# Analysis of the Guide Vane Jet-Vortex Flow and the Induced Noise in a Prototype Pump-Turbine
## 5 Results and Analysis
### Instaneous Turbulent-Flow-Induced Noise Field  
Based on the \(\mathrm{S_{A}}\) and \(\mathrm{S_{B}}\) surfaces, the instaneous turbulent-flow-induced noise fields were analyzed. Figure 8 shows the instaneous turbulent-flow-induced noise field on \(\mathrm{S_{A}}\) by plotting the \(L_{sp}\) contour. The indication numbers I to VII are kept on this figure. In the number I region in which the flow ring is between the runner trailing-edge and the guide vane, the \(L_{sp}\) value is around 80 dB. This is not a high noise region. The guide vane jet region number II is the highest \(L_{sp}\) region on \(\mathrm{S_{A}}\). The value of \(L_{sp}\) is up to 150 dB. In the twin-vortexes region numbers III and IV, \(L_{sp}\) becomes higher to about 100-120 dB. However, a low \(L_{sp}\) value lower than 90 dB can be also observed in the vortex core region of number IV. Figure 6: Flow regime on \(\mathrm{S_{A}}\) by plotting the \(C_{v}\) vectors. I: Flow ring between the runner trailing-edge and the guide vane; II: Guide vane jet; III and IV: Twin-vortexes adjacent to guide vane jet; V: Inter stay vane vortex; VI: Stay vane jet; VII: Volute vortex-ring; RSI: Rotor-stator interface. Figure 7: Flow regime on \(\mathrm{S_{B}}\) in volute at different locations by plotting the \(C_{v}\) vectors. (**a**) Section across the stay vane jet; (**b**) section across the volute vortex. This means that the clockwise rotating vortex produces more noise than the counter-clockwise rotating vortex. The inter stay vane vortex number V and the stay vane jet flow number VI are also high \(L_{sp}\) regions. The local highest \(L_{sp}\) value is in the stay vane vortex core region and reached about 130 dB. The value of \(L_{sp}\) in the volute vortex ring number VII region decreases to about 80-100 dB. However, it is also higher than in the other parts of volute. Based on Figure 9b, it can be seen that the local highest \(L_{sp}\) value is in the volute vortex core region. If the stay vane jet flows across the volute vortex ring, the local highest \(L_{sp}\) region disappears. \(L_{sp}\) is relatively high on the symmetry axis due to upper-lower flow interference. Figure 8: Instaneous turbulent-flow-induced noise field on S\({}_{\text{A}}\) by plotting the \(L_{sp}\) contour. I: Flow ring between the runner trailing-edge and the guide vane; II: Guide vane jet; III and IV: Twin-vortexes adjacent to guide vane jet; V: Inter stay vane vortex; VI: Stay vane jet; VII: Volute vortex-ring; RSI: Rotor-stator interface. Figure 9: Instaneous turbulent-flow-induced noise field on S\({}_{\text{B}}\) in volute at different locations by plotting the \(L_{sp}\) contour. (**a**) Section across the stay vane jet; (**b**) section across the volute vortex. Local high \(L_{sp}\) regions can be also found on the runner blade leading-edge, even if there is no obvious undesirable flow pattern. Figure 10 indicates the \(L_{sp}\) contours on the runner blade leading-edge, guide vane blade leading-edge, and stay vane blade leading-edge. Similarities can be found in that the leading-edge regions are all in high \(L_{sp}\). Specifically, two high \(L_{sp}\) regions can be found on one guide vane blade's leading-edge and on another guide vane blade's trailing-edge. On the contrary, the inter guide vane region where jet flow already generates is low in \(L_{sp}\). Thus, the local flow striking and separation are the reasons why flow noise generates. According to Equation (11), the turbulent-flow-induced noise strongly relates to the turbulence kinetic energy \(k\) and eddy dissipation rate \(\varepsilon\). To understand the reason why noise is generated in turbulent flow, the distribution of \(k\) and \(\varepsilon\) can be studied. The dimensionless turbulence kinetic energy coefficient \(C_{k}\) is used:  
\[C_{k}\ =\ \frac{k}{2 gR_{hi}} \tag{14}\]  
where \(g\) is the acceleration of gravity.