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Level of utilization of clean energy has grown dramatically in recent years due to increased pollution and environmental issues. For instance, the extra potential energy in water supply system is usually wasted, due to its low capacity. Design of a proper turbine has recently been given more attention by researchers to apply this clean energy. In the present paper, a modified Savonius turbine, suitable for use in a 4-inch pipe, is designed. Turbine with two blades is tested in a laboratory rig and also simulated with the FLUENT software. By matching numerical and laboratory results, simulations are expanded and the blades number effect on turbine performance is studied under determined hydraulic conditions. The flow field around the modified Savonius turbine is interpreted by the 3D streamlines and pressure contours. The obtained results indicate that increasing the turbine blade numbers up to 5 and more causes the turbine efficiency first to rise and then to fall, respectively.

The use of excess potential energy in urban and rural water pipelines is a new source of clean energy. This surplus energy can be created by hydraulic head generated as a result of the high altitude difference between the origin and the destination of the pipeline or by the pumping station. Generally, in the sense of reducing the excess pressure in the pipelines, a pressure relief valve or the atmospheric reservoir is employed [

The conventional turbines in small dimensions can potentially be the first idea to utilize hydraulic energy. However, the limitation of pressure drop in water pipelines along with the design requirements of the piping network, choosing an appropriate type of turbine type, is a challenging issue.

Several researchers have examined small scaled propeller or axial turbines [

Using the pump in reverse mode (pump as turbine or PAT) that was first proposed by Thoma and Kittredge [

As a third alternative, the use of vertical axis free flow turbines in a pipe has recently been raised. Darrieus and Savonius rotor turbines are the most commonly used vertical axis free flow turbines and work on the basis of lift and drag forces, respectively. These spherical-shaped turbines have 5 blades and the minimum diameter of the pipe for installation is 24 inches [

The effect of the number of the blades on the performance as well as the flow field around a small-scale in-pipe Savonius turbine has not been investigated yet. Firstly, an in-pipe drag-based turbine design procedure is described in the present paper. Secondly, in connection to the performed experimental studies, the effect of the blade numbers of a modified Savonius turbine on its performance under certain conditions is investigated numerically. Also, the effect of blade number on the flow field is explained by pressure contours and 3D streamlines graphically.

There is no comprehensive research on the effect of various small in-pipe turbine geometric parameters, such as blade profile, number of blades, height and thickness of blades, etc. In this research, except the number of blades, the other turbine geometry parameters are considered invariable and these mentioned parameters are chosen based on the related existing experiences. As the first parameter, the profile of the blade is taken into consideration. The blade profile of the modified turbine which is inspired by the Savonius turbine is part of a semicircle circumference. Chen et al. [

3-bladed in-pipe Savonius turbine: (a) Isometric view; (b) top view; (c) front view.

The modified turbine is designed in such a way to have the same profile for all sections. In other words, each section of a turbine with other sections is similar, and only its size varies with respect to the circle of the pipe section chord. Another important parameter is the height of the turbine, which is considered to be 70% pipe diameter due to the convenience of installation into the pipe. According to the dimensions provided by Chen et al. [

Earlier studies on the free flow Savonius turbine [

The schematic geometry of the deflector is shown in Figure

Essential geometry of the turbine and deflector parameters value.

Description | sign | value |
---|---|---|

Pipe diameter | | |

Circle arc degree | | |

Height of the turbine | | |

Clearance | | |

Deflector angle | | |

X-intercept | | |

Schematic of constant slope deflector: (a) upper view and (b) isometric view.

In order to investigate the turbine performance experimentally and validate numerical simulation, an experimental laboratory rig is designed and constructed. The laboratory rig is open and operates under a constant pressure difference which is created by a reservoir with a height of 4 meters. The test rig includes an atmospheric reservoir, a shut-off valve, a mercury manometer, a test section, a globe valve, and a flexible hose. Figure

Test rig and its components [

Since the main purpose of the experimental test is the validation of numerical simulation results, one turbine geometry consideration may be adequate. Based on this argument, a two-bladed turbine, as well as the described deflector, is made by a 3D printer and then installed in a 100-mm transparent pipe. Figure

Two-bladed turbine test section with deflector.

