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THERMO-MECHANICAL ANALYSIS OF A PWR CORE BAFFLE CONSIDERING THE IRRADIATION INDUCED CREEP OF THE

BOLTS

Eberhard Altstadt, Erwin Fischer1, Herrmann Kumpf, Gerhard Nagel1, Georg Sgarz1, and Frank-Peter Weiss

1. Introduction

In some PWRs the core baffle (Fig. 1) consists of sheets (light blue) and formers (red). The sheets are separated by small gaps (0.2 mm to 0.4 mm). The connection between the core baffle sheets and the formers and between formers and core barrel (blue) respectively is realized by a large number of bolts (about 900). During the manufacturing process of the core baffle the bolts are tightened with well defined pre-stress to guarantee the geometrical and me-chanical stability of the structure. During operation the pre-stress of the bolts is reduced as a consequence of thermal and mechanical loads and promoted by neutron irradiation possibly leading to expanding gaps and affecting the flow induced vibrations of fuel rods in outer fuel elements. These effects were investigated by an extensive structural analysis.

The core baffle of a PWR is loaded by the axial gradients of differential pressures in the bypass and the core and by temperature profiles originating from gamma heating and heat transfer into the coolant. Strain, deformation and gaps are assessed considering the effect of neutron irradiation induced creep of the core baffle bolts. The complete analy-sis requires three major steps:

• Evaluation of the three dimensional distributions of the neutron and gamma fluxes

• Calculation of the temperature distribution in the core baffle

• Calculation of time dependent deformations, stresses and strains

2. Neutron and gamma induced heating

The 3-dimensional distributions of the neutron and gamma fluxes and of the resulting heat deposition is calculated with the Monte Carlo code MCNP®. This program simulates the des-tiny of fission neutrons, fission gammas and of generated secondary particles from their birth in the pins until their absorption. The calculations are based on pin wise power distributions at the core edge for typical loading patterns. A 45°-symmetry is assumed. The neutron flux is calculated for neutrons with energies higher than 1 MeV. For the evaluation of the heat depo-sition two calculations are superimposed: 1) the transport of the prompt fission gammas and 2) the transport of neutrons and gammas from neutron capture and inelastic scattering. Fig-

1 E.ON Nuclear Power

Fig. 1: Core baffle (45° section)

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ure 2 shows the neutron flux and the en-ergy deposition over the circumference of the core baffle sheets (averaged over the height) for the so called low-leakage core load pattern.

Two typical core loading patterns are in-vestigated: In the early fuel cycles the fresh fuel elements (low burn-up) were placed into the outer regions of the core (classical core). In the mid nineties the strategy was changed to reduce neutron leakage from the core. The fuel elements with low burn-up were now placed in the central core region (low-leakage core).

3. Thermal finite element analysis

The finite element code ANSYS is ap-plied for the thermal and mechanical analyses. The FE-model comprises a complete 45° sector of the core baffle structure including the core barrel, the formers, the core baffle sheets. The ther-mal analysis is done for different opera-tional conditions and core loading pat-terns. The following effects are consid-ered: heat conduction in the components, internal heat sources (neutron and gamma heating) and convectional boundary con-ditions (heat transfer coefficients and bulk temperature of the coolant). Based on the coolant temperature and mass flow at different positions the heat transfer coef-ficients for the convectional boundary condition are calculated by:

H

water

DNu λ⋅

=α (1)

The Nusselt number follows from the empirical correlation [1]:

[ ]

vDRe;c

Pr:with

LD1Pr100Re0214.0Nu

Hwater

water

water

waterwater

667.0H4.08.0

⋅⋅µρ

=λ

⋅µ=

+⋅⋅−⋅=

(2)

where µ is the coolant viscosity, λ the heat conduction coefficient, ρ the density, v the mean velocity, DH and L the equivalent hydraulic diameter and length respectively. Figure 3 shows the typical temperature distribution for the low-leakage core during normal operation. It can be seen that the region of the highest temperature is the edge of the core baffle that is located closest to the core center. The maximum temperature exists inside the sheet. The heating up of

Fig. 2: Neutron flux [n/cm² s] for E > 1MeV and

energy deposition [W/cm³] in the core baf-fle sheets over the circumference with 0 = principal axis (0°); 75 = secondary axis (45°)

Fig. 3: Temperature distribution [°C] in the core

baffle for normal operation with a low-leakage core

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the bypass water (the coolant streaming through the core baffle formers) is also calculated, but it is negligible (about 1 K). The bolts are not modelled in the global thermal model. Instead of this, the bolt temperatures were evaluated with a local model of a single bolt with a variable heat power input according to the individual bolt position. The local model calculates the temperature difference in the bolt shaft relative to the temperature of the sheets at the bolt’s head and thread.

