atw 2018-09v3

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atw Vol. 63 (2018) | Issue 8/9 ı August/September OPERATION AND NEW BUILD 448 | | Fig. 4. Coherence and phase angles between different ex-core detectors (top), relative neutron flux measurements at six different elevations of the C04 in-core measurement rod (bottom); all measurements in a Vorkonvoi PWR. progressions of the curves are identical for all six elevations. It has to be emphasized that no time lag can be identified between measurements at the bottom of the reactor core compared with measurements at the top. The same signal pattern can be observed for all eight in-core measurement positions. All these observations are consistent with different measurements and analyses done during the last decades [6, 7, 8]. Fiedler [8] compared neutron flux fluctuation levels in different plant types. He found that the prominence of the 180° phase difference between opposing detectors (referred to as “beam mode”) is special to KWU type PWRs. Possible explanation based on thermo-hydraulics effects Already at the beginning of the 1970s, a model was published [9, 10] coupling a point-kinetics neutron physics model with a one-dimensional TH model. It allows predicting neutron flux fluctuation levels based on coolant temperature or density oscillations. Based on this model it is already possible to understand essential characteristics of the neutron | | Fig. 5. Simulated temperature fluctuations in frequency (top, left) and time (top, right) domain; layout of the coupled ATHLET-QUABOX/ CUBBOX model for a mini-core (bottom, left) and the resulting neutron flux fluctuations spectrum (bottom, right). noise spectrum qualitatively, e. g. the dependency of the neutron flux fluctuation amplitude on the value of the moderator temperature coefficient. Following this approach and based on some new simulations with the CTF/PARCS codes [11, 12] a model of the reactor core has been developed using a coupled version of ATHLET and QUABOX/CUBBOX [13]. In [12] temperature fluctuations at the core inlet were applied based on different spectral properties. Temperature oscil lations based on a white noise spectrum resulted in much smaller power/neutron flux oscillations than temperature oscillations based on a low-pass-filtered spectrum. A possible explanation for that observation might be alias-effects due to the limited spatial and temporal resolution of the coupled system. To avoid such problems with the coupled system of ATHLET and QUABOX/CUBBOX, a Kolmogorov type spectrum [14] has been applied for the temperature fluctuations at the inlet of the reactor core. Figure 5 (top row, left) shows the power spectral density of the temperature oscillations over the frequency. Such spectra were observed in different reactors [15, 16, 17]. Based on the assumption that the temperature fluctuations follow such a Kolmogorov type spectrum the time dependent temperature fluctuations are calculated (Figure 5, top right). The temperature fluctuations have the same variance as a sine-wave with an amplitude corresponding to 1 K. The TH model layout is shown in Figure 5 (bottom, left). It consists of nine interconnected core channels with common inlet and outlet thermofluid elements. The mini core has a typical neutron-physics characteristic of an end of fuel cycle (EOC). Figure 5 (bottom, right) shows the power spectral density of the resulting fluctuations in the reactor power production, which is proportional to the neutron flux amplitude. For frequencies smaller than 3 Hz the calculated power spectral density fits the measured ex-core detector signals of a Vorkonvoi PWR quite well over several orders of magnitude. This suggests that temperature fluctuations at the inlets of the core channels are part of the explanation. This model can also explain the correlation between the amplitude of the fluctuations and the moderator temperature coefficient. However, it is not possible to explain, why no phase differences could be observed between measurements of 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
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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