The tests are carried out for 7 operating conditions and the values of the flow rate, rotational speed, and pressure difference (as turbine head) are measured. The torque applied to the turbine shaft is only due to the friction of the mechanical seals and bearings. Thus, it is expected to remain constant during the tests.

The method of doing the test describes as follows. First, the globe valve rests in a constant state. Then, the atmospheric reservoir is fed by a pump to the overflow state. In the next step, the shut-off valve which is at the beginning of the 4-inch line opens completely. The flow passes through the turbine and, after ensuring the stability of the test conditions, the values of the pressure difference, rotational speed, and discharge are measured and recorded. Then, without changing the state of the globe valve, the experiment repeated several times for this condition, and, eventually, its average value is reported. By changing the position of the globe valve, a new operating condition for the turbine is created. Table

Test results in turbine different operating conditions.

Operating Conditions | | | |
---|---|---|---|

1 | 2.71 | 10 | 18.2 |

2 | 3.86 | 19 | 30.1 |

3 | 4.72 | 30 | 40.6 |

4 | 4.95 | 35 | 44.4 |

5 | 5.83 | 43 | 53.2 |

6 | 7.02 | 69 | 68.7 |

7 | 7.31 | 80 | 75.5 |

The simultaneous progress of computing tools and CFD techniques expanded the use of numerical simulations to examine various engineering issues. In the present study, numerical simulation is employed to investigate the number of turbine blades effect on turbine behavior. To simulate the flow field around the turbine a commercial software (FLUENT 18) is utilized. In order to validate the simulation, it is necessary to simulate the turbine condition in the experimental conditions essentially. After validating the simulation, the number of blades is changed and their numerical estimates are made. As the number of turbine blades changes from 2 to 10, a transient mode of the problem is considered. Although for multi-bladed turbines, it is possible to assume a steady state condition, transient mode is considered here. The sliding mesh technique has been used here. In the sliding mesh method, the domain of the solution is divided into two rotating and stationary zones. Rotating volume includes turbine blades and constant volume including inlet and outlet pipes and the deflector. The boundary conditions applied to the turbine, including the total and static pressure at the turbine inlet and outlet (approximate for head turbine values is 20 kPa), respectively and constant rotational speed (50 rad/s).

The flow field domain in numerical simulation consists of an inlet pipe, deflector zone, turbine and an outlet pipe which are shown in Figure

Numerical flow field domain components.

Modeling the fluid flow passing through the turbine is performed by using RANS equations. Among the turbulence models, the most suitable model to simulate turbomachines is the ^{−5} as well.

Increasing the number of elements, as well as reducing the time step, will increase the simulation accuracy. But, it also increases the time of simulation. The mesh used for fluid domain is such that average

Grid number vs. efficiency for all turbines.

| 1 | 2 | 3 | 4 | |
---|---|---|---|---|---|

Grid number | 2-bladed turbine | 1.5 | 2.8 | 5.1 | 7.6 |

| 19.22 | 16.01 | 14.15 | 14.12 | |

| - | 7.51% | 2.39% | 1.29% | |

| - | 4.9% | 3.21% | 1.86% | |

| |||||

Grid number | 3-bladed turbine | 5.3 | 7.9 | ||

| 22.10 | 22.09 | |||

| - | 1.72% | |||

| - | 1.96% | |||

| |||||

Grid number | 5-bladed turbine | 5.6 | 8.2 | ||

| 28.15 | 28.14 | |||

| - | 1.29% | |||

| - | 1.67% | |||

| |||||

Grid number | 8-bladed turbine | 5.8 | 8.8 | ||

| 26.41 | 26.41 | |||

| - | 1.11% | |||

| - | 1.37% | |||

| |||||

Grid number | 10-bladed turbine | 6.2 | 9.5 | ||

| 24.66 | 24.66 | |||

| - | 1.02% | |||

| - | 1.16% |

According to Table

Cell size, division number, and prism layer for all turbine are identical but the number of cells is different, because prism layer grid number increased by increasing blade number, i.e., walls.

