## 4 Results and Discussion
### Non-Linear Seismic-Induced Oscillations
#### 4.2.2 Seismic-Induced Oscillation of Parallel Three Channel System  
The seismic impact on the parallel channel system is related to the inherent natures of the initial operating state, particularly the resonance oscillation could be triggered while the seismic frequency approaches the natural frequency of the working flow. Figure 8 illustrates the variation in the dimensionless natural frequency (\(f^{+}\)) along with the stability boundary of three supercritical water heated channels with a heat flux ratio of 1.2:1.0:0.8 at a supercritical pressure of 25 MPa. This figure shows that the distribution of the dimensionless natural frequency on the stability boundary is ranged between 0.93 and 4.16. The parameter of \(N_{P\text{-}SUB}\) indicates the effect of inlet fluid temperature. A larger value of \(N_{P\text{-}SUB}\) infers a lower inlet fluid temperature, and vice versa. In the region with \(N_{P\text{-}SUB}\geq 1.67\), where the heavy fluid region would contribute a substantial role, the dimensionless natural  
Figure 6: The influence of parameter on the seismic-induced oscillation: (**a**) the effect of inlet loss coefficient; (**b**) the effect of outlet loss coefficient. frequency on the stability boundary is mildly increased as \(N_{P\text{-}SUB}\) is decreased. In addition, at a fixed value of \(N_{TPC}\) = 6.15, the dimensionless natural frequencies at the stable states with \(N_{P\text{-}SUB}\) = 2.882, 2.811 and 2.727 are 0.98, 1.1 and 1.14, respectively, as labeled in Figure 8. It also suggests the similar slight increasing trend in this region if the inlet fluid temperature is increased. However, when \(N_{P\text{-}SUB}\) is less than 1.67, the dimensionless natural frequency on the stability boundary would drastically increase as \(N_{P\text{-}SUB}\) is further decreased due to the expansion of the light fluid region dominating the channels. On the other hand, the parameter of \(N_{TPC}\) may include the effects of heat flux, heated length and channel diameter, which is generally proportional to heat flux (\(q^{\prime\prime}\)) and heated length (\(L_{H}\)) but inversely proportional to channel diameter (\(D_{H}\)). The increase of \(N_{TPC}\) can be reached by the increase of heating power (\(Q\)) or the reduction of total flow rate (\(W_{tot}\)), and vice versa. At a fixed value of \(N_{P\text{-}SUB}\) = 2.882, the dimensionless natural frequencies at the stable states with \(N_{TPC}\) = 6.15, 6.234 and 6.298 are 0.98, 1.05 and 1.09, respectively, as labeled in Figure 8. This implies that the dimensionless natural frequency would increase as the increase of \(N_{TPC}\) due to the expansion of light fluid region. For the supercritical water three-heated channels with an asymmetric radial power ratio of 1.2:1.0:0.8 considered in this study, the seismic-induced effect on the system transients is investigated in S1 stable state, i.e., normal operating state as denoted in Figure 3b. The inherent natural frequency of S1 state is approximately \(f^{+}\) = 1.1. Figure 9a assumes a set of external vertical sinusoidal acceleration waves, including two vertical acceleration waves with the same peak acceleration (\(a_{peak}\) = 0.1 g) but with different oscillation frequencies of \(f^{+}\) = 0.5 (non-resonance condition) and 1.1 (resonance condition), respectively. This study supposes that the total flow rate of parallel supercritical heated channels keeps constant under the impact of the external vertical acceleration wave, as shown in Figure 9b. As the vertical sinusoidal acceleration wave in Figure 9a is imposed on the system, Figure 9c shows the vibration-induced amplitude oscillations of the inlet flow velocity (\(\delta u_{i}^{+}\)) among these three supercritical heated channels. The channel oscillations triggered by the vertical acceleration wave can be regarded as the result of the inherent stability characteristics of the initial state combined with the influence of external vertical acceleration wave.