1Introduction

For centuries, mankind has used water wheels as a source of mechanical power near the rivers for mills, weaving factories and machine workshops. However, the theory of water wheels and their application to other water sources (such as tidal streams) has not been widely developed so far, from the end of the 19th century, the most develop technology took a significant leap into new turbines, especially with the emersion of steam turbines and diesel engines, thus causing water wheel development to cease for a period (Capecchi, 2013; Denny, 2004). Recently, due to a new perspective toward renewable energy and to local and smart electricity production, traditional water wheels are regarded again as a clean and accessible way for electricity generation from water, especially in sites with high potential of ocean energy, improving local economy and sustainable development. In fact, many countries surrounded by the oceans have rich marine energy resources, hence significant amount of electric power can be generated from the oceans. Besides that, marine currents offer a regular and predictable source of renewable energy (Charlier, 2003).

In general, water wheels can be classified into overshot, undershot, breast-shot (all of which work through extracting potential energy), and a stream design. In this paper, a stream water wheel was chosen to study as it is most suited to the low head flow as typified by near-shoe tidal induced currents, and as it is an impulse device, working through extraction of kinetic energy. There are several studies using numerical and experimental methods on water wheel turbines in order to evaluate the power performance of these devices. For instance, a study on a water wheel using CFD (Sam, 2010) was done for two kinds of blade shapes (triangle and rectangle). It indicated that the triangular blade design shows the weak performance compared to the rectangular one (about 30 % reduction in efficiency). Other researches on a water wheel turbine in different shapes and the flow field correlation between the experimental and numerical analysis were carried out by Yasuyuki et al. (2014; 2015), showing that the turbine efficiency of the straight blade runner was greater than that of the curved blade runner regardless of the rotational speed, and the experimental results on the performance of this turbine and the flow field were consistent with the numerical simulation. Other experimental tests on water wheels were also performed by Yelguntwar et al. (2014), Muller et al. (2007), and Turnock et al. (2007) in order to contribute to the development of water wheels and tidal current turbines in general.

The main purpose of the study in this paper was to design, test and evaluate a water wheel type turbine for tidal stream energy extraction using a numerical analysis method. In the study, water wheel turbine performances were compared for different numbers of rotor blades (including 10, 12, and 20 blades) and for different blade shapes at tip speed ratio (TSR) ranging from 0.7 to 1.2. By analyzing the numerical results, including power efficiency among all kinds of water wheel turbine, a best design for the tidal current energy application can be found.

2Numerical Experiment Model

Theoretically, water wheel is a kind of rotating mechanical element which converts water power (kinetic energy and potential energy) into useful energy (electricity). Water wheels are classified into four different types (overshot, undershot, breast-shot and stream wheels) (Muller, 2007). In this paper, a stream wheel was chosen for the study as it is an impulse device working through extraction of kinetic energy and most suitable for a very low head as typified by near shore tidal induced currents. In this paper, based on a floating model of water wheel developed by Turnock et al. (2007), which is suitable for the electricity generation in shallow waters as well as in stream line waters, the author and his colleagues designed a model water wheel type turbine for tidal current energy extraction as shown in Fig. 1.

The wheel has two main components:

Besides that, a stationary part is equipped with auxiliary and supporting machineries, including:

The design parameters for modelling in a computational study are summarized as shown in Table 1.

2.1Case Study on Rotor Blades in Different Shapes

Fig. 2 shows three kinds of stream wheels with different blade shapes, including Straight, Curved and Zuppinger types. The Straight type or Sagebien wheel in Fig. 2a is known as a traditional and original design of water wheel which is mostly utilized for undershot water wheels. The Curved type or Poncelet wheel in Fig. 2b is a water wheel invented by Jean-Victor Poncelet and applied to the undershot water wheel in order to improve efficiency. The last configuration, Zuppinger type in Fig. 2c is a common type of undershot water wheel used for very small head differences of 0.5 to 0.95 m³/s per meter of width (Muller, 2007). All three configurations of undershot water wheel in Fig. 2 are designed and tested for the stream wheel in order to be suitable for tidal current exploitation.

2.2Case Study on Different Numbers of Rotor Blades

In order to investigate the performance of the turbine, a series of numerical experiments was conducted with the purpose to determine the turbine characteristics based on the number of blades. In general, the blades are designed in three different numbers, 10, 12, and 20, as shown in Fig. 3 with the same dimensions for comparison of performance.

3Meshing and Setup Parameters

3.1Meshing Strategy

A three-dimensional model of water wheel turbines and their flow field was designed and numerically discretized in computational simulation. Power performance and characteristics of water wheel type turbine are analyzed using the CFD commercial code, ANSYS CFX 15.0. Meshing is done using the ANSYS Meshing. Tetrahedral grids are dominantly applied for the results in the mesh size of 450,000 elements for the stationary domain (including inlet, outlet, bed and side walls).