Another investigation that seems to be necessary is the interface location. The interface, which is, in fact, the boundary of the moving volume and stationary volume, is a 96-mm diameter sphere, where the clearance is 4 mm and turbine diameter is 92 mm. Also, with a change in the diameter of the interface sphere to 94 mm and 98 mm, there was insignificant effect on the results. It seems that the small dimensions of the turbine and the clearance have a negligible impact on the results of the interface diameter. Figure

Generated Grid: (a) around the 3-bladed turbine and (b) prism layer around the blade.

Time step may impact the accuracy of the simulation. Thus time step independency is considered separately. Time step was selected such that turbine rotated 1° during each time step which leads to average CFL (Courant Friedrichs Lewy condition) number of less than 5. CFL number defines a necessary condition for numerical stability of a hyperbolic partial equation [

Present CFD analysis was conducted with an implicit solver within Fluent for which CFL < 5 was acceptable [

Time step reduction effect on simulation.

Time step (s) | 1.7 | 1.0 | 7.0 | 3.5 | 1.7 |
---|---|---|---|---|---|

Degree(s) in a time step | | | | | |

2-bladed turbine efficiency | 17.11 | 15.34 | 14.37 | 14.15 | 14.13 |

10-bladed turbine efficiency | 28.52 | 25.86 | 24.93 | 24.66 | 24.66 |

Table

Before simulations are extended to turbines with more than two blades, a comparison between experimental results and numerical simulations of a 2-bladed turbine is proposed. Figure

Comparison between laboratory results and numerical simulation [

Although the average difference between numerical and experimental results is about 10%, the numerical simulation trend is completely in line with experimental results.

The almost linear relationship between rotational speed and flow rate indicates that this turbine can also be considered as a flowmeter. Due to complexities for geometric definitions such as surface blade roughness and turbine shaft that acts as a resistance in passing fluid flow it was not taken into account in numerical evaluation. This is probably the reason that numerical evaluation over predicts flow rate with respect to the experimental results; however, the difference within the numerical and the experimental results has decreased considerably with respect to the previous related studies [

The results are obtained at a constant pressure difference of 20 kPa and a rotational speed of 50 rad/s for a turbine with a number of blades from 2 to 10. Figure

Flow rate, efficiency, and torque change vs. blade number.

Obviously, increasing the number of blades causes a decrease in the flow through the turbine due to increased turbine hydraulic resistance.

In other words, adding any blade means increasing the hydraulic resistance. Because the flow with more obstacles (blades) collides, therefore, in boundary conditions, which is the difference in pressure between the two sides of the turbine (constant turbine head), increasing hydraulic resistance leads to a decrease in the flow through the turbine.

Another point is the rate of the flow rate changing, which is declined sharply from 2-bladed to 3-bladed turbine, but this rate becomes lower for more blades. The turbine leakage seems to be drastically reduced, with the number of blades increasing from two to three, but with a further increase in the number of blades from three, there is no dramatic reduction in leakage. Due to the large distance between the two blades in the 2-bladed turbine, in some angular positions of the turbine during its rotation, the flow does not collide with any blades and passes through the turbine. By increasing the number of blades to three, the positions where the flow does not collide with any blades are greatly reduced and the leakage from the turbine decreases accordingly. But more increasing in blades number (from 3 blades) does not have much effect on reducing leakage from the turbine during its rotation, which is why the rate of reduction in the discharge is reduced.

