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Influences of winglets on the hydrodynamic performance of horizontal axis current turbines
Applied Ocean Research 92 (2019) 101931
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Influences of winglets on the hydrodynamic performance of horizontal axis current turbines
T
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Ren Yirua,b, , Liu Bingwena,b, Zhang Tiantianc a
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, Hunan 410082, China College of Mechanical and Vehicle Engineering, Hunan University, Changsha, Hunan 410082, China c Strategic Development Department, China Three Gorges Corporations, Beijing 100038, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Tidal energy Horizontal axis current turbine Hydrodynamic performance Winglet Tip vortex
A novel tidal turbine with winglet is given, and the influences of winglets on the hydrodynamic performance of horizontal axis current turbines (HACT) are investigated. The incompressible Reynolds-Averaged Navier–Stokes (RANS) Equations with the k − ω shear stress transport (SST) turbulence model are solved. Two HACTs with the winglet that bent towards the pressure side or suction side are designed as the conceptual designs. The pressure distribution and tip vortices are analyzed and compared to investigate the effect of the winglets. Based on the simulation results, the parameter study of the winglet is performed to investigate the effect of length, tip chord and cant angle on the hydrodynamic performance. Results demonstrate that the numerical simulation shows good agreement with the experimental data. The performance of HACT could be improved only when the winglet bends towards the suction side. At the optimum tip speed ratio (TSR), the best design can achieve 4.66% power increase rate compared with that of the baseline turbine. The proper length, tip chord and cant angle of the winglet could improve power at the whole conditions.
1. Introduction The increasing world population, depleting fossil fuel resources, and uncontrolled CO2 emissions causing global warming make it an urgent affair to develop renewable energy [1]. Amongst in different types of renewable energy resources, during the last decades, tidal energy has been targeted and explored as one of the most promising type due to its high energy density, long-time predictability and potentially large resource [2,3]. If a cost-effective capturing method could be developed, tidal currents could be harnessed to help satisfy the world's growing energy needs. Thereinto, horizontal axis current turbine (HACT) is one promising technology that is being developed for this purpose [4,5]. Many studies about the flow field features of HACT have been carried out to better utilize the tidal energy. The blade element momentum theory (BEMT) and computational fluid dynamics (CFD) are the mainly two approaches for numerically analyzing the hydrodynamic performance of HACT. To better predict the hydrodynamic performance, fluid-structure interaction and CFD computational procedures are developed [6–8]. The flow field measurements in the wake behind a turbine are required to further understand the power extracting mechanism from a tidal turbine and interaction effects between flow and a turbine. The flow features in very-near weak including tip
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vortex is captured, and the quantitative evaluation approach on the transfer of inflow kinetic energy into mechanical work is provided [9]. The downstream wake field of a horizontal axis tidal turbine with three different numerical modeling techniques is investigated [10]. To gain advantages in the powertrain design, two shrouds are designed and experimentally tested to quantify their effect on the power of horizontal axis hydrokinetic turbines [11]. A HATST with leading-edge tubercles is designed, and its effects on cavitation and underwater radiated noise are also investigated [12]. To improve the efficiency, many innovative tidal turbines are proposed [13,14]. Though considerable studies have been conducted on HACT, the power efficiency of HACT which is still far from Betz limit has significant potential to be improved and the performance of the flow field needs to be further investigated. Due to the pressure difference between the pressure and the suction side, with the viscosity of the water, tip vortices would form behind the blade tip once two opposite flows from the both sides meet at the trailing edge. Tip vortices could cause power loss and affect the hydrodynamic performance of HACT. The winglet is an effect way to reduce the formation of tip vortices, and the effect on the marine propeller performance is given [15]. The first effective winglet is developed by Whitcomb, who designed a winglet installed on the winglet tip of a first-generation jet transport in 1970’s [16]. The
Corresponding author at: College of Mechanical and Vehicle Engineering, Hunan University, Changsha, Hunan 410082, China. E-mail address: [email protected] (Y. Ren).
https://doi.org/10.1016/j.apor.2019.101931 Received 16 March 2019; Received in revised form 2 September 2019; Accepted 2 September 2019 0141-1187/ © 2019 Elsevier Ltd. All rights reserved.
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2.2. Turbulence modeling
research result showed that proper designed winglet could reduce the intensity of the tip vortices, thereby, reduce the lift-induced drag and remarkably improve L/D ratios. Whitcomb's research set the ground upon the modern winglet design, after that, many researchers carried out a great deal of investigations on winglets. A winglet optimization procedure for a Medium Altitude Long Endurance Unmanned Aerial Vehicle is presented, and the study provided an increase in total flight time by approximately 10% [17]. To investigate the aerodynamic effects of blade tip tilting on power production of horizontal axis wind turbines, 16 geometries of wind turbines with tip tilting are studied and compared [18]. A HACT with a raked tip to mitigate the cavitation problem is designed [19]. Several different tidal turbine with winglets are compared by Ren et al. [20]. To obtain better HACT blade, a multifidelity optimization is proposed [21]. Though the winglet has been designed on HACT to improve the hydrodynamic performance, the investigation of the effect on the performance of the flow field is not clear enough. Therefore, the influences of winglet and its geometrical configurations on the hydrodynamic of HACT need to be further investigated. The main purpose is to investigate the influences of the winglet on the hydrodynamic performance of HACT. A CFD methodology is developed to simulate HACT performance and validated by existing experimental data. To improve the power efficiency of HACT, two winglet configurations are developed at first during the conceptual design and compared by using CFD. Then, a parameter study of the winglet is developed based on the simulation results of the conceptual designs to investigate the parameter change of winglet on HACT performance. Finally, the results are presented and compared to give design guidance of winglet on HACT.
The turbulence is modeled using the k − ω shear stress transport (SST) turbulence model [22], in which the transport equations for turbulence kinetic energy (k equation) and specific dissipation rate (ω equation) are
a1 k max(a1 ω, SF2)
(5)
4
⎧ k 500μl 4ρσω2 k ⎤ ⎫ ⎫ F1 = tanh ⎧min ⎡max( , 2 ), ⎢ ⎨⎨ ⎬ * β ωL Lω CDkω L2 ⎥ ⎣ ⎦⎬ ⎭ ⎭ ⎩⎩
(6)
1 ∂k ∂ω CDkω = max ⎛⎜2ρσω2 · , 10−10⎞⎟ ω ∂ x ∂ x j j ⎝ ⎠
(7)
2
⎡ ⎛ 2 k 500μl ⎞ ⎤ ⎤ F2 = tanh ⎢ ⎡ ⎢max ⎜ β *ωL , L2ω ⎟ ⎥ ⎥ ⎝ ⎠⎦ ⎦ ⎣⎣
(8)
∂u Pk = min ⎛⎜τij i , 10β *kω ⎞⎟ ⎝ ∂x j ⎠
(9)
In these equations, Pk is the turbulence production rate while α1 = 5/9, α2 = 0.44 , β1 = 3/40 , β2 = 0.0828, σk1 = 0.85, σk2 = 1.0 , σω1 = 0.5, σω2 = 0.856 are constant values. 3. Numerical model and validation The hydrodynamic performance of HACT is investigated by CFD in the current research. In order to validate the CFD procedure, comparisons are made with the experimental data [19,26]. A number of experiments to investigate the designed HACTs, and the experiments give an important guidance for the investigation of HACT. 3.1. Turbine blade modeling This turbine is equipped by a 3-blade rotor with the diameter of 700 mm. Seventeen blade sections are defined to control the blade profile. As demonstrated in Fig. 1, NACA63-418 is the profile along the blade span 15 sections (between r/R = 0.3–1.0), and a 2:1 ellipse is the hub fitting section shape. The chord of each spanwise section is from 24.3 mm to 59.9 mm, meanwhile the twist angle ranges from 2.5° to 16.98°. For the hub fitting section, there is no twist angle with 26.3 mm long chord.
