atw 2018-09v3

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atw Vol. 63 (2018) | Issue 8/9 ı August/September

SPNDs at the same horizontal but

different axial locations. The transport

of temperature fluctuations

through the core channels should

result in a delay of measurements

between detectors in lower regions

and the upper regions of the core.

Furthermore, this approach cannot

explain the strict 180° phase differences

between measurement positions

at opposing sides of the reactor

(neither for ex-core nor for in-core

detector combinations). If this

approach should be continued sensitivity

studies on the parameters of

the applied Kolmogorov typed spectrum

will be necessary.

Possible explanations based

on mechanical motions

For decades, the analyses of neutron

flux fluctuations have been used for

the detection of mechanical oscillations

inside the reactor pressure

vessel, see e.g. [6, 8, 18]. However, the

mechanical oscillations considered in

these analyses are harmonic oscillations

with resonance frequencies

exceeding 2 Hz. Nevertheless, the

simultaneousness of detector signals

of one measurement rod as well as the

location of the maximum of the neutron

noise level in the middle of the

core height indicate that mechanical

motions in the reactor core, which

behave synchronous and without

phase differences over the full core

height, also contribute to the observed

fluctuations at low frequencies.

Point Source Model

To check whether the observed fluctuations

are consistent with a core wide

mechanical motion a model based on

a point source for the neutron flux has

been developed. The model is based

on the assumption that the signal

| | Fig. 6.

Moving point source model (yellow circles:

detectors used for trilateration, black star:

idle position of point source, blue star: point

position derived by trilateration, red circle:

estimation for position uncertainty).

| | Fig. 7.

Different detector combinations used for trilateration (left), estimated horizontal point source locations over time (right).

strengths at the detectors depend linearly

on the distances between the

point source and the detectors (see

Figure 6). Based on this assumption

the position of the point source can

be calculated by trilateration using

different detector combinations (see

Figure 7 left). Additionally, an estimation

of the uncertainty of the

assumed position of the point source

can be derived. The three combinations

considered here are the four

ex-core detectors (marked red), three

in-core detectors located at the left

side of the reactor core (marked

green), and three in-core detectors

located at the right side (marked

blue).

Figure 7 (right) shows for different

time steps the pathways of the

assumed point source calculated

by a combination of the four ex-core

detectors (red), three left in-core

detectors (green) and three right incore

detectors (blue). The position

calculated by the ex-core detectors is

scaled by a factor of 1/3 relative to the

center of the reactor core. Also shown

are the estimated uncertainties of the

point source position for the different

detector combinations.

The model results in consistent

point source location estimations for

the three detector combinations. Also

the estimated uncertainties are small

compared with the pathways of the

point source. If instead of the detectors

marked in Figure 7 (left) the two

inner-most detectors (J06, G10) are

included in the calculation of the

trajectories, no consistent trajectories

can be derived.

This indicates that a phenomenon

involving the full reactor core plays a

significant role for explaining the

­observed neutron flux fluctuations.

But it cannot explain the shape of the

measured power spectral density.

Structural-Mechanics

Considerations on Core-Wide

Motions of Fuel Assemblies

and further Core Internals

A synchronous excitation or synchronization

via mechanical coupling

can lead to core-wide correlated

mechanical motions of fuel assemblies,

which effect both in- and excore

neutron flux instrumentation.

This explanation is supported by

both the successful simulation of

the detector signals by an empirical

model of a moving point source and

the correlation between the neutron

fluctuation levels and the use of fuel

assemblies with reduced lateral

stiffness due to changes in the spacer

design. It also explains the simultaneity

of signals at different vertical

levels and the bow-shaped vertical

amplitude characteristic with a maximum

at or slightly below middle core

height.

Core barrel, grid plate and the

collective of fuel assemblies form

an enhanced system of coupled

mechanical oscillators. Core barrel

motions can have additional effects

on the neutron flux signal via

modulation of absorption and

­reflection in the ­water gap between

core barrel and reactor pressure

vessel. The fuel assemblies within

this coupled oscillator differ in type

and service time and thus mechanical

parameters, which can lead to chaotic

motions and interaction effects and

thus oscillations in a broad frequency

band. In a low-leakage loading pattern

the fuel assemblies with the longest

service time and lowest remaining

stiffness are located at the core

periphery, which can evoke additional

effects on the ex-core and outer

in-coresensors, e.g. via water gap

modulation or motion in a strong

flux gradient.

OPERATION AND NEW BUILD 449

Operation and New Build

Analyses of Possible Explanations for the Neutron Flux Fluctuations in German PWR ı Joachim Herb, Christoph Bläsius, Yann Perin, Jürgen Sievers and Kiril Velkov

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