Runner Design and Internal Flow Characteristics Analysis for an Ns=200 Francis Hydro Turbine Model

2.1 Turbine runner model

This study is a continuation from a previous study [7]. In the previous study, a CFD analysis was conducted to investigate the internal flow characteristics of the Francis hydro turbine model with various internal flow passage shapes. However, the efficiency of the runner was still relatively low. Therefore, a similar design method was applied as in the previous study [4] to design the new Francis hydro turbine runner for Ns = 200 m-kW-min^-1.

The flow chart of the Francis hydro turbine design is shown in Figure 1. There are two redesign processes in this design flow chart. The turbine head is controlled by the guide vane opening at the design point condition. The outflow angle from the runner outlet is controlled by the blade loading and blade outlet angle. The guide vane angle and blade loading were modified until the turbine head and outflow angle from the runner were satisfactory.

The meridional shape of the Francis hydro turbine model is shown in Figure 2. The runner inlet diameter is D₁ = 377.5 mm, and the outlet diameter is D_e = 350 mm. The numbers of stay vanes and guide vanes are Z_s = Z_g = 16, and the number of runner blade vanes is Z_r = 13. The effective head of the Francis hydro turbine model is H = 18 m at the design condition, and the flow rate is Q = 0.45 m³/s. The rotational speed of the runner is N = 900 min^-1. The specific speed at the design point is Ns = 200 m-kW-min^-1. Table 1 shows the specifications of the Francis hydro turbine model runner. Figure 3 shows the three-dimensional model of the new Francis hydro turbine model runner and blade shape. Figure 4 shows the full fluid domain of the turbine model for CFD calculations, including the casing, stay vane, guide vane, runner, draft tube, and clearance gap.

Figure 1:

Flow chart of the Francis hydro turbine runner design

Figure 2:

Meridional shape of the Francis hydro turbine model runner

Table 1:

Design specifications of Francis hydro turbine model

Figure 3:

3D modeling of the Francis hydro turbine model runner and blade shapes

Figure 4:

3D fluid domain of the Francis hydro turbine model for CFD calculation

2.2 Numerical methods

The performance investigation and internal flow analysis of the turbine model was conducted by CFD analysis. The CFD analysis is a very useful tool for predicting hydraulic machinery performance at various operating conditions [2]-[11]. A turbulence model dependence test was conducted in the previous study [7] and a shear stress transport (SST) model has been applied in this analysis, which is well known to estimate both separation and vorticity occurring on the walls of complicated blade shapes. This study employs the commercial CFD code ANSYS CFX [12] to conduct CFD analysis. The operating condition maintains the head at 18 m and the flow rate range varies according to the guide vane openings. The boundary conditions are summarized in Table 2.

Moreover, according to the mesh dependence test as shown in Figure 5, a mesh number of approximately 11.0 × 10⁶ applied for all the cases, and y+ was approximately 59 for the runner blade surface. Figure 6 shows the fine numerical mesh used for Francis hydro turbine model components. The extended inlet pipe, stay vane, guide vane, and draft tube of the turbine model are modeled with a hexahedral numerical mesh. The casing part of the turbine model fluid domain is modeled with a tetrahedral mesh.

Table 2:

Numerical methods and boundary conditions

Figure 5:

Mesh dependence test result

Figure 6:

Numerical mesh for the Francis hydro turbine model components

3.1 Performance characteristic curves

For performance analysis of the Francis turbine model, all the flow rates and rotation speeds were normalized to unit flow and unit speed, respectively. Unit normalization was calculated through the following equations:

where N₁₁ is the unit speed, Q₁₁ is the unit flow, N is the rotational speed, D₁ is the diameter of the runner, Q is the flow rate, H is the head of the turbine, T is the torque, and ω is the rotational speed of the runner.

Performance curves with the characteristics of efficiency and unit flow with respect to unit speed at the design guide vane (GV) opening for the Francis hydro turbine model are presented in Figure 7. From the results, it can be inferred that this turbine model performs quite well. Moreover, there is a wide unit speed range with high efficiency, which means that there is a wide operation range with good performance. The head was maintained at 18 m, which is the design head of the Francis hydro turbine model. This efficiency takes into account the leakage loss, as well.

Figure 8 shows the relationship between unit flow (Q₁₁) and unit speed (N₁₁). It can be seen that there was an almost linear distribution between the unit flow and unit speed. The unit flow of the turbine was higher for the high guide vane opening in comparison to the low guide vane opening. The hill chart of the Francis hydro turbine model obtained by CFD analysis is shown in Figure 9. The efficiency in the hill chart was normalized by η/η_max. It can be seen that a high efficiency ratio of 0.99 was present at the guide vane opening from 30.4 mm to 37.3 mm. Therefore, the operation range with high performance for this turbine is relatively wide.

Figure 7:

Performance curve of the Francis hydro turbine model at design guide vane opening

Figure 8:

Relationship between unit flow (Q11) and unit speed (N11)

Figure 9:

Hill chart of the Francis hydro turbine model obtained by CFD analysis

3.2 Loss distribution

The losses in the clearance gap part mainly consisted of a degraded volumetric leakage flow rate. In order to study the Francis hydro turbine volumetric loss distribution in detail, the part load (PL), best efficiency point (BEP), and high load (HL) cases were typically selected for investigating the internal flow characteristics as shown in Figure 9.

Figure 10 shows the results of the volumetric leakage flow rate distribution in the clearance gap part. The volumetric leakage flow rates at all the operating points were relatively small. The volumetric leakage flow rate Q_leakage in the lower part was higher than that in the upper part. The main flow rate increased from partial load to high load while the volumetric leakage flow rate remained almost constant. As the head of the turbine was maintained, it can be conjectured that the volumetric leakage flow rate mainly depends on the pressure difference between the turbine inlet and outlet.

Figure 11 shows the loss distribution for each component. It can be seen that the BEP condition experienced its minimum loss in the runner and draft tube passage. Swirling flow occurs in the draft tube at off-design points, which contributes to losses in the turbine. There are only friction losses in the casing passage. Therefore, the HL condition at high velocity contributes to a large loss in the casing passage.

Figure 10:

Volumetric loss in the clearance gap part

Figure 11:

Loss distribution for each component

Figure 12:

Streamline distribution on the runner blade surface

3.3 Streamline distribution on the blade

Streamline distributions on runner blade surfaces clearly revealed the internal flow characteristics at the blade passages. In this study, the streamline on the blade surface at PL, BEP and HL was selected for further investigation.

The streamlines on the blade surface showed that there are better streamline distributions at both pressure and suction sides at the high-load operating condition than at others. Because of centrifugal force, secondary flow occurs to a large extent at both pressure and suction sides near the leading edge at the partial load condition where the loss occurs to a large extent, thereby reducing performance. The HL velocity was larger than that for the BEP. Therefore, the effect of centrifugal force on the secondary flow was weak for the HL condition, and the streamlines on the HL runner surfaces were relatively better than those for BEP. In general, the minimum loss in the runner and draft tube passage was located at the BEP condition.