# Design of a New Supersonic Shock Wave Generator and Application in Power Generation
## 4 Design of a Power Generation System Driven by Supersonic Shock Waves
### Power Generation Experiments and Analysis
Table 2 shows the average values of relevant monitoring data in each period, with \(S_{min}\) = 1200 rpm, where \(f_{g\text{-avg-}k}\), \(s_{\text{-avg-}k}\), \(f_{g\text{-avg-}k}\), \(V_{p\text{-avg-}k}\), \(I_{p\text{-avg-}k}\), and \(E_{p\text{-avg-}k}\) (\(k\) = 0, 1, 2, and 3) are the average values of the shock frequency, rotation speed, flow, voltage, current, and power in the period that \(k\) bulbs are turned on. The comparison results in Table 2 show  
\[f_{s\text{-avg-}0}< f_{s\text{-avg-}1}< f_{s\text{-avg-}2}< f_{s\text{-avg-}3} \tag{24}\] \[s_{r\text{-avg-}0}> s_{r\text{-avg-}1}> s_{r\text{-avg-}2}> s_{r\text{-avg-}3}\] (25) \[f_{g\text{-avg-}0}< f_{g\text{-avg-}1}< f_{g\text{-avg-}2}< f_{g\text{-avg-}3}\] (26) \[V_{p\text{-avg-}0}> V_{p\text{-avg-}1}> V_{p\text{-avg-}2}> V_{p\text{-avg-}3} \tag{27}\]  
Figure 14: Execution screen of the power generation monitoring software. \[I_{p\text{-}avg\textgreater}<I_{p\text{-}avg\textgreater}1<I_{p\text{-}avg\textgreater 2 }<I_{p\text{-}avg\textgreater 3} \tag{28}\] Figure 13:0  
We also set the control parameter \(S_{min}\) to 1500 rpm, keeping \(P_{min}\) and \(T_{d}\) unchanged (i.e., \(P_{min}\) = 3.5 kg/cm\({}^{2}\), \(S_{min}\) = 1500 rpm, and \(T_{d}\) = 2 s), then re-execute the power generation monitoring experiment and calculate each monitoring data as mentioned above. Table 3 shows the average values of relevant monitoring data in each interval when \(S_{min}\) = 1500 rpm. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Period** & **Zero Bulbs** & **One Bulb** & **Two Bulbs** & **Three Bulbs** \\ \hline \(f_{\text{-}avg\textgreater}\)(Hz) & 0.42 & 0.54 & 0.68 & 0.81 \\ \hline \(s_{\text{-}avg\textgreater}\)(rpm) & 1262.52 & 1243.65 & 1204.34 & 1170.82 \\ \hline \(f_{\text{-}avg\textgreater}\)(L/min) & 143.83 & 176.79 & 197.15 & 233.27 \\ \hline \(V_{p\text{-}avg\textgreater}\)(V) & 28.38 & 26.79 & 25.46 & 24.44 \\ \hline \(I_{p\text{-}avg\textgreater}\)(mA) & 0 & 51.33 & 98.63 & 143.26 \\ \hline \(E_{p\text{-}avg\textgreater}\)(mW) & 0 & 1375.13 & 2514.68 & 3501.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The average values of monitoring data in each period when \(S_{min}\) = 1200 rpm. Figure 15: Display screen of power generation monitoring experiment results. In Table 3, the comparison results of \(f_{s\text{-}avg\text{-}k}\), \(s_{r\text{-}avg\text{-}k}\), \(f_{g\text{-}avg\text{-}k}\), \(V_{p\text{-}avg\text{-}k}\), \(I_{p\text{-}avg\text{-}k}\), and \(E_{p\text{-}avg\text{-}k}\) (\(k=0\), 1, 2, and 3) are the same as Equations (24)-(29). Based on the calculation and comparison of the above monitoring results, we can analyze the performance of these shock wave-driven power generation experiments as follows:  
1. When there is no load (the number of bulbs is zero), the output current \(I_{p}\) and power \(E_{p}\) are zero. 2. It can be seen from Equation (24) that when the number of light bulbs that are turned on increases, the frequency of the generated shock waves also increases, which means that the greater the load, the greater the aerodynamic force that needs to be supplied. 3. Tables 2 and 3 show that the faster the rotation speed, the higher the voltage generated. Therefore, each average voltage \(V_{p\text{-}avg\text{-}k}\) generated when \(S_{min}=1500\) rpm is higher than the corresponding \(V_{p\text{-}avg\text{-}k}\) generated when \(S_{min}=1200\) rpm. 4. Equations (25) and (27) show that when the rotational speed \(S_{min}\) is the same, the greater the number of bulbs, the lower the voltage that can be generated. 5. Equation (26) shows that when the number of bulbs increases, to maintain a fixed speed, more high-pressure gas needs to be consumed so that the flow rate will increase significantly, and the greater the number of bulbs, the higher the gas flow rate. 6. Equations (28) and (29) indicate that when the number of light bulbs increases, both \(I_{p\text{-}avg}\) and \(E_{p\text{-}avg}\) become larger.