C. Bertrand, A. Allou, F. Beauchamp, E. Pluyette, P. Defrasne, and F. Baqué

Transcription

1 Scence and Technology of Nuclear Installatons, Artcle ID , 8 pages Research Artcle Thermomechancal Model and Burstng Tests to Evaluate the Rsk of Swellng and Burstng of Modfed 9Cr-1Mo Steel Steam Generator Tubes durng a Sodum-Water Reacton Accdent C. Bertrand, A. Allou, F. Beauchamp, E. Pluyette, P. Defrasne, and F. Baqué French Alternatve Energes and Atomc Energy Commsson (CEA), Nuclear Energy Drectorate, Cadarache Center, Sant Paul lez Durance, France Correspondence should be addressed to C. Bertrand; carole.bertrand@cea.fr Receved 29 July 2013; Revsed 4 December 2013; Accepted 5 December 2013; Publshed 9 January 2014 Academc Edtor: Marano Tarantno Copyrght 2014 C. Bertrand et al. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. The MECTUB code was developed to evaluate the rsk of swellng and burstng of Steam Generator (SG) tubes. Ths code deals wth the physc of ntermedate steam-water leaks nto sodum whch nduce a Sodum-Water Reacton (SWR). It s based on a one-dmensonal calculaton to descrbe the thermomechancal behavor of tubes under a hgh nternal pressure and a fast external overheatng. The mechancal model of MECTUB s strongly correlated wth the knd of the materal of the SG tubes. It has been developed and valdated by usng experments performed on the alloy 800. A change to tubes made of Modfed 9Cr-1Mo steel requres more knowledge of Modfed 9Cr-1Mo steel behavor whch nfluences the burstng tme at hgh temperatures (up to 1200 C). Studes have been ntated to adapt the mechancal model and to qualfy t for ths materal. The frst part of ths paper focuses on the mechancal law modellng (elastcty, plastcty, and creep) for Modfed 9Cr-1Mo steel and on overheatng thermal data. In a second part, the results of burstng tests performed on Modfed 9Cr-1Mo tubes n the SQUAT faclty of CEA are used to valdate the mechancal model of MECTUB for the Modfed 9Cr-1Mo materal. 1. Introducton and Context In the Steam Generator, the heat exchange tubes are the only physcalbarrerbetweenthesecondarysodumandthewater. If there s a leakage n the heat exchange tubes, then the water and the sodum are nto contact; thus an exothermc chemcal reacton occurs between the two reactants. Ths reacton produces sodum hydroxde and hydrogen. Overheatng of SG tubes can be due to the exothermc reacton. The temperature of the products of the reacton s hgh and t can reach the vaporzaton temperature of the sodum hydroxde (1390 C under 1 bar). The bolng temperature of the sodum s 880 Cwthapressureof1bar.The heat exchange between the hot reacton products and the neghborng tubes results n a rse of the temperature of these tubes. Then the mechancal characterstcs of the heated tubes decrease sgnfcantly; ths leads the creep phenomenon to become not neglgble. Due to the nternal pressure of the water/steam, the heat exchange tubes become sgnfcantly straned (swellng by a few tens %). Then the swelled tube may burst n a few tens of seconds, nvolvng large breaks. Thskndofaccdentcanoccurfthentalleakhas enough tme to evolve towards secondary and then a large leak: puncturng of another tube by wastage and propagatng to other tubes. Ths scenaro s only possble f the detecton s late (the secondary leak ntervene before the end of the depressurzaton of the steam-water n the SG) or f the detecton and protecton systems fal. Indeed, t s necessary to remnd that the accdent n PFR Superheater 2 n 1987 led to the burst of 40 tubes [1]. Ths accdent was able to occur because of the unavalablty of the hydrogen detecton n sodum. The Sodum-Water Reacton (SWR) was detected very late, by the measurement of the pressure ncrease n the ntermedate loop expanson tank plenum. The secondary loop was protected by the rupture of the burstng dscs wth trggerng of the sodum solaton, depressurzaton, and dranng sequence.

