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Design and numerical investigation of Savonius wind turbine with discharge flow directing capability
Energy 130 (2017) 327e338
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Design and numerical investigation of Savonius wind turbine with discharge flow directing capability Mojtaba Tahani a, *, Ali Rabbani a, Alibakhsh Kasaeian a, Mehdi Mehrpooya a, Mojtaba Mirhosseini b a b
Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran Department of Energy Technology, Aalborg University, Pontoppidanstraede 111, 9220, Aalborg East, Denmark
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 November 2016 Received in revised form 5 April 2017 Accepted 23 April 2017 Available online 24 April 2017
Recently, Savonius vertical axis wind turbines due to their capabilities and positive properties have gained a significant attention. The objective of this study is to design and model a Savonius-style vertical axis wind turbine with direct discharge flow capability in order to ventilate buildings. For this purpose, a modeling procedure is defined and validated using available experimental results in literature. In addition, two design modifications, variations in cross-section with respect to the height of rotor and conical shaft in the middle of wind rotor are proposed. The variable cut plane changes the pressure in inner region of rotor and enhances the discharge flow rate. However, this increases the negative torque acting on returning blade thus reducing the power coefficient. The inlet flow to Savonius wind rotor goes along the surface of conical shaft and is diverted to lower pressure in order to improve the discharge flow rate. Results indicate that the twist on Savonius wind rotor reduces the negative torque and improves its performance. According to the results, a twisted Savonius wind turbine with conical shaft is associated with 18% increase in power coefficient and 31% increase in discharge flowrate compared to simple Savonius wind turbine. Also, wind turbine with variable cut plane has a 12% decrease in power coefficient and 5% increase in discharge flow rate compared to simple Savonius wind turbine. Therefore, it can be inferred that twisted wind turbine with conical shaft indicated a proper aerodynamic performance. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Savonius turbine Discharge flow Conical shaft Twist Power coefficient
1. Introduction Fossil fuels pollution and their eventual resources depletion, creates an important challenge to reduce the emissions by applying alternative renewable energies. Wind energy has gained a significant attention in developed countries in comparison with other renewable energies, due to their better performance. Advantages such as being clean, having negligible safety issues and sustainable resources make wind energy one of the fastest-growing energy resources of the world. Wind turbine is one of the most common ways of capturing wind energy for the purpose of producing power. Generally, these turbines are categorized in two types: vertical and horizontal axis turbines. The Savonius wind rotor is a vertical axis wind turbine patented by the Finnish engineer Siguard Savonius in 1925 [1]. It is a drag driven wind turbine. While operating, in certain angular
* Corresponding author. E-mail address: [email protected] (M. Tahani). http://dx.doi.org/10.1016/j.energy.2017.04.125 0360-5442/© 2017 Elsevier Ltd. All rights reserved.
position of the rotor, and while the tip speed ratio is greater than one, the lift force acts on blades [2]. The Savonius wind turbine has several advantages such as low manufacturing cost, good selfstarting capability, low noise emission which is suitable for urban areas and low dependency on the wind direction. Many applications can be considered for Savonius turbines including but not limited to pumping water for irrigation, local electricity generation for low demands, heating, ventilation and air-conditioning in buildings and hybrid renewable energy systems [3e7]. Another type of vertical axis wind turbines are H-type rotors which are being widely utilized in several places. The focus of this research study is Savonius type wind turbines, therefore the literature review of H-type rotors is just summarized in Table 1. Numerous experimental and numerical investigations have been carried out to enhance the performance of the Savonius rotor due to the relatively lower efficiency of this turbine compared with other turbines. The Savonius rotor performance is presented by two aerodynamics coefficients: the power coefficient (CP) and torque coefficient (CT). These terms depend on various design parameters
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mT
Nomenclature CP CT TSR d D De e H
u P .
rg t
Power coefficient Torque coefficient Tip speed ratio Chord length of blade (m) Overall diameter (m) End plate diameter (m) Overlap distance (m) Height of the blade (m) Rotating speed of rotor (rpm) The static pressure (pa)
CTs T
r A V R Ts Pturbine Pavailabe R2
a Hc Dc
The gravity force (N) The stress tensor
Eddy viscosity (mm2/s) Static torque coefficient Dynamic torque (N.m) Air density (kg/m3) Swept area of the turbine (m2) Velocity of free stream wind (m/s) The radius of turbine (m) Static torque (N.m) The power produced by the turbine (w) The power available in the wind (w) Correlation coefficient Twist angle (degree) Height of conical shaft (m) Conical shaft diameter (m)
Table 1 The literature review for H-type vertical axis wind turbines. No.
Reference
Topic
1 2 3 4 5 6
Chong et al. [8] Zuo et al. [9] Li et al. [10] Li et al. [11] Li et al. [12] Li et al. [13]
Utilization of adaptive neuro-fuzzy methodology for the purpose of estimating the wind turbine rotational speed. Investigating the wake effect of a H-type vertical axis wind turbine on the downstream turbine using numerical simulations. Experimental investigation of the effect of flow field and aerodynamic forces on the turbine Experimental and numerical investigation of the aerodynamic loads on a two bladed vertical axis wind turbine Experimental and numerical investigation of the flow field on a two bladed vertical axis wind turbine Investigating the influence of number of blades on the aerodynamic forces of a vertical axis wind turbine
such as tip speed ratio (TSR), the aspect ratio (height of blade to diameter of blade), the overlap ratio, number of blades, the impact of end plates on aerodynamic performance, the rotor twist angle and cross-section profile [14]. Several researchers investigated these parameters to improve the aerodynamic performance of Savonius turbine [15e19]. Kianfar et al. [20] studied the effect of blade curve on the power coefficient of Savonius wind rotor by means of numerical simulation and compared it with wind tunnel tested results. Saha et al. [21] assessed the aerodynamic performance of single-, two-, and three-stage Savonius rotor systems. Both semicircular and twisted blades have been used in their investigations. Mahmoud et al. [22] compared different geometries of Savonius wind turbine to determine the most effective operation parameters. They reported that two-blade rotor is more efficient than three and four-blades and the rotor with end plates has a higher efficiency. Also, double stage rotors without overlap ratio have a higher performance. Moreover, Rashidi et al. [23] studied the effect of blade number on three different scaled-down helical Savonius vertical axis wind turbines systems performance. Driss et al. [24] studied the incidence angle effect on the aerodynamic structure of an incurved Savonius wind rotor. In this study, the numerical model was based on the Navier-Stokes equations in conjunction with the standard k-ε turbulence model. Soo Jeon et al. [25] experimentally studied the effects of the end plates with various shapes and sizes on the aerodynamic performance of helical Savonius wind turbines. Their results indicated that by increasing the end plate area ratio up to 1.0, the power coefficient and its tip speed ratio also will increase. Augmentation techniques can be used to improve the performance of Savonius wind rotor. Accordingly, several significant efforts have been done on numerical and experimental investigations to achieve an optimized geometry. Tartuferi et al. [26] enhanced the Savonius wind rotor aerodynamic performance with two approaches which was based on developing innovative airfoil-shaped
blades. Altan and Atilgan [27] designed a curtain to increase the performance of the Savonius wind rotor and experimental and numerical analysis was carried out on the static rotor performance equipped with this curtain. In addition, they introduced a new curtaining arrangement to improve the Savonius wind turbine performance. This curtain arrangement prevents the negative torque which is opposite to the direction of rotation [28,29]. During the rotation of the rotor, this negative torque constantly acts on the returning blade, in the flow direction. Twist of the Savonius wind turbine is one of the practical solutions to overcome this problem [30]. Saha and Rajkumar [31] investigated the feasibility of twisted bladed Savonius rotor for power generation. Their Experimental results indicated that the twisted bladed rotor shows a better smooth running, self-starting ability and higher efficiency compared to the conventional rotor. Kamoji et al. [32] tested a helical Savonius rotor with a twist of 90 in an open jet wind tunnel to measure the coefficient of static torque, coefficient of torque and coefficient of power. The results indicated that the helical Savonius rotor has a positive static torque coefficient at all the rotor angles. Driss et al. [33] carried out the numerical investigations to study the bucket design effect on the turbulent flow around unconventional Savonius wind rotors which results indicated that the bucket design has a direct effect on the local characteristics. Many researchers obtained innovative geometries to provide an effective wind rotor with high capabilities [34e36]. Roy and Saha [37] designed a novel developed two-bladed Savonius-style wind turbine which evolved from a series of experiments on different types of blades. Their investigation demonstrated a maximum power coefficient of 34.8%. Shaheen et al. [38] studied the development of a multi-turbine cluster for construction of efficient Savonius wind turbine farms and performed numerical investigations on a single Savonius wind turbine, clusters of two turbines in parallel and oblique positions, and triangular clusters of three wind turbines. Mohamad et al. [39] studied a considerably
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improved design to increase the output power of a classic Savonius turbine in the presence of the obstacle plate. Six design variables were considered in their optimization process. The final results revealed an increase in the output power coefficient of 40% compared to a standard Savonius turbine. Kamoji et al. [40] tested the rotors with and without central shaft between the end plates in a closed jet wind tunnel to modify the power coefficient of conventional Savonius wind rotor. The modified Savonius rotor with an overlap ratio of 0.0, blade arc angle of 124 , and an aspect ratio of 0.7 showed a maximum power coefficient of 0.21. In this research study, an innovative Savonius-style wind rotor which is capable of directing the discharge flow is designed to utilize the flow for ventilation and produce the power for electricity demand in buildings. Accordingly, a modeling procedure is defined and validated with experimental results. Moreover, grid and turbulence model are verified. In addition, two novel modifications, variable cut plane with respect to the height of rotor and conical shaft in middle of the rotor, are suggested as improvements to the rotor design. The innovative geometries can be summarized as follows:
Twisted Savonius rotor with the variable cut plane, Twisted Savonius rotor with conical shaft, Savonius rotor with conical shaft and variable cut plane, Twisted wind rotor with conical shaft and variable cut plane.
