## 3 Assessment of Flow-Induced Vibration of Fuel Assembly  
### Vibration Amplitude of the Fuel Assembly During Various Flow Conditions  
The foremost important quantity required to assess potential safety hazards related to the fuel assembly vibration is the vibration amplitude [30; 31]. During the operation of a nuclear reactor, many different operational conditions can occur in the coolant flow of a fuel assembly corresponding to different coolant flow velocities. These operational conditions should be investigated when studying the flow-induced vibration as the vibration amplitude in every condition can differ significantly. It is important to note that all references to vibration amplitude in this paper imply amplitudes of strain, rather than displacement since we measured the dynamic strain using the FBGs on the surface of the fuel pin in varying LBE flow rates. In addition, we have not elaborated on the frequencies associated with the vibration as the complex interaction of the densely packed fuel pins in the assembly will yield a set of overlapping frequency bands as illustrated in [11; 29]. The detailed analysis of this phenomenon is beyond the scope of the results reported in this paper. All experiments were performed at a constant LBE temperature of approximately 200 \({}^{\circ}\)C, as determined with thermocouples placed on the test section exterior wall. The measurement procedure was as follows. We increased the flow velocity in the test section in discrete steps from 1.08 m/s, up to the nominal flow velocity of 1.72 m/s (average flow velocity in the fuel assembly). For each flow condition, we allowed for the air-cooler to adapt to the new situation and to stabilize around a new steady-state. This also ensured that the flow was fully developed in the entire test facility. At each flow velocity, we determined the averaged vibration amplitude for all FBGs on the instrumented central fuel pin in the fuel assembly. We summarize the outcome of this sequence in Figure 6, which illustrates the average strain values with standard deviations as measured with all the FBGs, as a function of the average LBE flow velocity in the fuel assembly bundle. In addition, we observed a clear distinction between the vibration amplitudes corresponding to the directions parallel with and perpendicular to the support rails. The amplitudes were obtained by processing the measurements with a high-pass filter to obtain the rms value of the strain component. This high-pass filtering was essentially done to detrend the data. When increasing the flow velocity, we observed a corresponding increase in the vibration amplitude. It is important to note that during the experimental phase, the temperature fluctuations were also monitored with thermocouples, and were smaller than 0.2 \({}^{\circ}\)C across the test section. For LBE coolant flow velocities as anticipated in MYRRHA (equal to 1.72 m/s), we observed an average vibration amplitude just below 0.7 \(\upmu\varepsilon\) for the direction parallel with the support rails, and just over 0.5 \(\upmu\varepsilon\) for the direction perpendicular to the support rails. At the lowest tested flow velocity of 1.1 m/s, we measured vibration amplitudes close to 0.3 \(\upmu\varepsilon\) and 0.2 \(\upmu\varepsilon\), respectively, i.e., close to the limits of what we could detect. An important remark here is that the mean strain measured by a single FBG at a certain location can be up to twice the above mentioned overall mean strain values. This is further discussed in the subsequent Section 3.2. In any case, it is clear from these results that the vibration amplitudes (in terms of strain) of the fuel pins in a realistic mock-up of the MYRRHA fuel assembly are very small and will not be associated with vibration induced damage, as this would typically require amplitudes of at least 2 orders of magnitude more. Despite the challenging environment and small vibration levels, we were still able to record the Bragg wavelength shifts owing to our integration and interrogation scheme (explained in Section 2).