Performance of vertical axis water turbine with eye-shaped baffle for pico hydropower

Abstract

A series of inline pico hydropower systems, which could be used in confined space, especially for water distribution networks (WDNs), was designed and investigated. The turbine with an eye-shaped vertical water baffle was developed to evaluate the hydraulic performance. A three-dimensional dynamic mesh was employed and the inlet velocity was considered as the inlet boundary condition, whereas the outlet boundary was set as the outflow. Then, numerical simulations were conducted and the standard k-ε turbulence model was found to be the best capable of predicting flow features through the comparison with the experimental results. The effects of the opening diameter of the water baffle and installation angle of the rotor on the flow field in the turbine were investigated. The results suggested that the water baffle opening at d = 30 mm and the rotor at a 52° angle could achieve the highest efficiency of 5.93%. The proper eye-shaped baffle not only accelerates the fluid flow and generates positive hydrodynamic torque, but also eliminates the flow separation. The scheme proposed in this paper can be exploited for practical applications in the water pipelines at various conditions and power requirements.

Graphical abstract

Keywords

vertical axis water turbine / eye-shaped / vertical water baffle / pico hydropower

1 Introduction

The development of the economy has resulted in a tremendous increase in the consumption of non-renewable energy from fossil fuel. In recent years, renewable energy resources like water, wind, solar, and hydrogen have received global attention. Hydropower is cheap, clean, and environmentally friendly, which makes it a good candidate for renewable energy [1]. By the end of 1999, hydropower had produced 2650 Terawatt hour (TWh), which was 19% of the global total output of electricity. The hydropower produced nearly 3100 TWh at the beginning of 2009, and it is expected to reach 3606 TWh by 2020 [2]. China is improving upon wind and hydropower to put a cap on increased CO₂ emissions [3]. Generally, large and medium-sized hydropower projects with high costs provide the required electric power. Nevertheless, there is a massive population living in remote, rural, and hilly areas where as many as 1.3 billion people are without access to electricity [4–7]. Since grid extension is too expensive in these areas, pico hydropower (up to 5 kW capacity) can be an efficient and attractive option for off-grid electricity. It is an effective alternative to conventional energy because it is cheap, clean, and environmentally friendly. Pico hydropower has been widely applied in remote, rural, and hilly areas. Pico hydropower that is used in water distribution networks (WDNs) of urban areas can provide excess hydraulic energy. Only requiring small rivers, aquacultures, irrigation systems, or other pressurized systems to supply energy [8], the pico hydropower system is capable of providing enough electrical power for domestic use in remote and isolated areas that suffer from energy deficit [9].

Global warming, the requirement for electricity, low level of electrification in remote areas, and the publicity of pico in developing countries have aroused the interest of many researchers and policymakers to pay more attention to the research and development of pico hydro turbines. Lahimer et al. [10] reviewed the research and development of pico hydropower and discussed the factors contributing to the success of pico hydro projects in the rural areas, believing that pico hydro market would be booming in the future due to the extensive availability of low head and flow hydroelectric sites in developing countries. Based on a novel approach of turbine torque, Xu et al. [11] reported a sensitivity analysis of a Pelton hydropower station about hydraulic, mechanic, and electric parameters, whose results could provide some bases for design and stable operation of Pelton hydropower stations. Desai et al. [12] described a theoretical analysis that water flow rate and head were the most significant parameters for pico hydropower system design. The results suggested that the design with a water flow rate from 0.03 to 15 L per second and a head height from 1 to 30 m was most suitable for the electricity requirement of a typical village in rural areas. Susanto and Stamp [13] evaluated the major installation methods for low head pico hydropower. By observing local adaptations during field surveys in rural areas, they examined the performance and requirements of each installation method. Based on the experimental investigation and cost-benefit analysis, Morabito and Hendrick [14] reported the selection methodology and described the set-up application to choose the competitive pump as turbine (PAT). They also presented a case to demonstrate the practical application of the proposed methods.

Diverse types of pico hydro technology have been exploited for three decades and become relatively mature, mostly for rural electrification in developing countries [15–18]. While researches considered the confined space like WDNs as finite, WDNs have the potential to be used water head because the continuous fluid in pipelines can provide a large amount of extra hydraulic energy with a large pressure. Commonly pressure reducing valves (PRVs) are utilized to dissipate extra energy for pipe protection and leakage reduction [19]. However, the excess energy could be recovered for supplying power by pico hydropower systems. Compared with the monitoring sensor networks using batteries in water mains management [20], the electricity generated by the system is beneficial for maintenance and energy saving. Besides, it is a feasible approach to use the system in high-rise pumping mains given the existence of a high pressure [21,22].