2 2 Scence and Technology of Nuclear Installatons The PFR accdent led to reevaluaton of the leak evoluton scenaroduetoamechansmnottakenntoaccountprorto ths accdent, that s, the burstng of the tubes. Thus ths led to revse the safety strategy by takng nto account reference accdents nvolvng multple tube ruptures, nstantaneous ruptures, or those occurrng over a perod of tme. Consequently, a computatonal program called MECTUB code has been developed to calculate the local effects of the SWR that can nduce a secondary leak hazard wthn the tube bundle [2].The burstng crtera are lnked wth stran;ths code allows determnng the temperature and the stran of target tubes durng the SWR event. The mechancal model of the MECTUB code s strongly correlated wth the type of the materal of the SG tubes and ts ntrnsc behavor. It has been so developed and valdated wth regard to experments performed on the alloy 800 of the SUPERPHENIX helcal tubes SGs [2]. Modfed 9Cr-1Mo steel s one of the materals nvestgated for the SGU tubes of the future sodum-cooled fast reactors (SFRs). A change to straght tubes made of Modfed 9Cr-1Mo nduces dfferent result of the heatng-burstng tme at hgh temperatures (up to 1200 C); then t requres more n-depth knowledge of Modfed 9Cr-1Mo steel behavor. Studes have been ntated to adapt the mechancal model and to qualfy t for ths materal. The frst part of ths paper s focused on the descrpton of themechancallawmodellng(elastcty,plastcty,andcreep) for Modfed 9Cr-1Mo steel and on overheatng thermal data. In the second part, the paper presents elements of the valdaton of MECTUB mechancal model of the Modfed 9Cr-1Mo as the results of burstng tests performed on Modfed 9Cr-1Mo tubes n the SQUAT faclty of CEA Cadarache Center. 2. Overheatng Tubes Modellng 2.1. Overheatng-Swellng-Burstng Phenomenology. Under normal operatng condtons, a tube of SGU can be stressed by effects of nternal pressure (up to 200 bar) and by the radal heat flux across the tube (from 20 to 60 W/cm 2 for nomnal capacty, accordng to the exchange zone). Tubes are desgned to resst, whle the creep of the hottest part remans weak. When an mportant SWR occurs, the temperature of reacton products nduces a fast local heatng (the radal heat flux may exceed 200 W/cm 2 )tothetube.thenternalflud (steam water) can only remove a small amount of ths heat rse. Ths knd of forcng wll nduce stran of materal (accordng to ts elastcty, plastcty, and creep characterstcs), and the mechancal characterstcs of the materal drastcally fall wth the rse of the temperature. Fnally, the tube can burst after havng swollen under nternal pressure acton. Fgure 1 shows the boundary condtons, ntal condtons, and model data. Consderng overheatng, thermal condtons, mechancal characterstcs of materals, and mechancal laws of the tube, MECTUB thermomechancal code was developed to calculate swellng and burstng local effects whch can nduceasecondaryleak.thecodesabletopredctthe burstng tme of the tube and the stran rse durng tube swellng phase (wastage effects could also be taken nto account) Thermal Boundary Condtons Assocated to External Overheatng. The mechancal behavour laws strongly depend on the temperature. Thus an accurate knowledge of thetemperatureofthetubessrequred.theradalheat conducton equaton wthn the tube s solved to obtan the temperature dstrbuton n the thckness of the tube. Beyond thermal modellng resoluton tself, thermal boundary condtons have to be ntroduced as exactly as possble. The convecton between the hot sodum-water reacton products and the target tube wall produces an external overheatng flux. In the framework of CEA-ENEA collaboraton, ths thermal flux has been determned by analysng sodum-water reacton THETRA tests [3]performednItalyn1985. Phases of steady overheatng (hgh temperatures and gradent values) were analysed n order to calculate the overheatng flux of the reacton (steady-state calculatons). Among all the overheatng phases observed durng the fve THETRA tests, the followng conservatve values have been selected: () reacton products temperature: 1080 C, () heat transfer coeffcent between reacton products and tube: W/m 2 K. These values are used for safety calculatons as steadystate condtons Mechancal Behavour and Laws [2]. For each tme step the mechancal model uses 3 steps to compute stran and stress. Each step s based on one mechancal property of the materal n the followng order: () the elastcty, for small and reversble deformaton of the materal, see detals n Secton 2.3.1; () the plastcty effect, to model the rreversble deformaton. The plastcty underestmates the elastcty effect (tensle curve lower than the curve of plastcty of the alloy); see detals n Secton 2.3.2; () the creep effect nduces a relaxaton of the stress nvarants; see detals n Secton Asntheprevouslterature[2] aboutmectubcode, the nternal pressure of the tube allows to determne stress and stran components by the use of the balance equaton.

