The vibration and stress analysis program consists of hydraulic load analyses and structural response analyses. The program was performed before hot functional test of SKN unit 4 NPP and was performed additionally to reflect the measurement results after the vibration and stress measurement.

The hydraulic loads include the deterministic hydraulic loads caused by the pump pulsation and the random hydraulic loads induced by the turbulent flow. The deterministic loads and the random loads are assumed to be caused by independent sources. Therefore, those hydraulic loads can be calculated separately^(2,4~8). Fig. 1 shows the method of hydraulic and structural analysis^(2,4~8).

Fig. 1 
Summary of hydraulic and structural analysis method

The deterministic hydraulic load is due to the pulsations caused by the reactor coolant pumps. The pulsations propagate through the RVI as acoustic waves, independent of fluid velocity. The pulsations also occur at multiples of the rotor revolution frequency (20 Hz) and the blade passing frequency (120 Hz) of the reactor coolant pump. Therefore, the deterministic hydraulic loads were predicted with acoustic analysis for 6 frequencies (20 Hz, 40 Hz, 120 Hz, 240 Hz, 360 Hz and 480 Hz). The structural response analysis to the deterministic hydraulic loads was performed with the spectrum response analysis for the 6 frequencies. The total deterministic response was combined by the square root of the sum of squares (SRSS) method^(2,4,5,9~11).

The random hydraulic loads are due to the turbulent flow in the reactor vessel and were predicted with computational fluid dynamics in our study. Since random nature of the turbulence, a statistical method was used to define both the magnitude and frequency of the turbulence. Therefore, power spectral density (PSD) was used for both the random hydraulic load analysis and the structural response analysis. The flow except for the nearly stagnant flow in the upper guide structure (UGS) was selected as a turbulence analysis scope in the reactor vessel, because the bypass flow of the APR1400 reactor vessel is less than 3 % of total coolant flow and the flow in the inner barrel assembly (IBA) is too expensive to simulate. Natural frequencies and mode shapes of the RVI were calculated with block Lanczos method which is used a lot in commercial structural analysis programs and the spectrum analysis was used for the structural response analysis. The frequency range of the analysis was up to 500 Hz and the scale of the analysis results was 3-sigma. The hydrodynamic mass was considered, since the RVI are submerged by the coolant. Therefore, the added mass for each internal was calculated according to ASME B&PV Section III Appendix N^{(2,4,6,9,10,12)}.

The analysis and test conditions of SKN unit 4 RVI CVAP presented in prior Ko’s papers^(3,13), which are composed of 18 conditions based on the operation configurations of the pumps, operating pressures and temperatures. The transient state in the test conditions of the RVI CVAP corresponds to the start and stop of the reactor coolant pump. Since the hydraulic loads on the transient state do not give substantial effect on the results of the structural analysis in comparison with the loads on the steady state, the greater hydraulic load of the steady states before/after the transient was used⁽⁸⁾.

The vibration measurement program includes a data acquisition and reduction system as well as test conditions, consistent with the SKN unit 4 general guidelines for the vibration measurement program delineated in the US NRC RG 1.20 for prototype RVI. This program incorporates appropriate instrumentation to define the hydraulic loads and the responses of the internals that have been modified relative to the valid prototype, and demonstrates that the test acceptance criteria have been satisfied. In addition, the measurement program incorporates sufficient and appropriate instrumentation to monitor those RVI components that have not been modified relative to the valid prototype⁽¹⁾.

The vibration measurement program for the APR1400 RVI consists of twenty-three sensors (twenty-three data channels) located on the UGS assembly. In detail, two accelerometers (ACC.) and four strain gages (SG) for the IBA top plate, eight strain gages and one pressure transducer (PT) for the control element assembly (CEA) shroud assembly, and two accelerometers, two pressure transducers, and four strain gages for the UGS were installed as shown in Fig. 2^(3,13~17).