Gaining energy from large and medium-sized pipelines for water supply, Altan [23] optimized the performance of the water rotors. The effect of the design parameters of the water baffle plate on the torque values was discussed by performing theoretical computation and analyzing the numerical results. Pugliese et al. [19] experimentally investigated the PAT performance of two centrifugal pumps. Since the working range of a single PAT is narrow, a bypass must be coupled with the main power generation line. Samora et al. [24] presented a new pico axial turbine for a sub-grid of the drinking water system. A 45°-elbow was used to connect the main shaft of the runner and the generator. Through simulations based on the experiments, characteristics, and efficiency curves of the turbine were obtained.

The installation space in WDNs is limited due to the cost of land resources, especially in densely populated cities. The complex construction of pico hydropower tends to restrict installation sites. The drag-type vertical axis water turbine for generating electricity was given in WDNs [25], which could pick up power in any direction. Simultaneously, computational fluid dynamics (CFD) was widely applied in the simulation of turbomachinery to study the flow characteristics [26–28].

In this paper, the water turbine with an eye-shaped baffle is selected for further analysis and optimization. A water turbine experimental platform was established to test the performance characteristic of the water turbine. However, the results only from the experiment are limited, it is necessary to acquire the information of the flow field in the water turbine from the numerical simulation. A three-dimensional dynamic simulation model was established with different turbulent models. After comparing the experimental and numerical results, an appropriate turbulent model was incorporated and several design parameters were studied and analyzed to better understand the flow features of this type of water turbine.

2 Model geometry and experiment

2.1 Model geometry

Given the surging demand for the continuous water supply, the installation of the pico hydro-power system should be kept as simple as possible. As depicted in Fig. 1, the water turbine with an eye-shaped vertical water baffle cannot only greatly reduce the space and time of system installation, but also maintain the flow direction unchanged. At the beginning of design, there was only a vertical axis water turbine with five blades spaced of 72° in this inline system. In the pipe of 100-mm-diameter, the water striking the rotor with a diameter of 86 mm at a certain velocity created a positive torque on the concave surfaces of the 2-mm-thick blade and a negative torque on its convex surfaces [29]. The rotation movement was not distinct and the output power was very low. To improve the rotor performance, it is important to refrain from any negative torque which is formed in the opposite direction of the rotor rotating. Thus, a vertical eye-shaped water baffle placed in front of the water rotor is proposed to concentrate the internal flow in the pipe, which can tremendously reduce the negative torque as well as augment the positive one. The finally developed hydropower system is made up of two main components: a rotor and a water baffle. The geometric parameters of the water turbine are shown in Fig. 2, where D, whose value is 39.5 mm, represents the distance between the left border of the opening and the center-line; d, whose value is 26 mm, represents the distance between the opening center and the center-line. Under the condition of constant D, different openings were achieved by changing the value of d. To maintain a stable flow, the whole hydraulic passage is 1300 mm and is divided into the entry and exit sections. The lengths of entry and exit sections, namely L₁ and L₂, are 500 mm and 800 mm, respectively. The inner diameter of the water baffle is 46 mm. β is the blade installation angle and β = 73°. ω is the angular velocity of the rotor.

2.2 Experimental setup and measurements

The experimental arrangement consists of several pipelines of 100 mm diameter, a manufactured stainless steel water rotor, a circulation pump driven by a variable speed drive, a generator, a load, a reservoir, and the measurement devices. Figure 3 exhibits the schematic diagram of the experimental setup. The variable speed drive commanded the pump with a maximum power of 37 kW, sucked water from the reservoir, and offered different working conditions for testing the water turbine. The opening of the control valve regulated the water velocity under specified conditions. To guarantee a uniform flow, the straight pipes were sufficiently long and an electromagnetic flow-meter was installed relatively far away from the water turbine to get the more precise value. The excess water head was converted into mechanical energy by the water baffles of the turbine. The generator which was installed on the T-joint then converted the mechanical energy into electrical energy. The load that linked to the generator was used to manually correct the rotational speed of the water turbine. To monitor the differential pressure when the water turbine was running, two pressure sensors were installed at the entry and exit of the water turbine where upstream 5 times and downstream 4 times the diameter of the pipeline. Therefore, a micro permanent magnet power generator whose maximum output power can reach 50 W was applied because of the property for the low torque. Besides, the shaft power was also recorded to obtain the final power output. In the measurement apparatus described above, the precision of the flow meters and the pressure sensors are ±0.5% and ±0.25%. Uncertainty analysis was performed based on the Kline and McClintock method [30], and the uncertainties of the pressure, flow meter, and the efficiency of the turbine are 1.1%, 0.7%, and 1.5%, respectively.

