Francis turbines have been widely used globally because of their wide range of heads and flow rate applications. In addition, they also provide a good efficiency of approximately 90%. In most applications, the turbine is used for high heads and flow rates. However, in this study, the Francis turbine has been applied in a much smaller scale: it is designed for city water supply system. In general, a pressure-relief valve is normally used in the system because jet flow with high pressure will be formed when water is directly supplied to the public. However, a large amount of energy is wasted; therefore, a new type of Francis turbine with an inline casing is suggested in such situations to recycle the energy and decrease the pressure instead of using a pressure reducing valve.

In general, a spiral casing is preferred in a Francis turbine to supply water from the penstock to the vanes and through its unique shape of continual cross sectional area reduction, it maintains a near uniform velocity of water around the vanes. However, owing to the simplicity of the water supply piping system, an inline flow passage is required. Figure 1 shows the schematic view of the inline Francis turbine. The leakage and clearance parts are included in this study because the previous study showed that the leakage affects the performance considerably; especially, for small-scale turbines, the leakage can decrease the efficiency up to 3% at the normal operation.

Figure 1: 
Schematic view of the inline Francis turbine

This study is a continuation of the previous study conducted by the same authors [1]-[3]. However, there are some differences in the design specifications. The new runner has been designed with a lower head of 16m and flow rate of 0.028m³/s. Table 1 shows the similarities and differences in the design specifications. The same inline casing and piping dimensions have been used in the new design. The runner inlet diameter is the same but the exit diameter has been increased. The meridional shape of the new runner has been modified as illustrated in Figure 2. Some modifications have been made to the previous fluid domain, especially to the areas that connect to the new runner. These parts include the guide vane, leakage, and draft tube cone. The width B_g of the guide vane was modified from 15.5 to 18.8 mm. The draft tube cone was modified at the connection of the runner because the diameter changed from 100 to 112 mm. Furthermore, the leakage part was changed because the meridional shape of the new runner is different from that in the previous study. Figure 3 illustrates these modifications.

Figure 2: 
Comparison of N_s 80 to N_s 100 meridional shape

Figure 3: 
Separate isometric views of the modified regions for the fluid domain

The performance investigation and internal flow analysis of the turbine were conducted using computational fluid dynamics (CFD). The CFD analysis is very useful in predicting the hydraulic machinery performance at various operating conditions [4]-[7]. Therefore, the same procedure was followed from the previous studies [2-3]. A turbulence dependence test was conducted in the previous study, and similarly a shear stress transport (SST) model has been applied to this analysis. The model is well known to estimate both separation and vortex occurring on the wall of a complicated blade shape. This study employs a commercial CFD code ANSYS CFX to conduct CFD analysis [8]. The operating condition maintains the head at 16 m and the flow rate range varies according to the guide vane openings, as shown in Table 2. Table 3 summarizes the boundary conditions.

Additionally, shape and location of the stay vane with respect to guide vane was investigated. Table 4 and Figure 4 present the description of the four cases. Furthermore, the circumferential velocity and pressure were investigated at the locations of blue and red circles marked in the figure. The red circles represent the study of the stay vane outlet and the inlet distribution of the guide vane, whereas the blue circles represent the study of the outlet distribution of the guide vane. The initial design is commonly used with a spiral casing.

Figure 4: 
Stay vane investigation cases

In this study, the performance of a new inline Francis turbine was investigated and compared with the results of the previous study. Although, both turbines showed relatively similar efficiencies, the new turbine outperformed its predecessor, and the effect of the stay vanes was reduced. In the previous study, the effect of stay vanes showed considerable increase in the efficiency up to 5%. However, the stay vanes for the new turbine slightly affected the efficiency and, thus removing them could be more economical to the overall system. Another interesting discovery was the effect of leakage on the efficiency. Future studies could investigate the shape of the leakage to reduce the losses and improve the efficiency. The leakage part in the previous study was narrower and longer than that in the present study, and the internal flow results of the two differ considerably. However, there are limitations to the leakage because of the change in meridional shape.