Safety Analysis of the Reactor Pressure Vessel of NHR-200

Transcription

1 TECHNISCHE MECHANIK, Band 1s. Heft 4, (1998), Manuskripteingang. 4 März X998 Safety Anaysis of the Reactor Pressure Vesse of NHR-2 Xi-Qiao Feng, Shu-Yan He The safety features of the reactor pressure vesse (RPV) of the 2MW Nucear Heating Reactor (NHR-2), which has been deveoped by the Institute of Nucear Energy Technoogy of Tsinghua University of China, are investigated in this paper. The stress distribution, fatigue crack propagation and eak-before-break (LBB) of the RPV are anayzed. In comparison with RPVs of pressurized water reactors (PWRs) or boiing water reactors (BWRs), the stress eve and the fatigue crack growth rate ofthe RPV of NHR 2 are very ow. It is concuded from an LBB anaysis that postuated cracks wi not fracture in an unstabe fashion before they are detected. These features are very beneficia for the inherent and passive safety of the reactor. 1 Introduction In order to mitigate the probems of energy shortage, environmenta poution and overburdened transportation system, the research and deveopment of nucear district heating reactors (NHR) has been attracting much attention of scientists. During the past decade, a commercia size NHR with a therma output of 2MW (NHR-2) has been deveoped by the Institute of Nucear Energy Technoogy (INET) of Tsinghua University in China. Such an NHR-2 demonstration pant wi be buit in Daqing in northeast China. In the design of NHR-2, some specia considerations reated to safety features are reflected. A number of experimenta and theoretica anayses with the aid of numerica computation were carried out to gain or demonstrate the safety features of NHR-2. The NHR deveoped by INET is a vesse type, ight water reactor with an integrated arrangement, natura circuation, sef-pressurized performance and dua vesse structure. Due to its important roe in NHRQOO, the safety features of the reactor pressure vesse (RPV) were examined stricty. In this paper, some probems of deformation, fatigue and fracture, which are crucia for the characteristic features of the RPV, are anayzed, incuding stress distribution, fatigue crack propagation and eak-before break (LBB) behavior. The reported resuts may be usefu for the research and design of other nucear reactors. For carity, the RPV of NHR-2 is compared with that of Bibis B, another typica reactor. 2 Structure and Materias of the RPV The NHR-2 adopts an integrated arrangement of the primary oop components and a natura circuation of the primary cooant. Its primary heat exchangers are arranged on the periphery in the upper part of the RPV, and its core at the bottom. A containment vesse fits tighty around the RPV so that the core wi not become uncovered under any postuated eakage in the reactor cooant pressure boundary. As one of the most important components of NHR-2, the RPV has a sma wa thickness and a big inner diameter, as shown in Figure 1. It consists of the cyindrica she and a cosure head, which is connected to the she with 84 main bots of M 8 >< 4. The main fange is seaed with 2 metaic O-shaped rings. The inner surface of the vesse wa is a ayer of stainess stee cadding, which prevents the RPV from corrosion. The main design parameters of the RPV of NHR-2 are shown in Tabe 1. Some of these aspects concerning its safety characteristics are reviewed in what foows. By comparing with PWRs and BWRs, it is easiy seen that in some important aspects the RPV of NHR-2 is quite different from those of PWRs or BWRs. The RPV considered is fabricated with two carbon stees, SA516-7 and SA58-1a due to its ow operating parameters. These two materias are with ow strength, high ductiity and high toughness. Some of their basic mechanica properties are isted in Tabe 2, together with those of the materias used for the RPVs in PWRs and BWRs. During the whoe service period, the neutron irradiation damage to the materias of the RPV of NHR 2 coud be negigibe because of the very ow neutron flux (Tabe 1). The materias wi aways keep good toughness in a ife time of the reactor. 277