The incompressible fluid flow is solved by RANS equations. Mass and momentum conservation equations are solved as Eqs. (1)–(2)
(2)
(4)
The constant coefficient in the k equation and ω equation are solved by ϕ = ϕ1 F1 + ϕ2 (1 − F1), and ϕ1 is a constant coefficient in k − ε turbulence model equation, ϕ2 is a constant coefficient in k − ω turbulence model equation. In Eq. (4) closure coefficients and auxiliary relations are as Eqs. (6)–(9)
2.1. Governing equations
∂ρ ∂ ⎛ ∂ui ∂ ∂ + (ρui ) + (ρui uj ) = − − ρui′ u′j ⎞⎟ + Si ⎜μ ∂x i ∂x j ⎝ ∂x j ∂t ∂x j ⎠
∂ ∂ ∂ ⎡ ∂ω ⎤ + αρS 2 − βρω2 (ρω) + (ρuj ω) = (μl + σω μt ) ∂t ∂x j ∂x j ⎢ ∂x j ⎥ ⎣ ⎦ 1 ∂k ∂ω + 2(1 − F1) ρσω2 ω ∂x j ∂x j
μt =
A steady state CFD method is developed to investigate the hydrodynamic performance of HACT in the present research. The incompressible Reynolds-Averaged Navier–Stokes (RANS) Equations with the k − ω shear stress transport (SST) turbulence model are solved by a finite volume method. The SIMPLE algorithm is applied to deal with the pressure-based pressure–velocity coupling. The solution gradients at cell center are evaluated by the cell center-based Least Squares method. To discretize the convection terms, a second order accurate upwind interpolations scheme is used. The rotational flow field of HACT is complex and hard to numerically simulate. In consideration of the economy of the computation time, the multiple reference frame (MRF) model is used to handle the rotor revolution. MRF is a steady-state approximation method. The mesh remains fixed for the computation but the rotational speed of the local reference frame is set as that of the corresponding zone, thus the governing equations are solved in corresponding forms. In the rotor zone, the flow is solved using the rotating reference frame equations. However, the equations reduce to their stationary forms in the outer zone.
(1)
(3)
where the turbulence viscosity is as follows:
2. Mathematical and numerical method
∂ (ρui ) = 0 ∂x i
∂ ∂ ∂ ⎡ ∂k ⎤ (ρk ) + (ρuj k ) = (μl + σk μt ) + Pk − β *ρωk ∂t ∂x j ∂x j ⎢ ∂ xj ⎥ ⎣ ⎦
3.2. Numerical model with boundary conditions
where ρ is the fluid density, u is the fluid velocity, μ is the dynamic viscosity, and S is a source term. The − ρui′ u′j is Reynolds stress term that is modeled by a turbulence model.
The computational domain with boundary conditions is exhibited in Fig. 2. To consider the rotation of the blade, the rotational periodic 2
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Fig. 1. Tidal turbine blade with section profile.
conditions are imposed on the two side boundary, i.e., the flow across the two side boundaries is assumed to be identical. Therefore, only one blade of the turbine is modeled in a sector of 120°, and the hub is not considered in the present CFD model. This could improve modeling efficiency and computational accuracy. The turbine performance is analyzed for a yaw angle of 0∘, in other words, the velocity direction at the inlet is normal to the boundary. The velocity inlet boundary condition, i.e., a uniform and steady velocity is applied normal to the inlet boundary, located at 3D upstream. At 6D downstream, a pressure outlet boundary condition is applied on the outlet boundary, i.e., a reference pressure is given over the outlet boundary. On the top and the bottom boundary, the symmetry condition is applied to ensure no stress at outer boundaries. Between the adjacent subdomains, non-matching interfaces are applied on the overlap faces, and simple linear interpolation is utilized for the transport of the flow properties through the interfaces.
for the power coefficient with the coarse (0.78 million cells), medium (1.32 million cells), and fine (2.53 million cells) meshes in the rotational zone at TSR = 5. As illustrated in Fig. 4, when the cell number of the rotational zone is more than 1.32 million, the variation of the power coefficient is quite small. The relative difference of Cp between the medium meshes and the fine meshes is 0.98%, thus the effect of the cell number on the power coefficient is believed to be small. 3.4. Validation and result The validation result of the present CFD model is presented in Fig. 5, the power coefficient (CP = QΩ/0.5ρu3A , where Q, Ω, A are the torque of the turbine, the angular velocity of the turbine and the blade swept area, respectively) of the CFD results is compared with the experimental data over a range of TSRs (TSR = ΩR/ u , where R is the blade radius) [19,26]. In order to obtain a target TSR, the towing speed is changed while the turbine's angular velocity keeps constant (270 rpm) for both the experiments and the CFD simulations. The present CFD results agree well with the experimental data, but there still existed some quantitative discrepancies. Both the optimum TSRs occurred at approximately TSR = 5, where the CFD's Cp is about 0.408 and the experiment's Cp is about 0.422, the relative error is about 3.3%. The maximum relative error appeared at approximately TSR = 7.4, whose value is about 7.7%. The pressure coefficient contours with the streamlines on the selected span sections (r/R = 0.95/0.75/0.5/0.25) at TSR = 5 are demonstrated in Fig. 6, the pressure coefficient is defined by:
3.3. Grid strategy As illustrated in Fig. 3, the computational domain is divided in two zones, the stationary zone and the rotational zone. Due to the simple geometries in the stationary zone, approximately 0.24 million structured cells are generated to reduce the whole grids number and at the same time accelerate solution convergence and improve computational accuracy. In consideration of the complex geometries in the rotational zone, unstructured cells are meshed there to avoid the difficulty of mesh generation and improve computational efficiency. Due to the rotation of the blade, the flow near the blade tip, the leading edge and trailing edge is much complex. Therefore the rotational zone is divided into two subdomains to generate finer meshes near the blade surface to get a proper y+ and acquire accurate performance of the turbine blade. The y + of the blade surface is in the range of 30–300 which is acceptable for the high-Reynolds-number k − ω SST model. The grid-dependence in the computational simulations is assessed
Cpress =
P − Pref 0.5ρu2
where P and Pref are the local and the reference hydrostatic pressures, respectively. At the optimum TSR, the typical pattern for pressure distribution on the blade surface is well reproduced. The low pressure region on the suction side and the high pressure region on the pressure
Fig. 2. Tidal turbine blade. 3
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Fig. 3. Computational domain with boundary conditions.
side near the blade tip are observed. It's the pressure difference between the two sides that generates the lift force on the blade and thereby, the torque on the turbine to convert tidal energy. From the picture, it could be concluded that most of the power is produced near the blade tip, where most of the net pressure difference is produced. A well-behaved attached flow is observed at most of the span sections, which is correspond with the highest power production produced at TSR = 5. However, a near-separation flow occurred at 0.25 span section (which near the blade root transit from ellipse to airfoil) due to its large angle of attack. This would result in negative effect on the power production. 3.5. Discretization error The grid convergence index (GCI) is adopted to evaluate discretization error. Given by Noruzi, the numerical simulation result is acceptable if the grid refinement ratio is greater than 1.3, and the order of accuracy (p) and GCI can be given as Eqs. (10) and (11) [27].
ln
Fig. 4. Grid-dependence assessment.
(φM − φC ) (φF − φM )
+ ln
p=
GCI = Fs
(
nM / nC − sign ((φF − φM ) / (φM − φC )) nF / nM − sign ((φF − φM ) / (φM − φC ))
ln(nM / nC ) (φM − φF )/ φF nM / nC − 1
) (10)
(11)
where φ is the simulation variable such as rotor power output, pressure, velocity or lift coefficient, n is the grid number, the subscript F, M, C are the fine, medium and coarse grid, Fs is a safety factor equals 1.25. The order of accuracy and the GCI are 3.18 and 0.0029, respectively. It demonstrates that the numerical simulation result could be guaranteed. 4. The design of HACT with winglet The blade of the turbine is the key component to convert the tidal energy. Generally, the design of the blade is to select the appropriate types of the airfoils for corresponding section along the wingspan, and optimize its chord and twist angle to acquire the most lift-drag ratio. However, as mentioned before, the finite wingspan blade would produce tip vortices and suffer from the induced drag, which would cause power lose and affect the hydrodynamic performance. The winglet is utilized to reduce the intensity of the tip vortex and improve the hydrodynamic performance of HACT. The winglet is an effective way to weaken the tip vortex, which is able to carry a hydrodynamic load that produces a flow field that interacts with that of
Fig. 5. Validation of the CFD model.
