## 4 Results and Discussion
### Non-Linear Seismic-Induced Oscillations  
#### 4.2.1 Seismic-Induced Oscillation of Single Channel System  
An actual vertical seismic acceleration wave in Figure 4a is considered in the present study, which is extracted from the data recorded by the Linkou Station during the Chi-Chi earthquake in Taiwan that took place on 21 September 1999 [28]. The data were collected in a time step of 0.005 s during a time interval of 88 s upon this earthquake, which corresponds to a dimensionless time interval of nearly \(t^{+}\) = 35 and a dimensionless time step of almost \(\Delta t^{+}\) = 0.002. Supposing this actual vertical seismic acceleration wave is directly imposed on the S1 state, i.e., normal operating state as denoted in Figure 3b, of the single channel system, the inlet flow velocity oscillation in Figure 4b shows that the seismic wave dominates the channel oscillation. The flow oscillates chaotically following the vibration of seismic acceleration with the same frequency; however, the oscillation amplitudes remain bound in a certain range, inferring that seismic-induced oscillation of this supercritical uniformly-heated channel at S1 state is still small. The seismic-induced oscillation could result from the compound results of the inherent stability characteristics interacting with the effect of vertical seismic acceleration. The S1 state is very stable, as revealed in Figure 3b, such that the seismic acceleration just triggers a small oscillation. Figure 4: The influence of seismic acceleration on the single channel system at S1 state: (**a**) an actual vertical seismic acceleration recorded during the Chi-Chi earthquake in Taiwan [28]; (**b**) seismic-induced inlet velocity oscillation. On the other hand, at the same inlet fluid temperature with \(N_{P\text{-}SUB}\) = 1.55, the operating power is increased to another S2 stable state with \(N_{TPC}\) = 5.645, which is rather near the stability boundary of a single channel system, as revealed in Figure 3b. Assuming the same vertical seismic acceleration in Figure 4a is imposed on the S2 stable state, the results in Figure 5a illustrate that the seismic-induced oscillation in the S2 state is much larger than that in S1 state. This demonstrates that the strength of seismic-induced oscillation is related to the inherent stability characteristics of the initial state. For the S1 stable state, Figure 5b explores the effect of inlet fluid temperature on the seismic-induced oscillation of the single heated channel system. Under the same heating power (\(N_{TPC}\) = 3.232), the inlet fluid temperature is step decreased from \(N_{P\text{-}SUB}\) = 1.2, \(N_{P\text{-}SUB}\) = 1.55 (S1) to \(N_{P\text{-}SUB}\) = 2.02. The results in Figure 5b indicate that the reduction in inlet fluid temperature tends to stabilize the seismic-induced oscillation. It will increase the inlet fluid density to extend the heavy fluid region (region 1) inside the channel, thereby increasing the pressure drop contributed by the heavy fluid area; in addition, it will also drive the system to have a heavier inertial mass. Our previous study [14] showed that increasing the pressure drop of the heavy fluid region in the channel would have a stable effect on the supercritical forced convection heating channel system. Therefore, Figure 5b shows that due to the effects of both heavy fluid region and inertial mass, lowering the inlet fluid temperature will have a stable effect on the transient oscillation of the system caused by the seismic acceleration wave. In a supercritical water-heated channel system, such as the SCWR, the geometrical parameters may affect the transient oscillations of the system induced by the seismic acceleration wave. Under the same vertical seismic acceleration wave shown in Figure 4a and based on the S1 stable state, Figure 6a investigates the effect of inlet flow resistance (\(k_{i}\)) on the seismic-induced oscillation of a single supercritical heated channel.