# Analysis of the Guide Vane Jet-Vortex Flow and the Induced Noise in a Prototype Pump-Turbine
## 5 Results and Analysis
### Turbulence Kinetic Energy Pulsation  
To study the pulsation of turbulence kinetic energy, points were set, as shown in Figure 13, for monitoring the \(C_{k}\) variation in the indication regions numbers I to VII. Points P\({}_{1}\) to P\({}_{7}\) are, respectively, in the local flow regions I to VII. Figures 1-20 are the time-domain and frequency-domain plots of \(C_{k}\) on monitoring points P\({}_{1}\) to P\({}_{7}\). The time-domain data were acquired within 3600 timesteps that were five runner revolutions. The frequency-domain data was created based on the time-domain data by applying the fast-Fourier transformation (FFT) method with Hanning window. Figure 12: The contour of \(C_{\varepsilon}\) on the blade leading-edges. LE: Leading-edge. (**a**) Runner leading-edge; (**b**) Guide vane leading-edge and trailing-edge; (**c**) Stay vane leading-edge. The \(C_{k}\) pulsation on P\({}_{1}\) is shown in Figure 14. Multiple peaks can be found on the frequency-domain plot. Some important frequencies can be found including the blade frequency \(f_{b}\) of about 64.5 Hz and another frequency \(f_{2}\) of about 9.6 Hz. Three peaks are related to the blade frequency \(f_{b}\) are, respectively, \(f_{b}\), \(2f_{b}\), and \(3f_{b}\). Three other peaks are related to \(f_{2}\) are \(0.15f_{2}\), \(f_{2}\), and \(3f_{2}\). Generally, P\({}_{1}\) is under the strong influence of blade frequency \(f_{b}\), which is also a multiple of runner frequency \(f_{m}\). This is because P\({}_{1}\) is near the runner blade trailing-edge and faces the incoming flow from runner pumping. The frequency \(f_{2}\) is also strong and needs further analysis on points P\({}_{2}\) to P\({}_{7}\). The \(C_{k}\) pulsation on P\({}_{2}\) is shown in Figure 15. The runner blade frequency \(f_{b}\) is still obvious and stronger in amplitude than on P\({}_{1}\). However, the frequency \(f_{2}\) and its two-times multiple \(2f_{2}\) are relatively stronger than \(f_{b}\). P\({}_{2}\) is in the guide vane jet which is induced by both the runner pumping and the small guide vane opening. Thus, the runner blade frequency impressively influences P\({}_{2}\). Frequency \(f_{2}\) dominates with the \(C_{k}\) peak value up to about 0.23. Therefore, the \(f_{2}\)-series frequencies on P\({}_{1}\) are propagated from the guide vane jet region. Figure 14: Analysis of \(C_{k}\) pulsation on P\({}_{1}\). (**a**) Time-domain plot; (**b**) frequency-domain plot. Figure 13: Points P\({}_{1}\) to P\({}_{7}\) for monitoring the turbulence flow field. RSI: Rotor-stator interface; RD: Runner rotation direction. Figure 15: Analysis of \(C_{k}\) pulsation on P\({}_{2}\). (**a**) Time-domain plot; (**b**) frequency-domain plot. The \(C_{k}\) pulsation on P\({}_{3}\) is shown in Figure 16. P\({}_{3}\) is in one of the twin-vortexes which rotates in the same direction of runner rotation. The runner blade frequency \(f_{b}\) is no longer strong, but \(f_{2}\)-series dominates. \(1/3f_{2},f_{2}\), and \(2f_{2}\) are on a high amplitude level. Among them, the \(C_{k}\) amplitude of \(f_{2}\) is the highest that larger than 0.10. The \(C_{k}\) amplitude of 1/3\(f_{2}\) and 2\(f_{2}\) are also higher than 0.05. The \(C_{k}\) pulsation on P\({}_{4}\) is shown in Figure 17. P\({}_{4}\) is in another one of the twin-vortexes which rotates counter-rotationally against the runner. Frequency band becomes complex with 1/3\(f_{2},f_{2}\), 2\(f_{2}\), and 5.9 Hz and 33.6 Hz peaks. The \(C_{k}\) amplitude of these frequencies are no larger than 0.05 and are lower than that on P\({}_{3}\). This means that the turbulence kinetic energy is lower in the counter-runner-rotational vortex than in the runner-rotational vortex. According to the \(C_{k}\) pulsations on P\({}_{3}\) and P\({}_{4}\), the \(f_{2}\)-series frequencies also exist in the twin-vortexes adjacent to the guide vane jet. The \(C_{k}\) pulsation on P\({}_{5}\) is shown in Figure 18. The frequency \(f_{2}\) dominates with the \(C_{k}\) amplitude of about 0.15.