All types of turbine runners resulted in relatively similar mesh sizes, about 450,000 elements, despite of the different numbers of blades and the different shapes. This is enough for the given computational problem-solving and assures accurate results. Fig. 4 illustrates mesh formation for the three configurations of rotor.

Fig. 5 shows the dimensionless wall (Y-plus) near the rotor blade region. To investigate mesh dependency as shown in Table 2, the number of computational grids was approximately doubled, and the analysis was conducted at the same rotational speed and water flow velocity. It revealed that although the torque reduced by about 3 % from the results presented in this paper, the effect of computational grid size and number was comparatively small.

3.2Calculation Domain and Boundary Conditions

The computational domain is shown in Fig. 6. This domain consists of the wheel and the upstream and downstream domains. The length of the upstream and downstream domains to the center of the wheel is 5D and 15D, respectively (where D is the diameter of wheel).

In this paper, a three-dimensional unsteady flow was used to analyze considering the free surfaces. The multiphase flow model is the uniform model of the Euler-Euler approach, with acting fluids including water and air. The basic equations employed in the model are based upon mass, momentum and volume fraction conservation. The shear stress transport (SST) k-w model was adopted as the turbulent flow modelling, and the standard wall function was used to handle regions near the wall surfaces.

For boundary conditions, the "Cartesian velocity components" was set to the inlet boundary, free outflow (with a relative air pressure of 0 Pa) was applied to the outlet boundary, and the rotational speed was set for the wheel domain. Furthermore, the top surface of the computational domain was permeable to the atmosphere in order to allow the air to move freely in and out of the domain, while no-slip wall conditions were applied to all other walls of the domain. The boundary of the rotating and stationary domains was joined by the transient rotor-stator method. For initial conditions, the simulation was set at the value of the upstream flow velocity. The volume fraction VF_ih of water for the initial condition was defined in accordance with the following formula using the step function:

where, y is the coordinate of the height direction in the computational domain, and the water depth h uses the initial value of the upstream water depth. Thus, the position y ≤ h is the domain of water and the position h ≥ y is the domain of air.

Time dependent behaviour for transient simulation in CFD is specified through time duration and time step. In order to save computational resources and compare the turbine efficiency conveniently among all kinds of water wheel type in this paper, yet ensuring the accuracy of simulation results, the wheel would undergo one rotation every 144 steps, and the time step was recalibrated until fluctuations in the flow became negligible. Time dependency is set based on the values of rotational speed of the wheel to effectively get converged.

4Results and Discussions

4.1Comparison of Different Blade Shapes

1)Velocity vectors and streamlines

According to the simulation results, it indicated that the turbine performance of the three turbines showed the highest efficiency at the tip speed ratio (TSR) 0.9. For simplification, therefore, comparison of water velocity vectors and streamlines was done only at TSR 0.9.

Figs. 7a to 7c show the visualizations of water flow velocity vectors and streamlines of the three kinds of wheels (Straight, Curved and Zuppinger, respectively) at TSR 0.9. It is clearly seen that for the Curved-bladed type in Fig. 7b, the water flows appeared to be much more turbulent in the space of the blades than for the Straight and Zuppinger types. Moreover, the water has a tendency to flow backward against the incoming flows. As a result, there would be resistance or negative influence on the power generation of the Curved type turbine. In contrast, the Straight type has the least turbulence and reverse flows comparing to the others. Thus, it can be seen that the Straight-bladed turbine would extract more power than the Curved and Zuppinger types.

2)Flow interaction at different tip-speed ratios

To compare the flow interaction around the Straight-bladed wheel, water velocity direction and intensity are observed with a numerical analysis at different TSR values. The comparative analysis was done similarly for the Curved and Zuppinger types. Fig. 8 shows the reference water surface at water depth of 50 cm from the wheel's center for the comparison of flow interaction among the three TSR values (0.7, 0.9 and 1.2) as shown in Figs. 9a to 9c (from top view), respectively.

As depicted in Fig. 9a, velocity vectors at TSR 0.7 inside a space where the blades come into direct contact with the water (called "working area"), have a small size, and they appeared to be "calm" and did not have much intense interaction between the blades and water flow. On the contrary, at TSR 0.9 in Fig. 9b, the velocity vectors inside the working area are much more intense than at TSR 0.7. In addition, the velocity direction in the working area at TSR 0.9 has a tendency to flow in the same way as the incoming flow. As a result, this would positively affect the water energy extraction of the turbine. Meanwhile, at TSR 1.2 in Fig. 9c, the velocity vectors seemed to flow in the opposite way of the inflow, and consequently showed negative back flows that decreased the power generation of the wheel.

3)Power efficiency comparison

Power performances of water wheel type tidal turbine are evaluated by power coefficient (C_P) and torque coefficient (C_Q) (Behrouzi et al., 2014) as shown in Figs. 10 and 11, respectively. The figures express C_P and C_Q as a function of TSR and show the performances of three configurations of water wheel turbine with different blade shapes. The study is carried out with several TSRs by varying the rotational speed and keeping the inflow velocity fixed at 1m/s.

