d. araneo, g. agresta, f. d’auria grnspg -university of ... · grnspg -university of pisa, pisa,...

The 7-th International Conference “Safety Assurance of NPP with VVER” OKB “GIDROPRESS”, Podolsk, Russia

17-20 May, 2011

FRACTURE MECHANICS ANALYSIS FOR VVER1000 REACTOR PRESSURE VESSEL

D. Araneo, G. Agresta, F. D’Auria

GRNSPG -University of Pisa, Pisa, Italy This document deals with a research activity aimed at calculating the safety margin for brittle

crack propagation in the RPV (Reactor Pressure Vessel) of a VVER-1000 during a MSLB (Main Steam Line Break) transient. This problem is known as PTS (Pressurized Thermal Shock) and deserves a relevant role in the safety of a NPP (Nuclear Power Plant) because the RPV is the main component that limits the plant operational life due to the change of the mechanical property of the carbon steel material. High neutron flux on the welds close to the core region, thermal aging, etc., have the effect to increase the RPV material embrittlement and to decrease the safety margin for the crack propagation in case of transients that induce fast cooling rate on the primary side.

The approach to the analysis of such problem historically has been based on the introduction of conservative margins in all the steps of the analysis for the evaluation of the variables of interest: fluid temperature in the downcomer region and primary pressure. Nowadays, the scientific community is trying to change the approach to the PTS analysis toward a “Best Estimate” scheme with the aim to remove the excess of conservatism in each step of the analysis coming from the limited knowledge of the phenomena in the eighties when these kinds of problems have been considered in the safety analysis.

A methodology for PTS analysis has been developed in the years at University of Pisa based on a chain of specialized codes. This methodology starts with a system thermal-hydraulic calculation for evaluating the global behavior of the plant and to fix the boundary conditions for the CFD (Computation Fluid Dynamics) code able to simulate the mixing phenomena occurring at small scale in the downcomer region. The result of this step gives the thermal profile inside the RPV wall and the pressure as input for the structural mechanics analysis with a FE (Finite Element) code. The last step is represented by the Fracture Mechanics analysis for the calculation of the stress intensity factor at crack tip (KI) and the comparison with the critical stress intensity factor (KIc) for the quantifying the safety margin.

Keywords: PTS, CFD, Thermalhydraulics, safety, Fracture Mechanics.


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INTRODUCTION The present work deals with a Pressurized Thermal Shock (PTS) analysis in a VVER-1000

performed in a Main Steam Line Break (MSLB) scenario. The analysis has been conducted following a BE approach in the selection of the boundary conditions for the transient, and in all the steps of the analysis for the calculation of the stress intensity factor at crack tip.

The integrity of the reactor pressure vessel has to be maintained throughout the plant life since there are no feasible provisions which would mitigate a catastrophic vessel failure, therefore integrity is ensured by a margin between its load bearing capacity, given by vessel design and material properties and the acting loads, which could occur during the plant operation.

The degradation of material properties by neutron irradiation, in concurrence with fatigue, thermal ageing and other mechanisms, reduce the resistance of the vessel against brittle fracture.

The loads to be considered in the vessel integrity assessment are mainly related to plant states leading to a PTS events, characterized by rapid cool-down in the primary coolant system usually with high level of primary system pressure.

Historically, the PTS analysis for a NPP has been conducted following the approach established in the early 1980s with conservative treatment of several key parameters and model used. The most prominent of these conservatisms include the following factors:

• highly simplified treatment of plant transients (very coarse grouping of many operational sequences (on the order of 105) into very few groups (≈10), necessitated by limitations in the computational resources needed to perform multiple thermal-hydraulic calculations);

• characterization of fracture toughness using RTNDT, which has an intentional conservative bias;

• use of a flaw distribution that places all flaws on the inner surface of the RPV, and, in general, contains larger flaws than those usually detected in service inspection;

• a modeling approach that treated the RPV as entirely made of the most brittled of its constituent materials (welds, plates, or forgings);

These factors indicate the high likelihood that the current 10 CFR 50.61 PTS screening limits are unnecessarily conservative. Nowadays, the NRC staff believed that reexamining the technical basis for these screening limits, based on a modern understanding of all the factors that influence PTS, would most likely provide strong justification for substantially relaxing these limits (see ref.[1]).