Considering that the average water velocity in WDNs is 1.5 m/s [25], it is decided to adopt the flow velocity at values of 1.8 and 2.1 m/s in this paper, respectively. With the rotating speed changing from 162 to 621 r/min, the flow, velocity, and pressure are gradually generated at the measurement points. Moreover, for each flow velocity and rotational speed, the variable voltage imposed on the generator with the electronic load amperage was recorded to obtain the output power. After measuring each parameter, the flow velocity, the differential pressure, and the output power, the data of the water turbine are processed using [26]

(1)P=\rho \cdot Q\cdot E,

(2)E=\mathrm{g}{H}_{\mathrm{i}}-\mathrm{g}{H}_{\mathrm{o}}={\displaystyle \frac{p_{\mathrm{H}}-p_{\mathrm{L}}}{\rho }},

where P is the hydraulic power, Q denotes the volume flow rate, E is the specific energy available, g is the acceleration of gravity, and r is the density of water. The hydraulic power (H) in Eq. (2) is the difference between the pressure at the inlet and outlet, and p_H and p_L are the high pressure and low pressure, respectively. The shaft power of the water turbine is

(3)P_{\mathrm{out}}=UI=T\omega ,

where U and I are the voltage and current of the generator, respectively; T is the individual torque of rotor blades at the shaft; andω is the angular velocity of the rotor

(4)\omega ={\displaystyle \frac{\mathrm{2}\mathrm{\pi }N}{\mathrm{60}}},

where N is the revolutions per minute of the turbine.

The hydraulic efficiency is estimated as

(5)\eta ={\displaystyle \frac{P_{\mathrm{out}}}{P}}.

Tip speed ratio (TSR) is the ratio of the peripheral speed of the turbine rotor to the flow velocity, which can be calculated by

(6)TSR={\displaystyle \frac{r\omega }{V}},

where r is the rotor radius (m), and V is the flow velocity (m/s).

3 Numerical simulation

3.1 Governing equations

Considering that the flow in the pipeline is turbulent and incompressible, the governing equations are the averaged mass conservation and Reynolds averaged Navier-Stokes (RANS) equations [31], described as

(7){\displaystyle \frac{\partial {\overline{u}}_i}{\partial x_i}}=\mathrm{0},

where {\overline{u}}_i is the averaged velocity component in the i-direction.

(8){\displaystyle \frac{\partial \left(\rho {\overline{u}}_i\right)}{\partial t}}+{\displaystyle \frac{\partial }{\partial x_j}}\rho \stackrel{�����}{{u^{\prime }}_i{u^{\prime }}_j}=-{\displaystyle \frac{\partial \overline{p}}{\partial x_i}}+\mu {\displaystyle \frac{{\partial }^{\mathrm{2}}{\overline{u}}_i}{\partial x_j\partial x_j}}+\rho {\overline{F}}_i,

where ρ denotes the density, \rho \overline{{u^{\prime }}_i{u^{\prime }}_j} is the Reynolds stress, \overline{p} is the averaged pressure,μ denotes the viscosity, and {\overline{F}}_i is the averaged external force component.

The Reynolds stress, \rho \overline{{u^{\prime }}_i{u^{\prime }}_j}, is modeled using the Boussinesq approximation,

(9)-\rho \overline{{u^{\prime }}_i{u^{\prime }}_j}=-{\mu }_{\mathrm{t}}\left({\displaystyle \frac{\partial {\overline{u}}_i}{\partial x_j}}+{\displaystyle \frac{\partial {\overline{u}}_j}{\partial x_i}}\right)-{\displaystyle \frac{\mathrm{2}}{\mathrm{3}}}{\delta }_{ij}\left(\rho k+{\mu }_{\mathrm{t}}{\displaystyle \frac{\partial {\overline{u}}_i}{\partial x_j}}\right),

where μ_t denotes the turbulent viscosity and k is the turbulent kinetic energy which is defined as [32]

(10)k={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\rho \overline{{u^{\prime }}_i{u^{\prime }}_j}.