Fig. 2 
Locations where 23 Instruments were installed

The installation locations of the sensors were selected to provide, to the extent possible, data comparable to those from the measurement and inspection programs for Palo Verde 1 and OPR1000. There were restrictions on the APR1400 measurement program, however, which resulted from the necessity to minimize the risk of damage to the internals during site installation of the sensors and their leads, and hardware to protect them from flow-induced vibrations during the pre-core hot functional test (HFT)^(8,13). Fig. 3 shows two strain gages welded on a CEA guide tube and an accelerometer installed on the UGS support plate.

Fig. 3 
Strain gages and accelerometer installed on CEA guide tube and UGS support plate

The measurement for the APR1400 RVI was performed from April 13, 2016 through May 18, 2016. Although fifteen hard-lines for strain gages were unfortunately damaged and their data were not able to be acquired, the measurement for one strain gage (SG12), three pressure transducers, and four accelerometers for the APR1400 CVAP were carried out as a measurement procedure and the useful data were able to be acquired⁽¹³⁾.

The inspection program follows the related guidelines delineated in the US NRC RG 1.20 for a prototype RVI. The NRC RG 1.20 requires that the non-prototype RVI components be subjected to at least 1.0E6 cycles of vibration before the final inspection of the RVI. The minimum time duration of the hydraulic loads applied to the RVI was decided by the first natural frequency of the CSB. Therefore, the inspection program consists of a comparison of data gathered during the baseline (pre-HFT) inspection and data gathered during the post-HFT inspection to determine conformance with the acceptance criteria. The inspection program was performed for the high stressed areas of the RVI and interfaces between internals. The RVI to be inspected were a core support barrel, an in-core instrument support structure, a lower support structure, a core shroud, CEA guide tubes, a UGS barrel, a CEA shroud, an IBA, a hold-down ring, a reactor vessel, and a reactor vessel closure head. The baseline inspection for the APR1400 CVAP was conducted from January 4, 2016 to January 16, 2016 and the post-HFT inspection was conducted from December 9, 2016 to December 20, 2016⁽¹⁸⁾.

The comparisons of predictions and measured data were done for the IBA top plate, the CEA shroud assembly, and the UGS. The test conditions selected for evaluation were representative test cases, consisting mostly of operating conditions which provided the larger loading conditions for evaluation.

There are two hydraulic loads of interest: the pump-induced pressure pulsations and the random turbulence pressures. Table 1 and Table 2 presents the comparisons between predicted and measured pump-induced pressure pulsations at the pump forcing frequencies and rotor revolution frequencies for several test cases. As shown in Table 1, the measured pump-induced RMS (root mean square) pressure pulsations are very small for the pump forcing frequencies of 20 Hz, 40 Hz, 120 Hz, 360 Hz, and 480 Hz. The maximum RMS pressure pulsations measured at 0.077 psi at 240 Hz in the test condition 14 as 0.077 psi. The maximum measured total deterministic load also shows 0.077 psi in the test condition 14 too, and the maximum predicted RMS pressure presents 0.761 psi in the test condition 15. Although the measured data are higher than the predicted values in some test conditions, the total measured pump-induced RMS pressures are higher than the predicted pressures. In general, the total measured pump-induced RMS pressures are smaller than predicted those by approximately one order of magnitude or more for the locations PT1 within the CEA shroud assembly. From Table 2, the pump-induced RMS pressure pulsations for frequencies of 20 Hz, 40 Hz, 120 Hz, 360 Hz, and 480 Hz are very small. The highest measured RMS pressure occurred at 240 Hz. The maximum RMS pressure at 240 Hz in the test condition 16 was 0.143 psi. The maximum measured total deterministic load also shows 0.143 psi in the test condition 16 too, and the maximum predicted RMS pressure presents 2.12 psi in the test condition 14 and 16. In general, the measured values for pump-induced pressure pulsations are substantially smaller than the predicted values, especially at 240 and 480 Hz forcing frequencies.

