PROCEDURE FOR FRACTURE MECHANICS ANALYSIS OF WWER-1000 RPV IN PTS EVENT

D. Mazzini, M. Beghini, F. D’Auria, P. Vigni

Università degli Studi di Pisa Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione (DIMNP)

Via Diotisalvi 2, 56100 Pisa – Italy

ABSTRACT

The present work concerns on the research activity conducted at the University of Pisa to develop a computational tool able to evaluate the risk of brittle propagation of flaws in WWER-1000 Reactor Pressure Vessel (RPV). The aim is at evaluating the possibility to couple different codes for an accurate prediction of thermal and pressure loads as well as the induced nominal stress in the undamaged structure and the Stress Intensity Factor (SIF) for postulated crack sizes and localizations under Pressurized Thermal Shock (PTS).

The numerical models used to study the different aspects involved in this analysis by the codes RELAP 5.3 [1], FLUENT 5 [2] and ANSYS 5.5 [3] are presented, together with relevant results.

Keywords: coupled codes, PTS, PWR safety, CFD, fracture mechanics.

I. INTRODUCTION

The safety of nuclear power plants constitutes a global concern on the planet. This justifies interchanges of competences and information between Countries, especially on the application of advanced system codes for best estimate analyses.

The integrity of the RPV in Pressurized Water Reactors (PWRs) is of outmost importance as safety system are historically not designed to compensate the rupture of this component of the primary circuit, leading to insufficient core cooling condition. The RPV is subjected to temperatures and pressures which preclude unstable crack propagation even if located at critical positions. However, a set of accidental transients particularly dangerous for its integrity could take place. During PTS events, high thermal stresses are produced in the wall when a relatively cold fluid comes into contact with inner surface of the vessel wall, while the internal pressure may keep a high value. Brittle propagation of a preexisting defect could happen if the supplied SIF exceed the material crack toughness value.

A pre-operational PTS analysis able to assure a sufficient safety margin against the PTS induced catastrophic failure throughout the entire plant life is part of the licensing process [4], but the general target for the countries to extend the operation lifetime of existing plants needs best estimate theoretical and experimental investigations, since the neutron irradiation increases the

transition temperature of the structural material, reducing its toughness.

A research activity is carried out at “Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione” (DIMNP) of the University of Pisa to develop a computational tool able to perform parametric analysis of Fracture Mechanics assuming various shapes and locations of the flaw. Different computer codes are used, involving various tasks of technical field to achieve the best estimation of the SIF for the postulated defect.

For this purpose, the Kozloduy Nuclear Power Plant No 5 is taken as reference for an appropriate safety-related assessment of the numerical tools, assuming a Main Steam Line Break (MSLB) accident based on unlikely assumptions maximizing the PTS potential.

The thermal hydraulic response of the plant during the planned accident has been simulated by the RELAP 5.3 system code adopting a qualified nodalization for a WWER-1000 available at the DIMNP.

The fluid velocity field inside the downcomer and the temperature distribution inside the RPV wall have been investigated by the code FLUENT 5.3.

The nominal stress into the undamaged structure has been evaluated by the code for structural calculations ANSYS 5.5, while the assessment of the Stress Intensity Factor has been conducted by means of the Weight Function technique.

II. REFERENCE NUCLEAR POWER PLANT (NPP) AND THERMAL HYDRAULIC SCENARIO

WWER-1000 Plant. The Kozloduy Nuclear Power Plant No 5 is equipped with a WWER-1000/320 reactor (Fig. 1.a) and its main characteristics are given below [5-6-7]: • The reactor consists of 163 fuel assemblies,

producing up to 3000 MWt rated power. • The primary system has four primary loops equipped

with horizontal tube Steam Generators (SG) and Main Circulation Pumps (MCP) of centrifugal type.

• The RPV (Fig. 1.b) inner radius and wall thickness in the belt line region are 2068 mm and 199 mm, respectively.