3.2 Computational domain and mesh generation

The whole computational domain was divided into two parts: stationary and rotational domains. As revealed in Fig. 4, the stationary domain was composed of the water baffle, the entrance section, and the exit section of the pipe, whereas the rotational domain was the whole water rotor. In the stationary domain, the velocity inlet with a certain water velocity was located at the front of the water rotor while the outflow outlet was placed behind the water rotor primarily for the fully developed wake flows. In the rotational domain, the water rotor was placed over the symmetry section of the pipeline. The geometries of the rotor were highly complex because of the narrow regions and curved blades, the “unstructured tetrahedron mesh” was used to discretized the domains, and the “boundary layer mesh” was used for the grid generation in the domain near the blades. The average value of y + near the blade walls is around 5. Given the rotating domain was the most important part for analyzing the performance of the water turbine, the grid density of the rotational domain is increased to improve the mesh quality close to the water rotor.

To balance the computational time and numerical accuracy, a grid independence test was conducted to obtain the torque at the same runner rotating speed. An increased mesh density was performed near the blade and wall of the pipe to capture the flow details. Five different grid sizes, 1.5, 2.9, 6.7, 8.0, and 13.0 million cells, were simulated in preliminary computations. Table 1 lists the grid independence results. The maximum torque difference between the 8 and 13 million meshing schemes is more than 2% [33]. Hence, the total grid number of 0.80 million was applied in further study. The final three-dimension computational mesh is displayed in Fig. 5. The minimum mesh quality of 0.3 ensures the precision of the simulation.

3.3 Boundary conditions and solver set-up

The selection of the turbulence model poses a great challenge because none of the turbulence models can accurately predict the flow field in pipelines. Different turbulence models were compared in this paper to identify the most appropriate one. Since the rotation domain was unbaffled, an rotating reference frame (RRF) approach was used [34]. The inlet and outlet boundaries were determined according to the working condition. The inlet velocity was considered as the inlet boundary condition, whereas the outlet boundary was set as outflow. To separate stationary and rotational domains, two rotor-stator interfaces were set as the boundary condition. The non-slip wall boundary condition was applied to the water baffle, blade surface, and pipe wall.

The first-order upwind scheme was used to discretize the turbulent kinetic energy and turbulent dissipation rate terms. The second-order upwind scheme was used to discretize the momentum terms [35]. The semi-implicit method for pressure linked equations (SIMPLE) algorithm was applied to calculate the pressure and velocity distributions in many numerical simulations [36–39] where the pressure correction is solved to maintain the availability of the pressure area and mass conservation in each iteration. Therefore, it is also used in this paper. In the simulations performed, the turbulence intensity was set to be 8% whereas solution residuals of parameters were set to 10⁻⁵. Convergence was achieved when monitoring torque values generated by five blades of the water rotor became steady as the water turbine runs. It takes approximately 10 h to simulate each case on a 64-bit server with 24 cores. In other words, the performance curve of one working condition requires about 50 h.

4 Results and discussion

4.1 Comparison of experimental and simulation results

For each flow velocity described in Section 2.2, namely 1.8 m/s and 2.1 m/s, several groups of experiments were conducted at different rotational speeds. The rotational speed and the shaft power were recorded as tabulated in Table 2. It can be observed from Fig. 6 that with the increase of rotational speed from 226 r/min to 315 r/min, the power extracted by the turbines monotonically increases when the water velocity is 1.8 m/s. At a rotational speed of 424 r/min, the peak value of the power generated by the system reaches 8.2 W. Then, the power output begins to fall. At an incoming flow velocity of 2.1 m/s, the maximum power output (MPO) of the water turbine is 18.3 W when the rotational speed is 579 r/min. It is indicated that the rotational speed related to the MPO increases with increasing flow rate. Besides, as the water speed increases, the water power also increases, hence the turbine has the opportunity to extract more torque and power from the water stream.