Following this new trend toward a BE approach in the treatment of the parameters involved in the PTS analysis, IAEA published in the 2010 a TECDOC in ref. [2] that takes into account the new USNRC approach summarized in ref.[1]. The general suggestions resulting from the IAEA is that the selection of PTS transients should be performed in a comprehensive way starting from the accident scenarios identified in the safety analysis report. The main goal is to select initiating events which by themselves are PTS events or along with other consequences can lead to a PTS event. The sequences to be considered in the PTS analysis are frequently unit specific and all relevant and meaningful plant features should be taken into account.

The selection of the transients for deterministic analysis can be based on previous analyses and engineering judgment using the design basis accident analysis approach, combined with operational experience. It is important to consider several factors determining thermal and mechanical loading mechanisms in the down-comer during the overcooling events. These factors are:

• Final temperature in the down-comer; • Temperature decrease rate; • Non-uniform cooling of the RPV, characterized by cold plumes and their interaction and by the

non-uniformity of the coolant-to-wall heat transfer coefficient in the down-comer;


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• Level of primary pressure; • Width of cold plume; • Initial temperature in down-comer; • Stratification or stagnation of flow in cold leg. Nowadays the general trend followed in the PTS analysis is to move from a conservative approach

toward a BE approach in all the step of the analysis. This new trend has followed the development of always more sophisticated computer codes and several progresses in the understanding of the embrittled material behavior compared to the knowledge in the eighties. The benefit coming from this new approach is a larger safety margin for the operability of the RPV and a possible extension of the NPP operating life.


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UNIPI METHODOLOGY FOR PTS ANALYSIS University of Pisa developed a methodology summarized in ref. [1], concerning the use of a chain

of codes for the deterministic analysis of PTS scenarios; see ref. [2] and [3].

Thermal Hydraulic Transient

Thermal Hydraulic Analysis of the plant

Response

Multi Dimensional Study of Downcomer

Fluid Flow

Study of the Mechanical and Thermal Stress

Stress Intensity Factor(SIF)

Evaluation of the Possibility of Crack

Instable propagation

UN

IPIP

RO

POSA

L

Weight Function Model

Crack Model

NPP System Model

RPV Structural Model

RPV CFD Model

Material ToughnessModel

Material Toughness Curve

Material Neutron Sensitive Curve

RPV Model

AN

SYS

10C

FD

CFX

Rel

ap3D

PTS ProposalPTS ProposalW W ER -1000 G EN ER IC

P TS N OD AL IZAT ION SK ETC H1 /2

O V E RA L L SK E TC H( 1 o f 4 SG an d L O OP r epr ese nted )

XY

Z

1

2

MA

THC

AD

0

20

40

60

80

100

120

140

160

180

200

0 100 200 300 400 500 600 700 800

TEMPO [S]

[MPa

m0.

5] RTNDT=244°C

CRICCA ASSIALE

KI > KIC

3

4

Fig. 1: UNIPI Methodology for PTS Analysis

The methodology starts with the thermal hydraulic analysis of the Nuclear Power Plant (NPP)

using a System Thermal-Hydraulic (SYS TH) code such as Relap5, Cathare2, or equivalent, during a selected transient scenario. The goal of this step is to roughly calculate the cooling load induced on the internal RPV wall surface by the Emergency Core Coolant (ECC) injection or by the cooling plug following a (Main Steam Line Break) MSLB initiating event, to calculate the primary circuit pressure and to provide boundary conditions for the next step. If the transient evolves in single phase, a more detailed analysis of the mixing phenomena occurring in the down-comer region can be performed by mean a CFD code. The result of this step needed for the PTS analysis is the temperature distribution inside the down-comer. The thermal load to be applied to the Finite Element (FE) model for the stress analysis can be extrapolate from the Computational Fluid Dynamics (CFD) result considering the temperature profile at the interface down-comer model fluid RPV wall. This step is accomplished using suitable Matlab function developed for this purpose. The stresses due to mechanical load such self weight, pretension in bolts and internal pressure are also accounted in the Ansys FE calculation. In the last step of the analysis, the Stress Intensity Factor (SIF) KI is calculated by means the Weight Function method, once the stresses generated by the loads indentified before are known. The KI has to be compared with the critical SIF (KIc) of the material for the evaluation of the safety margin for the RPV operability. In the following paragraphs an example application to the methodology is provided.

