## 4 Results and Discussion
### Non-Linear Seismic-Induced Oscillations
#### 4.2.2 Seismic-Induced Oscillation of Parallel Three Channel System
Based on the case of normal operating state (S1), the results illustrate that as the outlet loss coefficient is increased from \(k_{e}\) = 0.5, 1.0 (S1), to 2.0, the most heated channel will show a smaller transient oscillation, which implies that vibration-induced oscillation is attenuated by the outlet flow resistance. However, if the outlet loss coefficient is further increased to an extraordinary condition with \(k_{e}\) = 20.0, the most heated channel will exhibit a dramatically larger vibration-induced oscillation in the case of resonance condition (\(f^{+}\) = 1.1), while a very small one is presented in the non-resonance condition (\(f^{+}\) = 0.5). Our previous study [14] revealed that increasing the outlet loss coefficient would destabilize the system of parallel supercritical heated channels in the static system, which strengthen the instability degree of the system. Thus, the unstable effect of outlet flow resistance combined with the resonance effect will cause the system to exhibit much larger oscillation than in the case of non-resonance. Moreover, the resonance oscillation with \(k_{e}\) = 20.0 is much stronger than that with \(k_{e}\) = 1.0 in Figure 9c. This suggests that the strength of vibration-induced resonance oscillation is closely related to the inherent stability characteristics of initial state. The feature of a multi-channel system would exhibit an asymmetric radial heat flux ratio distributed among channels, which may affect the seismic-induced oscillation. The power range relative to the average channel for three channel groups in SCWR is above 1.2 for group 1, 0.9 to 1.19 for group 2 and below 0.9 for group 3, as displayed in Table 1[25]. Therefore, supposing the same external vertical acceleration wave in Figure 9a is imposed on the normal operation point S1 of the parallel three supercritical heated channel system, as denoted in Figure 3b, the heat flux ratios of 1.1:1.0:0.9, 1.2:1.0:0.8 and 1.3:1.0:0.7 are selected to explore their effects on the vibration-induced oscillations, as indicated in Figure 11. The results suggest that the more difference in the heat flux among channels would drive a stronger channel-to-channel interaction, and thus cause a much larger vibration-induced oscillation as in the case of 1.3:1.0:0.7 shown in Figure 11.  
Figure 10: The parametric effects on vibration-induced oscillation of the most heated channel: (**a**) the effect of inlet loss coefficient at channel 1; (**b**) the effect of outlet loss coefficient. Based on the normal operation point S1 of the parallel three supercritical-heated channel system, as marked in Figure 3b, and assuming vertical seismic acceleration wave in Figure 4a imposed on the system, Figure 12 reveals the seismic-induced inlet velocity oscillations of parallel three supercritical heated channels with a heat flux ratio of 1.2:1.0:0.8 while a constant total flow rate is maintained at S1 state. It is found that since the normal operating point S1 is very stable, the interactions among parallel three channels are rather weak, thereby a vertical seismic acceleration wave would dominate the non-linear behaviors of the system oscillations. The inlet flow velocities among channels oscillate chaotically following the motion of vertical seismic acceleration wave with the same oscillation frequency. However, their oscillation amplitudes are still limited to a small range, indicating that the normal operating point S1 is still safe subject to this seismic wave. In addition, since the total flow rate is supposed to keep constant during the seismic motion, the inlet velocity oscillations among parallel three channels are out-of-phase, as illustrated in Figure 12.  
With the same pseudo subcooling number (\(N_{P\text{-}SUB}\) = 1.55), the seismic-induced effect is explored in another stable state of S3 with a high operating power of \(N_{\text{TPC}}\) = 5.505, which is more approximate to the stability boundary of a parallel three supercritical heated channel system with a heat flux ratio of 1.2:1.0:0.8, as denoted in Figure 3b.