atw 2018-09v3


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


There are three possibilities for an

excitation in general:

• Stochastic fluid forces from turbulent

flow would lead to oscillations

of components at their natural

frequencies. The lowest natural

frequency of the fuel assemblies is

reported around 2.6 to 4 Hz [6, 18],

which would not explain the coherence

maximum at 1 Hz. Calculations

with simplified finite element

models show that depending on

design and operational behavior,

i.e. lateral stiffness decrease due to

radiation induces spring relaxation

in the spacers, the lowest natural

frequency can be shifted significantly

towards lower values. In [6,

16] an additional mode of the fuel

assemblies around 1 Hz in form of

synchronously moving cantilevered

beams (fixed at the bottom) is supposed.

Nevertheless, regarding the

fixture of the fuel assemblies in the

grid plate, the manifestation of this

mode is questionable. A further

explanation is the excitation of the

coupled system of core barrel, grid

plate and fuel assemblies, which

might have additional natural

system frequencies below the natural

frequencies of the single fuel


• A second possibility would be the

existence of an excitation force,

which is oscillating at around 1 Hz

and evokes a subsequent transient

deflection of the fuel assemblies.

Pressure fluctuations from residual

imbalances of the coolant pump,

standing waves, cavity resonances

in the pressurizer or vibrations of

other components of the loop are

known to induce core barrel motions

which could propagate to the

fuel assemblies. Fluid mechanical

oscillating forces with direct effect

on the fuel assemblies, e.g. pressure

differences, are also possible.

• A third possibility would be a selfexcitation

of fuel assemblies in a

constant axial flow. Research on

fuel assembly bow gives hints that

in fluid-structure-interaction (FSI)

simulations local forces can arise

leading to instability of the zero

position of the fuel assembly [19].

To investigate and prove the mentioned

hypotheses, a coupled FSI

model of core components and the

surrounding fluid is essential.

Simulations of reflector


Further, the reflector influence has

been studied by means of a simplified

2D core model, in which the reflector

Case description

Maximum (relative)

increase on the left side

cross-sections are manipulated in

order to simulate the effect of varying

water gap between core barrel and

reactor pressure vessel, which corresponds

to the reflector region. These

variations could be caused by mechanical

motions, e.g. of core barrel or

fuel assemblies at the core periphery,

and their effect increases with decreasing

boron concentration. In this

model the TH parameters are homogeneous

and representative of the

hot full power state at zero burnup.

Further assumptions are: fuel temperature

= 900 K, moderator density =

702 kg/m 3 and boron concentration

= 1,300 ppm.

Table 1 summarizes the results

obtained for different variations of

the thermal absorption and fast-tothermal

scattering crosssection. The

reflector is modified only in one half of

the core (the left side) to reproduce

the spatial oscillations observed in the

PWR. The results show that the effects

of thermal absorption and scattering

are additive. The amplitude of the

power variation can reach the same

order of magnitude as observed in the


Additional study is necessary to

determine if actual mechanical motions

can cause such changes leading

to increase/decrease of the moderator

volume (coolant water) in the reflector

zone and in that way changing

the homogenized assembly crosssections.

In addition, time-dependent

simulations are needed to check if

the frequency observed in the PWR

can be reproduced. Nevertheless, this

preliminary result shows that this

hypothesis is very promising. The

recently published study [20] showed,

that a variation of the gap size

between fuel elements of about one

centimeter can result in changes

of the neutron flux amplitudes at

the ex-core detectors of up to the

order of magnitude of 10 %. Therefore,

the influence of mechanical

motions of the fuel elements relative

to each other and as an ensemble

­relative to the reflector cannot be

ruled out as explanation of the observed

neutron flux oscillations.

Summary and outlook

Several models based on single

­physical effects (TH fluctuations at

the core inlet, movement of a point

source, coupled oscillations of core

­internals, changes in the reflector

­coefficients) are used to simulate the

neutron flux. Each of these simple

models can reproduce some of the

characteristics of the observed neutron

flux fluctuations but does not

encompass all features observed in a

real reactor. This suggests that further

work on the combination of models

is needed. Thereby, the biggest challenges

will lie in FSI simulations of

fuel assemblies including further core

internals, neutron physics simulations

using time-dependent geometries,

and possibly the coupling of all three

physical models.


This work has been performed in the

framework of the German Reactor

Safety Research and was funded by

the German Federal Ministry for

Economic Affairs and Energy (BMWi,

project no. RS1533). The authors

would like to thank the operators of

one German Vorkonvoi PWR and one

Konvoi PWR for providing data of

­neutron flux measurements.


Maximum (relative)

decrease on the right side

-10 % thermal absorption 4 % -3 %

-10 % scattering 7 % -5 %

-10 % thermal absorption

-10 % scattering

10 % -8 %

-20 % thermal absorption 11 % -7 %

-20 % scattering 14 % -11 %

| | Tab. 1.

Summary of the reflector study results.

1. M. Seidl et al., Review of the historic

neutron noise behavior in German

GWU built PWRs, Progress in Nuclear

Energy 85, pp 668-675, 2015.

2. Reaktor-Sicherheitskommission,

Stellungnahme DWR-Neutronenflussschwankungen,

457. Sitzung vom


3. Bundesamt für Strahlenschutz,

Kurzbeschreibung und Bewertung der

meldepflichtigen Ereignisse in Kernkraftwerken

und Forschungsreaktoren

der Bundesrepublik Deutschland im

Zeitraum Januar 2011, Stand


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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