The CFD method has been widely used to analyze the flow field and performance of the hydro-turbine. Three turbulence models, i.e., the standard k-ε model, the RNG k-ε model, and the SST k-ε model, were adopted to simulate the flow field. To validate the feasibility of the numerical approach, seven performance points were simulated to compare with the test results. It is found that there is a certain deviation between the experimental and numerical results. The main reason for the deviation is the efficiency of the generator. In the simulations, the generator efficiency was not taken into consideration. However, part of mechanical energy was consumed by the generator in the experiments. Therefore, the values of torque obtained in simulations should be multiplied by the efficiency. Figure 7 exhibits the detail of the efficiency of the generator. With increasing rotational speed, the efficiency increases gradually. Only when the rotational speed surpasses 600 r/min, does the efficiency of the generator reach the maximum value of about 70%. Thus the energy loss increases which reinforces the difference between the experimental and numerical results with decreasing rotational speed. Furthermore, the energy loss caused by friction was also neglected in the simulations. After eliminating the effect of the efficiency of the generator, the comparison of hydrodynamic torque between the experimental and numerical results at different rotational speeds is depicted in Fig. 8. It can be seen that the error between simulated and experimental results of the standard k-ε model is the minimum, less than the SST k-ε and the RNG k-ε model. Therefore, the standard k-ε model is proved to be more accurate for further investigation.

There are two other reasons for the difference between the experimental and numerical results. First, the model of CFD simulation was simplified, leading to computational uncertainties which are difficult to eliminate. Next, deviations can also result from the experimental measuring error. It is observed from Fig. 8 that the error percentage is limited to 3%. For this reason, the proposed method is helpful for analyzing the performance of the vertical axis water turbine.

Figures 9 and 10 depict the streamline and vector of the internal flow field. A part of the fluid coming from the entrance passes through the baffle opening and has impact on the blade. The rest of the fluid is resisted by the water baffle and squeezed into the gap between the water baffle and the pipe wall. In the passageway of the water turbine impeller, the flow is stable. Only at the outlet of water baffle, is there an obvious vortex as a result of the collision between the uniform fluid and the solid components. After leaving the water turbine, the fluid flow is turbulent.

4.2 Parametric study and analysis

Several simulations were conducted to comprehensively study and analyze the water turbine system. As depicted in Fig. 2, the water baffle and rotor are two main components in the pico hydropower system, which have a great impact on the performance of the water turbine. The water baffle opening d was studied at first. The rotor installation angle β was also varied based on the modification of water baffle opening.

4.2.1 Water baffle modification and analysis

To investigate the effect of the opening size of water baffle on the performance of the water turbine, three different values of d (28 mm, 30 mm, and 32 mm) were assigned for the opening size while other parameters are kept unchanged. Under the working condition of a flow velocity of 2.1 m/s, the maximum efficiency point of the water turbine was obtained in several simulations. By using Eqs. (5) and (6), the efficiency of different d based on TSR was derived as presented in Fig. 11. It can be seen that with the increase in TSR, all the efficiencies increase first and then decrease afterward. The TSR related to the maximum efficiency increases gradually as the distance d increases. In the range of 26 mm<d<30 mm, the efficiency increases with increasing d. After reaching the peak at d = 30 mm, it begins to fall with increasing d. It is concluded that the opening size of water baffle, d, has a remarkable impact on the working range and the maximum efficiency. A larger d does not always mean a higher efficiency.

The data of differential pressure or pressure loss between the surfaces of the inlet and the outlet related to the maximum efficiency were collected for various water baffle opening conditions. Figure 12 depicts the maximum power output and differential pressure based on opening distance, d. As the distance d increases, both the differential pressure and MPO increase gradually. It can be seen that the power and the pressure loss increase synchronously in the opening distance range from 26 mm to 30 mm. When the opening distance changes from 30 mm to 32 mm, the power rises gently while the pressure loss surges rapidly. Consequently, the efficiency arrives at the highest when the distance d is 30 mm.

To obtain performance insight of the turbine with different baffle openings, the contour plots static pressure, and velocity magnitude are analyzed from the perspective of flow. Here, the objective is to see the contribution of static pressure and velocity distribution across the blades to hydrodynamic torque generation. The flow field of the water turbine system for different d values at the maximum efficiency is given in Fig. 13. It can be seen clearly that the proposed water baffle improves the flow velocity through the rotor, which means the water baffle increases the kinetic energy of the water flow. The entrance velocity of the water turbine increases with the increase of the opening distance, d. From Figs. 13(a)–13(c), it can be observed that the velocity through the water baffle opening surged, which results in a higher flow static pressure and shear force on advancing blade. The velocity scope of the water baffle entrance is 6–8 m/s, 8–9 m/s, and 9–10 m/s, corresponding to the opening of 26 mm, 28 mm, and 30 mm. Yet with the water baffle opening continues to shrink, the increase in velocity is not apparent in Fig. 13(d). With the consumption of kinetic energy, the accelerated fluid interacts with the concave surface of the rotor blades and promotes the rotation of the blade. The smaller d means a greater degree of opening, and the flow motivates one blade to rotate and produce a positive torque. Meanwhile, it also creates a negative torque on the convex surface of the adjacent blade to hinder the rotation. This effect is prominent in the case at d = 26 mm due to the more exposed area of the upstream blade facing the flow. For a larger opening diameter, the effect of the negative torque is weakened.