2 I The RPV of NHR-2 has a wide margin of safety to ensure its exceent performance. Its wa thickness of different parts is primariy determined based On the requirements of deformation, stiffness, diameter of main bots and manufacturing. The Stress distributions in the she and in the cosure head are cacuated by the finite eement program, NASTRAN. The numerous figures and tabes of stress distributions are omitted here. It was proved that the stress eve in the vesse wa is quite ow. The maxima equivaent stress is ower than 1 MPa. a532 Ii [W F. J 9. i 7 I O ä ~ a -F 12+s - Q O 3 ä ao+e 7o+s.1 I t, 69'. Figure 1. The RPV of NHR-2 Inner diameter (mm) 482 Wa thickness (mm) 65 Tota height (mm) 135 Tota weight (Mg) 19 Materia SA516-7 (pate) and SA58- a (forging) Cadding materia SA39-L and SA38 L Cadding thickness (mm) 6 Maxima neutron fux ( n/cmz) < 1 x 116 Design pressure (MPa) 3.1 Design temperature ( C) 25 Operating pressure (MPa) 2.5 Operating temperature ( C) 213 Tabe 1. Design Parameters of the RPV of NHR-2 Reactor Materia of the RPV ' y (MP3) O'b (MP3) y /' b SA516-7 NHR 2 SA58_1a SA58-3 PWR and BWR SA533_ Tabe 2. Materias of RPVs 278

3 The ow design parameters ead to the sma wa thickness of the RPV of NHR 2. According to the fatigue theory of surface cracks, defects tend to adopt preferred shapes as they propagate through the wa of a vesse or a pipe. Due to the arge diameter of the RPV discussed here, the buging effect on surface crack growth can be negected, A surface crack tends towards an equiibrium aspect ratio of crack depth b to haf ength a,.7 Sb/a S 9 provided that its initia aspect ratio is not too sma (Gichrist, et a., 1992; Feng and He, 1997). This means that the ength of a crack at through thickness is about 2.2~3. times the wa thickness. Therefore, it foows that when a surface crack penetrates through the thickness of the vesse its size wi be sti very sma, and that the wa-through crack wi be found before it reaches a size big enough to danger the safety of the RPV. In other words, the size of a wa-through crack at penetration is bigger for a thicker vesse. Furthermore, it wi be shown in the coming section that the possibiity of penetration of a postuated surface crack is very ow. In summary, the high toughness, the ow stress eve and the sma wa thickness are very beneficia to the safety properties of the RPV of NHR ZOO. 3 Anaysis of Fatigue Crack Growth It foows from the foregoing anaysis that the size of a wa-through crack at penetration from a postuated surface flaw in the wa usuay increases with the increase in the thickness of the vesse wa. It is aso we known that the fatigue crack growth rate (FCGR) under varying oads increases with the increase in crack sizcs. Because the wa thickness of the RPV in NHR-2 is ony about 1/3 of that in PWRs with the same output power, the sizes of possibe flaws at penetration in the wa of RPV of NHR-2 wi be much smaer than those in PWRs. In this artice, Bibis B is taken as a typica exampe of PWRs for the comparison the FCGRs of NHR-2 and PWRs. Some main parameters of Bibis B are given in Tabe 3 (Provan and Weein, 1987). Wa thickness (mm) 25 Inner diameter (mm) 5, Materia Operating pressure (MPa) 22MnMoNi Operating temperature (o C) 292.5~329.6 Design pressure (MPa) 17.5 Design temperature (o C) 35 Tabe 3. Design Parameters of the RPV of Bibis B (Provan and Weein, 1987) The FCGR of a mode-i crack can be cacuated by the famiiar Paris formua da dn z C( AK I) " (1) where n and C are materia constants, a is the depth of the surface crack, N is the number of oading cyces, AKI = Kmax KIM-n, KImax and Kmm are the maxima and the minima vaues of mode-i stress intensity factor during a oad cyce, respectivey. For some carbon stees, the exponentia and coefficient, n and CO, can be determined approximatey from the FCGR curves in Figure A-43-1 in Ref. (ASME, 1983a). The stress intensity factor KI for a crack in the wa of a pressure vesse can be cacuated by (ASME, 1983a) KI 2(amMm+'be) Ira/Q (2) where am and ab are the membrane stress and the bcnding stress norma to the crack pane, respectivey, Q is the modification factor depending upon the defect shape, M m and M b are modification coefficients of membrane stress and bending stress respectivey. For a surface crack, the parameters Q, M m and Mb can be found in Figs. A 43, A-43-3, A-43-5 in Ref. (ASME, 1983a), respectivey. Athough the possibe size of a postuated crack at penetration in Bibis B is arger than those in NHR-ZOO, for easy comparison, assume that there exists a semi eiptic, circumferentia surface crack of the same size and shape in both the interna was of RPVs of NHR 2 and of Bibis B. Such an assumption is conservative for 279

