- Email: [email protected]
Performance Investigation and Optimization of a Vertical Axis Wind Turbine with the Omni-Direction-Guide-Vane
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 67 (2013) 59 – 69
7th Asian-Pacific Conference on Aerospace Technology and Science, 7th APCATS 2013
Performance Investigation and Optimization of a Vertical Axis Wind Turbine with the Omni-Direction-Guide-Vane Y. C. Lima, W. T. Chonga,*, F. B. Hsiaob a
b
Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia Institute of Aeronautics and Astronautics, National Cheng Kung University, Tainan 70101, Taiwan, ROC
Abstract
This paper aims to present an approach on optimizing the design of the omni-direction-guide-vane (ODGV) in order to maximise the performance of the vertical axis wind turbine (VAWT). An analytical model had been developed based on the continuity equation for assessing the impact of each design parameter of the ODGV to the VAWT performance. A 2-level full factorial design was further utilized for the verification of analytical findings with the aid of computational fluids dynamics (CFD) simulation. Three parameters, i.e. two guide vanes angles (ș and ȕ) and ratio of VAWT diameter to distance between two guide vanes (b) were selected for the initial design of experiment (DOE) screening process. A total of 9 cases which include one centre point per block had been setup in CFD simulation. The DOE results suggested that the optimum point exists at the corner point (not at center point). Meanwhile, it was also pointed that strong interaction effect can be seen in ș with ȕ, ș with b and ȕ with b. It is worth to highlight that the analytical model overestimates the performance at larger ș since only one dimension steady flow is assumed. © TheAuthors. Authors.Published Published Elsevier © 2013 2013 The byby Elsevier Ltd.Ltd. Selection andpeer-review peer-reviewunder under responsibility of the National Chiao University. Selection and responsibility of the National Chiao TungTung University Keywords: guide vane; wind energy system; urban wind turbine; computational fluid dynamics; optimization; design of experiment
Nomenclature a b c
diameter ratio of VAWT to ODGV ratio of wind turbine diameter to m blade chord length (m)
* Corresponding author. Tel.: +6-012-723-5038; fax: +6-03-7967-5317 E-mail address: [email protected]
1877-7058 © 2013 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the National Chiao Tung University doi:10.1016/j.proeng.2013.12.005
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Y.C. Lim et al. / Procedia Engineering 67 (2013) 59 – 69
CFD computational fluids dynamics D diameter (m) DOE design of experiment h height of guide vane (m) K ratio of l to m l vertical distance between ODGV outer and inner (m) m minimum gap of two guide vanes (m) ODGV omni-direction-guide-vane Re blade Reynolds number V free stream velocity (m/s) VAWT vertical axis wind turbine w width of guide vane (m) Greek symbols ș guide vane angle (degree) ȕ guide vane angle (degree) Ȧ angular speed of turbine (rpm) μ air viscosity Subscripts at outer ODGV 1 at inner ODGV 2 1. Introduction Wind energy is one of the most sophisticated renewable energy sources for green and clean energy solution. Vertical axis wind turbine can be a cost-effective construction on the downtown skyscrapers for small scale power generation. Chong et al. [1-2] proposed a novel ODGV that surrounds a VAWT to further improve the VAWT performance, see Fig 1(a). This performance augmentation device can help to address the problem of low wind speed where the wind turbine can start producing energy at a lower wind speed in the urban areas. The VAWT’s self-starting behavior is improved where the cut-in speed was reduced with the integration of the ODGV. At 6 m/s, the power output at maximum torque was 3.48 times higher for the ODGV integrated with VAWT compared to the bare VAWT [1-2]. This has been reached a consensus with Daegyoum K. et al. [3] that the power output increases significantly on two counter-rotating straight-bladed VAWT with an upstream flat deflector. This is due to the turbines is positioned outside the near wake region where the local wind speed is larger than free-stream velocity. The authors concluded that the power output increases with the deflector installed is dependent on the width and height of the deflector and the turbine position relative to the deflector. The VAWT has an inherently unsteady aerodynamic characteristic [4-5] and becomes worse with deflector system due to variation of aerodynamic loading during revolution by unsteadiness of local flow field [3]. Numerical analysis was carried out by Marco R. et al. [5] to reduce the torque variation during the revolution of a VAWT. They found that the peak of power coefficient lowered with the increase of rotor solidity at lower tip speed ratio, and the maximum power coefficient can be reached with large number of blades for lower angular velocities, but the efficiency is affected. Foreseeing that many potential benefits that ODGV-VAWT configuration may further bring to the environment in resolving energy issue in urban areas, hence, this paper aims to present an approach on the optimization of the VAWT-ODGV performance by analytical study. The findings are further confirmed by full factorial design with the aid of computational fluid dynamics (CFD) simulation. 2. Omni-Direction-Guide-Vane (ODGV) Analytical Study A simple geometry, i.e. a rectangular shape (as shown in Fig. 1 (b)) instead of the circular design of the ODGV has been adopted in theoretical analysis. This is to allow a quick assess on the parameters in ODGV that are crucial to the VAWT performance. One dimensional steady flow is assumed to reach the outer of ODGV and
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Y.C. Lim et al. / Procedia Engineering 67 (2013) 59 – 69
enter the space between guide vanes. This will create the venturi effect to increase the wind speed before the wind stream interacts with wind turbine blades. As a result, the VAWT power output can be improved since it is proportional to V3. For simplicity, it is assumed that the flow is uniformly distributed without interaction with each other and fulfills the continuity equation without flow separation, see Fig. 1(a), and yields
V1 V2 | w2 h2 w1h1
(1)
where h2 and h1 are the height of outer and inner of guide vanes. w1 & w2 are the width of outer and inner guide vane, respectively. The velocity ratio of ODGV outer to inner, V1/V2 , can be rewritten as
V1 V2 | w2 h2 w1h1
^ D2 D1 2 tan T m`h2 ^ D2 D1 2 tan E m`h1
§ K tan T ·§ tan E ·§ h2 · ¨¨ K tan E ¸¸¨ tan T ¸¨¨ h ¸¸ ¹© 1 ¹ © ¹©
(2)
where
w1
l tan E m
w2
l tan T m
(3)
(4)
The ratio of vertical distance between ODGV outer and inner (l) to minimum gap of two guide vanes (m), i.e. K, can be expressed as
K
l m
D2 D1
2m
(5)
The Eq. (2) should satisfy three boundary conditions. Firstly, the minimum angle of ș is arccosine of diameter ratio of VAWT to ODGV, i.e. 1/a , due to the geometric limit for circular design of ODGV, see Fig. 2. In addition, the maximum ș angle has to be less than 900 due to undefined of this angle in tangent. However, the ș can be set to 900 in actual case as it is a circular design rather than rectangular.
cos D
°T min Omin ! cos 1 1 a D1 D2 ® °¯T max 90 0
(6)
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Y.C. Lim et al. / Procedia Engineering 67 (2013) 59 – 69
V1
w1
w2
V2
(a)
(b) Fig.1 Illustration of the ODGV 2D design (a) One dimension steady flow enters ODGV (b) A simplified geometry of the ODGV
Fig.2 Schematic of geometric limitation of the ODGV design
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Y.C. Lim et al. / Procedia Engineering 67 (2013) 59 – 69
The velocity at the inner of ODGV, V2, is expected to increase with the decreased in the cross sectional area (w2) . Hence,
w1 ! w2 (7)
? E T
Therefore, the angle of ȕ has to be smaller than ș in Eq.(2). Furthermore, the minimum gap of two guide vanes (m) should fulfill
m SD1 8 | 0.393D1 2.546 D1 m
(8)
b
3. Design of Experiment (DOE) Design of experiment (DOE) was utilized as a strategy to study the effects of several parameters that were highlighted on previous section by varying the level (i.e. the maximum and minimum design limit) of the said parameters simultaneously rather than one parameter at a time. A well-designed experiment can produce significantly more information from each experiment in limited resources [6]. The advantage of this approach is to provide a systematic way for verifying the analytical results with more time effective. In addition, it can be more robust in estimating the each parameter as well as understanding the interactions between the parameters. If one parameter’s effect is influenced by the level of another parameter then interaction effect can be confirmed. A 2level full factorial experiment was designed in this study based on analytical findings, i.e.