Figure 14 shows the pressure contour for the water turbine with different water baffle openings. The static pressure contour demonstrates a decrease in pressure from the upstream to the downstream of the turbine, which indicates the useful torque and power extraction by the turbine. It can be qualitatively realized that the total pressure is consumed by the water turbine system. A large blockage ratio, which is defined as the ratio of the water baffle opening to the cross-section of the pipe, results in a less pressure loss with decreasing d. From the pressure contours of the four cases, it is found that the pressure loss rises gradually with the increase in the opening size, which corresponds well with the variation as illustrated in Fig. 12.

The rotating turbine is realized by the fluid impact on the blade flowing through the different opening water baffles. The pressure of baffle inlet increases with the opening distance. In the case of d = 28 mm, the pressure loss is 10⁵ Pa. As shown in Figs. 14(a) and 14(b), as a result of a small baffle opening distance, the inlet pressure of the baffle are both low, which indicates that the fluid kinetic energy of the turbine is small. In addition, it can be seen from the pressure distribution around the blades that the pressure between the convex surface of blade 1 and the concave surface of blade 2 is large. Small high-pressure regions occur at the trailing edge, which has a negative impact on rotor torque output. From Figs. 14(c) and 14(d), it can be noticed that the high-pressure regions move toward the concave of blade 2, resulting in a gradual increase in the positive torque output. The water turbine efficiency is the ratio between the power output and pressure loss (see Eq. (5)). In the range of 26 mm to 30 mm, the power output may dominate the efficiency, which may rule in the range of 30 mm to 32 mm. To maintain the fluid flow, a smaller blockage ratio leads to an increase in a pressure loss, resulting in more energy consumption. The blockage ratio at d = 30 mm is most suitable for the highest efficiency.

4.2.2 Rotor installation angle modification and analysis

Based on the modification of water baffle opening, six values of β (38°, 45°, 52°, 59°, 66° and 73°) for rotor installation angles are chosen to analyze its effect on the performance of the water turbine. Figure 15 shows the computational rotor of the blade installation angle from 38° to 73°. The other parameters are unaltered: the opening size d is 30 mm and the blade diameter is 86 mm. Figure 16 depicts the efficiency of the rotor at different installation angles based on TSR. In the range of 38°<β<52°, the maximum efficiency increases with increasing angle β. However, in the range of 52°<β<73°, the larger β generates a lower maximum efficiency. The MPO related to pressure loss based on angle β is shown in Fig. 17. Different from the trend gained from the water baffle study, the power first increases and then decreases from 38° to 73°. On the contrary, the pressure loss decrease first and then increases. It indicates that the maximum efficiency peaks when the installation angle is 52°. When the installation angle is 38°, the water baffle has both a high-pressure loss and a high power output due to the large amount of extra water head.

Figures 18 and 19 show the velocity and pressure distributions of internal fields at different installation angles β. Under the condition that the other design parameters remain unchanged, the variation of blade installation angle will lead to various blade angles of attack and passageway between the two blades. As presented in Figs. 18(a)–18(c), a decreased angle of attack makes the impeller separate the high-velocity fluid. The flow separation is caused by a mismatching between the attack angle and the installation angle, which has a negative effect on the turbine performance. The higher velocity fluid has an impact on the convex of the blade which causes flow separation and greater pressure loss. When β>59°, the positive angle of attack makes fluid interact with the concave surfaces of blades. However, the high-velocity fluid would not attack the surface directly as shown in Figs. 18(d)–18(f).

