Introduction

The runner outlet diameter isD_e=350 mm, and the inlet diameter isD₁=377.5 mm. The number of the guide vanes areZ_g=16, and the number of the blade isZ_r=13. The guide vane opening can be fully opened to 64.4 mm, which is 100 % opening. The design point of the Francis turbine model is atH=18 m for the effective head,Q=0.45 m³/s for the water flow rate and the rotational speed isN=900 min^-1. The specific speed at the design point isN_S＝200 m-kW.Figure 1 shows the three-dimensional modeling view of the Francis turbine runner.Table 1 shows the detailed design specifications of the Francis turbine model.

Fig. 1 
3D modeling view of the Francis turbine runner model

Figure 2 shows the comparison of the Francis turbine model.Figure 2(a) is the comparison of the runner blade trailing edge shape. The curvature of runner blade trailing edge shape 1 is very small. In order to examine the runner blade trailing edge shape in regards to the performance and internal flow characteristics of the Francis turbine, a larger curvature of the runner trailing edge shape 2 is compared. The comparison of meridional shapes are also shown in this figure.

Fig. 2 
Francis turbine model shape design

For one-dimension loss analysis, the stay vane angle can be determined. For the stay vane profile optimization, Wu et. al.[4] concluded that the outflow from the stay vanes matches well with the inflow toward guide vanes after the profile of stay vane near the trailing edge is modified to protrude downstream. In this study, two types of stay vane leading edge shapes are investigated as shown inFig. 2(b), which has barely been studied before. The stay vane leading shape 1 is straight type, which is easy to manufacture. A curved corner shape at leading edge of the stay vane shape 2 is also studied. The comparison of meridional shapes are also shown in this figure.

Figure 2(c) shows that there are two cases with and without tongue wall at the ending of the spiral casing. As shown inFig. 2(c), location of the tongue wall is between the ending of the casing and the inlet of casing part. Tongue wall plays a role of stopping the water flow from recirculating into the casing.

Figure 2(d) shows the case with different stay vane number. Two kinds of stay vane number 8 and 16, are chosen to compare the influence on the performance and internal flow characteristics of the turbine model.

Computational Fluid Dynamics (CFD) analysis is a very useful tool for predicting hydro machinery performance at various operating conditions[5-8]. This study employs a commercial CFD code of ANSYS CFX[9] to conduct the internal flow analysis of Francis turbine model.

The numerical methods and boundary condition are set as shown inTable 2. The general connection is set as the frozen rotor condition between the rotational area and the fixed area in the flow field for steady state calculation. The total pressure boundary condition is applied at the inlet of the calculation domain, and the static pressure is set for the outlet of the domain.

Figure 3 show the results of the mesh and turbulence dependence at the design point of the turbine model. The results show that the efficiency of four turbulence models are similar. However, the Shear stress transport (SST) turbulence model has been well known to estimate both separation and vortex occurrence on the wall of a complicated blade shape. Therefore, TheSST is adopted as turbulence model.

Fig. 3 
Results of mesh and turbulence dependence

Moreover, the efficiency becomes constant after the mesh number excess of 3.0×10⁶. Therefore, the mesh number of about 3.0×10⁶ is selected for all the cases, for which the y⁺ is about 59 for runner blade surface.Figure 4 shows the fine numerical grids of the runner. The extended inlet pipe, stay vane, guide vane and draft tube of the turbine are made of hexahedral numerical grids. The casing part of the turbine fluid domain is made of tetrahedral grids because of the complex shape of the fluid domain.

Fig. 4 
Fine numerical grids of the runner

When the water flows through the turbine, hydro losses may occur due to eddy formation in different components, such as change in flow direction as well as due to loss in kinetic energy at the exit of the turbine.

Considering only the hydro loss, the turbine efficiency is calculated by the followingequation (1):

Whereη is the efficiency;T is the torque on the runner;ω is the angular speed of runner rotation on its own axis;ρ is the water density;g is the gravitational acceleration;Q is the flow rate;H is effective head.