4
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Fig. 6. Pressure coefficient contours with streamlines on selected span sections.
the main wing thereby reduces the amount of spanwise flow, thus the induced drag is reduced [23]. Adding winglets to HACT also causes an increase in wetted area and a corresponding increase in the profile drag [24]. The profile drag, which caused by viscosity of the water and the pressure drag, would make some energy taken from the water. The profile drag contribution of the winglet is more straight forward than that of the induced drag. Therefore, the design goal of a winglet is to produce the most reduction in induced drag for the smallest increase in profile drag. The profile drag is hard to predict, because it depends on many factors such as the wetted area of the blade, the shape of the blade airfoil and the angle of the attack [25]. However, the induced drag is also affected by these factors. Thus, it is hard to tradeoff and predict. Therefore, to get a proper design for HACT, the parameter study is necessary. In order to investigate the winglet design of HACT, only the blade tip of the baseline turbine is modified, while the other part kept the same. Besides, each design is insured to make the blade length constant. Firstly, two winglets are designed as an initial design stage to introduce the winglet concept to HACT. The configuration 1 of the two conceptual designs is demonstrated as Fig. 7. The three main parameters to define the winglet are illustrated in Fig. 8. The blade of configuration 1 is mounted with a blended winglet. The intersection between the blade tip and winglet is a smooth curve instead of a sharp angle to reduce the intersection drag formed at the junction of the blade and the winglet. The winglet bent towards the pressure side with the cant angle keep at
Fig. 7. Configuration1 of the conceptual design.
about 90∘. Each section shape of the winglet took the profile of ellipse with 16:1 major to minor axis ratio. The center line of the winglet is tangent to the center of the chord of the blade tip. The tip chord and height are 8 mm and 15 mm, respectively. The design of configuration 2 is the same as configuration 1 except that the winglet bends towards the suction side. Then, based on the conceptual design investigation results, the configuration 2 is modified with different parameters to investigate the effect of winglet length, tip chord and cant angle on the power efficiency.
5. Results and discussion The hydrodynamic performance of the HACTs with winglets is 5
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Fig. 8. Main parameters to define the winglet.
As shown in the picture, on 0.95 span section, from leading edge to about 0.5 chord, the pressure coefficient on pressure side of configuration 1 increases slightly compared with that of the baseline turbine. However, on the suction side, the pressure coefficient decreased slightly at most of the position. On the pressure side of configuration 2, the pressure coefficient also exhibited a slight increment. However, the pressure coefficient on the suction side decreased evidently compared with that of the baseline turbine. Therefore, the gap of the pressure coefficient between the pressure side and suction side of configuration 1 exhibited a slight decline. On the contrary, the gap of the pressure coefficient of configuration 2 is larger than that of the baseline turbine evidently. Thus the winglet of configuration 2 provided better flow pattern and generated higher torque near the blade tip region. Nevertheless, the negative effect on the torque generation near the blade tip is exhibited the winglet of configuration 1. The winglets have little effect on these sections on 0.75 and 0.5 span section. On 0.25 span section, the section which near the blade root transited from ellipse to airfoil, all the configurations encountered separation flow which have bad effect on the hydrodynamic performance. The difference of the net pressure coefficient of both the configurations with winglets is slight less than that of the baseline turbine, which revealed that the winglets have negative effect on the span near the blade root. It could be seen from Fig. 10, the pressure coefficient in 0.95 span section is the largest, and that of 0.25 span section is the smallest. The pressure coefficients of pressure side and suction side of 0.95 span section are seven and four times than that of 0.25 span section. As a result, the blade root contributes very little to the energy production, and the effect of the winglets on the blade root could be neglected. To reveal how the winglet influence on the tip vortex, the vorticity magnitude contours with streamlines of the three blade configurations behind the blade tip are presented in Figs. 11–13. Each plane of vorticity magnitude is plotted 22 mm far away from the blade tip, and the pressure side is in the right. The intensity of the tip vortices behind the tip of the baseline turbine is the greatest clearly. Both of the winglets suppressed the formation of the tip vortex. However, the intensity of vortex behind the blade tip of configuration 1 is similar to that of the baseline turbine. The intensity of the vortex behind the tip of configuration 2 is much lower than that of the baseline turbine. The vortex is significantly suppressed by the winglet of configuration 2. With the better flow pattern near the blade tip and the suppressed tip vortices, the configuration 2 results in improved power production. Though the winglet of configuration 1 decreases the intensity of the tip vortices as well, it has negative effect on the torque that generated near the blade tip. The torque decrease may be responsible for the power
investigated by the CFD method proposed in Section 2 and compared with that of the baseline turbine. The simulations are performed over a range of TSRs (4–10), where the target TSR is acquired by changing the current speed while kept turbine's angular speed at 270 rpm. 5.1. Conceptual design comparisons The comparisons of the power coefficient between the baseline turbine and the two conceptual designs are given as Fig. 9. As demonstrated in the picture, the power coefficient of the three cases all showed similar trend versus TSR. They all acquired peak power coefficient at approximately TSR = 5. Configuration 2, the winglet of which bent towards the suction side, showed power coefficient improvement at approximately all TSRs. However, configuration 1, the winglet of which bends towards the pressure side, performed power coefficient decline almost at all TSRs. The average decrease rate in Cp of configuration 1 is about 2.4% that of the baseline turbine, while the average increase rate in Cp of configuration 2 is about 3.1% than that of the baseline turbine. The maximum difference between configuration 1 and 2 is 5.03% and 4.34%, respectively. Fig. 10 presents the comparisons of pressure coefficient distribution on four span sections (r/R = 0.95/0.75/0.5/0.25) at TSR = 5 between the baseline turbine and the two conceptual designs. The horizontal axis (x/c) is cross-section of the span normalized.
Fig. 9. Power coefficient comparisons between the baseline turbine and the conceptual designs. 6
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Fig. 10. Comparisons of pressure coefficient distribution on four span sections at TSR = 5.
Fig. 12. Vorticity magnitude contour with streamlines behind the blade tip of configuration 1.
Fig. 11. Vorticity magnitude contour with streamlines behind the blade tip of the baseline turbine.
dubbed configuration l–13 and so on for the other HACTs with different winglet length. The Cp comparisons between the baseline turbine and configuration l − x (x = 10, 13, 15, 17, 19) is shown in Fig. 14. The increase rate in Cp of configuration l − x compared with that of the baseline turbine is demonstrated in Fig. 15. As shown in the Fig. 14, the Cp variation of configuration l − x show similar trend as that of the baseline turbine. All the HACTs with winglet performed power increase almost in all conditions compared with that of the baseline turbine. Overall, from TSR = 4 to TSR = 6.6 the winglet with the longest length results in the highest power coefficient increase of HACT. For each configuration, the increase rate versus TSRs is relatively stable. However, the increase rate in Cp all decreased dramatically from TSR = 6.6 to TSR = 7.4. The trend is consistent with the Cp variation in the same condition. The influence of winglet has little influence on the Cp if the TSR is above 7.4, and the Cp is a decreasing function with respect to TSR. When the TSR is larger than 7.4, the increase rate (except for configuration l–19) almost
decrease of configuration 1. 5.2. Parameter study For configuration 1 showed negative effect on HACT power efficiency, only configuration 2 is modified with different parameters (shown as Fig. 8) to investigate the effect of winglet length, tip chord and cant angle on the power efficiency. 5.2.1. Length effect To examine the effect of the winglet length on the hydrodynamic performance, the winglet length of configuration 2 is modified while other parameters are kept the same. Five HACTs with winglets are compared. The length of the winglets is 10 mm, 13 mm, 15 mm, 17 mm and 19 mm, respectively. The HACT with 10 mm winglet length is dubbed configuration l–10, the HACT with 13 mm winglet length is 7
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Fig. 13. Vorticity magnitude contour with streamlines behind the blade tip of configuration 2.
Fig. 16. Cp comparisons between the baseline turbine and configuration t − y.
all showed growth tendency but chaotic for the low Cp value and random factors. However, the configuration l–17 performed the best power coefficient increment when TSR is larger than 8.2, the power coefficient is still very low as that of the baseline turbine. The highest power increase rate at the optimum TSR (TSR = 5) is 3.82% which is achieved by configuration l–19. In order to acquire a power increase at the whole conditions, the length of the winglet shouldn't be less than 17 mm. 5.2.2. Tip chord effect To examine the effect of winglet tip chord on the hydrodynamic performance, the tip chord of the winglet of configuration l–19 is modified while other parameters are kept the same. Five HACTs with winglets are compared. The tip chords of the winglets are 4 mm, 8 mm, 10 mm, 12 mm and 16 mm, respectively. The HACT with 4 mm winglet tip chord is dubbed configuration t − 4, the HACT with 8 mm winglet tip chord is dubbed configuration t − 8 and so on for the other HACTs with different winglet tip chord. The Cp comparisons between the baseline turbine and configuration t − y (y = 4, 8, 10, 12, 16) is shown in Fig. 16. The increase rate in Cp of configuration t − y compared with that of the baseline turbine is demonstrated in Fig. 17. As demonstrated in Fig. 16, the tip chord of the winglet didn't show that much effect on the performance of HACT as the length. The increase rate in Cp didn't show much regularity along with
Fig. 14. Cp comparisons between the baseline turbine and configuration l − x.