4. Mechanical finite element analysis

The mechanical finite element model for the sheets, the formers and the core barrel is based on the same mesh as the thermal model. It considers additionally about 230 bolt connections, the non-linear contact between the single components, the effect of friction, and the creeping of the bolts. The load follows from the weight, the coolant pressure, the temperature fields for different operational situations and from the prestressing of the bolt connections. The pre-stress of the bolts is realized by a modified reference temperature TB,ref (where the thermal strain is zero):

α⋅

σ+=

ETT V

refref,B (3)

with Tref – analysis reference temperature of the components (except bolts), σV pre-stress of the bolt, E – elasticity modulus of the bolt material, α – thermal expansion coefficient of the bolt material. The irradiation induced creep of the bolts is correlated to the neutron flux φ and to the axial stress axσ as follows:

pax

n1

crax K σ⋅φ⋅=ε& (4)

The parameters K1, n and p were determined from results of relaxation experiments.

The viscoplastic analysis comprises a time frame of 30 full power years, which can roughly be subdivided into four large periods:

• Commissioning until bolt replacement (period 1) • Bolt replacement until change of core loading pattern (period 2) • Change of core loading pattern until core baffle modification (period 3) • Core baffle modification until 30 full power years (period 4)

The end of period 1 is marked by the replacement of the bolts in 2 former planes (Fig. 1). Af-ter the replacement the new bolts receive the nominal pre-stress of 250 MPa whereas the re-maining bolts exhibit already some relaxation due to creep. As a consequence of the change of the core loading pattern (end of period 2) the creep rate of the bolts is reduced (lower neu-tron flux, equation 4), likewise the average temperature level is slightly decreased (lower gamma heating). The core baffle modification is a hydraulic change in the upper former, which leads to a lower pressure in the bypass (between the core barrel and the core baffle sheets) during normal operation. For each of the four periods a heat-up and a cool-down load step has additionally been analyzed. The replacement of bolts required two more load steps in the cold state, so the mechanical analysis comprises 14 load steps in total. Each of the periods is characterized by a specific temperature-, pressure- and neutron flux field.

5. Results

The time dependent results of the mechanical analysis are: elastic deformation, stresses and strains in all core baffle components, creep strain in the bolts, self controlled and equalizing

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redistribution of bolt loads, gap widths between adjacent core baffle sheets, contact status between former and core barrel and between former and core baffle sheets. Figures 4 and 5 show axial stress and creep strain versus time for two different bolts. It can be seen that the heat-ups and cool-downs, which are connected with large thermal strains and therefore with sliding processes, can lead to significant changes in the axial bolt stresses and to a redistribu-tion of the loads amongst the bolts. The Figures 6 and 7 show the stress and strain curves for bolts of the former plane 2, where a bolt replacement took place. The results can be summa-rized as follows:

• The bolt pre-stresses in the sheet bolts of the former planes 2 to 4 are significantly re-duced over the load history

• The calculated maximum creep strain is 0.44% (former plane 2) • The gaps are not affected by creep and reduced pre-stress of the bolts • The bending stresses in the bolts are abolished by the neutron induced creep

The results show the equalizing effect of redistribution of bolt loads from high flux to lower flux exposure locations in a self controlled process, keeping the mechanical and geometrical stability of the core baffle structure and leaving the gaps between sheet edges unaffected.

References

[1] VDI-Wärmeatlas, 7. Auflage, VDI-Verlag, 1994

Fig. 4: Creep strain (red) and axial stress

(blue) versus time (baffle bolt number 7 plane 4)

Fig. 5: Creep strain (red) and axial stress

(blue) versus time (baffle bolt number 10 plane 4)

Fig. 6: Creep strain (red) and axial stress

(blue) versus time (bolt number 4 plane 2); old bolt

Fig. 7: Creep strain (red) and axial stress

(blue) versus time (bolt number 4 plane 2); new bolt