V1 V2 D K , E , T , h2 , h1
(9)
K D a , b
(10)
To simplify the DOE, the diameter ratio of ODGV to VAWT, a, was set to 1.8 and h2 and h1 can be discarded due to 2-D simulation. Hence, K, only depends on b. The level of parameters and test plan are summarized in Table 1 and 2. Three parameters, i.e. two guide vanes’ angle (ș and ȕ) and ratio of VAWT diameter to distance between two guide vanes (b) were selected for initial DOE screening process. A total of 9 simulations had been setup which include one center point per block (see Table 2). With the center points in factorial design, the presence of curvature can be detected during the optimization process, which usually is the point that the factors near to an optimum value. Table 1. Levels defined for parameters ș, ɴand b Level
Max
Center
Min
ș
900
73.50
570
ɴ
900
500
100
12
7.5
3
b
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Y.C. Lim et al. / Procedia Engineering 67 (2013) 59 – 69 Table 2. DOE test plan Case
ș
ɴ
b Min
1
Min
Min
2
Max
Min
Min
3
Min
Max
Min
4
Max
Max
Min
5
Min
Min
Max
6
Max
Min
Max
7
Min
Max
Max
8
Max
Max
Max
9
Centre
Centre
Centre
4. Computational Fluid Dynamics (CFD) Analysis Various configurations of ODGV were designed based on the proposed study in previous section. They were numerically analysed by using computational fluid dynamics (CFD) commercial package, ANSYS Fluent 14. The simulations were performed with a single bladed rotor (NACA 0015 airfoil) with constant free stream velocity of 6m/s and blade chord length of 0.1524m. The blade Reynolds number in this study is 3.95×105 which was calculated from
Re R 2Z c P
(11)
The computational domain consists of 3 main sub-grids (as shown in Fig.3), i.e. a) Free stream velocity sub-grid: a rectangular outer zone with a circular opening zone. b) ODGV sub-grid: guide vanes positioned in circular inner region adjacent with rotor sub-grid c) Rotor sub-grid: a circular inner zone and rotate at angular speed of turbine The free stream velocity sub-grid was constructed with the width and height equal to 10 times rotor diameter while the ODGV sub-grid with the diameter of 1.8 rotor diameters was centred at the free stream velocity sub-grid. The sliding mesh method was deployed on the rotor sub-grid for simulating the rotating of wind turbine [2,5]. Thus, the fluid area in this sub-grid was set to rotate at same angular velocity of the wind turbine. This will able to characterize the inherent unsteady aerodynamic behaviour of wind turbine with more time-accurate solution for ODGV-VAWT interaction. A quick convergence in solution can be obtained by having same mesh characteristic of cell size for both interfaces during computing the flux across the two non-conformal interfaces zones of each mesh interface [7]. The total amount of unstructured mesh element for each case is around 800,000 cells while 90% of total mesh elements were placed on ODGV and rotor sub-grid. The aspect ratio of mesh for each case was controlled at 30 ± 5 while the other cell qualities, for instance, maximum value of skewness and minimum value of orthogonal quality was kept below 0.95 and more than 0.1, respectively. Many of studies, e.g. Chong et al. [1,2] & Marco R et al. [5] pointed out that the SST (Shear Stress Transport) k-Ȧ turbulence model is capable to capture correct behavior in the near wall layers and separation flow. As a result, SST k-Ȧ turbulence model with two other transport equations were used in this study to solve the incompressible two-dimensional unsteady flow.
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Opening
ODGV Guide Vane
Interface
6m/s
10 Outlet Interface
10 Opening Free stream velocity sub-grid
Rotor sub-grid
NACA0015
Fig.3 Main Dimension and computational domain for each sub-grid
The SIMPLE algorithm was chosen due to its robustness in iterating the coupled parameters, available of high order differencing schemes as well as computational efficiency. Convergence at each simulation was determined by two aspects, i.e. residuals and global convergence. The residuals convergence criterion is set at 1×10-5 while variation of instantaneous torque value should be less than 1% at each simulation for global convergence. 5. Results The VAWT performance can be improved by altering the free stream velocity flow with a deflector or ODGV as reported in some studies [1-3]. A numerical study on Eq. (2) had been carried out in order to assess the parameters that would contribute significant impact to VAWT performance that integrated with the ODGV design. Theoretically, the combination of larger angle of ș with low ȕ angle gives a high velocity ratio in ODGVVAWT design. Fig. 4(b) demonstrates the relationship between K and velocity ratio by varying the ȕ angles. Higher velocity ratio of ODGV-VAWT design is found at lower ȕ angle and lager K value. It divulges that the velocity ratio is proportional to ratio of the vertical distance between inner and outer ODGV to minimum gap of two guide vanes, i.e. V2/V1 Į K. The 2-level full factorial experiment was conducted with only one replicate in CFD simulation. The peak torque of each case was selected as a response for the DOE. The Pareto chart of effects is shown in Fig. 5. Any bar extends beyond the reference line, i.e. value of 12.71 is considered as a significant effect at Į=0.05 significance level. However, Fig. 5 exhibits that there was no significant factor effects (no bar extending beyond reference line). This suggests that either all combinations are equally effective or the model has a problem [6]. Based on the analytical study in previous section as well as the experiment study by Chong et al. [2], it is strongly believed that the parameters selected are equally effective. It does make sense that the interaction effect of ș with ȕ or AB plays the most important role in VAWT performance. Meanwhile, the interaction effects of ș with b or AC as well as interaction of ȕ with b or BC are having a significant effects compared to the three main effects, i.e. ș, ȕ and b alone. As a result, only the interaction effect plot is discussed on Fig. 6.