2. Numerical model In order to design and achieve a proper geometry for vertical axis wind rotor, an appropriate modelling procedure should be applied. To achieve this target and validate the obtained results, a Savonius vertical axis wind rotor geometry from Ref. [37] has been modeled. It should be noted that the steady state conditions are considered for this modeling. ANSYS-CFX software has been utilized for the purpose of simulation and also validation. The, results are compared with experimental data reported in Ref. [37] and the error is evaluated.
Fig. 1. The schematic shapes of the validated geometry by proposed modeling procedure according to ref [36].
2.1. Geometry and computational domain Top view and isometric view of Savonius rotor presented in Ref. [37] has been shown in Fig. 1. This rotor has up and down end plates which two semi cylinder surfaces are relocated sideways. Also, dimensions of design parameters are shown in this figure. The 3D computational domain for the modeled Savonius rotor with circular plane is shown in Fig. 2. The domain consists of two parts that are separated by a sliding interface. The first region is stationary which represents wind tunnel test chamber. According to ref [37], the size of the stationary domain is assumed 500 mm 500 mm 700 mm. Rotational domain is the second region and is rotating around a perpendicular axis with respect to the specified plane passing through the center of rotor which is fixed at 250 mm from the inlet face of the stationary domain. The wind rotor is located in the middle of rotational domain and is rotating with the angular speed of the domain. The inlet velocity of wind that is presented in Ref. [37] is considered as the inlet boundary condition of the inlet face of the stationary domain with 250 mm distance from the axis of rotational domain. The outlet pressure of the outlet face is considered equal to atmospheric pressure. Also, the boundary condition on the blade of rotor is set as non-slip smooth wall. A particular attention was given to the grid in order to achieve a proper simulation of the flow field of the turbine rotor and its performance. The volume between stationary and rotating domain
Fig. 2. Layout of the 3D computational domain reproducing the test chamber and assumed boundary conditions.
has been discretized by means of structured mesh. The size of meshes increases as their distance from the interface increases. In the rotating domain, an unstructured triangular mesh was adopted. Due to the complex geometry of rotor, a significant effort was dedicated to adjusting the mentioned grid. In order to study more accurately the flow in the boundary layers of rotor blade, prismatic grids have been applied on sides of rotor blades to capture the boundary layer correctly. Accordingly, the value of the non-
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dimensional near-wall grid distance (yþ) is equal to 1. In addition, density of meshes was higher near the wall of rotor blades and interface. Fig. 3 shows the grid on rotor, rotating domain and stationary domain. 2.2. Governing equations Naturally, the flow around the Savonius rotor is turbulent. Therefore, the computational fluid dynamic simulation on the turbulence flow field around rotor is highly complex. CFD simulations were applied to solve the problem based on 3D steady finitevolume incompressible Reynolds Averaged Navier-Stokes (RANS) equations. The governing equations on turbulence flow are continuity, and Navier - Stokes equations that in conservative forms are represented as follows [41]:
vui ¼0 vxj
(1)
vP v v r ui uj ¼ þ tij ru0i u0j þ Sui vxj vxi vxj
(2)
where, P is the static pressure, r is the density and tij is the stress tensor and Sui is the centrifugal and Coriolis force term, which can be calculated using following equation:
h ! ! i 8 ! ! ! > Su i ¼ r 2 U u þ U U r > > < ! vui vuj > > > tij ¼ m þ : vxj vxi
(3)
To precisely model the turbulent phenomenon which occurs during the rotation of wind rotor, a robust turbulence model needs to be added in RANS CFD solvers. Several turbulence models have been applied to solve numerically the flow field around the wind rotor. The best model is the one which obtains results with the highest agreement with experiments. Plourde et al. used threedimensional SST k-u turbulence model and found that the results are in a great agreement with the experiment [14]. In another work, SST k-u turbulence model was used to analyze the transient forces that act on Savonius rotors [42]. SST turbulence model is based on k-u model and predicts the flow near the wall similar to k-u model. This model considers the transmission of stress tensor and has a significant performance in predicting the separation flow. While the k-ε turbulence model does not work well in vortex regions, SST model can accurately estimate this phenomenon. Moreover, results of SST model are in good agreement with experimental results. In order to gain proper results while applying k-u and SST turbulence models, the value of yþ must be small [43e45].
Fig. 3. (a) Computational grid (Isometric view of both domains), (b) Computational grid around blade (Isometric view of rotating zone), (c) Top view of unstructured meshing in rotating zone, (d) Top view of grid refinement near the blade.
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0.3 modeling
experimental [37]
Poly. (modeling)
CP
0.25 0.2 0.15 0.1 0.05 0 0.1
0.3
0.5
0.6
0.7
0.8
TSR
0.9
1
1.1
Fig. 4. Comparison of modeling and experimental power coefficient corresponding to tip speed ratios (TSR).
The governing equation on this turbulence model is the following:
Pk ¼ minðmt f; Clmt εÞ
(4)
CP ¼
PTurbine Tu T Ru ¼ CT TSR ¼ ¼ PAvailable 0:5rAV 3 0:5rAV 2 R V
(8)
In normal conditions, Clmt is assumed to be 1015. In SST model, a new parameter for dissipation rate was defined as follows:
ð1 F1 Þ2rsu2 vk vu vk vu vk vu þ þ vx vx vy vy vz vz u
CTS ¼ (5)
In this equation, F1 is mixture function near the wall surface which is zero in far way regions of wall surface. SST turbulence model applies k-u model in near the wall surface and k-ε model in far way surface. All factors in SST model are calculated as a function of F1 :
f ¼ F1 f1 þ ð1 F1 Þf2
(6)
f is the main factor in SST model and f1 is calculated from k-u model and f2 from k-ε. Based on the above discussions flow near the wall surface is analyzed by applying k-u. In this case, results are more accurate than those of k-ε model [14]. In this study, the SST model is used as the appropriate approach. 2.3. Performance calculation Generally, performance of a vertical axis wind turbines is demonstrated by torque coefficient (CT ), power coefficient (CP ) and static torque coefficient (CTS ) [33]:
CT ¼
T 0:5rAV 2 R
(7)
TS 0:5rAV 2 R
(9)
where, r is the air density, V is the free stream velocity, TSR is the tip speed ratio, A is the swept area of the turbine, R is the radius of turbine, u is the rotational speed, T represents the dynamic torque, TS is the static torque, PTurbine and PAvailable present the power produced by the turbine and the available power in the wind respectively. In order to validate the modeling procedure used in this study, various tip speed ratios (from 0.1 up to 1.1) for wind rotor were computed by the commercial software and the associated calculated power coefficients were compared with experimental results. Fig. 4 demonstrates a comparison between simulation and experimental results. According to Fig. 4, the proposed modeling procedure has a suitable agreement with experimental results thus can be applied as a procedure for designing and modeling. The coefficient of correlation is used to ensure the modeling procedure was efficient. According to ref [15], the coefficient of correlation is calculated from Eq. (10).
