# Sediment Erosion Characteristics and Mechanism on Guide Vane End-Clearance of Hydro Turbine
## 4 Results and Discussion
### Turbulence Characteristics in the End-Clearance of the Guide Vane  
The turbulence integral scales of each monitoring point in three directions were calculated by the direct integration of the autocorrelation function. The turbulence integral scale of different monitoring  
Figure 12: Velocity and pressure measurements along the clearance mid-span: (**a**) Pressure; and (**b**) velocity. Figure 13: Leakage flow. points is shown in Figure 14. The turbulence integral scale of each monitoring point in the X direction was small and the variable quantity was not large, which was mainly caused by the limitation of the clearance size. Meanwhile, the significant turbulence integral scale changes in the Y and Z direction were mainly due to a lack of restriction on the clearance size. By comparing the wear morphology in Figures 10 and 11, the turbulence integral scale in the Y and Z direction was large where the erosion regions were larger. The turbulence integral scale was larger, which showed that the vortex was larger. Then, more sand particles rolled up to the rotational motion by vortex, given that rotational motion makes sand particles have enough velocity and impingement angle to damage the flow-passage surfaces. That is, a larger turbulence integral scale makes a larger wear region, which was verified by the large and small wing surface wear. By comparing Figure 14a with Figure 13, the turbulence integral scale increased sharply at the Y and Z direction of C2. This was mainly affected by two factors: (1) The leakage vortex flowed down and only went through C2, and (2) the turbulence scale of the wake was larger at C2 due to the guide vane with a large eccentric shaft. A sediment-laden vortex with a large turbulence scale will cause serious wear of the runner inlet. To analyze the turbulent flow characteristics of monitoring points, turbulent kinetic energy (TKE) and coherent turbulence kinetic energy (CTKE) are defined, which is given as:  
\[TKE(t)=\frac{1}{2}\Big{[}u_{x^{\prime}}(t)^{2}+u_{y^{\prime}}(t)^{2}+u_{z^{ \prime}}(t)^{2}\Big{]}, \tag{22}\]  
where \(u_{x^{\prime}}(t)\), \(u_{y^{\prime}}(t)\), and \(u_{z^{\prime}}(t)\) are the fluctuation values of axial velocity, lateral velocity, and vertical velocity, respectively. \[CTKE(t)=\frac{1}{2}\Big{[}\Big{(}u_{x^{\prime}}(t)u_{y^{\prime}}(t)\Big{)}^{2 }+\big{(}u_{x^{\prime}}(t)u_{z^{\prime}}(t)\big{)}^{2}+\Big{(}u_{y^{\prime}}( t)u_{z^{\prime}}(t)\Big{)}^{2}\Big{]}^{1/2}. \tag{23}\]  
The horizontal flow angle \(\psi\prime(t)\) and the vertical flow angle \(\alpha\prime(t)\) of the velocity fluctuation can be calculated with Equations (4) and (5). Thus, the direction variant characteristics of turbulent fluctuation at monitoring points can be obtained:  
\[\psi\prime(t)=\tan^{-1}\Big{(}u_{y^{\prime}}(t)/u_{z^{\prime}}(t)\Big{)}. \tag{24}\]  
\[\alpha\prime(t)=\tan^{-1}(u_{x^{\prime}}(t)/u_{z^{\prime}}(t)). \tag{25}\]  
The TKE and CTKE of the monitoring points are shown in Figure 15. From Figure 15a, the TKE and CTKE in the clearance were greater than that outside the clearance. Combining Figure 10, Figure 12, and Figure 14, the TKE and CTKE of A5 was greater than A4, but there was almost no erosion at A5. This is because the pressure drop was obvious, the flow field was evenly distributed, the turbulence  
Figure 14: Turbulence integral scale: (**a**) Turbulence integral scale and average erosion rate of A3–A6; and (**b**) C1–C5. integral scale was small, and the particles were not deposited at A5. In addition, the wear region size and erosion rate of the wing surface of A4 were larger than that of A3, but the TKE and CTKE at A4 were smaller. The above results explain that TKE and CTKE were not a determinant for sediment wear.