• The Emergency Core Cooling Systems (ECCS) includes both the High Pressure Injection System (HPIS) and the Low Pressure Injection System (LPIS).

• Two independent feed-water loops are connected with each four SGs at four different locations.

(a)

(b)

Figure 1. (a) Primary Circuit of WWER-1000 NPP and (b)

RPV Sketch.

MSLB scenario. The transient here considered is of beyond Design Basis Accident type and it has been planned to enhance the thermal shock in presence of high pressure values. The assumptions adopted to depict the thermal-hydraulic scenario are: • One side 100% (related to the area of the steam line

pipe) break occurs at time zero at the top of the steam generator No. 1;

• Reactor scram occurs at 5 s into the transient; • Main Coolant Pumps are kept in operation, while

steam generators secondary sides are isolated; • Emergency feedwater is allowed to inject liquid only

in the broken steam generator loop, starting at 20 s into the transient.

• HPIS pumps are actuated in the three intact loops when the pressure achieves 9 MPa and they are not

isolated at the moment the primary system pressure overpasses that value. III. PLANT RESPONSE SIMULATION

RELAP 5.3 Nodalization. The RELAP calculation of the outlined accident has been conducted adopting a qualified nodalization of a WWER-1000 [7-8], modified in the present framework for a more detailed simulation in the zone where PTS is assumed to occur (allowing the calculation of data of direct interest in PTS analysis).

The original nodalization, developed in the frame of a cooperation also involving the Italian Licensing Authority (ANPA), the vendor Ansaldo and the University of Roma “La Sapienza” with the external support of Energoproekt [6-7-9], consists of more than one thousand nodes and it includes (Fig. 2):

• the vessel and the piping of the four loops of the

plant; • the bypass flow through the control rods and guide

tube that connects the lower plenum of the vessel to the upper head;

• the steam generators, reproduced with a appropriate nodding philosophy since their geometry;

• the ECCSs, directly connected with the downcomer and with the upper plenum of the main vessel, each modelled together with the Auxiliary Feedwater System;

• the relief valves at the top of the pressurizer and in the secondary side of the SGs.

Figure 2. Noding Scheme of the WWER-1000 NPP for the RELAP 5.3 Code (Only one Loop Shown).

Main Thermal Hydraulic results. When the rupture of the SG No. 1 takes place, the plant leaves the steady state condition (corresponding to the negative time interval in the

following figures). The primary system pressure decreases (Fig. 3) for the combined effect of reactor scram and heat removal growth in the SG No. 1, due to the secondary water boiling phenomena that takes place when the secondary side pressure assumes the atmospheric value (Fig. 3). The pressure of the primary side starts to increase at about 200. s into the transient, up to 15.0 Mpa, after the HPIS actuation. The pressuriser level rises due to (relatively) cold water inlet from the hot leg. Saturated water remains at the top of the pressurizer that did not completely drain during the initial phase of the transient. Therefore no mixing occurs in the pressurizer: cold water is entering the bottom and saturated fluid is buoyant on the top. Primary pressure increases till the values corresponding to the opening of the pressurizer PORV.

The flow through the cold legs keeps a high value since the MCP are working, and the isolation of the secondary SG sides enhance the difference in temperature between the flow through the cold leg No. 1 (connected to the broken SG) and the others (Fig. 4).

Primary Circuit

SG 1 Secondary Side

SG 2-3 Secondary Side

Figure 3. SG Primary and Secondary Side Pressure.

440

460

480

500

520

540

560

580

-50 0 50 100 150 200 250 300t [s]

[K]

Cold Leg 1

Cold Leg 2-3

Figure 4. Cold Leg Fluid Temperatures.

IV. THERMAL LOADS DOWNCOMER Model. The RELAP nodalization allows the evaluation of the temperature distribution in the RPV wall assuming the complete mixing of the vertical stacks that constitute the downcomer [10-11].

