Design and Performance of a Pico Propeller Hydro Turbine Model

2.1 Propeller turbine model test facility

The schematic of the propeller turbine model test facility is introduced in Fig. 1. Fig. 2 shows the axial pump model and propeller turbine model in detail. The propeller turbine model was horizontally installed in the test system which consists of an axial flow pump driven by a motor, two gate valves, a flow meter, a propeller turbine, a dynamometer and a water tank. The inner diameter of the pipe system is 155 mm but the casing inner diameters of the axial pump model and the propeller turbine model are both 151 mm with 0.5 mm tip clearance between the blade tip and the casing inner wall. As the tip gap less than 0.15 mm is not recommended [11], for manufacturing easier, the 0.5 mm tip gap was chosen. Pressure transducers are installed at the inlet and outlet pipes of the axial pump and the propeller turbine models to measure the pump and turbine heads, respectively. Dynamic torque meters are installed to measure the shaft speed and output torque. All measurement signals for each operating condition are recorded to a data logging system.

Fig. 1

The schematic of the propeller turbine model test facility with the old runner model

Fig. 2

The axial pump model(a) and (b)propeller turbine model

2.2 The old propeller turbine model performance

The old runner model which has a runner diameter of 150 mm was manufactured and installed within an inline pipe as shown in Fig. 3. In the experimental apparatus, the old runner model has no guide vane for the simplification of the pico propeller turbine model system. The experimental results of the old runner model are shown in Fig. 4. The efficiency of the old runner model at the design point is 66.5% which is a general value [4] but quite low yet for the commercialization of the pico propeller turbine. Therefore, a new propeller turbine needs to be designed to improve the performance.

Fig. 3

The existing old runner model (left) of the propeller turbine installed in the inline pipe (right)

Fig. 4

Measured performance of the propeller turbine model with the old runner model by experiment

3.1 Determination of the runner blade angle

Dixon [12] concluded that the free vortex method can be applied to the incompressible flow for Kaplan turbines as well as the compressible flow for gas turbine and compressors. K. Alexander [10] and P. Sing [8], used the free vortex method for their propeller turbine runner design. Therefore, the free vortex method has been applied to the flow from the guide vane outlet to the runner blade inlet in this study. The guide vane outlet angle and runner blade inlet angle have been calculated by the free vortex method with the assumption that there is no energy loss. The form of the free vortex principle comes from the conservation of angular momentum. This is illustrated by equation (2)

This is the starting point for calculating the runner blade inlet angle with the known constant k. The value of constant k can be found in equation (3) which is called the Euler’s head equation. Where H_th , V_u and u are the theoretical head, tangential velocity and peripheral velocity, respectively. Indicators 1 and 2 refer to the inlet and outlet of the runner blade, respectively. In order to achieve maximum energy transfer from the runner blade, the flow at the outlet of the runner blade should have no swirl flow. This means that V_u2 = 0.

Combining the equations (2) and (3) while considering the condition of no swirl flow at the runner outlet, the constant k can be substituted to form equation (4).

3.2 Design of runner blade shape

Fig. 7 represents the velocity diagrams of the runner blade and guide vane at a cylindrical section. In this study, from the hub to tip of the runner blade, five cylindrical sections are equally divided on the runner blade surface. In each section, the velocity triangle is calculated at the runner inlet and runner outlet points following the expressions:

Fig. 7

Velocity diagrams for a guide vane section (a) and runner blade section (b)

At the runner inlet point:

$$ {\beta }_1={\tan }^{-1}\left(\frac{V_{m1}}{u_1-V_{u1}}\right)$$

where $$ V_{u1}=\frac{\eta gH}{u_1};$$

　　　$$ \begin{array}{cc}{V}_{m1}=V_{m2};& u_1=u_2\end{array}$$

At the runner outlet point:

$$ {\beta }_2={\tan }^{-1}\left(\frac{V_{m2}}{u_2}\right)$$

where $$ \begin{array}{cc}{V}_{m2}=\frac{4Q}{\pi \left(D^2-D_h^2\right)};& u_2=\frac{\pi rn}{30}\end{array}$$

Where β, D_h , D and V_m are the runner blade angle, hub diameter, runner diameter and meridional velocity, respectively. The blade angle varies at each cylindrical section due to the variation of the relative flow angle from the hub to the tip of the blade inlet. The hub-tip diameter ratio,D_h /D, defines the hub diameter and annulus flow area for a propeller turbine. According to P. Singh [8], the choice of the hub to tip ratio and number of blades technically depends on the specific speed of the turbine. However, a designer's freedom can also be exercised in choosing the values. Table 2 shows the D_h /D from previous studies and includes the hub-tip diameter ratio used in this study. A hydrofoil was used in four sections, and the modified hydrofoil shape is utilized in the hub section of the new runner model due to its structural safety enhancement of the new runner model. The shape and dynamic characteristics of the hydrofoil are shown in Fig. 8. The hydrofoil characteristics were investigated at varying Reynolds number and angle of attack by using a commercial code of ANSYS CFX [13]. The figure shows that the highest lift to drag ratio was achieved at an angle of attack of 10 degrees in both cases. Figs. 9 and 10 compare the runner blade shape and 3D modeling between the old and new runner models. Table 3 compares the geometrical parameters of 2 runner models. Both of the runner models have same the solidity factor but different number of blade. As a result, the chord length in the new runner is shorter than that of the old runner model.