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Y.C. Lim et al. / Procedia Engineering 67 (2013) 59 – 69 5
4
ɽ 55 60 65 70 75 80 85
3
V2/V1 2
1
0 0
10
20
30
40
50
60
70
80
ɴ(degree) (a) 20
15
K 1.2 2.4
10
3.6
V2/V1
4.8 5
0 0
10
20
30
40
50
60
70
80
ɴ(degree)
(b) Fig.4 (a) Velocity ratio, V2/V1, under different combination of ș and ȕ angles at a=1.8, b=3,K=1.2, ,h12=1 (b) Relationship between K to velocity ratio with varying of different ȕ angles at a=1.8, ș =890,h12=1
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Y.C. Lim et al. / Procedia Engineering 67 (2013) 59 – 69
12.71 AB
F actor A B C
Term
AC
N ame Theta Beta b
BC B A C 0
2
4
6 8 Standardized Effect
10
12
14
Fig.5 Pareto chart of effects
10
50
90 (A)
3.0
7.5
12.0
(B) 2.6
Theta
2.4 2.2 (C)
2.6
Beta
2.4 2.2
Theta 57.0 73.5 90.0
Beta 10 50 90
Point Ty pe C orner C enter C orner
Point Ty pe C orner C enter C orner
b
Fig.6 Interaction effects plot
From the interaction effect plot, it is observed that the optimum point exists at the corner point, i.e. minimum or maximum level instead of the center points. In addition, the “cross” of each other describes that strong interaction of ș with ȕ, ș with b and ȕ with b. For the upper left plot in Fig. 6, it tells that the higher torque is obtained by configuration of either in both low ș and ȕ angles or both high ș and ȕ angles. The configuration of ș with 570 and ȕ with 100 give the highest torque value. This is aligned with the findings in Fig. 4(a). However, the velocity vector field in Fig. 7 suggests that more severe flow separation on higher ș, for instance, 900 , and results of lower torque, which analytical model is not taken into consideration. The upper and lower right plot on Fig. 6 explains the relation of b with ș & ȕ, respectively. The higher toque performance of VAWT is observed on lower ș and higher b same as the case of ȕ to b.
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Y.C. Lim et al. / Procedia Engineering 67 (2013) 59 – 69
y
y
(a)
x
(b)
y
(c)
x
y x
(d)
x
Fig.7 Velocity vector field (a) ș=570, ȕ=100 & b=12 (b) ș=570, ȕ=100 & b=3 (c) ș=900, ȕ=100 & b=3 (d) ș=900, ȕ=900 & b=12
6. Concluding Remarks A novel omni-direction-guide-vane that surrounds a vertical axis wind turbine is designed to improve the VAWT performance. An analytical study has indicated that ș, ȕ and b are more crucial to VAWT performance if a is fixed. A two-level full factorial has been deployed on screening process for the identification of the critical factors for VAWT performance. From two level full factorial, it further divulges that the strong interaction effect were observed at ș with ȕ, ș with b and ȕ with b compared to the main or individual effects. High torque performance is identified for ODGV-VAWT design at the configuration of ș with 570 and ȕ with 100 as well as larger b value, i.e. 12. It is worth to point out that angle of ș suggests at analytical model is much higher than in DOE results, i.e. 890 versus 570. This can be explained that the analytical model is derived based on the continuity equation with one dimension steady flow and the assumption of no flow is separated or circulated. The circulation flow can be clearly seen in velocity vector field in the CFD results at higher ș angle. Further study on the flow characteristic in the VAWT region is suggested for future works.
Y.C. Lim et al. / Procedia Engineering 67 (2013) 59 – 69
Acknowledgements This research work is supported by the Prototype Development Research Grant Scheme (PR002-2012A) awarded by the Malaysian Ministry of Higher Education (MOHE). References [1] W.T. Chong, K.C. Pan, S.C. Poh, A. Fazlizan, C.S. Oon, A. Badarudin, N.Nik-Ghazali, 2013. Performance Investigation of a Power Augmented Vertical Axis Wind Turbine for Urban High-rise Application, Renewable Energy, 51, p.388. [2] W.T. Chong, A. Fazlizan, S.C. Poh, K.C. Pan, W.P. Hew, F.B. Hsiao, 2013. The Design, Simulation and Testing of an Urban Vertical Axis Wind Turbine with the Omni-direction-guide-vane, Applied Energy, In Press. [3] Daegyoum Kim, Morteza Gharib,2013. Efficiency Improvement of Straight-bladed Vertical-axis Wind Turbines with an Upstream Deflector, J. Wind Eng. Ind. Aerodyn. Vol.115, p. 48–52. [4] S. Wang, Z. Tao, 2010. “Numerical Investigation on Dynamic Stall Associated with Low Reynolds Number Flows over Airfoils”, 2nd International Conference on Computer Engineering and Technology. [5] Marco R., Stefano D. B., Ernesto B., 2012. Effects of Blade Number on Straight-bladed Vertical-axis Darreius Wind Turbine, World Academy of Science, Engineering and Technology, 61, p.305-311. [6] Minitab Inc., Minitab Help, 2010. [7] Fluent Inc., Flunet User’s Manual, p.193-194, 2006.