Fig. 15. increase rate in Cp of configuration l − x with baseline turbine.
Fig. 17. increase rate in Cp of configuration t − y with baseline turbine. 8
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dubbed configuration ∂ − 80 and so on for the other HACT with different winglet cant angle. The Cp comparisons between the baseline turbine and configuration ∂ − z (z = 90, 80, 70, 60, 50) is shown in Fig. 18. The increase rate in Cp of configuration ∂-z compared with that of the baseline turbine is illustrated in Fig. 19. As shown in Fig. 19, the increase rate in Cp increased along with the cant angle increased from TSR = 4 to TSR = 6.6. Meanwhile, the effect of the TSR on the increase rate in Cp is not that much. The increase rate in Cp all decreases from TSR = 6.6 to TSR = 7.4, and then increases when TSR is larger than 7.4. Overall, the increase rate in Cp increased along with the cant angle decreased when TSR is larger than 9.2. However, when TSR is larger than 9.2 the power coefficient is quite low(less than 0.2). At the optimum TSR, the best power coefficient is acquired by configuration ∂ − 90, whose Cp is 3.70% higher than that of the baseline turbine. To acquire power increase at the whole conditions, the cant angle of the winglet shouldn't be less than 80∘. Fig. 18. Cp comparisons between the baseline turbine and configuration ∂ − z.
6. Conclusion The influences of the winglet on the hydrodynamic performance of HACT are investigated by CFD in the current research. Two conceptual designs with the winglet bent towards the pressure side or the suction side are designed to introduce the winglet concept to HACT. The CFD results show that only the HACT with the winglet that bent towards the suction side can HACT performed the power improvement at most of the TSRs. The results of the pressure coefficient on selected span sections and the vorticity magnitude contour behind the blade tip with streamlines reveals that, the winglet improve the power production by improving the torque near the blade tip and decreasing the intensity of tip vortices at the same time. Based on the simulation results of the conceptual designs, the parameter study of the HACT with the winglet that bend towards the suction side is conducted to investigate the influences of the length, tip chord and cant angle of the winglet on the hydrodynamic performance of HACT. The power coefficient comparisons results demonstrate that the power production increment depended on the length, the tip chord and the cant angle of the winglet. From TSR = 4 to TSR = 6.6, the power coefficient increases as the winglet length and cant angle increases. The tip chord would influence the power coefficient, but not that much as the other two parameters. All the configurations show a decrement in power coefficient from TSR = 6.6 to TSR = 7.4. The three parameters have significant effect on the power coefficient at high TSR, but no clear variation trends are found. To acquire a power increase at the whole conditions, length, tip chord and cant angle have effect on the hydrodynamics and should be carefully considered.At the optimum TSR, the best design has achieved 4.66% power increase rate compared with that of the baseline turbine.
Fig. 19. increase rate in Cp of configuration ∂ − z with baseline turbine.
the tip chord variation. Only configuration t − 4 and configuration t − 8 performs power increase at whole TSR compared with that of the baseline turbine. The configuration t − 16 with the longest tip chord shows the best power coefficient from TSR = 4 to TSR = 5.4. At the optimum TSR, configuration t − 16 achieves the best power coefficient, which is 4.66% higher than that of the baseline turbine. However, the power increment dramatically decreases when TSR is larger than 5.4. When TSR is larger than 7, the winglet of configuration t − 16 almost shows negative effect in the whole condition. The power coefficient of other configurations don't show much difference from each other from TSR = 4 to TSR = 5.4. The increase rate in Cp all demonstrates a downtrend from TSR = 6.6 to TSR = 7.4. When TSR is larger than 7.4, the HACT with the shortest tip chord performed a rising trend in Cp increase rate and showed the best power coefficient when TSR is larger than 9.2. To make the winglet increase the power production of the baseline turbine in the whole condition, the tip chord of the winglet shouldn't be larger than 8 mm.
Acknowledgments This research is funded by the Marine Renewable Energy Research Project of State Oceanic Administration of China (grant nos. GHME2013GC03 and GHME2015GC01), and the Fundamental Research Funds for the Central University (grant no. 2014044). References [1] M.S. Guney, K. Kaygusuz, Hydrokinetic energy conversion systems: a technology status review, Renew. Sustain. Energy Rev. 14 (2010) 2996–3004. [2] H.R. Charlier, A “sleeper” awakes: tidal current power, Renew. Sustain. Energy Rev. 7 (2003) 515–529. [3] D. Li, S.J. Wang, P. Yuan, An overview of development of tidal current in China: energy resource, conversion technology and opportunities, Renew. Sustain. Energy Rev. 14 (2010) 2896–2905. [4] Y.B. Ma, W.H. Lam, Y.G. Cui, T.M. Zhang, J.X. Jiang, C. Sun, J.H. Guo, S.G. Wang, S.S. Lam, G. Hamill, Theoretical vertical-axis tidal-current-turbine wake model using axialmomentum theory with CFD corrections, Appl. Ocean Res. 79 (2018)
5.2.3. Cant angle effect To examine the effect of winglet cant angle on the hydrodynamic performance of HACT, the cant angle of the configuration t − 4 is modified while other parameters are kept the same. Five HACTs with winglets are compared. The cant angle of the winglets is90∘, 80∘, 70∘, 60∘ and 50∘, respectively. The HACT with 90∘ winglet cant angle is dubbed configuration ∂ − 90, the HACT with 80∘ winglet cant angle is 9
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113–122. [5] K. Wang, K. Sun, Q.H. Sheng, L. Zhang, S.Q. Wang, The effects of yawing motion with different frequencies on the hydrodynamic performance of floating verticalaxis tidal current turbines, Appl. Ocean Res. 59 (2016) 224–235. [6] C.S.K. Belloni, R.H.J. Willden, G.T. Houlsby, An investigation of ducted and opencentre tidal turbines employing CFD-embedded BEM, Renew. Energy 108 (2017) 622–634. [7] J.H. Lee, S.H. Park, D.H. Kim, S.H. Rhee, M.C. Kim, Computational methods for performance analysis of horizontal axis tidal stream turbines, Appl. Energy 98 (2012) 512–523. [8] J. Liu, H. Lin, S.R. Purimitla, M. Dass, The effects of blade twist and nacelle shape on the performance of horizontal axis tidal current turbines, Appl. Ocean Res. 64 (2017) 58–69. [9] J.H. Seo, S.J. Lee, W.S. Choi, S.T. Park, S.H. Rhee, Experimental study on kinetic energy conversion of horizontal axis tidal stream turbine, Renew. Energy 97 (2016) 784–797. [10] J. Liu, H. Lin, S.R. Purimitla, Wake field studies of tidal current turbines with different numerical methods, Ocean Eng. 117 (2016) 383–397. [11] M. Shahsavarifard, E.L. Bibeau, V. Chatoorgoon, Effect of shroud on the performance of horizontal axis hydrokinetic turbines, Ocean Eng. 96 (2015) 215–225. [12] W.C. Shi, M. Atlar, R. Rosli, B.h. Aktas, R. Norman, Cavitation observations and noise measurements of horizontal axis tidal turbines with biomimetic blade leadingedge designs, Ocean Eng. 121 (2016) 143–155. [13] M.H. Yang, G.M. Huang, R.H. Yeh, Performance investigation of an innovative vertical axis turbine consisting of deflectable blades, Appl. Energy 179 (2016) 875–887. [14] J.N. Goundar, M.R. Ahmed, Design of a horizontal axis tidal current turbine, Appl. Energy 111 (2013) 161–174. [15] H.T. Gao, W.C. Zhu, Y.T. Liu, Y.Y. Yan, Effect of various winglets on the performance of marine propeller, Appl. Ocean Res. 86 (2019) 246–256. [16] R.T. Whitcomb, A Design Approach and Selected Wind-Tunnel Results at High
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Subsonic Speeds for Wing-Tip Mounted Winglets, NASA Langley Research Center, 1796, pp. 1–10 NASA TN D-8260. P. Panagiotou, P. Kaparos, K. Yakinthos, Winglet design and optimization for a MALE UAV using CFD, Aerosp. Sci. Technol. 39 (2014) 190–205. M.A. Alfarra, N.S. uzol, I.S. Akmandor, Investigations on blade tip tilting for hawt rotor blades using CFD, Int. J. Green Energy 12 (2015) 125–138. M. Song, M.C. Kim, I.R. Do, S.H. Rhee, J.H. Lee, B.S. Hyun, Numerical and experimental investigation on the performance of three newly designed 100 kW-class tidal current turbines, Intern. J. Nav. Archit. Ocean Eng. 4 (2002) 241–255. Y.R. Ren, B.W. Liu, T.T. Zhang, Q.H. Fang, Design and hydrodynamic analysis of horizontal axis tidal stream turbines with winglets, Ocean Eng. 144 (2017) 374–383. P.M. Kumar, J.H. Seo, W.C. Seok, S.H. Rhee, A. Samad, Multi-fidelity optimization of blade thickness parameters for a horizontal axis tidal stream turbine, Renew. Energy 135 (2019) 277–287. F. Menter, Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J. 32 (1994) 1598–1605. J.A. Blackwell Jr., Numerical Method to Calculate the Induced Drag or Optimum Loading for Arbitrary Non-Planar Aircraft, Vortex-Lattice Utilization, 1976, pp. 1–12 NASA SP-405, 49. M.D. Maughmer, Design of winglets for high-performance sailplanes, AIAA J. Aircr. 40 (2003) 1099–1106. F. Thomas, Fundamentals of Sailplane Design, College Park Press, MD, 1999 Translated by Judah Milgram. A.S. Bahaj, A.F. Molland, J.R. Chaplin, W.M.J. Batten, Power and thrust measurements of marine current turbines under various hydrodynamic flow conditions in a cavitation tunnel and a towing tank, Renew. Energy 32 (2007) 407–426. R. Noruzi, M. Vahidzadeh, A. Riasi, Design, analysis and predicting hydrokinetic performance of a horizontal marine current axial turbine by consideration of turbine installation depth, Ocean Eng. 108 (2015) 789–798.