Table 2

The hub-tip diameter ratio

Fig. 8

Dynamic characteristics of hydrofoil used for the new runner model at Reynolds number of 500000 and 1000000

Fig. 9

Comparison of old and new runner blade shapes

Fig. 10

The 3D modelling of the old (a) and new (b) runner models

Table 3

Comparison of geometrical parameters for 2 runner models

3.3 Design of the guide vane

The design of old runner model did not include a guide vane. However, a guide vane was designed for the new runner model in order to improve the turbine performance, especially in efficiency more. The design method of the guide vane is similar to the design of the runner blade. To determine the guide vane angle, the free vortex method was applied to calculate the guide vane outlet according to the following expressions:

$$ {\alpha }_{2g\upsilon }={\text{tan}}^{-1}\left(\frac{V_{m2g\upsilon }}{V_{u2g\upsilon }}\right);$$

$$ \begin{array}{cc}{v}_{1g\upsilon }=V_{2g\upsilon };V_{u1g\upsilon }=0;& {\alpha }_{1g\upsilon }=90°\end{array}$$

Where the character “gυ” represents the value at the guide vane. Like the runner blade model, the guide vane shape is also designed with a hydrofoil. The number of the guide vane is designed with 7 vanes.

5.1 Performance curves

Fig. 13 compares the turbine performance curves by the old and new runner models. The experimental efficiency of the old model is almost agree well with the CFD analysis result below the range of rotational speed of 1600 min^-1. The different efficiency of the old turbine between the experimental and CFD results may be due to mechanical loss increasing at high rotational speed (>1600 min^-1) in the system. The figure clearly shows that the efficiency and power curves by the new runner model are higher than those by the old runner model. According to the CFD analysis results, the maximum efficiency by the new runner model is 84.0% which is approximately 14% higher than that by the old runner model at the design point. The experimental result of the new turbine model will be compared with that of the old turbine model in the future.

Fig. 13

Comparison of the turbine performance curves by the old and new runner models

Moreover, unit power (P₁₁ ), shown in equation (5) was used to compare the performance of the two runner models. The unit power produced by the new runner model largely higher than that by the old runner model at the design rotational speed.

5.2 Loss analysis

To investigate the component losses of the propeller turbine, four sub-domains were divided in the flow field namely; inlet region, guide vane region, runner region and outlet region. The first domain is the inlet region and is defined from the intake pipe inlet to the inlet of the guide vane. The second domain is the guide vane region which is defined from the inlet of the guide vane to the runner inlet. The third domain is the runner region which is defined from the runner inlet to the inlet of the discharge pipe. The final domain is the outlet region from the inlet of the discharge pipe. Equations (6) and (7) are applied for the results of CFD analysis to calculate the losses at the inlet, guide vane, outlet and runner regions, respectively.

Where Δp is the total pressure difference in the analysis region. H is the total head and Q is the flow rate supply at the inlet of the propeller turbine. The character “RN ” represents the value at the runner region. Fig. 14 shows local losses distribution by the turbines at varying rotational speed. In the old model, when increasing the runner rotational speed, the swirl intensity decreases in the outlet region. It relates to reduction of the loss at the outlet region. However, the loss in the runner region of old model increased. The losses in the runner and outlet regions are significantly reduced by the new runner model in comparison with those by the old runner model. This may explain why the efficiency of the new model improves by 14% at the design point. The losses at the inlet and guide vane regions of the new model show almost no changes at different rotational speeds. The runner region’s loss gradually increases as the rotational speed increases in both runner models. The loss at the outlet region of the new turbine model shows the lowest value at the design point.

Fig. 14

Comparison of component losses by old and new models

5.3 Pressure coefficient and streamline distribution on the blade surface

The pressure coefficient (C_p ) is calculated by the following equation (8) using the CFD analysis results.

Where p and $$ \overline{p}$$ are the local static pressure and averaged reference static pressure on the blade surface. Fig. 15 shows the one blade pressure coefficient at the local span positions of the runner blade models. The output torque is generated by the pressure difference between the pressure and suction sides of the runner model. In the new runner blade model, the pressure difference between the pressure and suction sides is larger than that of the old runner model. As a result, there is significant increase in the unit power produced by all blades of the new runner model as seen in Fig. 13. Fig. 16 indicates comparison of streamline distribution on the old and new runner blade surfaces at the design rotational speed. The numerical result represents that the position of the stagnation line on the runner blade surface moves toward the pressure side for old runner model. In contrast, uniform streamline distribution along the new runner blade surfaces is found at the design point. It results in the better efficiency is achieved in the new turbine model in comparing with the old turbine model. Consequently, the efficiency of the runner model was relatively high with the uniform flow. However, near the tip (span 0.9) of the new runner model, the suction side pressure coefficient near the leading edge is relatively quite small which could result in cavitation near the tip area.

Fig. 15

Comparison of pressure coefficient on the old and new blade model surfaces at the design point (1800 min-1)

Fig. 16

Comparison of streamline distribution on the old and new runner blade model surfaces at the design point

5.4 Cavitation performance

In order to predict the cavitation performance on the runner blade surfaces, the value of air volume fraction (AVF) was examined on the two runner blade models at the design point (1800 min^-1). The range of AVF is from 0 to 1; where a value of “1” means that air bubbles are completely formed, resulting in high cavitation occurrence. Fig. 17 shows that the AVF values of the old runner blade model are almost “0” at the all local span positions on the runner blade surface; this means that the possibility of cavitation occurrence in the old runner blade model is very low. However, the maximum value of AVF of the new runner model is 0.43, which is much higher than that of the old runner model because the pressure coefficient distribution at the leading edge on suction side of the new runner blade model is lower than that of the old model as shown in Fig. 15. Nevertheless, the AVF value of the new runner blade model is quite below the limit of cavitation occurrence.

Fig. 17

Air volume fraction distribution on the old and new runner blade surfaces at the design point (1800 min-1)