3 Scence and Technology of Nuclear Installatons 3 Internal coolng Heat transfer coeffcent Temperature of water/vapour or nternal flux Target tube Water/steam Internal pressure 200 bar External heatng Heat transfer coeffcent = W/m 2 K Temperature of sodum water reacton (SWR) products = 1080 C Reacton products Water/ steam Materals Mechancal characterstcs: elastcty, plastcty, and creep Thermal characterstcs: conductvty and dffusvty Fgure 1: Boundary condtons, ntal condtons and model data. The creep part of the equaton gves stan varaton versus the tme. The mechancal algorthm s as follows: Δ(σ t+1 ) el =EΔε t+1, Δ(σ t+1 ) el+pl = mn (EΔε t+1 ;σ pl (ε t +Δεt ) σt ), Δ(σ t+1 ) creep = EA(σ t )n dt, Δ(σ t+1 )=mn (EΔε t+1 ;σ pl (ε t +Δεt ) σt ) EA(σ t )n dt, where pl s plastcty and el s elastcty. Beyond the elastcty and the plastcty laws correspondng to nstantaneous deformaton of mechancally or thermally loaded structures, t s essental to take nto account the creepeffectsassoonasthetemperaturebecomesveryhgh, even for short tme Elastcty. For deformatons whch are not exceedng 0.2%, stresses (σ) are proportonal to strans (ε)accordng to (1) Δσ = E Δε, (2) where E s Young s modulus. RCC-MR rules [4] provde the curve of the varaton of Young s modulus of Modfed 9Cr-1Mo steal accordng to temperature(ntherangefrom45upto600 C). Data untl 1200 Cwereobtanedbyafttngprocedureoftheparameters of the consttutve model of the Modfed 9Cr-1Mo. The data used to ft the parameters of the model were obtaned from expermental studes avalable n [5]. The values of Young s modulus for Modfed 9Cr-1Mo steel are gven n Table 1. In Fgure 2 tcanbeseenthatfortemperaturesupperthan 700 C the drop of the Modfed 9Cr-1Mo Young s modulus. Young modulus (MPa) Temperature ( C) 9Cr for <500 C 9Cr for <500 C Fgure 2: Young modulus of 9Cr. 9Cr Table 1: Values of Young s modulus. T ( C) E (MPa) Plastcty. For greater strans, there s no lnear varaton between stran and stress. On the bass of dynamc tensle tests at 600 C, the plastcs curves are known. The results are

4 4 Scence and Technology of Nuclear Installatons Stress (MPa) Stran (%) T=700 C T=600 C T = 800 C T=900 C T = 1000 C T = 1100 C T = 1200 C Fgure 3: Plastcty curves of 9Cr-MECTUB model. obtaned from a tracton test performed wth a stran rate of 0.42%/s [6]. Wth the hypothess that the curve (600 C) s the reference plastcty curve (Fgure 3), the othertemperature plastc curves are deduced, usng the followng emprcal formula: σ (T > 600 C)=σ(T=600 C) E (T > 600 C) E (T = 600 C). (3) For stran values exceedng 10%, t s assumed that the tube materal s perfectly plastc: the stran ncreases at constant stress Creep. It was clearly shown that durng permanent condtons tests, a sgnfcant ncrease of the tube stran could be observed up to rupture. Then the tme varaton of the stran s taken nto account by the mean of the creep term of the moton equaton. Three successve phases have to be consdered to gve an analytcal descrpton of the creep: prmary creep (stran rate decreases wth tme), secondary creep (stran rate ncreases lnearly wth tme), and tertary creep (stran rate ncreases wth tme up to rupture). Snce creep laws could not be establshed for 9Cr over a wde feld (of stran, stress, and temperature), t was decded to solve ths problem, usng only a smplfed secondary creep law (Norton s law), where stran rate ncreases lnearly wth respect to tme [7]: dε creep =Aσ n, (4) dt where t represents tme varable. Hgh head Support Pyrometer Feeders Feeders Sample Optcal bench Low head Protecton panel (e 20 mm) Vsble camera (strans measures) Fgure 4: SQUAT test faclty. Power supply (176 kva) Coolng crcut Table 2: Norton law coeffcents of MECTUB model. Temperature ( C) n log A A and n represent constant coeffcents whch depend only on the temperature. Norton s law coeffcents (A and n) are determned on the bass of tensle curve [6]. Ther values are gven n Table Burstng Tests of Modfed 9Cr-1Mo Tubes Theamofthetestsstoheatasfastaspossbleapressurzed tube untl t reaches a constant temperature. Sample tubes are all dentcal and representatve of the realty (such as dmensons and materals). Input data are the temperature and the nternal pressure. The man output data are the burstng tme, the temperatures, the pressure, and the stran versustme.resultsarenjectednthemodeltovaldatethe code, by comparng, for example, burstng tme calculated and burstng tme measured SQUAT Test Faclty. In order to valdate the mechancal model of the Modfed 9Cr-1Mo, burstng tests of SG tubes have been performed n the SQUAT faclty. The expermental results wll be compared wth the calculatons. The expermental devce SQUAT s shown n Fgure 4. It ncludes a heatng unt, a mechancal group ncludng a support, and top and bottom heads on whch the tube sample s welded, as well as a data acquston system whch s consttuted by measurng nstruments and by computng means. Heatng of the sample tube s performed by Joule effect Measurng Instruments. A pyrometer s used n order to measure the temperature. An magng devce and a telemetry laser are used n order to measure the stran. A pyrometer (Keller, Cellatemp PL22 AF3) s selected n order to measure the temperature at the surface of the tube. Ths devce works wthn the range of μm (the manufacturer recommends a target temperature falng n the range from 250 to 1600 C).

5 Scence and Technology of Nuclear Installatons 5 A laser dstance sensor (BAUMER OADM20I4440) s used for the stran measurement. Ths devce works wthn therangeof30 50mmwthanaccuracyof0.01mm. Furthermore the nternal pressure of the tubes s measured. The hgh-pressure gas crcut s fed by tanks stuated outsde the tests hall. A sensor of pressure SWAGELOK 0 250barSmodeltrans susedtorecoverthelevelofnternal pressure of the sample. Burstng temperature Landng temperature Pressure 3.3. Acqustons Systems and Control System. The control system conssts n a module ntegral PXI-1050: () a processor, () a record (dsk) of storage of the data, () a card of acquston (PXI-6259) connected wth varous modules of nput-output: (a) SCXI-1303 for the temperatures measurement (ambent temperature, temperature of the power cable), (b) SCXI-1161 for the flow, pressure, poston, temperature obtaned by pyrometer measurement, (c) SCB-68 for the analog ext of heatng nstructon, the commands output, and the nput (defects, safety, thresholds). Ths control system s managed by a program LabVIEW on After a phase of ntalzaton, 2 ndependent buckles are used: () a buckle s used for the acquston of the measurements and ther recordng (a perod of 120 ms), () a second buckle does the command and controlsystem part and nterfaces human machne (cadence of 100 ms) Data Explotaton. The data obtaned from the system LabVIEW are processed by usng Excel. The excel fle presents the man measures: () the temperature of the mddle of the tube s measured by the pyrometer, ()thesamplepressureandthetubeextenson, () the output voltage of the power supply transformer Test Procedure. The duraton of tests does not exceed halfanhour.thesetupphaseconsstsnpreheatngand pressurzng the sample tube. In the end of ths phase, the sample tube s heated to a nomnal temperature wth a controlled heatng rate of approxmately 100 C/s untl the burstng of the tube. The procedure of a test s presented Fgure Tests Parameters and Mans Results. The tested tubes are made wth Modfed 9Cr-1Mo steel. Ther length s 330 mm. The external