## 4 Results and Discussion
### Non-Linear Seismic-Induced Oscillations
#### 4.2.2 Seismic-Induced Oscillation of Parallel Three Channel System
Since the normal operating point (S1) is very stable, the channel-to-channel interaction among parallel heated channels is fairly weak. In the case of non-resonance condition (\(f^{+}\) = 0.5), Figure 9c indicates that the oscillation of each channel caused by the external vertical  
Figure 7: The influence of parameter on the seismic-induced oscillation: (**a**) the effect of heated length; (**b**) the effect of channel diameter. acceleration wave appeared to be very small due to the inherent stability nature of S1 state. In addition, under the external vertical acceleration, out-of-phase mode of inlet velocity oscillations is presented among channels to maintain a fixed total flow rate. In the case of resonance condition (\(f^{+}=1.1\)), the vibration-induced oscillation of each channel will become larger due to the resonance effect. However, as the normal operating point (S1) is very stable, the resonance effect seems to be not significant, which does not trigger the uncontrollable oscillations under the impact of the external vertical acceleration wave in Figure 9a. For a parallel supercritical heated channel system, such as SCWR, the inlet loss coefficient in each channel is set, as listed in Table 1, such that the similar power-to-flow ratio among channels is reached in the normal operating point (S1) of the forced circulation system. In general, the most heated channel, i.e., channel 1, is with the smallest inlet loss coefficient and thus the highest mass flow rate, while the least heated channel, i.e., channel 3, has the largest inlet loss coefficient that makes it have the lowest mass flow rate. Based on the normal operating point (S1) in Figure 3b as a reference case and under the same external vertical acceleration wave in Figure 9a, Figure 10a investigates the effect of inlet loss coefficient at the most heated channel (channel 1) on the vibration-induced oscillations among parallel supercritical heated channels. Assuming the group of inlet loss coefficient in Table 1 is step set to channel 1 from \(k_{i,1}=\) 22.7 (S1), 50.0, 93.0 to 241.1, the results in Figure 10a reveal that with the increase of inlet flow resistance set at the highest heating channel, the vibration-induced oscillation of the most heated channel firstly become smaller while the inlet loss coefficient is set to \(k_{i,1}=\) 50.0, due to both the stable  
Figure 8: The variation in the dimensionless natural frequency along with the stability boundary of three supercritical heated channels with a heat flux ratio of 1.2:1.0:0.8 at 25 MPa. effect and the attenuated effect of inlet flow resistance. However, if the inlet flow resistance of the hottest channel is further increased to \(k_{i,1}=93.0\) and \(241.1\), the most heated channel presents a larger vibration-induced oscillation, which infers an unstable influence on the system dynamics. This is caused by the more uneven power-to-flow distribution among channels resulted by the increase in the inlet loss coefficient of channel 1, particularly for the case with \(k_{i,1}=241.1\). The more difference among channels will induce a stronger channel-to-channel interaction to destabilize the vibration-induced oscillation when its effect is greater than the stable and attenuated effects of inlet flow resistance. Figure 9: The impact of external vertical acceleration on the parallel three channel system at S1 state: (**a**) external vertical sinusoidal acceleration with \(a_{peak}\)= 0.1g; (**b**) constant total flow rate under vertical vibrations; (**c**) vibration-induced inlet velocity oscillations among channels. Under the same external vertical acceleration wave in Figure 9a, Figure 10b further explores the influence of outlet flow resistance (\(k_{e}\)) on the transient oscillations of the parallel three supercritical heated channel system caused by external vertical sinusoidal acceleration wave.