4 the RPV of NHR-2. This case of cracks is designated as case 1 in Tabe 4. The surface cracks are assumed to be 1 mm deep and 5 mm ong. Three fluctuation magnitudes of cycic pressure, i.e., from to the operating pressure P, from 5 P to P, and from.95 P to 1.513, are considered in our anaysis. The stress intensity factors KI and the FCGRs da/dn for the RPVs of NHR 2 and of Bibis B are cacuated and given in Tabe 4. Under the three pressure fluctuations, the FCGRs of the RPV of Bibis B are about 6, 31 and 43 times of those of NHR-ZOO, respectivey. For further comparison, cracks with different sizes in the RPVs of NHR-2 and of Bibis B are aso considered. This case of cracks is referred to as case 2 in Tabe 4. The crack depth and ength are taken as 25 mm and 15 mm in the NHR ZOO, and 62.5 mm and 375 mm in Bibis B, respectivey. This is based on the correation between minimum crack size and wa thickness in vesses and pipes (ASME, 1983b). The FCGRs of these two cracks under the pressure fluctuation from.9 P to 1.1 Po are given in Tabe 4. In this case, da/dn of Bibis B is more than 1 times arger than that of NHR ZOO. It foows from the above anaysis that the FCGRs of the RPV in NHR-2OO are much ower than those in PWRs or BWRs under a conditions. Hence, it is expected that the RPV of NHR-2 has an exceent characteristic safety to guarantee its safe operation in a much onger period. Crack Reactor case 1 Pressure ' m al K1 AKI da/dn fluctuation (MP8) (MP3) (Mpa fr; ) (MPax/m ) (mm/cyce) ><1_ x 1 3 NHR-ZOO P Bibis B P 15g NHR-2 BbS B P )O P ' _ >< x 1 _4.95 PO NHR'2 1.5 P _IO _ B bhs B.95 P 1.5 PO.9 P '11 NHR ZOO ' X 1 A _ 8 th B.9 P '34 X 1 1'65 2'92 X 1 _8 1'26 X 1 _s _3 Tabe 4. Fatigue Crack Propagation Rate of RPVs 4 Leak-before-Break Anaysis The eak before-break (LBB) design for pressure vesses, high pressure pipes and tanks has recenty been attracting much attention from the standpoint of improved safety and economy. The LBB design aims to ensure that postuated cracks wi cause a detectabe eakage rate before they propagate in an unstabe fashion, even in emergencies. An appication of the LBB concept to protect the RPV of NHR-2 from a postuated break has been reviewed in INET to achieve the rationaization of structura design in the context of design improvements. Up to now, the LBB theory and its appication in reactor pressure vesses and pipes have been investigated in many countries. However, a unified criterion and methodoogy for LBB design have not been achieved. In our study, the LBB program deveoped by U. S. Nucear Reguatory Commission (USNRC, 1984, 1988) and one simpified program (Feng and He, 1998) based on inear eastic fracture mechanics and pasticity theory have been adopted. Aso, a detaied anaysis based on eastic pastic fracture mechanics has been performed with 28

5 the aid of a computer program deveoped by INET. The resuts from the theoretica and numerica methods show that the RPV of NHR ZOO meets the LBB conditions in a wide margin. Ony the main procedure of the second method, which is deveoped on the basis of the first one (USNRC, 1984, 1988), is described in this section. The detai LBB anaysis method based on a J integra method and some reevant experiments wi be pubished in another paper. 4.1 Vaidity of LBB Design Before the LBB concept is introduced into the safety anaysis of a pressure vesse or pipe, its vaidity must be assured first. Materia seection, design, fabrication, inspection and detection shoud be performed in accordance with the appicabe reguations, codes and standards. The LBB methodoogy is not usuay appied to components that have a history or possibiity of excessive or unusua oads or degradation mechanisms. The excessive or unusua oads or degradation mechanisms of concern mainy incude water hammer, corrosion, erosion, creep, fatigue and britte fracture. In the LBB anaysis of the RPV of NHR-ZOO, it is concuded from our review that a these potentia faiure mechanisms can be avoided by proper design, fabrication, instaation and operating condition. Therefore, it is appropriate to appy the LBB anaysis in the structura design and safety assessment of the RPV discussed here. Considering the stress distributions and the mechanica properties of materias, and accounting for the effects of weds, some critica positions for LBB evauation are determined. A these positions have to be demonstrated to meet the LBB criterion. In what foows, for conciseness, a postuated circumferentia or ongitudina crack in the RPV is assumed to iustrate the basic procedure adopted for the evauation of its LBB behavior. 