dameter s of 16.4 mm and the thckness s equal L+δ+γ Temperature ( C) Ambent temperature 15 mn 30 mn Fgure 5: Prncple of a burstng test. Austente (γ) 9% Cr L+δ α+γ+carbdes Lqud Ferrte +γ α+carbdes Chromum (wt%) Fe-0.1 C Tme Ferrte (hgh temperature allotrope (δ) and lower temperature (α)) Fgure 6: Modfed 9Cr-1Mo phase dagram. to 2.2 mm. Ten tests were performed. The parameters of the tests are shown n Table 3 as well as the man results. Each test starts n Martenstc phase wth a temperature of 300 C. For each test performed at a target temperature upper than 825 C, a phase change occurs durng the test. TemperaturephasechangelmtscanbeseennFgure 6. The dfference of 11 s between SQUAT9 and SQUAT10 tests (performed wth the same nstructons of temperature

6 6 Scence and Technology of Nuclear Installatons Table 3: Expermental results of SQUAT tests. SQUAT test Pressure (bar) Target temperature ( C) Burstng tme measured (s) Breakng elongaton (%) Stran rate (%/s) > Temperature ( C) Tme (s) Tme (s) SQUAT10 SQUAT09 Fgure 7: SQUAT09 and SQUAT10 temperatures operatng condtons Temperature ( C) P = 170 bars P=70bars Fgure 9: Burstng tme of the tests accordng to the target temperature. Fgure 9 shows the evoluton of the burstng tme accordng to the target temperature for a gven pressure. In the semlog space, the burstng tme decreases lnearly wth the ncrease of the temperature. 4. Results and Dscusson Fgure 8: Vew of the tube after the SQUAT 3 test. and pressure) s manly due to the dfferences on the temperature values obtaned between these 2 tests (the operatng condtons could be not exactly the same, see Fgure 7). On the bass of these 2 tests, we can clam that at least there s an uncertanty of ±11s on the measured burstng tme for a gven target temperature. Fgure 8 shows the sample number 3 after burstng. For every SQUAT experment, Table 4 gves rupture tmes obtaned expermentally and from calculaton wth MEC- TUB code. The comparson shows a good agreement between calculatons and experments. Ths good agreement s probably due to the fact that the measured temperature tme seres are mposed as nput temperature data to the code. In order to estmate the nfluence of the uncertantes of measurement n these computaton, the calculatons (shown n Table 3)are performed agan,by usng the lower and the upperboundsoftherangeofthesquatmeasurements (pressure ±0.5%/temperature ±0.5%). Consderng that the dscrepances on the computed burstng tme nduced by

7 Scence and Technology of Nuclear Installatons 7 SQUAT test Table 4: Comparson of rupture tme of the 9% Cr wth the expermental measures SQUAT. Target pressure (bar) Target temperature ( C) Burstng tme measured (s) Burstng tme calculated (s) MECTUB v2.0 Relatve error (%) >2150 > , Table 5: Sensblty calculatons on the SQUAT tests pressure and the temperature. SQUAT test Nomnal P, T T + 0.5% T 0.5% P + 0.5% P 0.5% No rupture No rupture the measurement uncertanty could be estmated. Table 5 gves results of these computatons. Effect of pressure varaton(±0.5%) on the rupture tme s neglgble (0.5 s), except for SQUAT4 test for whch the rupture tme s decreased n 8 seconds for pressure ncrease of 0.5%. The uncertanty of the temperature measurements (±0.5%) shows no or few varatons of rupture tmes for 6 tests over 9 (2 seconds at maxmum). The decrease of SQUAT8 tme to burstng s more mportant when the upperboundaryoftemperaturesappled( 8seconds).The SQUAT4 calculaton gves sgnfcant dfferences, as well as SQUAT3 for whch the crtera of rupture are not any more affected. Inthecodethechangeofphasestakenntoaccountby the changes n the materal mechancal propertes. Norton s lawcoeffcents(a and n, gvenntable 2) are determned by the use of some tensle