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Influences of winglets on the hydrodynamic performance of horizontal axis current turbines
T
⁎
Ren Yirua,b, , Liu Bingwena,b, Zhang Tiantianc a
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, Hunan 410082, China College of Mechanical and Vehicle Engineering, Hunan University, Changsha, Hunan 410082, China c Strategic Development Department, China Three Gorges Corporations, Beijing 100038, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Tidal energy Horizontal axis current turbine Hydrodynamic performance Winglet Tip vortex
A novel tidal turbine with winglet is given, and the influences of winglets on the hydrodynamic performance of horizontal axis current turbines (HACT) are investigated. The incompressible Reynolds-Averaged Navier–Stokes (RANS) Equations with the k − ω shear stress transport (SST) turbulence model are solved. Two HACTs with the winglet that bent towards the pressure side or suction side are designed as the conceptual designs. The pressure distribution and tip vortices are analyzed and compared to investigate the effect of the winglets. Based on the simulation results, the parameter study of the winglet is performed to investigate the effect of length, tip chord and cant angle on the hydrodynamic performance. Results demonstrate that the numerical simulation shows good agreement with the experimental data. The performance of HACT could be improved only when the winglet bends towards the suction side. At the optimum tip speed ratio (TSR), the best design can achieve 4.66% power increase rate compared with that of the baseline turbine. The proper length, tip chord and cant angle of the winglet could improve power at the whole conditions.
1. Introduction The increasing world population, depleting fossil fuel resources, and uncontrolled CO2 emissions causing global warming make it an urgent affair to develop renewable energy [1]. Amongst in different types of renewable energy resources, during the last decades, tidal energy has been targeted and explored as one of the most promising type due to its high energy density, long-time predictability and potentially large resource [2,3]. If a cost-effective capturing method could be developed, tidal currents could be harnessed to help satisfy the world's growing energy needs. Thereinto, horizontal axis current turbine (HACT) is one promising technology that is being developed for this purpose [4,5]. Many studies about the flow field features of HACT have been carried out to better utilize the tidal energy. The blade element momentum theory (BEMT) and computational fluid dynamics (CFD) are the mainly two approaches for numerically analyzing the hydrodynamic performance of HACT. To better predict the hydrodynamic performance, fluid-structure interaction and CFD computational procedures are developed [6–8]. The flow field measurements in the wake behind a turbine are required to further understand the power extracting mechanism from a tidal turbine and interaction effects between flow and a turbine. The flow features in very-near weak including tip
⁎
vortex is captured, and the quantitative evaluation approach on the transfer of inflow kinetic energy into mechanical work is provided [9]. The downstream wake field of a horizontal axis tidal turbine with three different numerical modeling techniques is investigated [10]. To gain advantages in the powertrain design, two shrouds are designed and experimentally tested to quantify their effect on the power of horizontal axis hydrokinetic turbines [11]. A HATST with leading-edge tubercles is designed, and its effects on cavitation and underwater radiated noise are also investigated [12]. To improve the efficiency, many innovative tidal turbines are proposed [13,14]. Though considerable studies have been conducted on HACT, the power efficiency of HACT which is still far from Betz limit has significant potential to be improved and the performance of the flow field needs to be further investigated. Due to the pressure difference between the pressure and the suction side, with the viscosity of the water, tip vortices would form behind the blade tip once two opposite flows from the both sides meet at the trailing edge. Tip vortices could cause power loss and affect the hydrodynamic performance of HACT. The winglet is an effect way to reduce the formation of tip vortices, and the effect on the marine propeller performance is given [15]. The first effective winglet is developed by Whitcomb, who designed a winglet installed on the winglet tip of a first-generation jet transport in 1970’s [16]. The
Corresponding author at: College of Mechanical and Vehicle Engineering, Hunan University, Changsha, Hunan 410082, China. E-mail address: [email protected] (Y. Ren).
https://doi.org/10.1016/j.apor.2019.101931 Received 16 March 2019; Received in revised form 2 September 2019; Accepted 2 September 2019 0141-1187/ © 2019 Elsevier Ltd. All rights reserved.
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2.2. Turbulence modeling
research result showed that proper designed winglet could reduce the intensity of the tip vortices, thereby, reduce the lift-induced drag and remarkably improve L/D ratios. Whitcomb's research set the ground upon the modern winglet design, after that, many researchers carried out a great deal of investigations on winglets. A winglet optimization procedure for a Medium Altitude Long Endurance Unmanned Aerial Vehicle is presented, and the study provided an increase in total flight time by approximately 10% [17]. To investigate the aerodynamic effects of blade tip tilting on power production of horizontal axis wind turbines, 16 geometries of wind turbines with tip tilting are studied and compared [18]. A HACT with a raked tip to mitigate the cavitation problem is designed [19]. Several different tidal turbine with winglets are compared by Ren et al. [20]. To obtain better HACT blade, a multifidelity optimization is proposed [21]. Though the winglet has been designed on HACT to improve the hydrodynamic performance, the investigation of the effect on the performance of the flow field is not clear enough. Therefore, the influences of winglet and its geometrical configurations on the hydrodynamic of HACT need to be further investigated. The main purpose is to investigate the influences of the winglet on the hydrodynamic performance of HACT. A CFD methodology is developed to simulate HACT performance and validated by existing experimental data. To improve the power efficiency of HACT, two winglet configurations are developed at first during the conceptual design and compared by using CFD. Then, a parameter study of the winglet is developed based on the simulation results of the conceptual designs to investigate the parameter change of winglet on HACT performance. Finally, the results are presented and compared to give design guidance of winglet on HACT.