In addition the comparison with the KI calculated with the J-integral method implemented in ANSYS FE code has been shown.


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TH ANALYSIS The PTS scenario selected is a MSLB in a VVER-1000 simulated by means of the RELAP5-

mod3.3 software code. The input deck nodalization (see Fig. 2) has been validated in the framework of the agreement between Institute Risk Research IRR, (Wien), and the University of Pisa: activity performed to investigate the peculiarities and or unexpected behavior of the Temelin VVER-1000 NPP during a MSLB transient, see ref.[18].

Fig. 2: VVER-1000 Nodalization sketch

The accident starts with the opening of the valve simulating the break on the steam line. The Scram

occurs in a few seconds and the stop signal of the main coolant pump and of the isolation of the Steam Generator (SG) follows immediately. The Primary side pressure increases and a pressurizer relief valve is taken into operation. Due to the heat exchange between primary and secondary side, the SG pressure increases too, and the atmospheric steam dump valves are taken into operation. After 30’ the 100 K/hr procedure starts and secondary side pressure starts to decrease. The emergency feed water in the intact SG is activated by the SG level signal. The fast depressurization of the SG improves the heat exchange between the primary and the secondary side preventing the power operated relief valve to open. After 40’ the primary side feed and bleeds procedure starts, and the primary side depressurizes up to the value of residual heat removal activation. Even if this transient has duration of about 4000 seconds, when the plant reaches stable conditions, for the purposes of the PTS analysis the phenomenological


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window of interest is restricted to the first 300 seconds because the cooling phase occurs inside this interval.

Fig. 3 shows the temperature and mass flow rate in the four Cold Legs (CL) calculated by RELAP5-mod3.3.

Fig. 3: Temperature and mass flow rate in cold legs at downcomer inlet


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CFD ANALYSIS Once the RELAP5-mod3.3 results are available is possible to set-up the boundary conditions for

the CFD analysis of the mixing phenomenon occurring at small scale in the downcomer region. The applicability of the CFD code is justified because the transient evolves in single phase. In this analysis a complete RPV VVER-1000 mesh has been developed using the APDL environment and imported into the CFX environment. The model is subdivided in two regions: a solid region representing the RPV structure, and a fluid region representing the downcomer flowing fluid. In fig. 4 the fluid region is represented in blue, emphasizing in yellow the CLs inlet and in red the downcomer outlet surfaces. The two regions have been modeled using respectively about one and four millions of elements.

Fig. 4: VVER-1000 RPV and downcomer CFD model

The CFD analysis has been set-up using the standard κ-ε turbulence model, the fluid streamline colored by temperature values at 100 sec are presented in fig. 5. The Conjugate Heat Transfer (CHT) model has been utilized to calculate the temperature distribution inside the RPV structure illustrated in fig. 6.

FLUID REGION

INLET CONDITION

OUTLET CONDITION


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Fig. 5: Streamline tubes at 100 sec colored by fluid temperature


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50 sec 90 sec 110 sec

150 sec 200 sec 300 sec Fig. 6: Temperature distribution into the RPV structure at different instants


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STRUCTURAL ANALYSIS The stress analysis has been performed within the ANSYS APDL environment using the same

structural mesh developed for the CFD analysis, see fig. 7. To perform the toughness assessment using the in the UNIPI methodology, the complete three dimensional geometry of the RPV has to be modeled because the Weight Function method adopted for the calculation of the KI requires the stress evaluated in the undamaged structure (see Fig. 7).

The calculation of the KI with the J-integral method requires that the crack is modeled inside the RPV. This approach has been done following the ANSYS FE code requirements for the mesh size and shape around the supposed cracks (see ref. [6]), see fig. 8. The two cracks have been modeled as semi-elliptical surface cracks with depth to thickness ratio of ¼ and depth to length ratio of ⅓. The RPV structure has been meshed using mainly hexahedral elements. A linear growth factor has been imposed to the elements through the thickness to calculate accurately the temperature and stress profile.