The small installation angle means a large flow angle of attack at the same opening. When β = 38°, the angle of attack is the largest. Since the flow separation occurs at the leading edge, the high-pressure region is produced in the convex surface of blade 2, which inhibits the creation of the positive torque. The pressure loss is 1.23 × 10⁵, and the torque output of the blade is negative or very small, which is consistent with the pressure distribution. Compared with the pressure contour of β = 38° and 45°, the high-pressure regions at the convex surface of blade 2 are smaller and the pressure loss is lower, because of the slight flow separation. From Figs. 19(a)–19(c) of pressure contour, it can be observed that a high-pressure region near the convex surfaces of blade 2 enlarges with a decreasing installation angle. For the installation angle of 66° and 73°, it can be seen from Figs. 19(e)–19(f) that the high-pressure regions are distributed on the trailing edge of blade 1 and blade 2, and a portion of fluid directly acts on the convex surfaces of blade 1, resulting in a fluid impact loss. Of the six models, the model with β = 52° offers good performance in terms of blade torque extraction, and its best efficiency is 5.93%. The reason for this is that the attack angle has a good matching with the installation angle, and the flow separation cannot be found in the blade passage. Besides, a pressure difference exists between the convex and concave of the blade, leading to the normal torque output of the rotor.

5 Conclusions

A water turbine with an eye-shaped vertical water baffle was proposed for pico hydropower and experimentally and numerically studied under different working conditions. The effects of water baffle opening, d, and rotor installation angle, β, were numerically analyzed based on the standard k-ε turbulence model. It is found that water baffles play an important role in the performance of the turbine because they convert part of the water head into kinetic energy and increase the flow velocity at the rotor inlet. The pressure difference between the upstream and downstream leads to a power output, and a pressure loss through the turbine. Of the four different water baffle openings, the water baffle at d = 30 mm has the highest efficiency (3.18%). The accelerated flow generates useful hydrodynamic torque with a reasonable pressure loss. The efficiency of the turbine could also be improved by reducing the negative torque at the rotor and eliminate the flow separation. The result suggest that the model at β = 52° could reach the maximum efficiency of 5.93%.

References

[1] Date A, Akbarzadeh A. Design and cost analysis of low head simple reaction hydro turbine for remote area power supply. Renewable Energy, 2009, 34(2): 409–415

[2] Elbatran A H, Yaakob O B, Ahmed Y M, Shabara H M. Operation, performance and economic analysis of low head micro-hydropower turbines for rural and remote areas: a review. Renewable & Sustainable Energy Reviews, 2015, 43: 40–50

[3] Pathak L, Shah K. Renewable energy resources, policies and gaps in BRICS countries and the global impact. Frontiers in Energy, 2019, 13(3): 506–521

[4] Chen C L, Chen H C, Lee J Y. Application of a generic superstructure-based formulation to the design of wind-pumped-storage hybrid systems on remote islands. Energy Conversion and Management, 2016, 111: 339–351

[5] Maher P, Smith N P A, Williams A A. Assessment of pico hydro as an option for off-grid electrification in Kenya. Renewable Energy, 2003, 28(9): 1357–1369

[6] Reddy V R, Uitto J I, Frans D R, Matin N. Achieving global environmental benefits through local development of clean energy? The case of small hilly hydel in India. Energy Policy, 2006, 34(18): 4069–4080

[7] Nfah E M, Ngundam J M, Vandenbergh M, Schmid J. Simulation of off-grid generation options for remote villages in Cameroon. Renewable Energy, 2008, 33(5): 1064–1072

[8] Bozorgi A, Javidpour E, Riasi A, Nourbakhsh A. Numerical and experimental study of using axial pump as turbine in Pico hydropower plants. Renewable Energy, 2013, 53(9): 258–264

[9] Haidar A M A, Senan M F M, Noman A, Radman T. Utilization of pico hydro generation in domestic and commercial loads. Renewable & Sustainable Energy Reviews, 2012, 16(1): 518–524

[10] Lahimer A A, Alghoul M A, Sopian K, Amin N, Asim N, Fadhel M I. Research and development aspects of pico-hydro power. Renewable & Sustainable Energy Reviews, 2012, 16(8): 5861–5878

[11] Xu B, Yan D, Chen D, Gao X, Wu C. Sensitivity analysis of a Pelton hydropower station based on a novel approach of turbine torque. Energy Conversion and Management, 2017, 148: 785–800

[12] Desai A, Mukhopadhyay I, Ray A. Theoretical analysis of a pico-hydro power system for energy generation in rural or isolated area. In: IEEE PES Asia-pacific Power & Energy Engineering Conference, Hong Kong, China, 2014

[13] Susanto J, Stamp S. Local installation methods for low head pico-hydropower in the Lao PDR. Renewable Energy, 2012, 44(4): 439–447

[14] Morabito A, Hendrick P. Pump as turbine applied to micro energy storage and smart water grids: a case study. Applied Energy, 2019, 241: 567–579

[15] Paish O. Small hydro power: technology and current status. Renewable & Sustainable Energy Reviews, 2002, 6(6): 537–556