4.2 Cacuation of Leakage Rate A cacuation of eakage rate is essentia for the determination of the crack ength, 2aeak, which is defined as the minima crack ength detectabe for the eakage monitoring system of the reactor primary cooant. It is we accepted that the eakage rate of gaon/minute in a reactor primary pressure boundary shoud be detected within one hour by the monitoring system. The margin on eakage detection is often chosen to be 1. Therefore, the eakage rate of 1 gaon/minute is used to determine the detectabe crack ength Zaeak. Introducing the damage of materias into the anaysis of fatigue crack growth, Feng and He (1997) presented a theoretica method based on continuum damage mechanics to simuate crack shape deveopment. According to their resuts, it shoud be noticed that the crack ength that wi be used in the fracture mechanics evauation in the seque shoud aso be arger than 3~4 times of wa thickness, depending upon the initia aspect ratio of the surface crack and the oading conditions. It is important but difficut to carify the reation of eakage rate with respect to interna temperature and pressure, geometric dimension of the structure, crack shape, crack surface roughness and varying bending moment. Up to now, many theoretica or empirica modes have been deveoped to sove the probem of cacuating the eakage rate from a crack (Bahandari, 1993; Feng et a., 1998; Moody, 1966; Swarmy, 1986). Under different conditions of temperature, pressure, and properties of the iquid, different methods can be adopted in order to have a high accuracy. After some numerica comparison, the present authors adopt a twophase critica flow mode (Xu et a., 1995) to obtain the eakage rate for a through-wa crack in the RPV of NHR-ZOO. This two-phase critica flow is rather simpe to be appied and is accurate enough for our LBB anaysis, athough its shortcoming and imitations are aso noticed. For the considered probems, the eakage rate through a crack, m, can be cacuated by (Xu et a., 1995) m=ga=ax.6 2pp( I]) 77=psa,(T)/p (3) where G is the eakage rate per unit flow area, A is the crack opening area, p and T are respectivey the pressure and temperature in the vesse, p is the density of iquid, 77 is the critica pressure ratio, psm is the saturated pressure at temperature T. psat and r] can be obtained from tabes of physica properties of water in many textbooks on fluids. 281

6 For comparison, the Moody s two phase fow mode (Moody, 1966) is aso used to cacuate the eakage rate, The resuts of many exampes from the two methods are in a good accordance under the operating condition of the RPV of NHR Cacuation of Stresses and Stress Intensity Factors In the LBB anaysis, the most dangerous oading state to which the RPV may be exposed shoud be considered. Therefore, it is necessary to specify the types and magnitudes of a possibe oads, which incude the static forces and moments due to norma operation and those associated with the safe shutdown earthquake. Then, the tota force and moment can be obtained by adding a the components according to the foowing equations Ftota =[FDWI+ FT + FPi+ FSSEi+Fother (Mi)tota1= (Mi)DW + (Mi)T + (Mi)Pi+ (Mi)SSE + (Mi)otheri /2 Mtota =[(M1)tota +(A42)tota +(M3)tota] where F denotes the axia force, M the moment. The subscripts i (i=1,2,3) denote the three components of moment, the subscripts,,tota,,,dw, p, T, SSE and,,other denote the tota oads and its components due to dead-weight, interna pressure, temperature, safe shutdown earthquake and other reasons, respectivey. To obtain the stress distribution in an eastic pastic structure, a compete three-dimensiona constitutive reation of the materia and an anaysis of eastic-pastic mechanics are often needed. As