Fig. 7: ANSYS structural mesh model


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The node temperature calculated by CFX at various instant of the transient has been imported as body loads into ANSYS and several runs has been performed. The CFX temperature transfer in this case results more complicated because each structural node doesn't have a corresponding node with the CFX mesh used for the calculus of the temperature field. Suitable MATLAB® functions have been developed for this purpose performing for each ANSYS node a trimap interpolation using the temperature values at the corner of each CFX hexahedral element, see ref. [7]. Fig. 10 and fig. 11 show the equivalent Von Mises stresses due to the operating internal pressure of 16 MPa and the stresses near the two postulated flaws.

Fig. 9: ANSYS cracks mesh

definition and temperature transfer Fig. 8: ANSYS FE model cracks location


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Fig. 10: Equivalent Von Mises stresses due to the internal pressure (16 MPa)

Fig. 11: Circunferential and axial stresses due to internal pressure (16 MPa) near the cracks


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STRESS INTENSITY FACTOR EVALUATION J-Integral The Stress Intensity Factor (SIF) has been evaluated with the ANSYS built-in APDL macro

CINT. T theory introduced by ref. his macro is based on the J-integral [6] and [7]. J is defined as:

limΓ 0 Γε

Γ

• · is the stress-work density

• 12· is the and kinetic energy density

• is the density, are stresses and the strains

• and are displacements and displacement gradients

• are components of the unit normal vector to the J integral contour Γ Γ integrals are performed along contours surrounding the crack tip. Ref. [9] shows that for

small-scale yielding the stress energy release rate G is equal to the J and the SIF can be obtained by: 2

• for plane stress and 1 2 for plane strain

In the ANSYS calculations a plane strain condition has been assumed. Fig. 14 and fig. 15 illustrate the SIF due to thermal shock result at various time instant calculated with the J-Integral methodology respectively for the circumferential and axial crack.

Fig. 12: Thermal KI curves for the axial crack

The 7-th International Conference “Safety Assurance of NPP with VVER”

OKB “GIDROPRESS”, Podolsk, Russia 17-20 May, 2011

Fig. 13: Thermal KI curves for the circumferential crack

Fig. 14: Thermal KI results for the circumferential crack

Fig. 15: Thermal KI results fcrack

or the axial

Fig. 16: SIF due to RPV internal pressure (16 MPa) for the axial and the circumferential

postulated defect


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Weight Function The KI at the crack tip has been calculated by mean the weight function method developed by

Verfolomeyer and Hodulak (ref. [3] and [4]) on the basis of a bi-dimensional crack scheme. puted once the stresses on the crack border are known by mean a simply

integ

∫= dxaxHxKI0

),()(σ

Where

The KI is comration with the formula:

a

)(xσ is the stress distribution perpendicular to the crack surface in the un-cracked component and is the weight function for the geometry.

The weight function is considered independent from the stress distribution and can be obtained from a reference load case.

For heJ-Integral method have been supposmodel. In Fig. 17 the temperature at the crack ferential) has been plotted. It is important to note that the minimum temperature is not reached at the same time because the two cracks have different locations inside the RPV (see Fig. 8). Furthermore the cooling effect depends on the evolution of the mixing phenomena in the downcomer region calculated by CFX code.

),( axH

the application of this method two cracks of the same size of the previous analyzed with ted to be present in the same position in the RPV undamaged

tip for both cracks (Axial and Circum

245

250

255

260

265

270

275

50 100 150 200 250 300

Ti me [sec]

Tem

pera

ture

[°C

]

Tempera ture at Axia l c rac k tip

Tempera ture at Circumfere nti al cra ck tip

Fig. 17: Temperature at the cracks tip for the Axial and the Circumferential crack

The pressure and the thermal loads have been used for the calculation of the stresses inside the RPV wall to be integrated in the previous formula. The integral executed at different time with different stress profile along the crack length gives the KI (Axial and Circumferential) at the crack tip for this transient. Fig. 18 and Fig. 19 show directly the comparison between the total given by the two contributions, pressure and temperature variation, to the stress KI


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Fig. 18: KI total calculated with JINT and WF KI comparison for the Axial crack

Fig. 19: KI total calculated with JINT and WF KI comparison for the Circumferential crack

The results show that the WF is more conservative for the axial crack, while the J-Integral method more conservative with the circumferential crack. It should be noted that from one side the

calculation performed with the ANSYS subroutine needs additional validation because this model has been not extensively adopted for this kind of problems, while the WF method has been already

is


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adopted in the framework of international project (see ref. [5]). In addition the WF method results more conservative in case of Axial crack that are subject to more high circumferential stresses compared with the axial stresses. Anyway for the calculation of the KI it can be a good practice to perform the same calculation with different methods and to compare the results.

CONCLUSION This paper describes all the steps needed to calculate the KI for a during MSLB PTS scenario

in a VVER-1000 NPP. The methodology developed at University of Pisa based on a chain of specialized codes has been applied to the one circumferential and one axial crack. The results have been compared with the results obtained with the J-integral method implemented in the ANSYS code. The comparison has shown that the two methods calculate the KI with the same order of magnitude. WF is more conservative for the axial crack while J-integral is more conservative with the circumferential crack.

In this paper the approach to the PTS analysis has follow a best estimate approach in all the step of the analysis starting from the selection of the boundary conditions for the transients till the calculation of the fracture mechanics analysis. This is a new trend in such kind of analysis that historically has been based on a conservative approach in the selection of the parameters.


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REFERENCES

[1] M. EricksonKirk, M. Junge, W. Arcieri, B.R. Bass, R. Beaton, D. Bessette, T.H.J. Chang, T. Dickson, C.D. Fletcher, A. Kolaczkowski, S. Malik, T. Mintz, C. Pugh, F. Simonen, N.

tehead, P. Williams, R. S. Yin, NUREG-1806 Vol.1/Vol.2, “Technical Basis

[5] D’Auria, F., Galassi, G., Giannotti, W., “Temelin Wwer 1000 Mslb Transient Scoping Calculations”, Dipartimento Di Ingegneria Meccanica Nucleare e della Produzione DIMNP NT-507,Pisa, 2003.

[6] ANSYS® Academic Research, Release 12.0, Help System, Structural Analysis Guide: Fracture Mechanics, ANSYS, Inc.

[7] Shangyou, Z., “Subtetrahedral test for the positive Jacobian of hexahedral elements”, preprint, http://www.math.udel.edu/~szhang/

Siu, D. Whifor Revision of the Pressurized Thermal Shock (PTS) Screening Limit in the PTS Rule (10 CFR 50.61)”, August 2007.

[2] INTERNATIONAL ATOMIC ENERGY AGENCY, “Pressurized Thermal Shock in Nuclear Power Plants: Good Practices for Assessment Deterministic Evaluation for the Integrity of Reactor Pressure Vessel”, IAEA-TECDOC-1627, IAEA, Vienna (2010). http://www-pub.iaea.org/MTCD/publications/PDF/te_1627_web.pdf

[3] Araneo, D., “Procedura di analisi integrata di PTS per il RPV in un impianto nucleare WWER-1000/320 per mezzo dei codici accoppiati Relap5, Trio_U e Ansys”, F. D’Auria, M. Beghini, D. Mazzini, Pisa 2003.

[4] Frustaci, L., “Analisi dello shock termico in un RPV tipo WWER1000 in condizioni di DEGB”, F. D’Auria, M. Beghini, D. Mazzini, Pisa 2005.

, 2005.

[8] Cherepanov, G. P., “The Propagation of Cracks in A Continuous Media”, J. Appl. Math. Mech., vol. 31,1967, pp. 503–512.

[9] Rice, J. R., “A path independent integral and the approximate analysis of strain concentrations by notches and cracks”, J. Appl. Mech. ASME, 35:1968, pp. 379-386.

d. araneo, g. agresta, f. d’auria grnspg -university of ... · grnspg -university of pisa, pisa,...

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