The turbulence is modeled using the k − ω shear stress transport (SST) turbulence model [22], in which the transport equations for turbulence kinetic energy (k equation) and specific dissipation rate (ω equation) are
a1 k max(a1 ω, SF2)
(5)
4
⎧ k 500μl 4ρσω2 k ⎤ ⎫ ⎫ F1 = tanh ⎧min ⎡max( , 2 ), ⎢ ⎨⎨ ⎬ * β ωL Lω CDkω L2 ⎥ ⎣ ⎦⎬ ⎭ ⎭ ⎩⎩
(6)
1 ∂k ∂ω CDkω = max ⎛⎜2ρσω2 · , 10−10⎞⎟ ω ∂ x ∂ x j j ⎝ ⎠
(7)
2
⎡ ⎛ 2 k 500μl ⎞ ⎤ ⎤ F2 = tanh ⎢ ⎡ ⎢max ⎜ β *ωL , L2ω ⎟ ⎥ ⎥ ⎝ ⎠⎦ ⎦ ⎣⎣
(8)
∂u Pk = min ⎛⎜τij i , 10β *kω ⎞⎟ ⎝ ∂x j ⎠
(9)
In these equations, Pk is the turbulence production rate while α1 = 5/9, α2 = 0.44 , β1 = 3/40 , β2 = 0.0828, σk1 = 0.85, σk2 = 1.0 , σω1 = 0.5, σω2 = 0.856 are constant values. 3. Numerical model and validation The hydrodynamic performance of HACT is investigated by CFD in the current research. In order to validate the CFD procedure, comparisons are made with the experimental data [19,26]. A number of experiments to investigate the designed HACTs, and the experiments give an important guidance for the investigation of HACT. 3.1. Turbine blade modeling This turbine is equipped by a 3-blade rotor with the diameter of 700 mm. Seventeen blade sections are defined to control the blade profile. As demonstrated in Fig. 1, NACA63-418 is the profile along the blade span 15 sections (between r/R = 0.3–1.0), and a 2:1 ellipse is the hub fitting section shape. The chord of each spanwise section is from 24.3 mm to 59.9 mm, meanwhile the twist angle ranges from 2.5° to 16.98°. For the hub fitting section, there is no twist angle with 26.3 mm long chord.
The incompressible fluid flow is solved by RANS equations. Mass and momentum conservation equations are solved as Eqs. (1)–(2)
(2)
(4)
The constant coefficient in the k equation and ω equation are solved by ϕ = ϕ1 F1 + ϕ2 (1 − F1), and ϕ1 is a constant coefficient in k − ε turbulence model equation, ϕ2 is a constant coefficient in k − ω turbulence model equation. In Eq. (4) closure coefficients and auxiliary relations are as Eqs. (6)–(9)
2.1. Governing equations
∂ρ ∂ ⎛ ∂ui ∂ ∂ + (ρui ) + (ρui uj ) = − − ρui′ u′j ⎞⎟ + Si ⎜μ ∂x i ∂x j ⎝ ∂x j ∂t ∂x j ⎠
∂ ∂ ∂ ⎡ ∂ω ⎤ + αρS 2 − βρω2 (ρω) + (ρuj ω) = (μl + σω μt ) ∂t ∂x j ∂x j ⎢ ∂x j ⎥ ⎣ ⎦ 1 ∂k ∂ω + 2(1 − F1) ρσω2 ω ∂x j ∂x j
μt =
A steady state CFD method is developed to investigate the hydrodynamic performance of HACT in the present research. The incompressible Reynolds-Averaged Navier–Stokes (RANS) Equations with the k − ω shear stress transport (SST) turbulence model are solved by a finite volume method. The SIMPLE algorithm is applied to deal with the pressure-based pressure–velocity coupling. The solution gradients at cell center are evaluated by the cell center-based Least Squares method. To discretize the convection terms, a second order accurate upwind interpolations scheme is used. The rotational flow field of HACT is complex and hard to numerically simulate. In consideration of the economy of the computation time, the multiple reference frame (MRF) model is used to handle the rotor revolution. MRF is a steady-state approximation method. The mesh remains fixed for the computation but the rotational speed of the local reference frame is set as that of the corresponding zone, thus the governing equations are solved in corresponding forms. In the rotor zone, the flow is solved using the rotating reference frame equations. However, the equations reduce to their stationary forms in the outer zone.
(1)
(3)
where the turbulence viscosity is as follows:
2. Mathematical and numerical method
∂ (ρui ) = 0 ∂x i
∂ ∂ ∂ ⎡ ∂k ⎤ (ρk ) + (ρuj k ) = (μl + σk μt ) + Pk − β *ρωk ∂t ∂x j ∂x j ⎢ ∂ xj ⎥ ⎣ ⎦
3.2. Numerical model with boundary conditions
where ρ is the fluid density, u is the fluid velocity, μ is the dynamic viscosity, and S is a source term. The − ρui′ u′j is Reynolds stress term that is modeled by a turbulence model.
The computational domain with boundary conditions is exhibited in Fig. 2. To consider the rotation of the blade, the rotational periodic 2
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Fig. 1. Tidal turbine blade with section profile.
conditions are imposed on the two side boundary, i.e., the flow across the two side boundaries is assumed to be identical. Therefore, only one blade of the turbine is modeled in a sector of 120°, and the hub is not considered in the present CFD model. This could improve modeling efficiency and computational accuracy. The turbine performance is analyzed for a yaw angle of 0∘, in other words, the velocity direction at the inlet is normal to the boundary. The velocity inlet boundary condition, i.e., a uniform and steady velocity is applied normal to the inlet boundary, located at 3D upstream. At 6D downstream, a pressure outlet boundary condition is applied on the outlet boundary, i.e., a reference pressure is given over the outlet boundary. On the top and the bottom boundary, the symmetry condition is applied to ensure no stress at outer boundaries. Between the adjacent subdomains, non-matching interfaces are applied on the overlap faces, and simple linear interpolation is utilized for the transport of the flow properties through the interfaces.
for the power coefficient with the coarse (0.78 million cells), medium (1.32 million cells), and fine (2.53 million cells) meshes in the rotational zone at TSR = 5. As illustrated in Fig. 4, when the cell number of the rotational zone is more than 1.32 million, the variation of the power coefficient is quite small. The relative difference of Cp between the medium meshes and the fine meshes is 0.98%, thus the effect of the cell number on the power coefficient is believed to be small. 3.4. Validation and result The validation result of the present CFD model is presented in Fig. 5, the power coefficient (CP = QΩ/0.5ρu3A , where Q, Ω, A are the torque of the turbine, the angular velocity of the turbine and the blade swept area, respectively) of the CFD results is compared with the experimental data over a range of TSRs (TSR = ΩR/ u , where R is the blade radius) [19,26]. In order to obtain a target TSR, the towing speed is changed while the turbine's angular velocity keeps constant (270 rpm) for both the experiments and the CFD simulations. The present CFD results agree well with the experimental data, but there still existed some quantitative discrepancies. Both the optimum TSRs occurred at approximately TSR = 5, where the CFD's Cp is about 0.408 and the experiment's Cp is about 0.422, the relative error is about 3.3%. The maximum relative error appeared at approximately TSR = 7.4, whose value is about 7.7%. The pressure coefficient contours with the streamlines on the selected span sections (r/R = 0.95/0.75/0.5/0.25) at TSR = 5 are demonstrated in Fig. 6, the pressure coefficient is defined by:
3.3. Grid strategy As illustrated in Fig. 3, the computational domain is divided in two zones, the stationary zone and the rotational zone. Due to the simple geometries in the stationary zone, approximately 0.24 million structured cells are generated to reduce the whole grids number and at the same time accelerate solution convergence and improve computational accuracy. In consideration of the complex geometries in the rotational zone, unstructured cells are meshed there to avoid the difficulty of mesh generation and improve computational efficiency. Due to the rotation of the blade, the flow near the blade tip, the leading edge and trailing edge is much complex. Therefore the rotational zone is divided into two subdomains to generate finer meshes near the blade surface to get a proper y+ and acquire accurate performance of the turbine blade. The y + of the blade surface is in the range of 30–300 which is acceptable for the high-Reynolds-number k − ω SST model. The grid-dependence in the computational simulations is assessed
Cpress =
P − Pref 0.5ρu2
where P and Pref are the local and the reference hydrostatic pressures, respectively. At the optimum TSR, the typical pattern for pressure distribution on the blade surface is well reproduced. The low pressure region on the suction side and the high pressure region on the pressure
Fig. 2. Tidal turbine blade. 3
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Fig. 3. Computational domain with boundary conditions.
side near the blade tip are observed. It's the pressure difference between the two sides that generates the lift force on the blade and thereby, the torque on the turbine to convert tidal energy. From the picture, it could be concluded that most of the power is produced near the blade tip, where most of the net pressure difference is produced. A well-behaved attached flow is observed at most of the span sections, which is correspond with the highest power production produced at TSR = 5. However, a near-separation flow occurred at 0.25 span section (which near the blade root transit from ellipse to airfoil) due to its large angle of attack. This would result in negative effect on the power production. 3.5. Discretization error The grid convergence index (GCI) is adopted to evaluate discretization error. Given by Noruzi, the numerical simulation result is acceptable if the grid refinement ratio is greater than 1.3, and the order of accuracy (p) and GCI can be given as Eqs. (10) and (11) [27].
ln
Fig. 4. Grid-dependence assessment.