aforementioned, the finite eement program package, NASTRAN, is adopted in our anaysis. For pressure pipes and vesses in LBB anaysis, wide margins are required to ensure their safety and stabiity. Hence, the mechanica response of the pipes and vesses is often eastic. Under such cases, ony an eastic anaysis is necessary, and the constitutive reation and the stress computation become much simper. Longitudina and circumferentia through-wa cracks are two typica cases in LBB anaysis of pressure pipes or vesses. Herein, the stress intensity factor is taken as the contro parameter of unstabe crack growth. Assume that a circumferentia or ongitudina crack with haf ength a exists in a vesse with average radius R and thickness 1. If the vesse is subjected to axia force N, bending moment M and interna pressure p, the mode I stress intensity factor can be expressed as K; =ZK;fl=ZMafiK;O ß (a=1,2,,6:1,2,3) (5) ß where K113 denote the stress intensity factors of a crack with the same size in a pate subjected to the same oads, Maß modification coefficients. The subscripts (2 =1 and 2 correspond to the circumferentia and ongitudina crack cases, and 8:1, 2 and 3 correspond to the oading cases of axia tension, bending and interna pressure, respectivey. For exampe, M12 denotes the modification coefficient of stress intensity factor of a circumferentia crack under bending, and K11 the stress intensity factor in a pate under tension. Some other factors (for exampe, the eipticity and ovaization of pipes, weds and transformation geometry) shoud aso be accounted for in the cacuation of stresses and stress intensity factors (Feng et a., 1998). These factors may exert an evident infuence on the magnitudes of stresses and stress intensity factors. 4.4 Crack Instabiity Anaysis To demonstrate the LBB behavior of a component, both the goba and the oca stabiity evauations are required. A simpe effective method of goba pastic instabiity anaysis is the pastic instabiity method, based on traditiona pastic imit oad concepts, but accounting for strain-hardening effects and taking into account the presence of a crack (Swarmy, 1986). A widey adopted method of oca instabiity anaysis, which is aso used in the LBB anaysis of NHR-2, is based on the concept of J integra in eastic pastic fracture mechanics. The corresponding crack instabiity criterion can be found in many textbooks on fracture 282

7 mechanics. Due to the compexity in the cacuation ofj integra and in the measurement of J resistance curve, however, some methods based on inear eastic fracture mechanics are Often adopted to make an estimation of LBB characteristics of a component. According to the Reguations of Chinese Vesse Defect Assessment (CVDA, 1984), the concept of stress intensity factor can be used to review the stabiity of crack growth in pressure vesses and pipes provided that the equivaent tensie stress is ower than the yied stress of materia. The ow stresses in the RPV of NHR 2OO meet this condition. Then, it is thought that unstabe britte fracture wi not occur in a crack provided that its stress intensity factor satisfies the inequaity K <.6 Kg (6) where KcI is the critica vaue of stress intensity factor of the materia. For comparison, the R6 method is aso adopted, in which the interaction between britte fracture and pastic coapse is accounted for. A non-dimensiona stress intensity factor Kr and a non dimensiona pastic oad factor Lr are defined by _ K I P K _ L = - (7) K! r PL respectivey, where P is the appied oad, and PL the pastic coapse oad. If an assessment point (Kr, Lr) for a component ies inside the curve of the faiure assessment diagram, the crack wi not ead to faiure under the appied oads. ' 4.5 Cacuation of Crack Opening Area The crack opening area of a component is another important parameter in LBB anaysis. Its importance incudes two aspects. First, the eakage rate of a through-wa crack is directy reated to its crack opening area. The eakage can be detected more quicky for a arger crack opening area. Second, the jet force of cooant acting on the vesse or pipe is aso reated to the crack opening area. The crack opening area can be cacuated from severa theoretica approaches on the basis of eastic r eastic-pastic fracture mechanics (Bahandari, 1993; Feng et a., 1998). Here, the crack opening area is evauated approximatey by A = 21:4: o.16 12)/E (8) for a postuated through-wa ongitudina crack or by A = 21ra2(+.117/i.2)1/2/E (9) for a postuated through-wa circumferentia crack (Wiithrich, 1983). In equations (8) and (9), I =12(1 v2)a4/(r2t2) (1) E is Young s moduus, v is Poisson s ratio, ' is the tensie stress norma to the crack surfaces, a is the hafength of the crack, and R and tare the average radius and the thickness of the vesse, respectivey. 