Obtained results also indicate an optimum value for the efficiency and the torque. It seems that this behavior comes from the fluid flow and turbine blades interaction. In the turbine with a low blade number, a major portion of the fluid flow passes inside the turbine without having effective contacts with the blades. This causes lower useful torque and consequently efficiency reduction. Over there, in the turbine with more than a specified blade number which is evidently dependent on the blade size and its rotational speed; the passing flow does not have completely positive influences on the turbine blades (as a result of blades overlapping). Thereby, torque decreasing as well as flow rate reduction due to the increasing blade number causes a reduction in turbine efficiency. In other words, the lower blades cause more leakage and more blades, due to overlapping, prevent the proper flow impact on the blades. Given that the rate of the torque and the efficiency changing for turbines with blades more than 5 is less than the rate of the changes for turbines with blades less than 5, it can be concluded that the negative effect of leakage is greater than the negative effect of overlapping on the efficiency.

Since the study on the fluid flow passing through the turbine might provide a deeper understanding of the above descriptions, the pressure contours and the streamlines are investigated. In this regard, one turbine position is chosen from the 360° trip. Selected state is the case where one blade is completely in front of the flow.

Figure

The position of the turbine blades for comparison.

The simulated fluid flow around the 3-bladed turbine: (a) pressure contours (i) in the direction of flow view and (ii) in the opposite direction of flow view and (b) top view of streamlines.

The simulated fluid flow around the 5-bladed turbine. (a) pressure contours (i) in the direction of flow view and (ii) in the opposite direction of flow view and (b) top view of streamlines.

The simulated flow field around the 8-bladed turbine. (a) Pressure contours (i) in the direction of flow view and (ii) in the opposite direction of flow view and (b) top view of streamlines.

Considering the direction of turbine rotation (clockwise), increasing pressure in concave surfaces means increasing the positive torque and increasing the pressure on the convex surfaces means reducing the positive torque generation. Figure

But in the turbine of the 5 blades, except for the concave surface of the blade No. 1, the concave surfaces of blades Nos. 3 and 4 also have a higher pressure than their convex surfaces (see pressure contour of Figure

By comparing the streamlines of 3-bladed and the 5-bladed turbines (Figures

For this reason, the generated torque of the 5-bladed is increased compared to the 3-bladed turbine; however, the flow rate is decreased. In other words, the proper fitting of the blades in the 5-bladed turbine causes the flow to meet twice with each blade in a 360°. The streamlines in Figure

According to Figure

It seems that the cause of the reduction in the efficiency of the 8-bladed turbine is related to several factors. The first is to reduce the flow rate, which reduces the pressure on the blades generally. The second is to divide the flow into blades No. 1 and No. 2, which causes the surfaces to not be under maximum pressure (compare pressure contours of Figures

In order to detect more precisely, the normalized flow rate and net torque at 360° of turbine rotation are plotted for turbines 3, 5, and 8 of the blade in Figures

(a) Normalized flow rate and (b) generated torque for one revolution.

.

As it is clear in Figure

In the present study, an in-pipe drag-based turbine which is inspired by a Savonius rotor turbine for a diameter of 4 inches is designed. A prototype of the turbine is examined in the test rig, and, after assuring matching the results of numerical simulation and laboratory, the effect of increasing the number of turbine blades is investigated numerically. The results show

Increasing the number of in-pipe turbine blades up to 5 blades efficiency is improved.

Increasing the number of blades, more than 5, reduces the efficiency due to increased turbine hydraulic resistance and inadequate impact of the fluid with blades.

Turbines with a number of blades less than 5 are less efficient than the optimum mode because they cannot use all of the potential flow capacity.

The use of the hollow shaft turbine could allow the flow to pass properly through turbine blades and bring increased efficiency.

Uniformity of the flow and torque is the effect of increasing the number of turbine blades.

No data were used to support this study. In this study we used our experiments that are included within the article.

Amir F. Najafi is a Visiting Professor at the Institute of Fluid Mechanics, KIT, 76131 Karlsruhe, Germany.

The authors declare that there are no conflicts of interest regarding the publication of this paper.