(φM − φC ) (φF − φM )
+ ln
p=
GCI = Fs
(
nM / nC − sign ((φF − φM ) / (φM − φC )) nF / nM − sign ((φF − φM ) / (φM − φC ))
ln(nM / nC ) (φM − φF )/ φF nM / nC − 1
) (10)
(11)
where φ is the simulation variable such as rotor power output, pressure, velocity or lift coefficient, n is the grid number, the subscript F, M, C are the fine, medium and coarse grid, Fs is a safety factor equals 1.25. The order of accuracy and the GCI are 3.18 and 0.0029, respectively. It demonstrates that the numerical simulation result could be guaranteed. 4. The design of HACT with winglet The blade of the turbine is the key component to convert the tidal energy. Generally, the design of the blade is to select the appropriate types of the airfoils for corresponding section along the wingspan, and optimize its chord and twist angle to acquire the most lift-drag ratio. However, as mentioned before, the finite wingspan blade would produce tip vortices and suffer from the induced drag, which would cause power lose and affect the hydrodynamic performance. The winglet is utilized to reduce the intensity of the tip vortex and improve the hydrodynamic performance of HACT. The winglet is an effective way to weaken the tip vortex, which is able to carry a hydrodynamic load that produces a flow field that interacts with that of
Fig. 5. Validation of the CFD model.
4
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Fig. 6. Pressure coefficient contours with streamlines on selected span sections.
the main wing thereby reduces the amount of spanwise flow, thus the induced drag is reduced [23]. Adding winglets to HACT also causes an increase in wetted area and a corresponding increase in the profile drag [24]. The profile drag, which caused by viscosity of the water and the pressure drag, would make some energy taken from the water. The profile drag contribution of the winglet is more straight forward than that of the induced drag. Therefore, the design goal of a winglet is to produce the most reduction in induced drag for the smallest increase in profile drag. The profile drag is hard to predict, because it depends on many factors such as the wetted area of the blade, the shape of the blade airfoil and the angle of the attack [25]. However, the induced drag is also affected by these factors. Thus, it is hard to tradeoff and predict. Therefore, to get a proper design for HACT, the parameter study is necessary. In order to investigate the winglet design of HACT, only the blade tip of the baseline turbine is modified, while the other part kept the same. Besides, each design is insured to make the blade length constant. Firstly, two winglets are designed as an initial design stage to introduce the winglet concept to HACT. The configuration 1 of the two conceptual designs is demonstrated as Fig. 7. The three main parameters to define the winglet are illustrated in Fig. 8. The blade of configuration 1 is mounted with a blended winglet. The intersection between the blade tip and winglet is a smooth curve instead of a sharp angle to reduce the intersection drag formed at the junction of the blade and the winglet. The winglet bent towards the pressure side with the cant angle keep at
Fig. 7. Configuration1 of the conceptual design.
about 90∘. Each section shape of the winglet took the profile of ellipse with 16:1 major to minor axis ratio. The center line of the winglet is tangent to the center of the chord of the blade tip. The tip chord and height are 8 mm and 15 mm, respectively. The design of configuration 2 is the same as configuration 1 except that the winglet bends towards the suction side. Then, based on the conceptual design investigation results, the configuration 2 is modified with different parameters to investigate the effect of winglet length, tip chord and cant angle on the power efficiency.
5. Results and discussion The hydrodynamic performance of the HACTs with winglets is 5
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Fig. 8. Main parameters to define the winglet.
As shown in the picture, on 0.95 span section, from leading edge to about 0.5 chord, the pressure coefficient on pressure side of configuration 1 increases slightly compared with that of the baseline turbine. However, on the suction side, the pressure coefficient decreased slightly at most of the position. On the pressure side of configuration 2, the pressure coefficient also exhibited a slight increment. However, the pressure coefficient on the suction side decreased evidently compared with that of the baseline turbine. Therefore, the gap of the pressure coefficient between the pressure side and suction side of configuration 1 exhibited a slight decline. On the contrary, the gap of the pressure coefficient of configuration 2 is larger than that of the baseline turbine evidently. Thus the winglet of configuration 2 provided better flow pattern and generated higher torque near the blade tip region. Nevertheless, the negative effect on the torque generation near the blade tip is exhibited the winglet of configuration 1. The winglets have little effect on these sections on 0.75 and 0.5 span section. On 0.25 span section, the section which near the blade root transited from ellipse to airfoil, all the configurations encountered separation flow which have bad effect on the hydrodynamic performance. The difference of the net pressure coefficient of both the configurations with winglets is slight less than that of the baseline turbine, which revealed that the winglets have negative effect on the span near the blade root. It could be seen from Fig. 10, the pressure coefficient in 0.95 span section is the largest, and that of 0.25 span section is the smallest. The pressure coefficients of pressure side and suction side of 0.95 span section are seven and four times than that of 0.25 span section. As a result, the blade root contributes very little to the energy production, and the effect of the winglets on the blade root could be neglected. To reveal how the winglet influence on the tip vortex, the vorticity magnitude contours with streamlines of the three blade configurations behind the blade tip are presented in Figs. 11–13. Each plane of vorticity magnitude is plotted 22 mm far away from the blade tip, and the pressure side is in the right. The intensity of the tip vortices behind the tip of the baseline turbine is the greatest clearly. Both of the winglets suppressed the formation of the tip vortex. However, the intensity of vortex behind the blade tip of configuration 1 is similar to that of the baseline turbine. The intensity of the vortex behind the tip of configuration 2 is much lower than that of the baseline turbine. The vortex is significantly suppressed by the winglet of configuration 2. With the better flow pattern near the blade tip and the suppressed tip vortices, the configuration 2 results in improved power production. Though the winglet of configuration 1 decreases the intensity of the tip vortices as well, it has negative effect on the torque that generated near the blade tip. The torque decrease may be responsible for the power
investigated by the CFD method proposed in Section 2 and compared with that of the baseline turbine. The simulations are performed over a range of TSRs (4–10), where the target TSR is acquired by changing the current speed while kept turbine's angular speed at 270 rpm. 5.1. Conceptual design comparisons The comparisons of the power coefficient between the baseline turbine and the two conceptual designs are given as Fig. 9. As demonstrated in the picture, the power coefficient of the three cases all showed similar trend versus TSR. They all acquired peak power coefficient at approximately TSR = 5. Configuration 2, the winglet of which bent towards the suction side, showed power coefficient improvement at approximately all TSRs. However, configuration 1, the winglet of which bends towards the pressure side, performed power coefficient decline almost at all TSRs. The average decrease rate in Cp of configuration 1 is about 2.4% that of the baseline turbine, while the average increase rate in Cp of configuration 2 is about 3.1% than that of the baseline turbine. The maximum difference between configuration 1 and 2 is 5.03% and 4.34%, respectively. Fig. 10 presents the comparisons of pressure coefficient distribution on four span sections (r/R = 0.95/0.75/0.5/0.25) at TSR = 5 between the baseline turbine and the two conceptual designs. The horizontal axis (x/c) is cross-section of the span normalized.
Fig. 9. Power coefficient comparisons between the baseline turbine and the conceptual designs. 6
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Fig. 10. Comparisons of pressure coefficient distribution on four span sections at TSR = 5.
Fig. 12. Vorticity magnitude contour with streamlines behind the blade tip of configuration 1.