A better evaluation of thermal loads can be obtained taking into consideration the non uniformity of the fluid temperature (i.e. cold plumes) and of the coolant-to-wall heat transfer coefficients in the downcomer. This has been done defining a downcomer model suitable for the CFD code FLUENT.

Only a half of the downcomer and the “nozzles” of three cold legs have been modeled (Fig. 5) for the symmetry reasons of the analytical model (the meridian plane passing through the axis of the cold leg connected with the broken SG is a symmetry plane).

Figure 5. FLUENT Downcomer Space Discretization.

The geometrical grid is built by hexahedral elements

both for the fluid flow region and the wall material, assuming a non-uniform spacing both in the transversal and in the parallel directions with respect to the main flow velocity component, both in the fluid and the solid regions.

The water physical properties are expressed as function of the temperature, avoiding the pressure dependence, the steel has been described with heat capacity and thermal conductivity depending from temperature. The high Reynolds RNG-κ ε model [12] has been adopted, handling the turbulence next to the wall with the Standard Wall Function technique [13].

The boundary conditions has been derived from the RELAP calculation by defining the cold leg mass flow rate and temperatures as time dependent functions. The heat exchange is allowed with the inner surface of the RPV and

cold leg walls, while heat fluxes towards the environment and the barrel have been set to zero (adiabatic boundary condition). Wall temperature distribution. General views of the wall temperature evaluated at different times are given in Figs. 6 - 7 In Fig. 6, it is evident the large cooled area of the RPV inner surface (resulting from the main coolant pump operation) as well as the difference in temperature between the cold leg flows. In Fig. 7 the thermal wave propagation in the vessel steel is showed plotting the temperature distribution on the symmetry plane.

5.60e+02

5.51e+02

5.42e+02

5.33e+02

5.23e+02

5.14e+02

5.05e+02

4.96e+02

4.87e+02

4.78e+02

4.69e+02Z

Y

X

Figure 6. Downcomer Inner Surface Temperature at 45. s Calculated by FLUENT Code.

5.60e+02

5.51e+02

5.42e+02

5.33e+02

5.25e+02

5.16e+02

5.07e+02

4 .98e+02

4 .89e+02

4 .80e+02

4 .71e+02

Z

Y

X

Figure 7. Wall Temperature Distribution on the Symmetry Plane in the Cold Leg nozzle Region at 200. s Calculated by

FLUENT Code.

V. STRUCTURAL CALCULATION AND FRACTURE MECHANICS ANALYSIS

RPV Discretization. The pressure and thermal loads evaluated by the codes RELAP and FLUENT have been applied to the RPV model suitable for the ANSYS 5.5 code in order to estimate the nominal stress in the undamaged structure.

The adopted RPV grid is given in Fig. 8. It reproduces a half of the lower part of the vessel, assuming again the existence of a meridian symmetry plane. Constraints at the node displacement have been defined on the symmetry plane (in the perpendicular direction), and on the circumference corresponding to the vertical support (Fig. 1,b).

A non-uniform spatial node distribution in the wall thickness (parallel to the thermal wave propagation direction) has been defined to allow the temperature gradient prediction in the region lower to the cold legs nozzles where circumferential welds are located.

Figure 8. RPV Grid for Structural Calculation by the ANSYS Code.

Since the input conditions for the structural analysis came from the RELAP and FLUENT outputs, an interface Fortran program has been written to create the correct data for the ANSYS model. The major difficulties encountered are related to the temperature transferring because of the different nodding scheme of the three-dimentional grids.

The structural assesment is focused to the evaluation of the possibility for an assigned thermal transient to produce unstable propagation of flaws. The following assumptions have been postulated: • a pre-existing surface defect in the inner side of the

wall exist;

• the flaw is located on the second welding below cold leg No. 1 on the symmetry plane;

• the crack is virtually infinite, having a constant through-thickness depth. The formulated hypothesis are justified in view of

the fact that:

• a pre-existing defect is commonly associated with vessel welds;

• that most severe irradiation are expected in the RPV belt line region;

• a flaw of general three-dimentional shape usually shows a first propagation in the direction perpendicular to the wall thickness. The temperature at the crack location is reported at

for different times in Fig. 9.