For random turbulence pressure in the UGS support plate region, Fig. 4 shows comparisons of predictions versus measurements on location PT3 for the test condition 18⁽¹⁹⁾. The figure indicates that the predicted PSD trend matches or envelopes the measured random turbulence pressure. Meanwhile, we do not compare the measured values with the predicted values for random hydraulic loads inside the UGS in this paper, because the flow in the CEA shroud assembly isn't the main flow of reactor coolant and so the flow wasn’t predicted with CFD. Also due to the reason, the conservative hydraulic loads among the hydraulic loads predicted on the UGS support plate were used for the structural analysis of the CEA shroud assembly.

Fig. 4 
Comparison of measured and predicted pressure PSD distribution at PT3 in test condition 18

The total hydraulic loads predicted and measured are shown in Table 3. Comparing Table 3 to Table 1 or Table 2, the deterministic hydraulic loads are generally smaller than the random hydraulic loads. The hydraulic loads (PT1) in the CEA shroud assembly were measured to be considered even if the flow in the CEA shroud assembly isn't the mainstream. The predicted values are generally larger than the measured values. However, the random hydraulic loads used for the structural response analysis of the CEA shroud assembly need to be applied more conservatively for the test condition 1 ~ 4.

Table 4 show the natural frequencies of the CEA shroud assembly predicted from the first to the fifth mode. Fig. 5 shows measured strain PSD distribution in narrow band of the SG12 in the test condition 6.

Fig. 5 
Measured strain PSD distribution in narrow band at SG12 in test condition 6

This plot shows peaks at approximately 29.5 Hz, as com-pared to the predicted value of 30.8 Hz (126.7℃, test condition 6). However, several peaks are observed at frequencies different from the natural frequencies in Fig. 5. Those frequencies are about 10.5 Hz, 12.2 Hz, 14.7 Hz, 20 Hz, and 38.5 Hz. Similar results were seen in other test conditions. strain PSD distribution in narrow band at SG12 in test condition 6.

The frequency ranges for those peaks are 10.5 Hz ∼ 11.5 Hz, 12 Hz ∼ 13.5 Hz, 14.5 Hz ∼ 17 Hz, 20 Hz ∼ 22 Hz, and 38.5 Hz ∼ 39.5 Hz. The peaks of 20 Hz ∼ 22 Hz and 38.5 Hz∼ 39.5 Hz are judged to be from the deterministic hydraulic loads. For the other peaks, it is estimated that the responses of the UGS and the CSB have an effect on the CEA shroud assembly, since the CEA shroud assembly is welded to the UGS assembly and is fixed with the CSB assembly by alignment keys, or those peaks can be generated by rigid body motion induced by fluid coupling between the UGS assembly and the CEA shroud assembly.

The total RMS responses of the UGS assembly in the SKN unit 4 RVI CVAP tests and the responses of the internals in the analysis are shown in Table 5. The responses of the UGS assembly to the deterministic and random hydraulic loads are the results of structural responses of entire UGS assembly as well as of individual components such as the UGS barrel, the UGS support plate, the IBA barrel, the IBA top plate, the CEA guide tubes, the CEA shroud tubes, and the CEA shroud webs. The structural responses of the UGS assembly were measured by the strain gages and the accelerometers. From Table 5, it is clear that the measured responses in the UGS assembly are generally lower than predicted values. The maximum strain was measured by the SG12 in the test condition 11 at 7.17 με (micro-strain) RMS. This is smaller than the maximum predicted value of 9.92 με. The maximum measured displacement is 4.54 mils for the IBA top plate (A1) in the test condition 14. This is lower than the predicted value of 36.9 mils RMS in the test condition 15. The maximum measured displacement of the UGS support plate (A4) is 4.28 mils in the test condition 16. This is smaller than the predicted value of 15.6 mils in the test conditions 10 and 11. This shows that the response analysis for the UGS assembly was performed conservatively. Unlike the measurement, the predicted displacements of the A1 are much larger than those of the A4. This is due to very conservative hydraulic load input method used for the structural response analysis for the IBA top plate.