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ScienceDirect Procedia Engineering 67 (2013) 59 – 69
7th Asian-Pacific Conference on Aerospace Technology and Science, 7th APCATS 2013
Performance Investigation and Optimization of a Vertical Axis Wind Turbine with the Omni-Direction-Guide-Vane Y. C. Lima, W. T. Chonga,*, F. B. Hsiaob a
b
Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia Institute of Aeronautics and Astronautics, National Cheng Kung University, Tainan 70101, Taiwan, ROC
Abstract
This paper aims to present an approach on optimizing the design of the omni-direction-guide-vane (ODGV) in order to maximise the performance of the vertical axis wind turbine (VAWT). An analytical model had been developed based on the continuity equation for assessing the impact of each design parameter of the ODGV to the VAWT performance. A 2-level full factorial design was further utilized for the verification of analytical findings with the aid of computational fluids dynamics (CFD) simulation. Three parameters, i.e. two guide vanes angles (ș and ȕ) and ratio of VAWT diameter to distance between two guide vanes (b) were selected for the initial design of experiment (DOE) screening process. A total of 9 cases which include one centre point per block had been setup in CFD simulation. The DOE results suggested that the optimum point exists at the corner point (not at center point). Meanwhile, it was also pointed that strong interaction effect can be seen in ș with ȕ, ș with b and ȕ with b. It is worth to highlight that the analytical model overestimates the performance at larger ș since only one dimension steady flow is assumed. © TheAuthors. Authors.Published Published Elsevier © 2013 2013 The byby Elsevier Ltd.Ltd. Selection andpeer-review peer-reviewunder under responsibility of the National Chiao University. Selection and responsibility of the National Chiao TungTung University Keywords: guide vane; wind energy system; urban wind turbine; computational fluid dynamics; optimization; design of experiment
Nomenclature a b c
diameter ratio of VAWT to ODGV ratio of wind turbine diameter to m blade chord length (m)
* Corresponding author. Tel.: +6-012-723-5038; fax: +6-03-7967-5317 E-mail address: [email protected]
1877-7058 © 2013 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the National Chiao Tung University doi:10.1016/j.proeng.2013.12.005
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Y.C. Lim et al. / Procedia Engineering 67 (2013) 59 – 69
CFD computational fluids dynamics D diameter (m) DOE design of experiment h height of guide vane (m) K ratio of l to m l vertical distance between ODGV outer and inner (m) m minimum gap of two guide vanes (m) ODGV omni-direction-guide-vane Re blade Reynolds number V free stream velocity (m/s) VAWT vertical axis wind turbine w width of guide vane (m) Greek symbols ș guide vane angle (degree) ȕ guide vane angle (degree) Ȧ angular speed of turbine (rpm) μ air viscosity Subscripts at outer ODGV 1 at inner ODGV 2 1. Introduction Wind energy is one of the most sophisticated renewable energy sources for green and clean energy solution. Vertical axis wind turbine can be a cost-effective construction on the downtown skyscrapers for small scale power generation. Chong et al. [1-2] proposed a novel ODGV that surrounds a VAWT to further improve the VAWT performance, see Fig 1(a). This performance augmentation device can help to address the problem of low wind speed where the wind turbine can start producing energy at a lower wind speed in the urban areas. The VAWT’s self-starting behavior is improved where the cut-in speed was reduced with the integration of the ODGV. At 6 m/s, the power output at maximum torque was 3.48 times higher for the ODGV integrated with VAWT compared to the bare VAWT [1-2]. This has been reached a consensus with Daegyoum K. et al. [3] that the power output increases significantly on two counter-rotating straight-bladed VAWT with an upstream flat deflector. This is due to the turbines is positioned outside the near wake region where the local wind speed is larger than free-stream velocity. The authors concluded that the power output increases with the deflector installed is dependent on the width and height of the deflector and the turbine position relative to the deflector. The VAWT has an inherently unsteady aerodynamic characteristic [4-5] and becomes