probability of basic action 2 and failure probability of action 2 recovery are assessed as 0.1 on this particular example in Figure 2. No dependency is assumed in the example. Resulted HEP is written in lower right corner of the figure: 2.97E-2. 2.4.1. Consideration of Simulator Experience into HRA The training of plant operators on a full scope simulator is a complex process. One of the features of this process is that simulator personnel collect and analyse responses of operators on real scenarios and real events. The consideration of simulator experience into HRA is proposed as follows: □ Human failure events, which are part of probabilistic safety assessment, are identified and their descriptions are provided to simulator personnel. □ Simulator personnel recognize and assess experience of operators with each particular human failure event in a way that the events, which are better or worse than the average, are identified. The events with average success of response of operators are marked with N. The events, for which more difficulties in success of response of operators than average are identified, are marked with N+. The events, for which less difficulties in success of response of operators than average are identified, are marked with N-. Such expert opinion of simulator personnel is performed separately for diagnosis phase of the event and separately for action phase of the event. Human reliability assessment is modified as follows. The human error probabilities of human failure events marked with N+ (either diagnosis phase or action phase or both) increase their probability for 10%. The human error probabilities of human failure events marked with N- (either diagnosis phase or action phase or both) reduce their probability for 10%. If both: N+ and N- exist for the same human failure event: one for diagnosis phase and the other for action phase, HEP is not changed. 2.5. Consideration of dependencies between human failure events Consideration of dependencies between human failure events is an important issue, which is described in more details in reference (Cepin, 2008). 3. MODEL A full plant specific Probabilistic Safety Assessment (PSA) model of a two loop nuclear power plant is selected for the analysis. The model is developed for the computer code Risk Spectrum PSAP. The probabilistic safety assessment model for normal operation is a detailed model consisting of thousands of basic events and gates, hundredths of system and subsystem fault trees and tenths of event trees. The model integrates the internal and external events, but only the portion for internal events is selected for purposes in this paper. 4. ANALYSIS AND RESULTS Table 1 shows the selected human failure events with their respective human error probabilities, which are calculated using the IJS-HRA method. Table 1. Part of the calculated human error probabilities Description Human Error Probability Type False calibration 1,91E-3 Pre-initiator Block valve - incorrect position after test 1,07E-2 Pre-initiator Wrong line up of valve 2,27E-4 Initiator Wrong line up at cross connection of service water 4,09E-4 Post-initiator Failure to start the service water pump B 1,15E-2 Post-initiator Operator fails to align containment spray system recirculation - Train A 1.97E-2 Post-initiator Operator fails to establish main feedwater 2,2E-2 Post-initiator Operator fails to check and isolate faulted steam generator 2,76E-2 Post-initiator Operator fails to manually initiate safety injection 5E-2 Post-initiator Table 2 and table 3 show the importance measures: risk increase factor and risk decrease factor, of the most important human failure events in the nuclear power plant probabilistic safety assessment. Risk increase factor of specific human failure event shows, how much the risk of the plant increases, if the human error probability of the respective human failure event increases to 1. Risk decrease factor of specific human failure event shows, how much the risk of the plant decreases, if the human error probability of the respective human failure event decreases to 0. Those human failure events, which are identified as the most important, are candidates for simulator training, which consequently lead to improvement of sa- -25- ASÍGURAREA CALITÁTII - QUALITY ASSURANCE lanuarie - Martie 2009 Volumul XV Numárul 57 fety. Namely, better trained operators for specific actions perform them more reliably, which means decrease of human error probability. Table 2. Identification of Selected Human Failure Events with the largest Risk Increase Factor Basic Event Risk Increase Factor Description HE-POST-INI-004 226 Operator fails to establish auxiliary feedwater & secondary cooling (in transients) HE-POST-INI-012 75,6 Operator fails to establish auxiliary feedwater & secondary cooling (at loss of offsite power) HE-POST-INI-105 44,6 Operator fails to align cold leg high pressure recirculation (small loss of coolant accident) HE-POST-INI-100 36,4 Operator fails to trip the reactor coolant pumps HE-INI-001 23,3 Wrong lineup of valve HE-POST-INI-107 22,2E Operator fails to align cold leghigh pressure recirculation (transients) HE-POST-INI-033 6,68 Operator fails to start one out of three containment spray pumps within 5 min HE-POST-INI-034 3,17 Operator fails to start one out of three containment spray pumps within 10 min HE-POST-INI-074 2,67 Operator fails to initiate cooling and depressurization of reactor coolant system HE-POST-INI-068 2,61 Operator fails to initiate cooldown of the reactor coolant system Table 3. Identification of Selected Human Failure Events with the largest Risk Decrease Factor Basic Event Risk Increase Factor Description HE-POST-INI-047 1,13 Operator fails to initiate reactor coolant pump seal injection HE-POST-INI-068 1,09 Operator fails to initiate cooldown of the reactor coolant system HE-POST-INI-093 1,09 Operator fails to action for reactor coolant system inventory restoring The overall contribution of human failure events to the core damage frequency is large. This means that contribution of human is still an important contributor to risk in spite of a wide automation, which took place in recent decades. Figure 1 shows the risk contributions of selected groups of components based on quantified minimal cut sets. Group HUMAN-ERRORS includes all basic events corresponding to human failure events, group DIESELGEN includes all basic events corresponding to diesel generators, group AFW-PUMPS includes all basic events corresponding to auxiliary feedwater pumps, group HUMAN-E-INI includes all basic events corresponding to initiator human failure events, group HUMAN-E-PRE-INI includes all basic events corresponding to pre-initiator human failure events, group MOVS includes all basic events corresponding to motor operated valves and group AOVS includes all basic events corresponding to air operated valves. Result on Figure 3 show that the risk contribution of all human failure events is similar to the risk contribution of all basic events connected with safety system diesel generators and a little larger that the risk contribution of all basic events connected with auxiliary feedwater system. CONCLUSIONS The method for the human reliability analysis is developed with consideration of current requirements and good practice. The selected features of existing methods and selected specific features are introduced into the method. The method is described and applied. The human error probabilities that are calculated according to the method are applied in the probabilistic safety assessment model and the subsequent analyses were performed. The analysis of the probabilistic safety assessment model shows, that the contribution of human error probabilities is a notable contributor to risk in spite to a large automation in recent years. The results of eva- 1.0E-03 1.0E-02 1.0E-01 Figure 3. Fractional Contribution for Selected Groups of Events -26- ASÍGURAREA CALITÁTII - QUALITY ASSURANCE lanuarie - Martie 2009 Volumul XV Numárul 57 luating the probabilistic safety assessment model show and quantify the key human failure events, which mainly contribute to risk. Those can be subjected to simulator training, which may subsequently decrease their human error probability, which consequently leads to improved safety. The problem of human reliability analyses lays in subjectivity of the models and their quantifications. The subjectivity could be decreased with development of more detailed guidelines and procedures for specific detailed examples of human failure events. The factors, which largely impact the subjectivity of the models and subsequently the uncertainty of the results, are performance shaping factors and the features of dependency. Future activities connected with decreasing the subjectivity of human reliability analysis should be focused to those two fields. REFERENCES [1] ASME RA-S-2002 (2002), Standard for Probabilistic Risk Assessment for Nuclear Power Plant Applications, The American Society of Mechanical Engineers. [2] Y.H.J. Chang & A. 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