Figure 5 shows the result of efficiencies compared by different internal flow passage shapes. The best efficiency point is taken as reference condition. The initial turbine model consists of runner blade shape 1, stay vane shape 1, tongue wall shape 1 (no volute tongue wall) and stay vane number of 8. The efficiency of initial model (dashed line) is slightly higher than that of design point. The CFD analysis only considers the hydro loss at the clearance gap between runner and fixed casing, hence the efficiency of experiment appears lower than CFD results. Attaching the tongue wall at the end of spiral casing and increasing the stay vane number to 16 are effective to improve the efficiency of the Francis turbine model. As the boundary condition of total pressure at inlet and static pressure at outlet is used, the head of the turbine almost constant by different internal flow passage shapes. Moreover, the effect of internal flow passage shapes on the flow rate slightly.

Fig. 5 
Comparison of efficiencies by different internal flow passage shapes

Figure 6 shows the pressure contours at the pressure and suction side of the runner blade surface. In comparison with the runner blade shape 1, the pressure at the runner blade shape 2 has a larger difference. There is a low pressure region near the blade leading edge at pressure side and near trailing edge at the suction side at the blade shape 2. This low pressure region may cause the efficiency to drop, which is unwanted in turbine performance improvement.

Fig. 6 
Pressure contours on the runner blade surface

Figure 7 presents the streamline distribution on the runner blade surface. The result shows that the streamline at the suction side has smooth distribution at the both blade shapes. However, the secondary flow occurs at the pressure side by both blade shapes. Moreover, the secondary flow occurs at the leading edge of the runner blade shape 2 with curvature shape of trailing edge.

Fig. 7 
Streamline distribution on the runner blade surface

The velocity vectors distribution on the center plane of the casing are shown inFig. 8. It clearly indicates that there is secondary flow at the pressure side of the runner blade for both the two cases with different runner blade trailing edge shapes. The effect of trailing edge shapes for suppressing secondary flow at the pressure side of the runner blade is poor.

Fig. 8 
Velocity vectors distribution

Figure 9 shows the streamline distribution on the stay vane surface. Smooth streamlines appear on the stay vane surface with straight corner leading edge (Stay vane shape 1). However, the secondary flow occurs when the curved leading edge was attached at the leading edge of stay vane (Stay vane shape 2). As a result, the secondary flow loss at the stay vane flow passage increases and the efficiency drops.

Fig. 9 
Streamline distribution on stay vane surface

Figure 10 presents the velocity vector distribution on the cross section plane. Recirculation flow appears at the stay vane inlet area of stay vane shape 2, which increases the energy loss and decreases the efficiency. The curved coner leading edge of stay vane contributes to the secondary flow loss at the stay vane passage, where the turbine efficiency drops.

Fig. 10 
Velocity vectors distribution by different stay vane shape

Figures 11 and12 show the velocity distribution at the inlet and outlet of stay vane with and without tongue wall, respectively. The tangential velocity fluctuation of the turbine with tongue wall deceases. This means the loss by fluctuation of velocity is reduced by tongue wall.

Fig. 11 
Tangential velocity distribution without tongue wall

Fig. 12 
Tangential velocity distribution with tongue wall

The flow angle at stay vane outlet is the flow angle at inlet of guide vane. These two angles should be similar for maximum efficiency. However, it is very difficult to match these angles. Therefore, these angles should be as close as possible for increasing efficiency.

The flow tangential angle in the region of stay vane inlet at the location ofθ from 0∽150˚ increases effectively near to the stay vane angle by attaching the tongue wall as shown inFigs 13 and14. In addition, the tangential angle of stay vane outlet becomes closer to the guide vane inlet angle by attaching the tongue wall. This means that the effect of tongue wall suppresses the incidence loss by correcting the flow angle.

Fig. 13 
Flow tangential angle without tongue wall

Fig. 14 
Flow tangential angle with tongue wall

The results ofFigs. 15 and16 show that the flow tangential angle of stay vane outlet is closer to the guide vane angle with the stay vane number of 16, which means that the energy loss reduces with a closer angle between the flow tangential angle of stay vane outlet and guide vane inlet. That is why the efficiency improves with the stay vane number of 16.

Fig. 15 
Tangential velocity distribution with stay number of 8

Fig. 16 
Tangential velocity distribution with stay number of 16