worse with deflector system due to variation of aerodynamic loading during revolution by unsteadiness of local flow field [3]. Numerical analysis was carried out by Marco R. et al. [5] to reduce the torque variation during the revolution of a VAWT. They found that the peak of power coefficient lowered with the increase of rotor solidity at lower tip speed ratio, and the maximum power coefficient can be reached with large number of blades for lower angular velocities, but the efficiency is affected. Foreseeing that many potential benefits that ODGV-VAWT configuration may further bring to the environment in resolving energy issue in urban areas, hence, this paper aims to present an approach on the optimization of the VAWT-ODGV performance by analytical study. The findings are further confirmed by full factorial design with the aid of computational fluid dynamics (CFD) simulation. 2. Omni-Direction-Guide-Vane (ODGV) Analytical Study A simple geometry, i.e. a rectangular shape (as shown in Fig. 1 (b)) instead of the circular design of the ODGV has been adopted in theoretical analysis. This is to allow a quick assess on the parameters in ODGV that are crucial to the VAWT performance. One dimensional steady flow is assumed to reach the outer of ODGV and
61
Y.C. Lim et al. / Procedia Engineering 67 (2013) 59 – 69
enter the space between guide vanes. This will create the venturi effect to increase the wind speed before the wind stream interacts with wind turbine blades. As a result, the VAWT power output can be improved since it is proportional to V3. For simplicity, it is assumed that the flow is uniformly distributed without interaction with each other and fulfills the continuity equation without flow separation, see Fig. 1(a), and yields
V1 V2 | w2 h2 w1h1
(1)
where h2 and h1 are the height of outer and inner of guide vanes. w1 & w2 are the width of outer and inner guide vane, respectively. The velocity ratio of ODGV outer to inner, V1/V2 , can be rewritten as
V1 V2 | w2 h2 w1h1
^ D2 D1 2 tan T m`h2 ^ D2 D1 2 tan E m`h1
§ K tan T ·§ tan E ·§ h2 · ¨¨ K tan E ¸¸¨ tan T ¸¨¨ h ¸¸ ¹© 1 ¹ © ¹©
(2)
where
w1
l tan E m
w2
l tan T m
(3)
(4)
The ratio of vertical distance between ODGV outer and inner (l) to minimum gap of two guide vanes (m), i.e. K, can be expressed as
K
l m
D2 D1
2m
(5)
The Eq. (2) should satisfy three boundary conditions. Firstly, the minimum angle of ș is arccosine of diameter ratio of VAWT to ODGV, i.e. 1/a , due to the geometric limit for circular design of ODGV, see Fig. 2. In addition, the maximum ș angle has to be less than 900 due to undefined of this angle in tangent. However, the ș can be set to 900 in actual case as it is a circular design rather than rectangular.
cos D
°T min Omin ! cos 1 1 a D1 D2 ® °¯T max 90 0
(6)
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Y.C. Lim et al. / Procedia Engineering 67 (2013) 59 – 69
V1
w1
w2
V2
(a)
(b) Fig.1 Illustration of the ODGV 2D design (a) One dimension steady flow enters ODGV (b) A simplified geometry of the ODGV
Fig.2 Schematic of geometric limitation of the ODGV design
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Y.C. Lim et al. / Procedia Engineering 67 (2013) 59 – 69
The velocity at the inner of ODGV, V2, is expected to increase with the decreased in the cross sectional area (w2) . Hence,
w1 ! w2 (7)
? E T
Therefore, the angle of ȕ has to be smaller than ș in Eq.(2). Furthermore, the minimum gap of two guide vanes (m) should fulfill
m SD1 8 | 0.393D1 2.546 D1 m
(8)
b
3. Design of Experiment (DOE) Design of experiment (DOE) was utilized as a strategy to study the effects of several parameters that were highlighted on previous section by varying the level (i.e. the maximum and minimum design limit) of the said parameters simultaneously rather than one parameter at a time. A well-designed experiment can produce significantly more information from each experiment in limited resources [6]. The advantage of this approach is to provide a systematic way for verifying the analytical results with more time effective. In addition, it can be more robust in estimating the each parameter as well as understanding the interactions between the parameters. If one parameter’s effect is influenced by the level of another parameter then interaction effect can be confirmed. A 2level full factorial experiment was designed in this study based on analytical findings, i.e.
