# Design of a New Supersonic Shock Wave Generator and Application in Power Generation
## 3 Supersonic Shock Wave Monitoring
### Experimental Analysis of Supersonic Shock Wave Monitoring  
In this study, we used the LabVIEW graphical language [29; 30; 31] to develop the monitoring software for the shock wave monitoring system. Figure 10 shows the screen of the shock wave monitoring results, the upper left corner shows that the sample number \(n_{s}\) of this monitoring system is 100,000 points (Pt), and the sampling rate \(r_{s}\) is 100,000 Pt/s; namely, the sampling time \(t_{s}\) of each Pt is 1/100,000 s. Buffered sampling [28] was adopted in this study. At a sampling rate of 100,000 points per sec, the pressure values of 100,000 points measured at each end were collected (lasting for 1 s) to draw the pressure curve in the middle of the screen. A monitoring result display zone is located on the right side of the screen to display the monitored data and the calculated result of shock wave speed and shock wave pressure. The pressure curve chart shows two curves in blue and red. The blue curve represents the front-end pressure curve, while the red curve represents the rear-end pressure curve. Figure 10: Shock wave monitoring results. Figure 9: Entity of the shock wave monitoring system. The system automatically displays the pressure pulses with the maximum peak (namely, the first measured shock wave) in the center of the chart. In this chart, a blue (front-end) pressure pulse appears first, followed by a red (rear-end) pressure pulse (we can ignore noises with slight pressure), indicating that the shock wave first passes through the front-end pressure sensor and then the rear-end pressure sensor. After that, a red-pressure pulse follows another red-pressure pulse, giving rise to another blue-pressure pulse. This phenomenon indicates that after passing through the rear-end pressure sensor for the first time, the shock wave reaches the bottom of the shock tube and is reflected; the reflected shock wave first passes through the rear-end pressure sensor and then the front-end pressure sensor. The measurements and calculated parameters in the monitoring result display zone on the right side of Figure 10 are analyzed from top to bottom as follows:  
1. Maximum voltage measured: The maximum peak voltage of the pressure pulse measured appears at the peak, where \"Ch1 Max\" represents the maximum voltage (\(v_{fmax}\)) of the front-end pressure curve (channel 1), and \"Ch2 Max\" represents the maximum voltage (\(v_{max}\)) of the rear-end pressure curve (channel 2). At this point, \(v_{fmax}\) = 6.756 V and \(v_{max}\) = 6.728 V.
2. Location with the maximum pressure: \"Ch1 Max Pos\" represents the location (\(l_{fmax}\)) with the maximum value of the front-end pressure curve, and \"Ch2 Max Pos\" represents the location (\(l_{max}\)) with the maximum value of the rear-end pressure curve. At this point, \(l_{fmax}\) = 8959 Pt and \(l_{max}\) = 8983 Pt. 3. Distance and time differences between both ends: The distance \(\Delta d\) between the front-end pressure sensor and the rear-end pressure sensor was 0.35 m, and the system calculates the time difference \(\Delta t\) of two pressure pulses based on the difference between the rear end and the front end in positions of the maximum pressure, namely,  
\[\Delta t=(l_{max}-l_{fmax})\times t_{s} \tag{18}\]  
Therefore, \(\Delta t\) = (8983 - 8959) \(\times\) 0.00001 = 24 \(\times\) 0.00001 = 0.00024 s, where \(t_{s}\) is the time of each sampling (0.00001 s). 4. Shock wave velocity and Mach: The shock wave velocity in the \(x\) direction can be calculated by dividing the distance between the front end and rear end by the time difference between the shock wave passing through the front-end and rear-end sensors. Namely, shock wave velocity \(v_{x}\) (m/s) was calculated as follows: \[v_{x}=\Delta d/\Delta t\] (19)  
Therefore, \(v_{x}\) = 0.35 m/0.00024 s = 1458.33 m/s. In addition, because Mach 1 (Ma) was about 340.3 m/s, the shock wave velocity \(M_{x}\) in Mach was calculated as follows:  
\[M_{x}=v_{x}/340.3=1458.33/340.3=4.29\text{ (Mach)} \tag{20}\]
5.