460

480

500

520

540

560

580

0 0.2 0.4 0.6 0.8 1(r -r i )/(r e -r i ) [-]

[K]

0. s10. s20 s40. s70. s130. s170. s200. s

Figure 9. Temperature Distribution through the Wall Thickness at the Assumed Crack Location.

Nominal Stresses. The axial stresses evaluated by the ANSYS model at the crack location for the undamaged structure are shown in Figs. 10-11, respectively corresponding to the pressure and thermal loads of interest for a circumferential crack. However, the following discussion is also valid for axial defects since the calculated circumferential tensions have similar trend and intensity.

Stresses due to the internal pressure are plotted only at the initial instant (t = 0. s), as they vary in time proportionally to the primary pressure (Fig. 3). The trend showed in Fig. 10 differs from the nominal one obtained for an infinitely long cylinder with an internal pressure as a consequence of the thickness changing in the wall material next to the assumed crack location.

The induced difference in temperature of about 100 K causes a peak of stress higher than the one related to the pressure (Fig. 11). The stress level remain at big level even in the following for the progressive decrease of the temperature of the cooling fluid.

40

50

60

70

80

90

100

0 0.2 0.4 0.6 0.8 1(r -r i )/(re -r i ) [-]

[MPa

]

Figure 10. Axial Stress Distribution through the Wall Thickness, Calculated for the Initial Pressure Value

(t = 0. s) at the Assumed Crack Location.

-50

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8 1(r -r i )/(r e -r i ) [-]

[MPa

]

0. s10. s20 s40. s70. s130. s170. s200. s

Figure 11. Axial Thermal Stress Distributions through the Wall Thickness Calculated at the Assumed Crack Location

for Different Times. Stress Intensity Factor. The SIF has been determined by means of Weight Functions proposed by Verfolomeyev and Hodulak [14], on the base of a bi-dimentional scheme. In Figs. 12-13 the evolutions of the SIF produced by pressure and thermal loads are reported. The Stress Intensity Factor has been calculated for few crack depths from relatively shallow to deep defects, for a time interval of 200 s.

The SIF value induced by the pressure decreases in time following the trend of the primary circuit pressure (the HIPS start its injection at 200. s). The thermal SIF evolution is affected by the temporary temperature increase at 40 s. Its subsequent growth is related to the continuos thermal power transfer between primary fluid and secondary side in the SG No. 1.

For the shallow cracks (that may be found with major likelihood) the total SIF is more affected by the thermal load than by the pressure.

The condition of propagation has been examined in relation to the 5 mm circumferential crack by comparing the calculated SIF with the ASMR KIc reference function. In Fig. 14 it can be observed that a very high transition temperature (RNDT = 280 °C) is necessary to promote the brittle propagation. The increasing of the transition temperature takes place for every steel by the neutron irradiation, depending mainly by the chemical composition of the alloy (the ASME reference curve is a lower bound curve).

0

10

20

30

40

50

60

70

80

0 25 50 75 100 125 150 175 200t [s]

[MPa

·m0.

5 ]

a = 5 mma = 10 mma = 25 mma = 50 mma = 100 mm

Figure 12. Evolution of the SIF Due to Primary Circuit Pressure Calculated for Different Circumferential Crack

Depth.

0

10

20

30

40

50

60

0 25 50 75 100 125 150 175 200t [s]

[MPa

·m0.

5 ]

a = 5 mma = 10 mma = 25 mma = 50 mma = 100 mm

Figure 13. Evolution of the Thermal SIF Calculated for Different Circumferential Crack Depth.

020406080

100120140160180200

0 25 50 75 100 125 150 175 200t [s]

[MPa

m0.