curves [6]. The results of the tests SQUAT3 and SQUAT4 show that mechancal propertes mplemented nto the code are not accurately ftted for a temperature of 950 C. Our mechancal model suffers from a lack of data n ths temperature range. Except for SQUAT10 test, t s notced that rupture tme vary n a logcal way when the lower boundares are appled: a decrease n the pressure or the temperature tends to delay theburstng.theoppostecomestrueforthepressure:an ncrease tends to reduce the tme to break. Furthermore, thetmetobreaktendstodecreaseforanncrease(0.5%)of the temperature. Concernng SQUAT10 case, the computed burstng tme dfferences reman lower than 0.6%. 5. Conclusons The MECTUB code has been developed n order to model the thermomechancal behavour of pressurzed tubes under overheatng load. Ths code has been set up and valdated usng experments performed on the alloy 800 of the SUPER- PHENIX helcal tubes SGs. A new test bench was set up and qualfed to burst heated tubes. The tme to burst was successfully detected usng the nternal pressure measurements. The results obtaned wth ths test bench hghlght a logarthmc trend n the decrease of the burstng tme versus the ncrease of the overheatng temperature for a gven nternal pressure. The expermental studes shown n ths paper allowed us to adapt the mechancal model and to qualfy t for Modfed 9Cr-1Mo materal. Mechancal modellng takes nto account the elastc, plastc, and creep effects up to hgh temperature (1200 C). The creep law has been reduced to a smpler Norton s law. On the bass of burstng tests on the Modfed 9Cr- 1Mo steel, t appears that the MECTUB code s able to be

8 8 Scence and Technology of Nuclear Installatons conservatve n the estmate of the rupture tme. Then t could beusedforsafetyanalyssofsgofsfrs. Nomenclature MECTUB: Modélsaton d EClatement de Tubes (model of tubes burstng) PFR: Prototype Fast Reactor SFR: Sodum-Cooled Fast Reactor SG: Steam Generator SGU: Steam Generator Unt SQUAT: Secton of Qualfcaton of the Accdental codes for Tubes heat exchangers SWR: Sodum-Water Reacton THETRA: THErmal TRAnsfer A, n: Norton s law coeffcents E: Young smodulus σ: Stress ε: Stran T: Temperature el: Elastcty pl: Plastcty. Conflct of Interests The authors declare that there s no conflct of nterests regardng the publcaton of ths paper. Acknowledgment The authors would lke to express ther thanks to EDF and AREVA for ther fnancal support. References [1] A. M. Judd and R. Curre, The under-sodum leak n PFR superheater 2, February 1987, Nuclear Technology, vol. 31, no. 3, pp , [2] F. Baqué, A thermomechancal model for overheatng studes of LMFBR steam generator tubes durng a sodum/water reacton, n Proceedngs of the IAEA Specalsts Meetng on Steam Generator Falure and Falure Propagaton Experence, Ax-en- Provence, France, September [3] F. Baqué, P. Martn, P. Agostn, and L. Lorenzell, Thermal characterzaton of sodum-water reacton: the THETRA program, n Proceedngs of the Internatonal BNES Conference, Paper 590, pp , Brtsh Nuclear Energy Socety, Guernsey, UK, May [4] RCC-MR, Règles de concepton et de constructon des matérels mécanques des îlots nucléares RNR. [5] G. Roux, Prévson des contrantes résduelles ndutes par le soudage TIG dun acer martenstque (X10CrMoVNb9-1) [Ph.D. thess], Perre et Mare Cure Unversty, Pars, France, [6] A.Bougault,C.Jans,andJ.C.Brachet, Expermentaldescrpton of the mechancal behavor of 9Cr up to 1200 C to antcpate the behavor of materal durng weldng and manufacturng of thck plates or accdental condtons, Meetng on weldablty of modfed 9Cr1Mo, CEA unpublshed data, [7] F. H. Norton, Creep of Steel at Hgh Temperatures, Mc Graw-Hll, 1929.

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