4.6 Resuts In the LBB evauation of the RPV of NHR ZOO, some used parameters are as foows: K} 222 MPam/z, '), 2262 MPa, ab =483 MPa, [123.] MPa, T=213 C, Pat =2.31 MPa, R= mm, t=65 mm, and p=848.7 Kg/m3, E: 2.1x 15 MPa and V=O.28. Among them, the materia parameters are conservativey obtained from our experiments or reated handbooks. The resuts of the LBB anaysis of the RPV of NHR-2 are given in Tabe 5. In this tabe, A and aeak correspond to the eakage rate of 1 gaon/minute, whie KI, Kr and Lr correspond to the crack with the haf ength 2aeak. Apparenty, the RPV has the LBB property, S 283

8 and hence the possibiity of britte faiure can be excuded from it. This stems mainy from its sma wa thickness and ow stress intensity. In the authors Opinion, it is often difficut for the RPVs of PWRs or BWRs to meet the LBB conditions due to their big wa thickness and high stress eve. crack A (m2) KI (MPamm) Kr Lr Longitudina crack 26 X1'5 aeak Circumferentia crack 2.6 X Tabe 5. Resuts of LBB Anaysis of the RPV of NHR-2. 5 Concusions Some safety features of the RPV of NHR-ZOO designed by INET of China are anayzed. Theoretica anaysis and numerica computation show that both the stress eve and the FCGR in the RPV are very ow, and that it can operate safey during the whoe ife of the reactor. The LBB evauation demonstrates that postuated cracks in the RPV wi cause a detectabe eakage rate before they propagate in an unstabe fashion, even in emergencies. Therefore, the possibiity of britte fracture can be excuded from the RPV. It is expected that the RPV of NHR-ZOO have a much ower probabiity of faiure than those of PWRs and BWRs. Acknowedgment This project is supported by the Nationa High Technoogy Deveopment Program of China. Literature 1. ASME: ASME Standards on Boier and Pressure Vesses, Section XI-IWA, App. A, (1983a). 2. ASME: ASME Standards on Boier and Pressure Vesses, Section III-, App. G, (1983b). 3. Bahandari, S.; Leroux, J. C.: Evauation of crack opening times and eakage areas for ongitudina cracks in a pressure pipe, Nuc. Eng. Design, 142, (1993), CVDA: Reguations of Chinese Vesse Defect Assessment, Beijing, (1984). Feng, X. Q.; He, S. Y.: A continuum damage mechanics method for fatigue grth of surface cracks, J. Tsinghua University, 37, (1997), Feng, X. Q.; He, S. Y.: A simpified LBB anaysis method for pressured pipes, Nuc. Power Eng. (in Chinese), 19, (1998), Feng, X. Q.; He, S. Y.; Dong, D.: LBB anaysis of pressurized pipes and vesses in nucear reactors, Advances in Mechanics (in Chinese), 28, (1998), Gichrist, M. D.; Chipao, M. I.; Smith, R. A.: Shape deveopment of surface defects in tension fatigued finite thickness pates, Int. J. Pres. Ves. Piping, 49, (1992), Moody, F. J.: Maximum two-phase vesse bowdown from pipes, J. Heat Transfer, 88, (1966), Provan, J. W.; Weein, R.: Probabiistic Fracture Mechanics and Reiabiity, Nijhoff, Dordrecht, (1987). Swarmy, S. A.: Appication of the Leak-Before-Break Approach to Westinghouse PWR Piping, EPRI Report NP-4971, Pao Ato, (1986). USNRC: NUREG-161, Vo. 3, Evauation of potentia for pipe breaks, Report of the US Nucear Reguatory Commission Piping Review Committee, Washington, (1984). USNRC: Reguatory Guide 1.45, Reactor Cooant Pressure Boundary Leakage Detection Systems, 14. Wüthrich, C.: Crack opening areas in pressure vesses and pipes, Eng. Fract. Mech., 18, (1983), Xu, J. L.; Chen T. K.; Yang, L. W.: Two-phase critica discharge of initiay saturated or subcooed water 12. Washington, (1988) flowing in sharp edged tubes at high temperatures, J. Therma Science, 4, (1995), Addresses: Dr. Xi-Qiao Feng, Technische Universität Darmstadt, InStitt für MCChanik», HochSChUStr- 1' D64289 DarmStad; PrOfCSSOT ShU-Yan He, INET, Tsinghua University, Beijing 184, P. R. China 284