[16] Gladstone S, Tersigni V, Francfort K, Haldeman J A. Implementing pico-hydropower sites in rural Rwanda. Procedia Engineering, 2014, 78: 279–286

[17] Nfah E M, Ngundam J M. Feasibility of pico-hydro and photovoltaic hybrid power systems for remote villages in Came-roon. Renewable Energy, 2009, 34(6): 1445–1450

[18] Vicente S, Bludszuweit H. Flexible design of a pico-hydropower system for Laos communities. Renewable Energy, 2012, 44(4): 406–413

[19] Pugliese F, De Paola F, Fontana N, Giugni M, Marini G. Experimental characterization of two pumps as turbines for hydropower generation. Renewable Energy, 2016, 99: 180–187

[20] Younis M, Akkaya K. Strategies and techniques for node placement in wireless sensor networks: a survey. Ad Hoc Networks, 2008, 6(4): 621–655

[21] Li S L, Chen H, Wang Q. Series-parallel combined constant pressure water supply pipeline design of high-rise building. Advanced Materials Research, 2013, 760–762: 1369–1375

[22] Swamee P K. Design of high-rise pumping mains. Urban Water, 2001, 3(4): 317–321

[23] Altan B D. The numerical simulation of the performances of water rotors used in pipelines with the water baffle plates. Journal of Mechanical Science and Technology, 2014, 28(11): 4555–4562

[24] Samora I, Hasmatuchi V, Münch C, Franca M J. Energy production with a tubular propeller turbine. In: 28th IAHR Symposium on Hydraulic Machinery and Systems, Grenoble, France, 2016

[25] Chen J, Yang H X, Liu C P, Lau C H, Lo M. A novel vertical axis water turbine for power generation from water pipelines. Energy, 2013, 54(2): 184–193

[26] Ranjan R K, Alom N, Singh J, Sarkar B K. Performance investigations of cross flow hydro turbine with the variation of blade and nozzle entry arc angle. Energy Conversion and Management, 2019, 182: 41–50

[27] Du J Y, Shen Z C, Yang H X. Numerical study on the impact of runner inlet arc angle on the performance of inline cross-flow turbine used in urban water mains. Energy, 2018, 158: 228–237

[28] Fernandez A. Numerical prediction of the turbulent wakes generated by a row of marine turbines. International Journal of Marine Energy, 2016, 16: 41–50

[29] Altan B D, Atılgan M. The use of a curtain design to increase the performance level of a Savonius wind rotors. Renewable Energy, 2010, 35(4): 821–829

[30] Kline S J, McClintock F A. Describing uncertainties in single-sample experiments. Mechanical Engineering (New York, N.Y.), 1953, 75: 3–8

[31] Ameur H. 3D hydrodynamics involving multiple eccentric impellers in unbaffled cylindrical tank. Chinese Journal of Chemical Engineering, 2016, 24(5): 572–580

[32] Williamson S J, Stark B H, Booker J D. Experimental optimisation of a low-head pico hydro turgo turbine. In: 2012 IEEE 3rd Internatioanal Conference on Sustainable Energy Technologies, 2012, 322–327

[33] Cao W, Huang W, Wei G, Jin Y, Jiang F. A numerical study of non-Darcy flow in heat reservoirs during heat extraction. Frontiers in Energy, 2019, 13(3): 439–449

[34] Ameur H. Energy efficiency of different impellers in stirred tank reactors. Energy, 2015, 93: 1980–1988

[35] Ameur H. Effect of the shaft eccentricity and rotational direction on the mixing characteristics in cylindrical tank reactors. Chinese Journal of Chemical Engineering, 2016, 24(12): 1647–1654

[36] Mohamed M. Performance investigation of H-rotor Darrieus turbine with new airfoil shapes. Energy, 2012, 47(1): 522–530

[37] Torresi M, Fortunato B, Camporeale S. Numerical investigation of a darrieus rotor for low-head hydropower generation. Procedia Computer Science, 2013, 19(5): 728–735

[38] Ameur H. Mixing of shear thinning fluids in cylindrical tanks: effect of the impeller blade design and operating conditions. International Journal of Chemical Reactor Engineering, 2016, 14(5): 1025–1033

[39] Yadav A S, Bhagoria J L. Heat transfer and fluid flow analysis of an artificially roughened solar air heater: a CFD based investigation. Frontiers in Energy, 2014, 8(2): 201–211

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