5 ]

KI (a = 5 mm)

KIc (RTNDT = 200 °C)

KIc (RTNDT = 220 °C)

KIc (RTNDT = 280 °C)

Figure 14. Comparison of the Total SIF and Fracture Toughness for a Shallow Crack for Different Brittle-Ductile

Transition Temperature.

V. CONCLUSIONS In order to extend the lifetime of a NPP, the likelihood of brittle propagation of defects has to be evaluated. In this paper, a hypothetical accidental transient has been studied, making use of complex codes (RELAP5/Mod3, FLUENT5.3 and ANSYS 5.5) for a complete analysis of the different aspects involved: pressure and thermal loads estimation, induced stress calculation. The Stress Intensity Factor has been evaluated by the Weight Function Technique that produces accurate results comparable to a complete finite element study.

Assuming the presence of a circumferential crack in a weld of the vessel, the propagation condition has been investigated on the basis of various hypotheses on its shape and on the thermal transient. The obtained result highlights the relevant rule of thermal shock of shallow cracks that produces high SIF increments.

Possible improvements in the study include:

• code to code linking; • adoption of a three-dimentional scheme for the

Fracture Mechanics analysis; • consideration of the actual material properties; • consideration of actual defect; • consideration of the presence of the liner; • realistic thermal-hydraulic transient.

The present study shows the capability achieved at

DIMNP on performing complete coupled Thermal Hydraulic and Fracture Mechanics analyses.

REFERENCES

[1] The Thermal Hydraulics Group, SCIENTECH Inc., RELAP5/Mod3 Code Manual, Volume I: Code Structure, System Models and Solution Methods, Idaho, June 1999. [2] Fluent Incorporated, FLUENT User’s Guide Version 4.3, 1995. [3] Ansys User’s Guide Manual, 1997. [4] IAEA-EBP-WWER-08, Guidelines on Pressurised Thermal Shock Analysis for WWER Power Plant, June 1997. [5] Kolev N.P., Tomov E., Ovchatova I., Angelov D.K., Kozloduy Nuclear Plant Analyzer. Specification of a WWER-1000 reference plant for NPA modelling Purposes, Energoproekt Report, Sofia (BG), 1992. [6] Hinovsky I., Personal Communications to F. D’Auria, Sofia (BG), March and June 1995. [7] Gatta P., Mastrantonio L., Thesis in Nuclear Engineering, Università di Roma ‘La Sapienza’, 1995. [8] Cerullo N., D’Auria F., Frogheri M., Hinovsky I., Data Base for Transient Analysis in WWER-1000 Nuclear Plants, ICONE-4 Conf., New Orleans (US), March 10-14 1996. [9] Aprile G., D’Auria F., Frogheri M., Galassi G., Application of a qualified WWER-1000 plant nodalization for Relap5/mod3.2 computer code, Int. Conf. on Nuclear Option in Countries with Small and Medium Electricity Grid, Opatija (Croazia), Oct 7-9 1996. [10] Beghini M., D’Auria F., Galassi G.M., Vitale E., Evaluation of the PTS Potential in a WWER-1000 Following a Steam Line Break, IAEA Specialist Meeting on Methodology for Pressurized Thermal Shock Evaluation, Esztergom (Hungary), May 5-8 1997. [11] Magliolo P., Beghini M., D'Auria F., Morasso R., Methodology for Stress-Strain State Evaluation in the WWER RPV in case of Pts. [12] Launder, B.E., and Spalding, D.B., The Numerical Computation of Turbulent Flows, Imperial College of Science and Technology, London, NTIS N74-12066, January 1973. [13] Launder, B.E., and Spalding, D.B., Lectures in Mathematical Models of Turbulence, Academic Press, London, 1972. [14] Varfolomeyev I. V., Hodulak, Improved Weight Functions for Infinitely Long Axial and Circumferential

Cracks in a Cylinder, in press on Int. J. Pres. Ves. & Piping, 1997.