P
2 fExp fpred R2 ¼ 1 P 2 fExp fExp
(10)
where
Table 2 List of properties of elements size for different defined grids. Case number
Cells number
Element size of stationary domain (m)
Element size of rotating domain (m)
Element size on blade (m)
1 2 3 4 5 6
704218 1537443 2819955 5223980 8531780 12140524
0.013 0.0098 0.008 0.0065 0.0055 0.005
0.01 0.0093 0.0075 0.006 0.005 0.0045
0.0085 0.0063 0.005 0.004 0.0035 0.0025
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Table 3 Calculated errors from comparison of numerical and experimental results. cells number
Torque (N m)
CP
Error (%)
0.7milion 1.5milion 2.8milion 5milion 8.5milion 12milion
0.04226 0.04388 0.04486 0.04491 0.04496 0.04496
0.2189 0.2274 0.2324 0.02327 0.2328 0.2329
12.41 9.05 7.02 6.92 6.85 6.81
Pn fExp ¼
i¼1 fExp
(11)
n
“n” presents the number of experimental results. According to calculations, the value of coefficient of correlation is 0.93 which demonstrates the high reliability of the obtained results. In order to further evaluate the modeling procedure used in this study, in the following subsections, gird independency and turbulence model are verified. 2.4. Mesh study
Table 4 Coefficient of correlation for different turbulence models according to experimental results. Turbulence model
SST
k-omega
k-epsilon
RNG k-epsilon
R2 (In comparison to [37])
0.856
0.835
0.774
0.73
As mentioned earlier, the coefficient of correlation can be used as a criterion to determine an appropriate turbulence model. In Table 4, the values of correlation coefficient for different turbulence models are given. Based on calculated results, the SST turbulence model has a superior performance compared to the others. 2.6. Design procedure In order to define innovative blade geometry while considering the direct discharge flow as the main target, several ideas were adopted. Twist in vertical axis wind rotor is one of these ideas to improve the power coefficient and discharge flow of the turbine. Variations in cross-section with respect to the height of rotor will be defined as another idea to design the new wind turbine. The third idea is designing a vertical axis wind rotor with a centrically
A grid sensitivity analysis was done to reduce the computational time and guarantee a minimum discretization error from experimental results. In this section, six different grids on model with various element sizes for similar TSR equal to 0.7 are investigated and their calculated power coefficients are compared with experimental results. Table 2 shows the properties of different grids. Table 3 indicates the obtained error from comparing the calculated results with experimental ones in different grids. Results indicate a small dependence on grid resolution and by considering run time of modelling, cell numbers around 2.8 million have a good agreement with experimental results of ref [37]. Therefore, the element size of grids with 2.8 million cell numbers is used for final modelling. 2.5. Turbulence study In order to evaluate the turbulence model for modelling Savonius wind rotor and verifying the reliability of the utilized model, a comparison between different turbulence models including k-u, kε, RNG k-ε and SST is carried out according to the obtained experimental results from Ref. [37]. Fig. 5 shows the calculated results for CP using different turbulence models in various TSR. 0.3
SST
k-omega
Fig. 6. Design flowchart.
k-epsilon
RNG K-epsilon
experimental [37]
CP
0.25 0.2 0.15 0.1 0.05
TSR 0 0.3
0.5
0.7
Fig. 5. Comparison of various turbulence models power coefficient.
1
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Fig. 7. The schematic shapes diagram of the helical Savonius wind rotor with a twist of 30 .
3. Results of modeling
0.25
Based on the mentioned assessments modeling procedure, design and modeling of a vertical axis wind turbine in Savonius form with direct discharge flow capability will be discussed. The design process is started from the simple Savonius wind rotor with circular cross section and novel modifications will be implemented to improve the power coefficient and discharge flow rate of the turbine. In these modellings, the value of TSR is 0.7 for all the suggested geometries. The difference between the experimental and simulated results of proposed geometry from Ref. [37] and highest value of power coefficient is the reason of this assumption.
0.2
CP
0.15 0.1 0.05 0 0
10
20
30
40
50
3.1. Design of different novel geometries
twist angle
3.1.1. Simple and twisted circular Savonius rotor As reported in Ref. [31], according to the Savonius wind rotor form and the direction of flow impact on blades, the negative torque on convex blade relative to the flow is applied constantly which decreases the power coefficient of the wind turbine. Therefore, the
Fig. 8. Improvement of the power coefficient by the twist angle.
Discharge flow rate
shaft in conical form. Fig. 6 shows the flowchart of the design procedure.
0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 0
10
20
30
40
Twist angle discharge flow form up
discharge flow from down
Fig. 9. Improvement of discharge flow rate by the twist angle.
50
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Fig. 10. The schematic shapes of the variable cut plane Savonius-style wind rotor.
Table 5 Calculated discharge flow rate and power coefficient for different turbines.
Wind rotor with fixed cut plane Twisted wind rotor with fixed cut plane (30 ) Wind rotor with variable cut plane Twisted wind rotor with variable cut plane
CP
Discharge flow from down of rotor (kg/s)
Discharge flow from up of rotor (kg/s)
0.17 0.205 0.15 0.16
0.0312 0.0363 0.03204 0.0328
0.03 0.0349 0.0305 0.031
Fig. 11. The schematics shapes of Savonius wind rotor with conical shaft, (a) the top view, (b) the isometric view and (c) the front view of wind rotor.
M. Tahani et al. / Energy 130 (2017) 327e338 Table 6 Calculated discharge flow rate and power coefficient for different rotors, comparison of wind rotor with conical shaft with simple Savonius wind rotor.
Wind rotor without a shaft and twist Two blades wind rotor with conical shaft Three blades wind rotor with conical shaft Twisted wind rotor without shaft Twisted wind rotor with conical shaft
CP
Discharge flow from down of rotor kg= s
0.17 0.158 0.14 0.205 0.2
0.0312 0.0368 0.0317 0.0363 0.0401
Table 7 Calculated discharge flow rate and power coefficient for different rotors, comparison of wind rotor with conical shaft and variable cut plane with simple Savonius wind rotor.