V1 V2 D K , E , T , h2 , h1
(9)
K D a , b
(10)
To simplify the DOE, the diameter ratio of ODGV to VAWT, a, was set to 1.8 and h2 and h1 can be discarded due to 2-D simulation. Hence, K, only depends on b. The level of parameters and test plan are summarized in Table 1 and 2. Three parameters, i.e. two guide vanes’ angle (ș and ȕ) and ratio of VAWT diameter to distance between two guide vanes (b) were selected for initial DOE screening process. A total of 9 simulations had been setup which include one center point per block (see Table 2). With the center points in factorial design, the presence of curvature can be detected during the optimization process, which usually is the point that the factors near to an optimum value. Table 1. Levels defined for parameters ș, ɴand b Level
Max
Center
Min
ș
900
73.50
570
ɴ
900
500
100
12
7.5
3
b
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Y.C. Lim et al. / Procedia Engineering 67 (2013) 59 – 69 Table 2. DOE test plan Case
ș
ɴ
b Min
1
Min
Min
2
Max
Min
Min
3
Min
Max
Min
4
Max
Max
Min
5
Min
Min
Max
6
Max
Min
Max
7
Min
Max
Max
8
Max
Max
Max
9
Centre
Centre
Centre
4. Computational Fluid Dynamics (CFD) Analysis Various configurations of ODGV were designed based on the proposed study in previous section. They were numerically analysed by using computational fluid dynamics (CFD) commercial package, ANSYS Fluent 14. The simulations were performed with a single bladed rotor (NACA 0015 airfoil) with constant free stream velocity of 6m/s and blade chord length of 0.1524m. The blade Reynolds number in this study is 3.95×105 which was calculated from
Re R 2Z c P
(11)
The computational domain consists of 3 main sub-grids (as shown in Fig.3), i.e. a) Free stream velocity sub-grid: a rectangular outer zone with a circular opening zone. b) ODGV sub-grid: guide vanes positioned in circular inner region adjacent with rotor sub-grid c) Rotor sub-grid: a circular inner zone and rotate at angular speed of turbine The free stream velocity sub-grid was constructed with the width and height equal to 10 times rotor diameter while the ODGV sub-grid with the diameter of 1.8 rotor diameters was centred at the free stream velocity sub-grid. The sliding mesh method was deployed on the rotor sub-grid for simulating the rotating of wind turbine [2,5]. Thus, the fluid area in this sub-grid was set to rotate at same angular velocity of the wind turbine. This will able to characterize the inherent unsteady aerodynamic behaviour of wind turbine with more time-accurate solution for ODGV-VAWT interaction. A quick convergence in solution can be obtained by having same mesh characteristic of cell size for both interfaces during computing the flux across the two non-conformal interfaces zones of each mesh interface [7]. The total amount of unstructured mesh element for each case is around 800,000 cells while 90% of total mesh elements were placed on ODGV and rotor sub-grid. The aspect ratio of mesh for each case was controlled at 30 ± 5 while the other cell qualities, for instance, maximum value of skewness and minimum value of orthogonal quality was kept below 0.95 and more than 0.1, respectively. Many of studies, e.g. Chong et al. [1,2] & Marco R et al. [5] pointed out that the SST (Shear Stress Transport) k-Ȧ turbulence model is capable to capture correct behavior in the near wall layers and separation flow. As a result, SST k-Ȧ turbulence model with two other transport equations were used in this study to solve the incompressible two-dimensional unsteady flow.
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Opening
ODGV Guide Vane
Interface
6m/s
10 Outlet Interface
10 Opening Free stream velocity sub-grid
Rotor sub-grid
NACA0015
Fig.3 Main Dimension and computational domain for each sub-grid
The SIMPLE algorithm was chosen due to its robustness in iterating the coupled parameters, available of high order differencing schemes as well as computational efficiency. Convergence at each simulation was determined by two aspects, i.e. residuals and global convergence. The residuals convergence criterion is set at 1×10-5 while variation of instantaneous torque value should be less than 1% at each simulation for global convergence. 5. Results The VAWT performance can be improved by altering the free stream velocity flow with a deflector or ODGV as reported in some studies [1-3]. A numerical study on Eq. (2) had been carried out in order to assess the parameters that would contribute significant impact to VAWT performance that integrated with the ODGV design. Theoretically, the combination of larger angle of ș with low ȕ angle gives a high velocity ratio in ODGVVAWT design. Fig. 4(b) demonstrates the relationship between K and velocity ratio by varying the ȕ angles. Higher velocity ratio of ODGV-VAWT design is found at lower ȕ angle and lager K value. It divulges that the velocity ratio is proportional to ratio of the vertical distance between inner and outer ODGV to minimum gap of two guide vanes, i.e. V2/V1 Į K. The 2-level full factorial experiment was conducted with only one replicate in CFD simulation. The peak torque of each case was selected as a response for the DOE. The Pareto chart of effects is shown in Fig. 5. Any bar extends beyond the reference line, i.e. value of 12.71 is considered as a significant effect at Į=0.05 significance level. However, Fig. 5 exhibits that there was no significant factor effects (no bar extending beyond reference line). This suggests that either all combinations are equally effective or the model has a problem [6]. Based on the analytical study in previous section as well as the experiment study by Chong et al. [2], it is strongly believed that the parameters selected are equally effective. It does make sense that the interaction effect of ș with ȕ or AB plays the most important role in VAWT performance. Meanwhile, the interaction effects of ș with b or AC as well as interaction of ȕ with b or BC are having a significant effects compared to the three main effects, i.e. ș, ȕ and b alone. As a result, only the interaction effect plot is discussed on Fig. 6.