Fig. 11. Vorticity magnitude contour with streamlines behind the blade tip of the baseline turbine.
dubbed configuration l–13 and so on for the other HACTs with different winglet length. The Cp comparisons between the baseline turbine and configuration l − x (x = 10, 13, 15, 17, 19) is shown in Fig. 14. The increase rate in Cp of configuration l − x compared with that of the baseline turbine is demonstrated in Fig. 15. As shown in the Fig. 14, the Cp variation of configuration l − x show similar trend as that of the baseline turbine. All the HACTs with winglet performed power increase almost in all conditions compared with that of the baseline turbine. Overall, from TSR = 4 to TSR = 6.6 the winglet with the longest length results in the highest power coefficient increase of HACT. For each configuration, the increase rate versus TSRs is relatively stable. However, the increase rate in Cp all decreased dramatically from TSR = 6.6 to TSR = 7.4. The trend is consistent with the Cp variation in the same condition. The influence of winglet has little influence on the Cp if the TSR is above 7.4, and the Cp is a decreasing function with respect to TSR. When the TSR is larger than 7.4, the increase rate (except for configuration l–19) almost
decrease of configuration 1. 5.2. Parameter study For configuration 1 showed negative effect on HACT power efficiency, only configuration 2 is modified with different parameters (shown as Fig. 8) to investigate the effect of winglet length, tip chord and cant angle on the power efficiency. 5.2.1. Length effect To examine the effect of the winglet length on the hydrodynamic performance, the winglet length of configuration 2 is modified while other parameters are kept the same. Five HACTs with winglets are compared. The length of the winglets is 10 mm, 13 mm, 15 mm, 17 mm and 19 mm, respectively. The HACT with 10 mm winglet length is dubbed configuration l–10, the HACT with 13 mm winglet length is 7
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Fig. 13. Vorticity magnitude contour with streamlines behind the blade tip of configuration 2.
Fig. 16. Cp comparisons between the baseline turbine and configuration t − y.
all showed growth tendency but chaotic for the low Cp value and random factors. However, the configuration l–17 performed the best power coefficient increment when TSR is larger than 8.2, the power coefficient is still very low as that of the baseline turbine. The highest power increase rate at the optimum TSR (TSR = 5) is 3.82% which is achieved by configuration l–19. In order to acquire a power increase at the whole conditions, the length of the winglet shouldn't be less than 17 mm. 5.2.2. Tip chord effect To examine the effect of winglet tip chord on the hydrodynamic performance, the tip chord of the winglet of configuration l–19 is modified while other parameters are kept the same. Five HACTs with winglets are compared. The tip chords of the winglets are 4 mm, 8 mm, 10 mm, 12 mm and 16 mm, respectively. The HACT with 4 mm winglet tip chord is dubbed configuration t − 4, the HACT with 8 mm winglet tip chord is dubbed configuration t − 8 and so on for the other HACTs with different winglet tip chord. The Cp comparisons between the baseline turbine and configuration t − y (y = 4, 8, 10, 12, 16) is shown in Fig. 16. The increase rate in Cp of configuration t − y compared with that of the baseline turbine is demonstrated in Fig. 17. As demonstrated in Fig. 16, the tip chord of the winglet didn't show that much effect on the performance of HACT as the length. The increase rate in Cp didn't show much regularity along with
Fig. 14. Cp comparisons between the baseline turbine and configuration l − x.
Fig. 15. increase rate in Cp of configuration l − x with baseline turbine.
Fig. 17. increase rate in Cp of configuration t − y with baseline turbine. 8
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dubbed configuration ∂ − 80 and so on for the other HACT with different winglet cant angle. The Cp comparisons between the baseline turbine and configuration ∂ − z (z = 90, 80, 70, 60, 50) is shown in Fig. 18. The increase rate in Cp of configuration ∂-z compared with that of the baseline turbine is illustrated in Fig. 19. As shown in Fig. 19, the increase rate in Cp increased along with the cant angle increased from TSR = 4 to TSR = 6.6. Meanwhile, the effect of the TSR on the increase rate in Cp is not that much. The increase rate in Cp all decreases from TSR = 6.6 to TSR = 7.4, and then increases when TSR is larger than 7.4. Overall, the increase rate in Cp increased along with the cant angle decreased when TSR is larger than 9.2. However, when TSR is larger than 9.2 the power coefficient is quite low(less than 0.2). At the optimum TSR, the best power coefficient is acquired by configuration ∂ − 90, whose Cp is 3.70% higher than that of the baseline turbine. To acquire power increase at the whole conditions, the cant angle of the winglet shouldn't be less than 80∘. Fig. 18. Cp comparisons between the baseline turbine and configuration ∂ − z.
6. Conclusion The influences of the winglet on the hydrodynamic performance of HACT are investigated by CFD in the current research. Two conceptual designs with the winglet bent towards the pressure side or the suction side are designed to introduce the winglet concept to HACT. The CFD results show that only the HACT with the winglet that bent towards the suction side can HACT performed the power improvement at most of the TSRs. The results of the pressure coefficient on selected span sections and the vorticity magnitude contour behind the blade tip with streamlines reveals that, the winglet improve the power production by improving the torque near the blade tip and decreasing the intensity of tip vortices at the same time. Based on the simulation results of the conceptual designs, the parameter study of the HACT with the winglet that bend towards the suction side is conducted to investigate the influences of the length, tip chord and cant angle of the winglet on the hydrodynamic performance of HACT. The power coefficient comparisons results demonstrate that the power production increment depended on the length, the tip chord and the cant angle of the winglet. From TSR = 4 to TSR = 6.6, the power coefficient increases as the winglet length and cant angle increases. The tip chord would influence the power coefficient, but not that much as the other two parameters. All the configurations show a decrement in power coefficient from TSR = 6.6 to TSR = 7.4. The three parameters have significant effect on the power coefficient at high TSR, but no clear variation trends are found. To acquire a power increase at the whole conditions, length, tip chord and cant angle have effect on the hydrodynamics and should be carefully considered.At the optimum TSR, the best design has achieved 4.66% power increase rate compared with that of the baseline turbine.
Fig. 19. increase rate in Cp of configuration ∂ − z with baseline turbine.
the tip chord variation. Only configuration t − 4 and configuration t − 8 performs power increase at whole TSR compared with that of the baseline turbine. The configuration t − 16 with the longest tip chord shows the best power coefficient from TSR = 4 to TSR = 5.4. At the optimum TSR, configuration t − 16 achieves the best power coefficient, which is 4.66% higher than that of the baseline turbine. However, the power increment dramatically decreases when TSR is larger than 5.4. When TSR is larger than 7, the winglet of configuration t − 16 almost shows negative effect in the whole condition. The power coefficient of other configurations don't show much difference from each other from TSR = 4 to TSR = 5.4. The increase rate in Cp all demonstrates a downtrend from TSR = 6.6 to TSR = 7.4. When TSR is larger than 7.4, the HACT with the shortest tip chord performed a rising trend in Cp increase rate and showed the best power coefficient when TSR is larger than 9.2. To make the winglet increase the power production of the baseline turbine in the whole condition, the tip chord of the winglet shouldn't be larger than 8 mm.
Acknowledgments This research is funded by the Marine Renewable Energy Research Project of State Oceanic Administration of China (grant nos. GHME2013GC03 and GHME2015GC01), and the Fundamental Research Funds for the Central University (grant no. 2014044). References [1] M.S. Guney, K. Kaygusuz, Hydrokinetic energy conversion systems: a technology status review, Renew. Sustain. Energy Rev. 14 (2010) 2996–3004. [2] H.R. Charlier, A “sleeper” awakes: tidal current power, Renew. Sustain. Energy Rev. 7 (2003) 515–529. [3] D. Li, S.J. Wang, P. Yuan, An overview of development of tidal current in China: energy resource, conversion technology and opportunities, Renew. Sustain. Energy Rev. 14 (2010) 2896–2905. [4] Y.B. Ma, W.H. Lam, Y.G. Cui, T.M. Zhang, J.X. Jiang, C. Sun, J.H. Guo, S.G. Wang, S.S. Lam, G. Hamill, Theoretical vertical-axis tidal-current-turbine wake model using axialmomentum theory with CFD corrections, Appl. Ocean Res. 79 (2018)
5.2.3. Cant angle effect To examine the effect of winglet cant angle on the hydrodynamic performance of HACT, the cant angle of the configuration t − 4 is modified while other parameters are kept the same. Five HACTs with winglets are compared. The cant angle of the winglets is90∘, 80∘, 70∘, 60∘ and 50∘, respectively. The HACT with 90∘ winglet cant angle is dubbed configuration ∂ − 90, the HACT with 80∘ winglet cant angle is 9
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