Wind rotor without shaft Two blades wind rotor with conical shaft Wind rotor with conical shaft and variable cut plane Twisted wind rotor with conical shaft and variable cut plane Twisted wind rotor with conical shaft
CP
Discharge flow from down of rotor kg= s
0.17 0.158 0.145
0.0312 0.0368 0.0373
0.155
0.0377
0.2
0.0401
twist on blades can reduce the negative torque. In the first step, the Savonius wind rotor and after that the twisted Savonius wind rotor
335
are modeled and the calculated results, indicated the effectiveness of this design. In addition, the twisted wind rotor has a positive effect on the discharge flow rate of the turbine. Fig. 7 shows the Savonius wind rotor with a 30 twist angle. Figs. 8 and 9 indicate the effect of twist angle on the improvement of power coefficient and discharge flow rate. 3.1.2. Simple and twisted Savonius rotor with the variable cut plane One of the ideas which is presented in this study is circular cut plane with a various arc with respect to wind rotor height. The top cross section of the rotor has a 270 arc angle and then the angle of the arc is dropped with respect to the height and in the final cross section of the rotor has an 180 arc. The reason is that by decreasing the cut plane arc angle along the height, the pressure is changed and causes an increase in discharge flow rate. Fig. 10 shows the Savonius-style wind rotor with the variable cut plane. In the next step, the effect of twist angle on vertical axis wind rotor with the variable cut plane on changing the blade height is investigated. The Purpose of this section is to evaluate all of possible conditions for power coefficient and discharge flow of wind turbine improvement and obtain the appropriate and optimized design. The values of discharge flow rate and power coefficient for four different turbines are shown in Table 5. According to the results, the wind rotor with the fixed cut plane and a twist of 30 has a better performance in power coefficient and discharge flow compared to the conventional case. Therefore, this idea will be applied in the final design. The wind rotor with variable cut plane indicates a small improvement in discharge flow rate and power coefficient. The reason is the increase in negative torque surface and the inner space pressure of rotor. Therefore, the results suggest that twist in
Fig. 12. The schematic shapes of Savonius wind rotor with conical shaft and variable cut plane, (a) the top view, (b) the isometric view and (c) the front view of wind rotor.
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Fig. 13. The velocity contours on different plane, (a) with 0.03 m height, (b) 0.06 m height, (c) 0.09 m height, (d) 0.12 m height, (e) 0.15 m height, (f) 0.18 m height, (g) the plane with 0.23 m height from down of the blade.
wind rotor improves its aerodynamic performance. 3.1.3. Simple and twisted Savonius rotor with conical shaft Incorporation of a conical shaft as the central shaft can be considered as another proposed idea in designing the Savonius wind rotor with direct discharge flow capability. The radial centrifugal compressor has a middle structure in the conical form which can produce a 90 diversion in the inlet flow. Therefore, the central shaft of the rotor is designed with a capability that the wind flow by passing from its inclined surface is being discharged with 90 deviation from the down or upper parts of the rotor. On the other hand, from the results of modeling it can be seen that the output rate from down the rotor is more than upper part of the rotor due to gravity. For this reason, wind turbine shaft is designed in a way that the upper part of the rotor is closed and the slope of the conical shaft is in direction that the inlet flow into the rotor diverts downwards. Fig. 11 shows the schematic shapes of the Savonius wind rotor with the conical shaft. As discussed in the previous section, twist in wind turbine can
improve the power coefficient and discharge flow of turbine. Due to mentioned point, in the proposed innovative design of the vertical axis wind rotor with conical shaft, a twist angle with 30-degree angle is considered. Table 6 indicates the calculated discharge flow and power coefficient results for the proposed wind rotor. Based on the obtained results associated with two-bladed wind rotor with and without shaft, it can be concluded that this design has a significant impact on the wind turbine discharge flow rate but causes negligible reductions in power coefficient. Therefore, the use of this design will be appropriate. Indeed, using a conical shaft in wind rotor will improve the discharge flow rate up to 18%. In order to study the effect of number of blades on the aerodynamic operation, the wind rotor with three blades is also modeled. The results reveal that the three blade wind turbine with conical shaft does not have a proper performance for discharge flow rate and power coefficient. Results indicate that a twisted wind rotor with conical shaft compared to wind rotor without shaft and twist, is associated with 29% and 18% increase in discharge flow rate and power coefficient
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Fig. 14. The velocity vector, (a) the simple Savonius rotor, (b) the twisted Savonius rotor with conical shaft.
respectively. Also, it has 11% improvement in discharge flow rate compared to the twisted wind rotor without shaft. As the calculated results suggest, the twisted wind rotor with conical shaft has a great performance for defined purpose. 3.1.4. Savonius rotor with conical shaft and variable cut plane A vertical axis wind rotor with the conical shaft and variable cut plane is the other proposed design modification. Two models of the wind rotor with and without twist will be considered to evaluate all possible cases in order to help selecting an appropriate design. Table 7 shows the calculated results for power coefficient and discharge flow rate of four different wind rotors. Fig. 12 shows a Savonius wind rotor with the conical shaft and variable cut plane with a twist angle equal to 30 . Calculated results indicate that using wind turbine with the conical shaft and variable cut plane causes a decrease in power coefficient compared to fixed cut plane. However, the amount of improvement for discharge flow rate is about 1% which is not sufficient for the design. The twist in this type of turbine has a little improvement thus is not suitable to use in the design. If a vertical axis wind rotor with the conical shaft and variable cut plane is compared with a twisted vertical axis wind rotor with the conical shaft and fixed cut plane, results will indicate that for both cases, the twisted wind turbine with 30 angle has a better performance. Fig. 13 presents the distribution of the velocity on the various plane with different height from end of twisted Savonius wind turbine with conical shaft. The velocity contour is shown on plane with 0.03 m distance from the top and down planes and the value of twist is 30 . According to the Fig. 13, the separation and also velocity reduction can be seen in the edge of advancing blade in all geometries. On the other hand, the velocity is increased on the convex side of returning blade. This is because of reduction in cross sectional area and also the direction of blade rotation. In general, all geometries presented in Fig. 13 have the same behavior and the velocity contours indicate that the flow is being separated after the blades. In Fig. 14, the velocity vectors for simple Savonius rotor and twisted Savonius rotor with conical shaft is presented for comparing the flow direction. According to the figure, it can be seen that the flow direction has been changed the velocity is increased in twisted Savonius rotor with conical shaft. 4. Conclusion In this research study it was aimed to design a vertical axis wind
rotor with direct discharge flow capability. In this section, results associated with different designs are summarized. The first step of design process is to determine the variation of twist in wind turbine. According to the calculated results, twisted wind turbine has an appropriate performance based on the obtained power coefficient and discharge flow rate. In order to direct the discharge flow from wind turbine, two novel modifications which are variable cut plane along height and using the conical shaft in the middle of wind rotor are suggested. Power coefficient and discharge flow rate for variable cut plane are compared to simple Savonius wind rotor and the results indicated that power increases 12% and the discharge flow rate decreases 5%. And in comparison to the wind rotor with conical shaft, power decreases 7% and discharge flow rate increases 18%. Twist in proposed design of this paper causes an improvement in the results. Therefore, power coefficient and the discharge flow rate for twisted wind rotor with variable cut plane in comparison to twisted wind rotor has a 25% decrease and 9.6% increase and compared to wind rotor with conical shaft has a 2% decrease and 10.5% increase respectively. Moreover, results of simple Savonius wind rotor compared to twisted wind turbine with conical shaft shows 18% increase and 31% increase in CP and discharge flow rate respectively. This suggest that this innovative idea is a suitable design to satisfy the main target. In order to consider all possible cases for suggested design ideas, two wind rotors with variable cut plane and conical shaft with and without twist were evaluated. The results suggest that compared to twisted wind rotors with conical shaft, these rotors have a weaker operation. References [1] Ushiyama I, Nagai H. Optimum design configurations and performance of Savonius rotors. Wind Eng 1988;12(1):59e75. [2] Tartuferi M, D'Alessandro V, Montelpare S, Ricci R. Enhancement of Savonius wind rotor aerodynamic performance: a computational study of new blade shapes and curtain systems. Energy 2015;79:371e84. [3] Roy S, Saha UK. An adapted blockage factor correlation approach in wind tunnel experiments of a Savonius-style wind turbine. Energy Convers Manag 2014;86:418e27. [4] Goodarzi M, Keimanesh R. Numerical analysis on overall performance of Savonius turbines adjacent to a natural draft cooling tower. Energy Convers Manag 2015;99:41e9. [5] Chong WT, Poh SC, Fazlizan A, Yip SY, Chang CK, Hew WP. Early development of an energy recovery wind turbine generator for exhaust air system. Appl Energy 2013;112:568e75. [6] Maleki A, Khajeh MG, Rosen MA. Weather forecasting for optimization of a
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Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Design and numerical investigation of Savonius wind turbine with discharge flow directing capability Mojtaba Tahani a, *, Ali Rabbani a, Alibakhsh Kasaeian a, Mehdi Mehrpooya a, Mojtaba Mirhosseini b a b
Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran Department of Energy Technology, Aalborg University, Pontoppidanstraede 111, 9220, Aalborg East, Denmark
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 November 2016 Received in revised form 5 April 2017 Accepted 23 April 2017 Available online 24 April 2017
Recently, Savonius vertical axis wind turbines due to their capabilities and positive properties have gained a significant attention. The objective of this study is to design and model a Savonius-style vertical axis wind turbine with direct discharge flow capability in order to ventilate buildings. For this purpose, a modeling procedure is defined and validated using available experimental results in literature. In addition, two design modifications, variations in cross-section with respect to the height of rotor and conical shaft in the middle of wind rotor are proposed. The variable cut plane changes the pressure in inner region of rotor and enhances the discharge flow rate. However, this increases the negative torque acting on returning blade thus reducing the power coefficient. The inlet flow to Savonius wind rotor goes along the surface of conical shaft and is diverted to lower pressure in order to improve the discharge flow rate. Results indicate that the twist on Savonius wind rotor reduces the negative torque and improves its performance. According to the results, a twisted Savonius wind turbine with conical shaft is associated with 18% increase in power coefficient and 31% increase in discharge flowrate compared to simple Savonius wind turbine. Also, wind turbine with variable cut plane has a 12% decrease in power coefficient and 5% increase in discharge flow rate compared to simple Savonius wind turbine. Therefore, it can be inferred that twisted wind turbine with conical shaft indicated a proper aerodynamic performance. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Savonius turbine Discharge flow Conical shaft Twist Power coefficient
1. Introduction Fossil fuels pollution and their eventual resources depletion, creates an important challenge to reduce the emissions by applying alternative renewable energies. Wind energy has gained a significant attention in developed countries in comparison with other renewable energies, due to their better performance. Advantages such as being clean, having negligible safety issues and sustainable resources make wind energy one of the fastest-growing energy resources of the world. Wind turbine is one of the most common ways of capturing wind energy for the purpose of producing power. Generally, these turbines are categorized in two types: vertical and horizontal axis turbines. The Savonius wind rotor is a vertical axis wind turbine patented by the Finnish engineer Siguard Savonius in 1925 [1]. It is a drag driven wind turbine. While operating, in certain angular
* Corresponding author. E-mail address: [email protected] (M. Tahani). http://dx.doi.org/10.1016/j.energy.2017.04.125 0360-5442/© 2017 Elsevier Ltd. All rights reserved.
position of the rotor, and while the tip speed ratio is greater than one, the lift force acts on blades [2]. The Savonius wind turbine has several advantages such as low manufacturing cost, good selfstarting capability, low noise emission which is suitable for urban areas and low dependency on the wind direction. Many applications can be considered for Savonius turbines including but not limited to pumping water for irrigation, local electricity generation for low demands, heating, ventilation and air-conditioning in buildings and hybrid renewable energy systems [3e7]. Another type of vertical axis wind turbines are H-type rotors which are being widely utilized in several places. The focus of this research study is Savonius type wind turbines, therefore the literature review of H-type rotors is just summarized in Table 1. Numerous experimental and numerical investigations have been carried out to enhance the performance of the Savonius rotor due to the relatively lower efficiency of this turbine compared with other turbines. The Savonius rotor performance is presented by two aerodynamics coefficients: the power coefficient (CP) and torque coefficient (CT). These terms depend on various design parameters
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mT
Nomenclature CP CT TSR d D De e H
u P .
rg t
Power coefficient Torque coefficient Tip speed ratio Chord length of blade (m) Overall diameter (m) End plate diameter (m) Overlap distance (m) Height of the blade (m) Rotating speed of rotor (rpm) The static pressure (pa)
CTs T
r A V R Ts Pturbine Pavailabe R2
a Hc Dc
The gravity force (N) The stress tensor
Eddy viscosity (mm2/s) Static torque coefficient Dynamic torque (N.m) Air density (kg/m3) Swept area of the turbine (m2) Velocity of free stream wind (m/s) The radius of turbine (m) Static torque (N.m) The power produced by the turbine (w) The power available in the wind (w) Correlation coefficient Twist angle (degree) Height of conical shaft (m) Conical shaft diameter (m)
Table 1 The literature review for H-type vertical axis wind turbines. No.
Reference
Topic
1 2 3 4 5 6
Chong et al. [8] Zuo et al. [9] Li et al. [10] Li et al. [11] Li et al. [12] Li et al. [13]
Utilization of adaptive neuro-fuzzy methodology for the purpose of estimating the wind turbine rotational speed. Investigating the wake effect of a H-type vertical axis wind turbine on the downstream turbine using numerical simulations. Experimental investigation of the effect of flow field and aerodynamic forces on the turbine Experimental and numerical investigation of the aerodynamic loads on a two bladed vertical axis wind turbine Experimental and numerical investigation of the flow field on a two bladed vertical axis wind turbine Investigating the influence of number of blades on the aerodynamic forces of a vertical axis wind turbine
such as tip speed ratio (TSR), the aspect ratio (height of blade to diameter of blade), the overlap ratio, number of blades, the impact of end plates on aerodynamic performance, the rotor twist angle and cross-section profile [14]. Several researchers investigated these parameters to improve the aerodynamic performance of Savonius turbine [15e19]. Kianfar et al. [20] studied the effect of blade curve on the power coefficient of Savonius wind rotor by means of numerical simulation and compared it with wind tunnel tested results. Saha et al. [21] assessed the aerodynamic performance of single-, two-, and three-stage Savonius rotor systems. Both semicircular and twisted blades have been used in their investigations. Mahmoud et al. [22] compared different geometries of Savonius wind turbine to determine the most effective operation parameters. They reported that two-blade rotor is more efficient than three and four-blades and the rotor with end plates has a higher efficiency. Also, double stage rotors without overlap ratio have a higher performance. Moreover, Rashidi et al. [23] studied the effect of blade number on three different scaled-down helical Savonius vertical axis wind turbines systems performance. Driss et al. [24] studied the incidence angle effect on the aerodynamic structure of an incurved Savonius wind rotor. In this study, the numerical model was based on the Navier-Stokes equations in conjunction with the standard k-ε turbulence model. Soo Jeon et al. [25] experimentally studied the effects of the end plates with various shapes and sizes on the aerodynamic performance of helical Savonius wind turbines. Their results indicated that by increasing the end plate area ratio up to 1.0, the power coefficient and its tip speed ratio also will increase. Augmentation techniques can be used to improve the performance of Savonius wind rotor. Accordingly, several significant efforts have been done on numerical and experimental investigations to achieve an optimized geometry. Tartuferi et al. [26] enhanced the Savonius wind rotor aerodynamic performance with two approaches which was based on developing innovative airfoil-shaped
blades. Altan and Atilgan [27] designed a curtain to increase the performance of the Savonius wind rotor and experimental and numerical analysis was carried out on the static rotor performance equipped with this curtain. In addition, they introduced a new curtaining arrangement to improve the Savonius wind turbine performance. This curtain arrangement prevents the negative torque which is opposite to the direction of rotation [28,29]. During the rotation of the rotor, this negative torque constantly acts on the returning blade, in the flow direction. Twist of the Savonius wind turbine is one of the practical solutions to overcome this problem [30]. Saha and Rajkumar [31] investigated the feasibility of twisted bladed Savonius rotor for power generation. Their Experimental results indicated that the twisted bladed rotor shows a better smooth running, self-starting ability and higher efficiency compared to the conventional rotor. Kamoji et al. [32] tested a helical Savonius rotor with a twist of 90 in an open jet wind tunnel to measure the coefficient of static torque, coefficient of torque and coefficient of power. The results indicated that the helical Savonius rotor has a positive static torque coefficient at all the rotor angles. Driss et al. [33] carried out the numerical investigations to study the bucket design effect on the turbulent flow around unconventional Savonius wind rotors which results indicated that the bucket design has a direct effect on the local characteristics. Many researchers obtained innovative geometries to provide an effective wind rotor with high capabilities [34e36]. Roy and Saha [37] designed a novel developed two-bladed Savonius-style wind turbine which evolved from a series of experiments on different types of blades. Their investigation demonstrated a maximum power coefficient of 34.8%. Shaheen et al. [38] studied the development of a multi-turbine cluster for construction of efficient Savonius wind turbine farms and performed numerical investigations on a single Savonius wind turbine, clusters of two turbines in parallel and oblique positions, and triangular clusters of three wind turbines. Mohamad et al. [39] studied a considerably
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improved design to increase the output power of a classic Savonius turbine in the presence of the obstacle plate. Six design variables were considered in their optimization process. The final results revealed an increase in the output power coefficient of 40% compared to a standard Savonius turbine. Kamoji et al. [40] tested the rotors with and without central shaft between the end plates in a closed jet wind tunnel to modify the power coefficient of conventional Savonius wind rotor. The modified Savonius rotor with an overlap ratio of 0.0, blade arc angle of 124 , and an aspect ratio of 0.7 showed a maximum power coefficient of 0.21. In this research study, an innovative Savonius-style wind rotor which is capable of directing the discharge flow is designed to utilize the flow for ventilation and produce the power for electricity demand in buildings. Accordingly, a modeling procedure is defined and validated with experimental results. Moreover, grid and turbulence model are verified. In addition, two novel modifications, variable cut plane with respect to the height of rotor and conical shaft in middle of the rotor, are suggested as improvements to the rotor design. The innovative geometries can be summarized as follows:
Twisted Savonius rotor with the variable cut plane, Twisted Savonius rotor with conical shaft, Savonius rotor with conical shaft and variable cut plane, Twisted wind rotor with conical shaft and variable cut plane.
2. Numerical model In order to design and achieve a proper geometry for vertical axis wind rotor, an appropriate modelling procedure should be applied. To achieve this target and validate the obtained results, a Savonius vertical axis wind rotor geometry from Ref. [37] has been modeled. It should be noted that the steady state conditions are considered for this modeling. ANSYS-CFX software has been utilized for the purpose of simulation and also validation. The, results are compared with experimental data reported in Ref. [37] and the error is evaluated.
Fig. 1. The schematic shapes of the validated geometry by proposed modeling procedure according to ref [36].
2.1. Geometry and computational domain Top view and isometric view of Savonius rotor presented in Ref. [37] has been shown in Fig. 1. This rotor has up and down end plates which two semi cylinder surfaces are relocated sideways. Also, dimensions of design parameters are shown in this figure. The 3D computational domain for the modeled Savonius rotor with circular plane is shown in Fig. 2. The domain consists of two parts that are separated by a sliding interface. The first region is stationary which represents wind tunnel test chamber. According to ref [37], the size of the stationary domain is assumed 500 mm 500 mm 700 mm. Rotational domain is the second region and is rotating around a perpendicular axis with respect to the specified plane passing through the center of rotor which is fixed at 250 mm from the inlet face of the stationary domain. The wind rotor is located in the middle of rotational domain and is rotating with the angular speed of the domain. The inlet velocity of wind that is presented in Ref. [37] is considered as the inlet boundary condition of the inlet face of the stationary domain with 250 mm distance from the axis of rotational domain. The outlet pressure of the outlet face is considered equal to atmospheric pressure. Also, the boundary condition on the blade of rotor is set as non-slip smooth wall. A particular attention was given to the grid in order to achieve a proper simulation of the flow field of the turbine rotor and its performance. The volume between stationary and rotating domain
Fig. 2. Layout of the 3D computational domain reproducing the test chamber and assumed boundary conditions.
has been discretized by means of structured mesh. The size of meshes increases as their distance from the interface increases. In the rotating domain, an unstructured triangular mesh was adopted. Due to the complex geometry of rotor, a significant effort was dedicated to adjusting the mentioned grid. In order to study more accurately the flow in the boundary layers of rotor blade, prismatic grids have been applied on sides of rotor blades to capture the boundary layer correctly. Accordingly, the value of the non-
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dimensional near-wall grid distance (yþ) is equal to 1. In addition, density of meshes was higher near the wall of rotor blades and interface. Fig. 3 shows the grid on rotor, rotating domain and stationary domain. 2.2. Governing equations Naturally, the flow around the Savonius rotor is turbulent. Therefore, the computational fluid dynamic simulation on the turbulence flow field around rotor is highly complex. CFD simulations were applied to solve the problem based on 3D steady finitevolume incompressible Reynolds Averaged Navier-Stokes (RANS) equations. The governing equations on turbulence flow are continuity, and Navier - Stokes equations that in conservative forms are represented as follows [41]:
vui ¼0 vxj
(1)
vP v v r ui uj ¼ þ tij ru0i u0j þ Sui vxj vxi vxj
(2)
where, P is the static pressure, r is the density and tij is the stress tensor and Sui is the centrifugal and Coriolis force term, which can be calculated using following equation:
h ! ! i 8 ! ! ! > Su i ¼ r 2 U u þ U U r > > < ! vui vuj > > > tij ¼ m þ : vxj vxi
(3)
To precisely model the turbulent phenomenon which occurs during the rotation of wind rotor, a robust turbulence model needs to be added in RANS CFD solvers. Several turbulence models have been applied to solve numerically the flow field around the wind rotor. The best model is the one which obtains results with the highest agreement with experiments. Plourde et al. used threedimensional SST k-u turbulence model and found that the results are in a great agreement with the experiment [14]. In another work, SST k-u turbulence model was used to analyze the transient forces that act on Savonius rotors [42]. SST turbulence model is based on k-u model and predicts the flow near the wall similar to k-u model. This model considers the transmission of stress tensor and has a significant performance in predicting the separation flow. While the k-ε turbulence model does not work well in vortex regions, SST model can accurately estimate this phenomenon. Moreover, results of SST model are in good agreement with experimental results. In order to gain proper results while applying k-u and SST turbulence models, the value of yþ must be small [43e45].
Fig. 3. (a) Computational grid (Isometric view of both domains), (b) Computational grid around blade (Isometric view of rotating zone), (c) Top view of unstructured meshing in rotating zone, (d) Top view of grid refinement near the blade.
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0.3 modeling
experimental [37]
Poly. (modeling)
CP
0.25 0.2 0.15 0.1 0.05 0 0.1
0.3
0.5
0.6
0.7
0.8
TSR
0.9
1
1.1
Fig. 4. Comparison of modeling and experimental power coefficient corresponding to tip speed ratios (TSR).
The governing equation on this turbulence model is the following:
Pk ¼ minðmt f; Clmt εÞ
(4)
CP ¼
PTurbine Tu T Ru ¼ CT TSR ¼ ¼ PAvailable 0:5rAV 3 0:5rAV 2 R V
(8)
In normal conditions, Clmt is assumed to be 1015. In SST model, a new parameter for dissipation rate was defined as follows:
ð1 F1 Þ2rsu2 vk vu vk vu vk vu þ þ vx vx vy vy vz vz u
CTS ¼ (5)
In this equation, F1 is mixture function near the wall surface which is zero in far way regions of wall surface. SST turbulence model applies k-u model in near the wall surface and k-ε model in far way surface. All factors in SST model are calculated as a function of F1 :
f ¼ F1 f1 þ ð1 F1 Þf2
(6)
f is the main factor in SST model and f1 is calculated from k-u model and f2 from k-ε. Based on the above discussions flow near the wall surface is analyzed by applying k-u. In this case, results are more accurate than those of k-ε model [14]. In this study, the SST model is used as the appropriate approach. 2.3. Performance calculation Generally, performance of a vertical axis wind turbines is demonstrated by torque coefficient (CT ), power coefficient (CP ) and static torque coefficient (CTS ) [33]:
CT ¼
T 0:5rAV 2 R
(7)
TS 0:5rAV 2 R
(9)
where, r is the air density, V is the free stream velocity, TSR is the tip speed ratio, A is the swept area of the turbine, R is the radius of turbine, u is the rotational speed, T represents the dynamic torque, TS is the static torque, PTurbine and PAvailable present the power produced by the turbine and the available power in the wind respectively. In order to validate the modeling procedure used in this study, various tip speed ratios (from 0.1 up to 1.1) for wind rotor were computed by the commercial software and the associated calculated power coefficients were compared with experimental results. Fig. 4 demonstrates a comparison between simulation and experimental results. According to Fig. 4, the proposed modeling procedure has a suitable agreement with experimental results thus can be applied as a procedure for designing and modeling. The coefficient of correlation is used to ensure the modeling procedure was efficient. According to ref [15], the coefficient of correlation is calculated from Eq. (10).
P
2 fExp fpred R2 ¼ 1 P 2 fExp fExp
(10)
where
Table 2 List of properties of elements size for different defined grids. Case number
Cells number
Element size of stationary domain (m)
Element size of rotating domain (m)
Element size on blade (m)
1 2 3 4 5 6
704218 1537443 2819955 5223980 8531780 12140524
0.013 0.0098 0.008 0.0065 0.0055 0.005
0.01 0.0093 0.0075 0.006 0.005 0.0045
0.0085 0.0063 0.005 0.004 0.0035 0.0025
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Table 3 Calculated errors from comparison of numerical and experimental results. cells number
Torque (N m)
CP
Error (%)
0.7milion 1.5milion 2.8milion 5milion 8.5milion 12milion
0.04226 0.04388 0.04486 0.04491 0.04496 0.04496
0.2189 0.2274 0.2324 0.02327 0.2328 0.2329
12.41 9.05 7.02 6.92 6.85 6.81
Pn fExp ¼
i¼1 fExp
(11)
n
“n” presents the number of experimental results. According to calculations, the value of coefficient of correlation is 0.93 which demonstrates the high reliability of the obtained results. In order to further evaluate the modeling procedure used in this study, in the following subsections, gird independency and turbulence model are verified. 2.4. Mesh study
Table 4 Coefficient of correlation for different turbulence models according to experimental results. Turbulence model
SST
k-omega
k-epsilon
RNG k-epsilon
R2 (In comparison to [37])
0.856
0.835
0.774
0.73
As mentioned earlier, the coefficient of correlation can be used as a criterion to determine an appropriate turbulence model. In Table 4, the values of correlation coefficient for different turbulence models are given. Based on calculated results, the SST turbulence model has a superior performance compared to the others. 2.6. Design procedure In order to define innovative blade geometry while considering the direct discharge flow as the main target, several ideas were adopted. Twist in vertical axis wind rotor is one of these ideas to improve the power coefficient and discharge flow of the turbine. Variations in cross-section with respect to the height of rotor will be defined as another idea to design the new wind turbine. The third idea is designing a vertical axis wind rotor with a centrically
A grid sensitivity analysis was done to reduce the computational time and guarantee a minimum discretization error from experimental results. In this section, six different grids on model with various element sizes for similar TSR equal to 0.7 are investigated and their calculated power coefficients are compared with experimental results. Table 2 shows the properties of different grids. Table 3 indicates the obtained error from comparing the calculated results with experimental ones in different grids. Results indicate a small dependence on grid resolution and by considering run time of modelling, cell numbers around 2.8 million have a good agreement with experimental results of ref [37]. Therefore, the element size of grids with 2.8 million cell numbers is used for final modelling. 2.5. Turbulence study In order to evaluate the turbulence model for modelling Savonius wind rotor and verifying the reliability of the utilized model, a comparison between different turbulence models including k-u, kε, RNG k-ε and SST is carried out according to the obtained experimental results from Ref. [37]. Fig. 5 shows the calculated results for CP using different turbulence models in various TSR. 0.3
SST
k-omega
Fig. 6. Design flowchart.
k-epsilon
RNG K-epsilon
experimental [37]
CP
0.25 0.2 0.15 0.1 0.05
TSR 0 0.3
0.5
0.7
Fig. 5. Comparison of various turbulence models power coefficient.
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Fig. 7. The schematic shapes diagram of the helical Savonius wind rotor with a twist of 30 .
3. Results of modeling
0.25
Based on the mentioned assessments modeling procedure, design and modeling of a vertical axis wind turbine in Savonius form with direct discharge flow capability will be discussed. The design process is started from the simple Savonius wind rotor with circular cross section and novel modifications will be implemented to improve the power coefficient and discharge flow rate of the turbine. In these modellings, the value of TSR is 0.7 for all the suggested geometries. The difference between the experimental and simulated results of proposed geometry from Ref. [37] and highest value of power coefficient is the reason of this assumption.
0.2
CP
0.15 0.1 0.05 0 0
10
20
30
40
50
3.1. Design of different novel geometries
twist angle
3.1.1. Simple and twisted circular Savonius rotor As reported in Ref. [31], according to the Savonius wind rotor form and the direction of flow impact on blades, the negative torque on convex blade relative to the flow is applied constantly which decreases the power coefficient of the wind turbine. Therefore, the
Fig. 8. Improvement of the power coefficient by the twist angle.
Discharge flow rate
shaft in conical form. Fig. 6 shows the flowchart of the design procedure.
0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 0
10
20
30
40
Twist angle discharge flow form up
discharge flow from down
Fig. 9. Improvement of discharge flow rate by the twist angle.
50
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Fig. 10. The schematic shapes of the variable cut plane Savonius-style wind rotor.
Table 5 Calculated discharge flow rate and power coefficient for different turbines.
Wind rotor with fixed cut plane Twisted wind rotor with fixed cut plane (30 ) Wind rotor with variable cut plane Twisted wind rotor with variable cut plane
CP
Discharge flow from down of rotor (kg/s)
Discharge flow from up of rotor (kg/s)
0.17 0.205 0.15 0.16
0.0312 0.0363 0.03204 0.0328
0.03 0.0349 0.0305 0.031
Fig. 11. The schematics shapes of Savonius wind rotor with conical shaft, (a) the top view, (b) the isometric view and (c) the front view of wind rotor.
M. Tahani et al. / Energy 130 (2017) 327e338 Table 6 Calculated discharge flow rate and power coefficient for different rotors, comparison of wind rotor with conical shaft with simple Savonius wind rotor.
Wind rotor without a shaft and twist Two blades wind rotor with conical shaft Three blades wind rotor with conical shaft Twisted wind rotor without shaft Twisted wind rotor with conical shaft
CP
Discharge flow from down of rotor kg= s
0.17 0.158 0.14 0.205 0.2
0.0312 0.0368 0.0317 0.0363 0.0401
Table 7 Calculated discharge flow rate and power coefficient for different rotors, comparison of wind rotor with conical shaft and variable cut plane with simple Savonius wind rotor.
Wind rotor without shaft Two blades wind rotor with conical shaft Wind rotor with conical shaft and variable cut plane Twisted wind rotor with conical shaft and variable cut plane Twisted wind rotor with conical shaft
CP
Discharge flow from down of rotor kg= s
0.17 0.158 0.145
0.0312 0.0368 0.0373
0.155
0.0377
0.2
0.0401
twist on blades can reduce the negative torque. In the first step, the Savonius wind rotor and after that the twisted Savonius wind rotor
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are modeled and the calculated results, indicated the effectiveness of this design. In addition, the twisted wind rotor has a positive effect on the discharge flow rate of the turbine. Fig. 7 shows the Savonius wind rotor with a 30 twist angle. Figs. 8 and 9 indicate the effect of twist angle on the improvement of power coefficient and discharge flow rate. 3.1.2. Simple and twisted Savonius rotor with the variable cut plane One of the ideas which is presented in this study is circular cut plane with a various arc with respect to wind rotor height. The top cross section of the rotor has a 270 arc angle and then the angle of the arc is dropped with respect to the height and in the final cross section of the rotor has an 180 arc. The reason is that by decreasing the cut plane arc angle along the height, the pressure is changed and causes an increase in discharge flow rate. Fig. 10 shows the Savonius-style wind rotor with the variable cut plane. In the next step, the effect of twist angle on vertical axis wind rotor with the variable cut plane on changing the blade height is investigated. The Purpose of this section is to evaluate all of possible conditions for power coefficient and discharge flow of wind turbine improvement and obtain the appropriate and optimized design. The values of discharge flow rate and power coefficient for four different turbines are shown in Table 5. According to the results, the wind rotor with the fixed cut plane and a twist of 30 has a better performance in power coefficient and discharge flow compared to the conventional case. Therefore, this idea will be applied in the final design. The wind rotor with variable cut plane indicates a small improvement in discharge flow rate and power coefficient. The reason is the increase in negative torque surface and the inner space pressure of rotor. Therefore, the results suggest that twist in
Fig. 12. The schematic shapes of Savonius wind rotor with conical shaft and variable cut plane, (a) the top view, (b) the isometric view and (c) the front view of wind rotor.
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Fig. 13. The velocity contours on different plane, (a) with 0.03 m height, (b) 0.06 m height, (c) 0.09 m height, (d) 0.12 m height, (e) 0.15 m height, (f) 0.18 m height, (g) the plane with 0.23 m height from down of the blade.
wind rotor improves its aerodynamic performance. 3.1.3. Simple and twisted Savonius rotor with conical shaft Incorporation of a conical shaft as the central shaft can be considered as another proposed idea in designing the Savonius wind rotor with direct discharge flow capability. The radial centrifugal compressor has a middle structure in the conical form which can produce a 90 diversion in the inlet flow. Therefore, the central shaft of the rotor is designed with a capability that the wind flow by passing from its inclined surface is being discharged with 90 deviation from the down or upper parts of the rotor. On the other hand, from the results of modeling it can be seen that the output rate from down the rotor is more than upper part of the rotor due to gravity. For this reason, wind turbine shaft is designed in a way that the upper part of the rotor is closed and the slope of the conical shaft is in direction that the inlet flow into the rotor diverts downwards. Fig. 11 shows the schematic shapes of the Savonius wind rotor with the conical shaft. As discussed in the previous section, twist in wind turbine can
improve the power coefficient and discharge flow of turbine. Due to mentioned point, in the proposed innovative design of the vertical axis wind rotor with conical shaft, a twist angle with 30-degree angle is considered. Table 6 indicates the calculated discharge flow and power coefficient results for the proposed wind rotor. Based on the obtained results associated with two-bladed wind rotor with and without shaft, it can be concluded that this design has a significant impact on the wind turbine discharge flow rate but causes negligible reductions in power coefficient. Therefore, the use of this design will be appropriate. Indeed, using a conical shaft in wind rotor will improve the discharge flow rate up to 18%. In order to study the effect of number of blades on the aerodynamic operation, the wind rotor with three blades is also modeled. The results reveal that the three blade wind turbine with conical shaft does not have a proper performance for discharge flow rate and power coefficient. Results indicate that a twisted wind rotor with conical shaft compared to wind rotor without shaft and twist, is associated with 29% and 18% increase in discharge flow rate and power coefficient
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Fig. 14. The velocity vector, (a) the simple Savonius rotor, (b) the twisted Savonius rotor with conical shaft.
respectively. Also, it has 11% improvement in discharge flow rate compared to the twisted wind rotor without shaft. As the calculated results suggest, the twisted wind rotor with conical shaft has a great performance for defined purpose. 3.1.4. Savonius rotor with conical shaft and variable cut plane A vertical axis wind rotor with the conical shaft and variable cut plane is the other proposed design modification. Two models of the wind rotor with and without twist will be considered to evaluate all possible cases in order to help selecting an appropriate design. Table 7 shows the calculated results for power coefficient and discharge flow rate of four different wind rotors. Fig. 12 shows a Savonius wind rotor with the conical shaft and variable cut plane with a twist angle equal to 30 . Calculated results indicate that using wind turbine with the conical shaft and variable cut plane causes a decrease in power coefficient compared to fixed cut plane. However, the amount of improvement for discharge flow rate is about 1% which is not sufficient for the design. The twist in this type of turbine has a little improvement thus is not suitable to use in the design. If a vertical axis wind rotor with the conical shaft and variable cut plane is compared with a twisted vertical axis wind rotor with the conical shaft and fixed cut plane, results will indicate that for both cases, the twisted wind turbine with 30 angle has a better performance. Fig. 13 presents the distribution of the velocity on the various plane with different height from end of twisted Savonius wind turbine with conical shaft. The velocity contour is shown on plane with 0.03 m distance from the top and down planes and the value of twist is 30 . According to the Fig. 13, the separation and also velocity reduction can be seen in the edge of advancing blade in all geometries. On the other hand, the velocity is increased on the convex side of returning blade. This is because of reduction in cross sectional area and also the direction of blade rotation. In general, all geometries presented in Fig. 13 have the same behavior and the velocity contours indicate that the flow is being separated after the blades. In Fig. 14, the velocity vectors for simple Savonius rotor and twisted Savonius rotor with conical shaft is presented for comparing the flow direction. According to the figure, it can be seen that the flow direction has been changed the velocity is increased in twisted Savonius rotor with conical shaft. 4. Conclusion In this research study it was aimed to design a vertical axis wind
rotor with direct discharge flow capability. In this section, results associated with different designs are summarized. The first step of design process is to determine the variation of twist in wind turbine. According to the calculated results, twisted wind turbine has an appropriate performance based on the obtained power coefficient and discharge flow rate. In order to direct the discharge flow from wind turbine, two novel modifications which are variable cut plane along height and using the conical shaft in the middle of wind rotor are suggested. Power coefficient and discharge flow rate for variable cut plane are compared to simple Savonius wind rotor and the results indicated that power increases 12% and the discharge flow rate decreases 5%. And in comparison to the wind rotor with conical shaft, power decreases 7% and discharge flow rate increases 18%. Twist in proposed design of this paper causes an improvement in the results. Therefore, power coefficient and the discharge flow rate for twisted wind rotor with variable cut plane in comparison to twisted wind rotor has a 25% decrease and 9.6% increase and compared to wind rotor with conical shaft has a 2% decrease and 10.5% increase respectively. Moreover, results of simple Savonius wind rotor compared to twisted wind turbine with conical shaft shows 18% increase and 31% increase in CP and discharge flow rate respectively. This suggest that this innovative idea is a suitable design to satisfy the main target. In order to consider all possible cases for suggested design ideas, two wind rotors with variable cut plane and conical shaft with and without twist were evaluated. The results suggest that compared to twisted wind rotors with conical shaft, these rotors have a weaker operation. References [1] Ushiyama I, Nagai H. Optimum design configurations and performance of Savonius rotors. Wind Eng 1988;12(1):59e75. [2] Tartuferi M, D'Alessandro V, Montelpare S, Ricci R. Enhancement of Savonius wind rotor aerodynamic performance: a computational study of new blade shapes and curtain systems. Energy 2015;79:371e84. [3] Roy S, Saha UK. An adapted blockage factor correlation approach in wind tunnel experiments of a Savonius-style wind turbine. Energy Convers Manag 2014;86:418e27. [4] Goodarzi M, Keimanesh R. Numerical analysis on overall performance of Savonius turbines adjacent to a natural draft cooling tower. Energy Convers Manag 2015;99:41e9. [5] Chong WT, Poh SC, Fazlizan A, Yip SY, Chang CK, Hew WP. Early development of an energy recovery wind turbine generator for exhaust air system. Appl Energy 2013;112:568e75. [6] Maleki A, Khajeh MG, Rosen MA. Weather forecasting for optimization of a
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