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4
ɽ 55 60 65 70 75 80 85
3
V2/V1 2
1
0 0
10
20
30
40
50
60
70
80
ɴ(degree) (a) 20
15
K 1.2 2.4
10
3.6
V2/V1
4.8 5
0 0
10
20
30
40
50
60
70
80
ɴ(degree)
(b) Fig.4 (a) Velocity ratio, V2/V1, under different combination of ș and ȕ angles at a=1.8, b=3,K=1.2, ,h12=1 (b) Relationship between K to velocity ratio with varying of different ȕ angles at a=1.8, ș =890,h12=1
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12.71 AB
F actor A B C
Term
AC
N ame Theta Beta b
BC B A C 0
2
4
6 8 Standardized Effect
10
12
14
Fig.5 Pareto chart of effects
10
50
90 (A)
3.0
7.5
12.0
(B) 2.6
Theta
2.4 2.2 (C)
2.6
Beta
2.4 2.2
Theta 57.0 73.5 90.0
Beta 10 50 90
Point Ty pe C orner C enter C orner
Point Ty pe C orner C enter C orner
b
Fig.6 Interaction effects plot
From the interaction effect plot, it is observed that the optimum point exists at the corner point, i.e. minimum or maximum level instead of the center points. In addition, the “cross” of each other describes that strong interaction of ș with ȕ, ș with b and ȕ with b. For the upper left plot in Fig. 6, it tells that the higher torque is obtained by configuration of either in both low ș and ȕ angles or both high ș and ȕ angles. The configuration of ș with 570 and ȕ with 100 give the highest torque value. This is aligned with the findings in Fig. 4(a). However, the velocity vector field in Fig. 7 suggests that more severe flow separation on higher ș, for instance, 900 , and results of lower torque, which analytical model is not taken into consideration. The upper and lower right plot on Fig. 6 explains the relation of b with ș & ȕ, respectively. The higher toque performance of VAWT is observed on lower ș and higher b same as the case of ȕ to b.
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y
y
(a)
x
(b)
y
(c)
x
y x
(d)
x
Fig.7 Velocity vector field (a) ș=570, ȕ=100 & b=12 (b) ș=570, ȕ=100 & b=3 (c) ș=900, ȕ=100 & b=3 (d) ș=900, ȕ=900 & b=12
6. Concluding Remarks A novel omni-direction-guide-vane that surrounds a vertical axis wind turbine is designed to improve the VAWT performance. An analytical study has indicated that ș, ȕ and b are more crucial to VAWT performance if a is fixed. A two-level full factorial has been deployed on screening process for the identification of the critical factors for VAWT performance. From two level full factorial, it further divulges that the strong interaction effect were observed at ș with ȕ, ș with b and ȕ with b compared to the main or individual effects. High torque performance is identified for ODGV-VAWT design at the configuration of ș with 570 and ȕ with 100 as well as larger b value, i.e. 12. It is worth to point out that angle of ș suggests at analytical model is much higher than in DOE results, i.e. 890 versus 570. This can be explained that the analytical model is derived based on the continuity equation with one dimension steady flow and the assumption of no flow is separated or circulated. The circulation flow can be clearly seen in velocity vector field in the CFD results at higher ș angle. Further study on the flow characteristic in the VAWT region is suggested for future works.
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Acknowledgements This research work is supported by the Prototype Development Research Grant Scheme (PR002-2012A) awarded by the Malaysian Ministry of Higher Education (MOHE). References [1] W.T. Chong, K.C. Pan, S.C. Poh, A. Fazlizan, C.S. Oon, A. Badarudin, N.Nik-Ghazali, 2013. Performance Investigation of a Power Augmented Vertical Axis Wind Turbine for Urban High-rise Application, Renewable Energy, 51, p.388. [2] W.T. Chong, A. Fazlizan, S.C. Poh, K.C. Pan, W.P. Hew, F.B. Hsiao, 2013. The Design, Simulation and Testing of an Urban Vertical Axis Wind Turbine with the Omni-direction-guide-vane, Applied Energy, In Press. [3] Daegyoum Kim, Morteza Gharib,2013. Efficiency Improvement of Straight-bladed Vertical-axis Wind Turbines with an Upstream Deflector, J. Wind Eng. Ind. Aerodyn. Vol.115, p. 48–52. [4] S. Wang, Z. Tao, 2010. “Numerical Investigation on Dynamic Stall Associated with Low Reynolds Number Flows over Airfoils”, 2nd International Conference on Computer Engineering and Technology. [5] Marco R., Stefano D. B., Ernesto B., 2012. Effects of Blade Number on Straight-bladed Vertical-axis Darreius Wind Turbine, World Academy of Science, Engineering and Technology, 61, p.305-311. [6] Minitab Inc., Minitab Help, 2010. [7] Fluent Inc., Flunet User’s Manual, p.193-194, 2006.
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