Both of the graphs C_P and C_Q show the same patterns with a tendency to rise up from TSR 0.7 to a peak at TSR 0.9, and then decrease gradually down to TSR 1.2. According to the results shown in Fig. 10, the Straight-bladed type obtains the highest value of power coefficient (C_P) compared to the other types of blade shapes in all cases of TSR. At TSR 0.9, the power coefficient (C_P) of the Straight-bladed type reaches up to 43 % which is about 1.7 times that of TSR 0.7. For the Curved and Zuppinger types, they absorb the most water current energy at TSR 0.9, with the power coefficient of (C_P) about 38 % and 30 %, respectively. However, at higher TSRs, namely TSRs 1.1 and 1.2, the distinction in performance pattern is more evident between the Straight type and the Curved and Zuppinger types together. It is obvious that the Curved-bladed type mostly generates the lowest power efficiency in comparison with the others, especially at high TSRs.

Similar to the power coefficient (C_P) chart, as shown in Fig. 22 for the torque coefficient (C_Q) from a similar non-dimensional analysis of torque, the Straight type keeps showing its predominant performance comparing to the others at various TSRs, meaning that the torque extracted from the rotor's shaft of this turbine always achieves higher energy than the two other kinds of water wheel turbines. Conversely, it is clearly seen that the tidal current energy conversion capability of the Curved-bladed type is the smallest compared to the others at the same TSR, and the difference is clearer at higher TSRs, corresponding to higher rotational speeds.

All these results of turbine efficiency are reasonable and can be explained by the characteristics of flow patterns, including visualizations of velocity vectors and water volume fraction as discussed above, where high efficiency is found in the cases with clear changes in the velocity vectors of water flow before and after the rotor's blades that come into direct contact with water.

In summary, from the curves of C_P and C_Q, the turbine with Straight blades shows the best performance at all TSRs, especially at TSR 0.9 as shown by the change of flow pattern in Figs. 7 to 9.

4.2Comparison of Different Numbers of Rotor Blades

1)Flow pattern visualizations

An analysis of flow patterns for comparison of the three kinds of rotor blades in different numbers was done using a combination of water volume fraction and stream velocity vectors.

Figs. 12a to 12c show a difference in water volume fraction and velocity vector intensity of four types of studies on the number of blades at TSR 0.9. It is clearly seen that at the same TSR, the water amount passing through the 20-bladed type turbine (marked by black ellipse) is much less than that passing through the other types of water wheels. In addition, the velocity vectors' magnitude and intensity in the space between the blades of the 20-bladed type turbine that come into direct contact with water are very small compared to others, and the direction of velocity vectors shows a trend of tangential flow to the outer circumference of the wheel. Therefore, the water current energy transferring to the rotor in case of 20-bladed type is very small, and as a result, the extracted power on the wheel's shaft is small as well. On the contrary, the amount of water flowing through the 10-bladed type turbine is most dominant in all cases. Moreover, the difference in velocity vector intensity in case of 12-bladed types is not much considerable and smaller than that of 10-bladed turbine.

2)Turbine efficiency comparison

Figs. 13 and 14 illustrate a comparison of the performances (power and torque coefficients, respectively) of the three kinds of water wheel type tidal turbines with different numbers of rotor blades. For all turbines, the computed torque (represented by torque coefficient, C_Q) increase up to TSR 0.9 and then gradually decreased as the rotational speed increased. Accordingly, the computed power output (as represented by the power coefficient, C_P) increased as well when the rotational speed was raised, but with a slightly different torque coefficient (C_Q) pattern.

Obviously, the 10-bladed type generates the highest power and torque compared to the other types in the study with up to 43 % C_P and 48 % C_Q at TSR 0.9. In contrast, the 20-bladed type achieves the lowest performance. Albeit the most number of blades, the power efficiency of this turbine is six times lower than that of the 10-bladed turbine at TSR 0.9. In addition, in all cases of TSR, the performance of the 20-bladed type does not change too much when the rotational speed increases.

Meanwhile, although the 12-bladed turbine has two blades more than the 10-blade one, but its power efficiency is approximately two times less than that of the 10-blade type, especially at TSR 0.9. However, the power and torque generations of both types are much less than those of the 20-bladed type at all TSRs.

All computed results of turbine efficiency are compatible with the characteristics of water volume fraction and velocity vectors as discussed above, whereas high efficiency is found in cases with clear changes in flow patterns through the wheel.

To sum up, it can be seen that at the same operating conditions, the 10-bladed type attains the highest possibility of tidal current energy extraction compared to the others in the study. Conversely, the 20-bladed type shows the lowest power efficiency.

5Conclusions

This paper present a numerical analysis of a water wheel turbine for tidal current conversion application with a variety of blade counts and blade shapes. It has several obvious advantages, such as simple structure, easy manufacture and repair, and environmentally friendly operation. The following conclusions are derived: