Hydrodynamic Performance and Flow Field Characteristics of Tidal Current Energy Turbine with and without Winglets

: In order to gain a more comprehensive understanding of the inﬂuence of winglets on the hydrodynamic performance and ﬂow ﬁeld characteristics of tidal current energy turbines, two different shapes of winglets are designed, and numerical simulation results for turbines with and without winglets are compared and analyzed. The results show that both shapes of winglets can improve the energy conversion efﬁciency, and the winglets with a cant angle (60 ◦ ) are more effective than the ﬂat (0 ◦ ) winglets; the winglets transfer the tip vortices to the winglet tips and weaken the tip vortices, increase the pressure coefﬁcients of the cross-section in the tip region, and inhibit the three-dimensional ﬂow phenomenon in the tip region; the winglets will make the wake axial velocity deﬁcit larger in the near-wake region, and with the axial distance increases, the axial velocity of the wake ﬂow with winglets recovers faster than that without winglets; winglets can make the vortex pairing and breaking of the turbine tip vortex faster, which can also be observed by the change in the turbulent kinetic energy (TKE).


Introduction
Sustainable development has become an increasingly important issue in China with the announcement of a "dual carbon goal" in 2020 and the promotion of sustainable development policies in the 14th Five-Year Plan [1].Transitioning the energy structure to renewable energy is an important way to achieve sustainable development.The oceans contain a large amount of renewable resources, and the development and utilization of ocean energy provides a necessary path for the transformation of the energy structure with great potential [2].Generally speaking, ocean energy includes tidal current energy, tidal energy, wave energy, temperature difference energy, salt difference energy, and so on [3].As tidal current energy has the advantages of strong regularity, predictability, and high energy conversion efficiency of tidal current energy compared with other ocean energy, the development and utilization of tidal current energy turbines have received the attention of many scholars.
Improving the energy conversion efficiency of tidal current energy turbines is an important way to promote the commercialization of tidal current energy turbines.Owing to the influence of the marine environment, the tidal current energy turbine cannot directly increase the blade length to improve the energy conversion efficiency of the turbine [4].Some scholars have used other methods to increase the energy conversion efficiency of tidal current energy turbines.
Cardona-Mancilla et al. [5] conducted numerical simulations of turbines with and without a deflector, and their comparison found that the turbine with a deflector had a higher energy conversion efficiency.Coiro et al. [6] proposed a new type of tidal current energy utilization device, which is also known as an underwater kite; there are two ducted turbines installed on the device, and the device is connected to the seabed through a tether.The movement of the underwater kite enables the velocity of the water flowing through the turbine to be increased to ten times the actual tidal velocity, which can increase the energy conversion efficiency of the turbine.Xiaodong Liu et al. [7] investigated the interaction between two counter-rotating rotors in a counter-rotating tidal current energy turbine and showed that a counter-rotating tidal current energy turbine could balance the axial torque, accelerate the recovery of the wake, and be more conducive to the arrayed layout in the tidal current field.Menghao Fan et al. [8] designed a bionic blade by changing the shape of leading-edge tubercles and found that the turbine equipped with bionic blades had a better energy conversion efficiency at high tip speed ratios, and the structure of the leading edge of the blade also altered the pressure distribution on the suction surface of the blade and the flow separation phenomenon.The above methods, by adding extra parts to the tidal current energy turbine or changing the blade structure of the tidal current energy turbine, can indeed increase the energy conversion efficiency of the turbine, but they will also increase the manufacturing cost and the maintenance cost of the produced equipment.
When the fluid passes through the blades, the fluid will flow from the pressure surface to the suction surface, generating radial flow, which results in the formation of tip vortices as well as the generation of induced drag [9].This phenomenon leads to a reduction in the energy conversion efficiency of the turbine, which cannot approach the theoretical efficiency of Betz's Law.By adding winglets at the tip of the blade, this phenomenon can be suppressed, the energy loss at the tip of the blade can be reduced, and some of the energy wasted in the tip vortex can be converted into apparent thrust, which improves the energy conversion efficiency of the turbine.Initially, winglets were used on the wings of airplanes, and with the commercialization of wind turbines, researchers used winglets on horizontal axis wind turbine blades.Gupta et al. [10] performed numerical simulations using the single-blade analysis method by varying the height and cant angle of the winglet at the tip of the wing, with the winglet facing toward the pressure plane, and found that the winglet with a cant angle of 45 • performed better than the winglet with a cant of 90 • .Khaled et al. [11] analyzed the performance of horizontal axis wind turbines with and without winglets through numerical simulation and the results showed that the presence of a winglet at the tip of the wing showed a significant increase in the power and thrust coefficients, and the best performance improvement was observed when the winglet length was 6.32% and cant angle was 48.3 • .Mourad et al. [12] investigated the effect of winglet geometry on the performance of horizontal axis wind turbines and found that the power coefficient increased with increasing toe angle and reached its maximum at a toe angle of 20 • .Saravanan et al. [13] investigated the effect of winglets on the performance of horizontal-axis wind turbines through modeling tests and found that the wind turbine with winglets could capture more wind energy in low-wind-speed regions.Mühle et al. [14] conducted an experimental study on the near wake characteristics of a horizontal axis wind turbine with winglets.Their experiments investigated the near-wake in 4D behind the rotor, and it was found that the optimized winglets not only contributed to the energy extraction at the tip of the blade, but also accelerated the tip vortex interactions, which had a positive effect on the recovery of the mean kinetic energy of the wake.
As the blade size of a horizontal-axis tidal turbine is smaller than that of a horizontalaxis wind turbine, the positive effect of winglets on reducing the tip energy loss will be more obvious than in the wind turbine [15].In recent years, some scholars have applied winglets to horizontal-axis tidal turbines.Nedyalkov et al. [16] studied the effect of winglets on tip vortex cavitation in tidal turbines and found that, at higher angles of attack, winglets had a significant advantage in suppressing tip vortices.Zhu et al. [17] studied the issue of winglet tip orientation using numerical simulation and produced three design options for winglet tip orientation by adding winglets to the suction and pressure surfaces alone, as well as by adding winglets to both sides, and found that the addition of winglets had a positive effect on the turbine's energy conversion efficiency in general, but the power of the turbine with winglets added to both sides increased more.Ren et al. [18] designed and studied the hydrodynamic performance of three types of horizontal-axis tidal current energy turbines with different winglets and found that the turbine with triangular winglets had the best hydrodynamic performance, with a power factor increase of 4.34% at the optimal tip speed ratio.Kunasekaran et al. [19] designed and optimized the cant angle and height of the winglets and found that a cant angle of 33.2 • and a height of 2.04%R resulted in a decreased area of the return zone at the trailing edge of the winglet, a larger pressure gradient, and a 7% increase in the power coefficient of the turbine.Barbarić et al. [15] investigated the effects of winglet height and sweep angle on the hydrodynamic performance and flow field characteristics of a horizontal-axis tidal current energy turbine using numerical simulation and found that the power coefficient of the turbine increased with an increase in the winglet height when the tip-speed ratio was greater than 3.5; meanwhile, the maximum increase in power coefficient for all tip speed ratios occurred at a sweep angle of 40 • and turbines with winglets created stronger vortices in the far-wake region, which may have had an effect on the turbines in the array.Olvera-Trejo [4] experimentally investigated the hydrodynamic performance of horizontal-axis tidal turbines with winglets using an oil-based paint flow visualization technique to determine the mechanism behind the phenomenon of winglets affecting the suction side, and the experimental results showed that the winglet should be oriented toward the pressure surface.
In this paper, two different shapes of winglets were designed, firstly, to compare the hydrodynamic performance of the tidal current energy turbine with and without winglets and to analyze the reasons for the influence of winglets on the hydrodynamic performance in terms of the changes in the pressure coefficients of the blade cross-section and vortices at the tip of the blade, and secondly, to study the influence of the winglets on the wake field of the tidal current energy turbine by comparing the recovery of the mean axial velocity of the wake flow and the evolution of the wake vortices of the tidal current energy turbine without winglets and with winglets.The effects of winglets on the wake field characteristics of tidal current energy turbines are investigated.

Tidal Current Energy Turbine Model
The tidal current energy turbine model used in this paper originates from previous work, and was developed by the Institute of Marine Renewable Energy of Harbin Engineering University [20,21].The turbine blade was designed using the leaf element body momentum theory (BEM), and the specific design parameters are shown in Table 1.r is the direction along the blade radius and R is the blade radius; to ensure the strength of the root of the turbine blade, the transition region of the blade root is within the interval of r/R = 0.15-0.20,and the airfoils at the positions within the interval of r/R = 0.20-1.0are adopted in the S809 airfoils; Figure 1a shows the distribution of chord lengths and torsion angles at different radiuses of the blade, and Figure 1b shows the distribution of chord lengths and torsion angles at different radiuses of the blade.In the preliminary experimental study, the 3D model of this tidal current energy turbine was machined and fabricated by a five-axis CNC machine tool, and its hydrodynamic performance tests and PIV flow field measurements were carried out in the towing pool laboratory and circulating flume laboratory of Harbin Engineering University, respectively.The hydrodynamic performance tests in the towing pool laboratory are described in reference [22].The PIV flow field measurement experiments in the recirculation tank laboratory are shown in Figure 2b, where a movable table was used to facilitate the adjustment of the position of the tidal energy turbine in the experimental section of the circulating flume, as well as the flow field measurement.In the preliminary experimental study, the 3D model of this tidal current energy turbine was machined and fabricated by a five-axis CNC machine tool, and its hydrodynamic performance tests and PIV flow field measurements were carried out in the towing pool laboratory and circulating flume laboratory of Harbin Engineering University, respectively.The hydrodynamic performance tests in the towing pool laboratory are described in reference [22].The PIV flow field measurement experiments in the recirculation tank laboratory are shown in Figure 2b, where a movable table was used to facilitate the adjustment of the position of the tidal energy turbine in the experimental section of the circulating flume, as well as the flow field measurement.

Model of Tidal Current Energy Turbine with Winglets
The winglet concept first appeared in jet airplanes, and the main design parameters of winglets are the airfoil shape, chord length distribution, height, radius of curvature, twist angle, sweep angle, cant angle, and toe angle [9].In this study, the height, radius, cant angle, and chord length distribution of the winglet were mainly designed as shown in Figure 3.The airfoil shape used for the winglets was kept the same as the airfoil shape of the blade tip section, and the wing chord length of the winglet tip was kept the same as the wing chord length of the blade tip; as the designed winglets were all facing the suction   In the preliminary experimental study, the 3D model of this tidal current energy turbine was machined and fabricated by a five-axis CNC machine tool, and its hydrodynamic performance tests and PIV flow field measurements were carried out in the towing pool laboratory and circulating flume laboratory of Harbin Engineering University, respectively.The hydrodynamic performance tests in the towing pool laboratory are described in reference [22].The PIV flow field measurement experiments in the recirculation tank laboratory are shown in Figure 2b, where a movable table was used to facilitate the adjustment of the position of the tidal energy turbine in the experimental section of the circulating flume, as well as the flow field measurement.

Model of Tidal Current Energy Turbine with Winglets
The winglet concept first appeared in jet airplanes, and the main design parameters of winglets are the airfoil shape, chord length distribution, height, radius of curvature, twist angle, sweep angle, cant angle, and toe angle [9].In this study, the height, radius, cant angle, and chord length distribution of the winglet were mainly designed as shown in Figure 3.The airfoil shape used for the winglets was kept the same as the airfoil shape of the blade tip section, and the wing chord length of the winglet tip was kept the same as the wing chord length of the blade tip; as the designed winglets were all facing the suction

Model of Tidal Current Energy Turbine with Winglets
The winglet concept first appeared in jet airplanes, and the main design parameters of winglets are the airfoil shape, chord length distribution, height, radius of curvature, twist angle, sweep angle, cant angle, and toe angle [9].In this study, the height, radius, cant angle, and chord length distribution of the winglet were mainly designed as shown in Figure 3.The airfoil shape used for the winglets was kept the same as the airfoil shape of the blade tip section, and the wing chord length of the winglet tip was kept the same as the wing chord length of the blade tip; as the designed winglets were all facing the suction surface, the design parameters of the winglets were defined based on the winglets facing the suction surface, the cant angle was measured from the blade plane toward the suction surface, and the height of the winglet was the percentage of the blade radius; the specific design parameters defining the geometry of the winglet are shown in Table 2.As shown in Figure 4, two types of tidal current energy turbines with winglets, W1 and W2, were designed in this study, among which W1 adopted a circular transition with a certain height at the connection between the winglet and the blade to ensure the strength of the winglet and the blade connection.
height at the connection between the winglet and the blade to ensure the strength of the winglet and the blade connection.

Control Equations
Numerical simulation of the tidal current energy turbine with winglets is carried out following the CFD method, in which the Navier-Stokes equations for incompressible viscous fluid are used for the controlling equations, and the equations of conservation of mass and momentum are shown in Equations ( 1) and ( 2).The finite volume method (FVM) is used to discretize the control equations, and the second-order upwind scheme (SOUS) is used to determine the difference in the discretized equations; the SST k-ω turbulence model is used to close the discretized equations, and the discretized equations are solved by the SIMPLE method.design parameters defining the geometry of the winglet are shown in Table 2.As shown in Figure 4, two types of tidal current energy turbines with winglets, W1 and W2, were designed in this study, among which W1 adopted a circular transition with a certain height at the connection between the winglet and the blade to ensure the strength of the winglet and the blade connection.

Control Equations
Numerical simulation of the tidal current energy turbine with winglets is carried out following the CFD method, in which the Navier-Stokes equations for incompressible viscous fluid are used for the controlling equations, and the equations of conservation of mass and momentum are shown in Equations ( 1) and ( 2).The finite volume method (FVM) is used to discretize the control equations, and the second-order upwind scheme (SOUS) is used to determine the difference in the discretized equations; the SST k-ω turbulence model is used to close the discretized equations, and the discretized equations are solved by the SIMPLE method.

Control Equations
Numerical simulation of the tidal current energy turbine with winglets is carried out following the CFD method, in which the Navier-Stokes equations for incompressible viscous fluid are used for the controlling equations, and the equations of conservation of mass and momentum are shown in Equations ( 1) and ( 2).The finite volume method (FVM) is used to discretize the control equations, and the second-order upwind scheme (SOUS) is used to determine the difference in the discretized equations; the SST k-ω turbulence model is used to close the discretized equations, and the discretized equations are solved by the SIMPLE method.
To describe the hydrodynamic performance of the tidal current energy turbine, the dimensionless parameters of the tip speed ratio (λ), energy conversion efficiency (C P ), and drag coefficient (C D ) are defined as follows: where Ω: angular velocity of turbine rotation, (rad/s); R: radius of turbine, m; U T : incoming flow velocity, (m/s); Q: torque generated by the turbine, (N•m); ρ: fluid density, (kg/m 3 ); D: axial resistance arising from the rotating work of turbine, (N); A T : swept area of turbine, (m 2 ).

Boundary Conditions and Meshing
In this study, only the computational domain of the numerical simulation of the tidal current energy turbine with winglets is described, but the definition of the boundary conditions and the mesh delineation are consistent with those of the numerical simulation of the tidal current energy turbine without winglets.The size of the computational domain for numerical simulation is consistent with the size of the PIV flow field measurement test section described in the previous section.To unify the reference value, the reference value of the computational domain size in this paper is the diameter of the turbine without winglets D. The basin inlet boundary condition is set as a uniform velocity inlet with an inlet turbulence intensity of 1%, which is located at 10 D upstream of the turbine, and the basin outlet boundary condition is set as a pressure outlet, which is located at about 26 D downstream of the turbine; Figure 5 presents the detailed boundary condition settings.As shown in Figure 5, the coordinate axes in this paper are defined as the x-axis direction being inward in the vertical paper direction, y-axis direction being vertically upward, and z-axis direction being horizontally to the right; special attention is paid to the direction of the coordinate axes considering that the positive and negative relationships of the flow velocity are closely related to the direction of the coordinate axes.The numerical computation domain is equipped with a rotational domain and a stationary domain, and the data are transferred through the interface between them.The tidal current energy turbine with winglets is located in the rotational domain, and the solver adopts an implicit unsteady model during the numerical simulation process; the time step is the time needed to rotate the blades by 3°.In mesh encryption, to further reflect the flow characteristics of the tip and root of the turbine blade, this study carries out body encryption for these two regions.In addition, the leading edge, following edge, suction surface, pressure surface, and marking of the turbine blade and the winglets on the blade are marked, and the marked feature lines and feature surfaces are encrypted by using the curve control and the surface control; Figure 6 shows a grid diagram of a tidal current energy turbine with winglets.The numerical computation domain is equipped with a rotational domain and a stationary domain, and the data are transferred through the interface between them.The tidal current energy turbine with winglets is located in the rotational domain, and the solver adopts an implicit unsteady model during the numerical simulation process; the time step is the time needed to rotate the blades by 3 • .In mesh encryption, to further reflect the flow characteristics of the tip and root of the turbine blade, this study carries out body encryption for these two regions.In addition, the leading edge, following edge, suction surface, pressure surface, and marking of the turbine blade and the winglets on the blade are marked, and the marked feature lines and feature surfaces are encrypted by using the curve control and the surface control; Figure 6 shows a grid diagram of a tidal current energy turbine with winglets.
time step is the time needed to rotate the blades by 3°.In mesh encryption, to further reflect the flow characteristics of the tip and root of the turbine blade, this study carries out body encryption for these two regions.In addition, the leading edge, following edge, suction surface, pressure surface, and marking of the turbine blade and the winglets on the blade are marked, and the marked feature lines and feature surfaces are encrypted by using the curve control and the surface control; Figure 6 shows a grid diagram of a tidal current energy turbine with winglets.The grid independence of the numerical simulation method used in this paper was verified in detail in the authors previous work [23] and analyzed accordingly using Richardson extrapolation [24,25], which will not be repeated in this paper.

Validation of Numerical Simulation Method
To verify the numerical simulation method used in this study more comprehensively, the numerical simulation results of the tidal current energy turbine without winglets were used in this study for verification.Firstly, the authors compared the experimental results The grid independence of the numerical simulation method used in this paper was verified in detail in the authors' previous work [23] and analyzed accordingly using Richardson extrapolation [24,25], which will not be repeated in this paper.

Validation of Numerical Simulation Method
To verify the numerical simulation method used in this study more comprehensively, the numerical simulation results of the tidal current energy turbine without winglets were used in this study for verification.Firstly, the authors compared the experimental results and numerical simulation results of the hydrodynamic performance of the tidal current energy turbine without winglets, and Figure 7 shows the comparison between the energy conversion efficiency and the drag coefficient of the turbine without winglets under a flow velocity of 1.5 m/s.and numerical simulation results of the hydrodynamic performance of the tidal current energy turbine without winglets, and Figure 7 shows the comparison between the energy conversion efficiency and the drag coefficient of the turbine without winglets under a flow velocity of 1.5 m/s.In Figure 7, it can be firstly seen that the numerical simulation results of the energy conversion efficiency and drag coefficient of the turbine without winglets were closer to the experimental results of the model, the error between the numerical simulation results of the energy conversion efficiency of the turbine (0.3662) and the experimental results (0.3651) in the design tip speed ratio (λ = 5) was 0.3%, and the error between the numerical simulation results of the drag coefficient of the turbine (0.7334) and the experimental results (0.7610) was −3.63%.It can be verified that the numerical simulation method used in this paper was accurate in solving the hydrodynamic performance of the tidal turbine.In the region with a low tip speed ratio, the error between the numerical simulation results and experimental results was relatively large, which was because the turbine rotational speed was low under a low tip speed ratio, and the water flowed into the turbine blades at a larger angle of attack, resulting in the formation of a larger separation at the trailing edge of the blades, as shown in Figure 8.The existing turbulence model was partially distorted in simulating the separation of the fluid, which led to a large relative error in the energy conversion efficiency of the turbine in the low tip speed ratio.In Figure 7, it can be firstly seen that the numerical simulation results of the energy conversion efficiency and drag coefficient of the turbine without winglets were closer to the experimental results of the model, the error between the numerical simulation results of the energy conversion efficiency of the turbine (0.3662) and the experimental results (0.3651) in the design tip speed ratio (λ = 5) was 0.3%, and the error between the numerical simulation results of the drag coefficient of the turbine (0.7334) and the experimental results (0.7610) was −3.63%.It can be verified that the numerical simulation method used in this paper was accurate in solving the hydrodynamic performance of the tidal turbine.
In the region with a low tip speed ratio, the error between the numerical simulation results and experimental results was relatively large, which was because the turbine rotational speed was low under a low tip speed ratio, and the water flowed into the turbine blades at a larger angle of attack, resulting in the formation of a larger separation at the trailing edge of the blades, as shown in Figure 8.The existing turbulence model was partially distorted in simulating the separation of the fluid, which led to a large relative error in the energy conversion efficiency of the turbine in the low tip speed ratio.In the region with a low tip speed ratio, the error between the numerical sim results and experimental results was relatively large, which was because the turbi tional speed was low under a low tip speed ratio, and the water flowed into the blades at a larger angle of attack, resulting in the formation of a larger separatio trailing edge of the blades, as shown in Figure 8.The existing turbulence model w tially distorted in simulating the separation of the fluid, which led to a large relati in the energy conversion efficiency of the turbine in the low tip speed ratio.The near-domain flow field numerical simulation results of the tidal turbine without winglets were compared with the experimental results of PIV flow field measurement.Before comparing and analyzing the near-domain flow field characteristics of the hydraulic turbine, firstly, the method of selecting velocity profiles in this study is described, such as the A-A profile in Figure 5, which is the selected velocity profile; since the numerical simulation adopted the non-constant computation, the axial flow rate and radial flow rate in this paper comparing the numerical simulation of the turbine with the modeling experiments was the instantaneous flow rate, not the average flow rate of the profiles.In this paper, the velocity profile was selected by intercepting the longitudinal profile A-A (numerical simulation)/laser sheet light (model experiment) in the basin, and then intersecting the transverse profile with the longitudinal profile A-A at distances of 0.5 D, 0.1 D, and 0.05 D in front of the blade and behind the blade, respectively, to further obtain the flow velocity data of the profiles at different axial positions of the blades at a distance of the turbine in the proximity domain.Figure 9 shows the comparison of numerical simulation and experimental results of the axial flow velocity and radial flow velocity in the near-domain flow field of the hydraulic turbine without winglets at different profiles at 0.8 m/s flow velocity.
As can be seen in Figure 9, the numerical simulation results of the near-domain flow field of the turbine without winglets were in good agreement with the experimental results, which further verified the accuracy of the numerical simulation method used in this paper.Comparing the instantaneous axial flow velocity and radial direction at 0.5 D, 0.1 D, and 0.05 D profile positions in front of the blade (Figure 9a-c), it can be seen that, close to the turbine blade, the axial flow velocity in the blade region showed a gradual decreasing tendency.Meanwhile, the radial flow velocity was close to 0 in front of the blade at 0.5 D, but accompanied by the closer the distance to the turbine disk, the radial velocity showed a gradually increasing tendency with the increase in radius in the blade region; however, after passing through the tip of the blade, there was a rapidly decreasing trend.In addition, as shown in Figure 9c, at the 0.05 D profile in front of the blade, the axial velocity at the blade region was about 0.53 m/s, and the axial flow velocity at the blade under the Betz's Law-deduced limiting energy conversion efficiency (0.593) was 0.5333 m/s (incoming velocity 0.8 m/s), which shows that the axial velocity at the turbine blade stayed in the same line as the theoretical axial velocity, but the energy conversion efficiency of the turbine without winglets under the design tip speed ratio was 0.345 (incoming velocity 0.8 m/s).To explore the reason for the decrease in the energy conversion efficiency compared with the Betz limit efficiency, this paper further analyzes the distribution of axial and radial velocities at the different profiles after the blades.
The near-domain flow field numerical simulation results of the tidal turbine without winglets were compared with the experimental results of PIV flow field measurement.Before comparing and analyzing the near-domain flow field characteristics of the hydraulic turbine, firstly, the method of selecting velocity profiles in this study is described, such as the A-A profile in Figure 5, which is the selected velocity profile; since the numerical simulation adopted the non-constant computation, the axial flow rate and radial flow rate in this paper comparing the numerical simulation of the turbine with the modeling experiments was the instantaneous flow rate, not the average flow rate of the profiles.In this paper, the velocity profile was selected by intercepting the longitudinal profile A-A (numerical simulation)/laser sheet light (model experiment) in the basin, and then intersecting the transverse profile with the longitudinal profile A-A at distances of 0.5 D, 0.1 D, and 0.05 D in front of the blade and behind the blade, respectively, to further obtain the flow velocity data of the profiles at different axial positions of the blades at a distance of the turbine in the proximity domain.Figure 9 shows the comparison of numerical simulation and experimental results of the axial flow velocity and radial flow velocity in the near-domain flow field of the hydraulic turbine without winglets at different profiles at 0.8 m/s flow velocity.As can be seen in Figure 9, the numerical simulation results of the near-domain flow field of the turbine without winglets were in good agreement with the experimental results, which further verified the accuracy of the numerical simulation method used in this paper.Comparing the instantaneous axial flow velocity and radial direction at 0.5 D, 0.1 D, and 0.05 D profile positions in front of the blade (Figure 9a-c), it can be seen that, close to the turbine blade, the axial flow velocity in the blade region showed a gradual decreasing tendency.Meanwhile, the radial flow velocity was close to 0 in front of the blade at 0.5 D, but accompanied by the closer the distance to the turbine disk, the radial velocity showed a gradually increasing tendency with the increase in radius in the blade region; however, after passing through the tip of the blade, there was a rapidly decreasing trend.In addition, as shown in Figure 9c, at the 0.05 D profile in front of the blade, the axial As shown in Figure 9c,f, comparing the radial velocity distribution at the 0.05 D profile in front of the blade and the 0.05 D profile after the blade, the radial velocity at the tip of the leaf in front of the blade was +0.236 m/s, and the radial velocity at the tip of the leaf after the blade was −0.142 m/s.It should be noted that the positive and negative of the radial velocity were related to the coordinate system, which was positive in the same direction as the coordinate axis and negative in the opposite direction, and the coordinate axis is shown in Figure 5. Through the above comparison, it can be seen that, in front of the blade, the radial flow velocity flows to the tip of the blade and shows a gradually increasing trend in the blade area; after the blade, the fluid at the tip of the blade flows to the blade root area, which has an obvious "downwash" trend, and then produces an obvious three-dimensional effect in the tip of the blade area, which decreases the energy conversion efficiency of the turbine without the winglets.

Hydrodynamic Performance of Tidal Current Energy Turbine with Winglets
Numerical simulation of a tidal current energy turbine with winglets was carried out using the numerical simulation method verified earlier.Firstly, the hydrodynamic performances of the tidal current energy turbines with winglets and without winglets were compared under a flow velocity of 1.5 m/s. Figure 10 shows a comparison of the energy conversion efficiencies and drag coefficients of the turbine without winglets and the turbine with winglets in W1 and W2.From Figure 10, it can be seen that the energy conversion efficiency of the turbine with winglets was significantly higher than that of the turbine without winglets, and the increase reached the peak value under the designed tip speed ratio of 5.With a design tip speed ratio of 5, the energy conversion efficiency of the turbine with winglets was 46%, that of the turbine without winglets was 36.6%, and the energy conversion efficiency of the turbine with winglets was increased by 25.7%.The energy conversion efficiency of W2 was lower than that of W1, but with the increase in tip speed ratio, the energy conversion efficiency of W2 was higher than that of W1 when the tip speed ratio was more than 6.The drag coefficients of W1 and W2 were larger than that of the turbine without winglets, and the difference in their drag coefficients was larger with the increase in tip speed ratio.To analyze the causes of the above phenomenon, the distribution of pressure coefficients at five cross-sections of 30%, 47%, 63%, 95%, and 98% of the length of the blade spread along the blade length of the turbine without winglets, W1, and W2, is provided in this paper, as shown in Figure 11.The pressure coefficients are defined as follows: where P : local static pressure, (Pa); P ∞ : free-stream static pressure, (Pa); U ∞ : incoming velocity, (m/s); r: radial distance from hub center to blade section, (m); ρ : fluid density, (kg/m 3 ); and ω : angular velocity, (rad/s).To analyze the causes of the above phenomenon, the distribution of pressure coefficients at five cross-sections of 30%, 47%, 63%, 95%, and 98% of the length of the blade spread along the blade length of the turbine without winglets, W1, and W2, is provided in this paper, as shown in Figure 11.The pressure coefficients are defined as follows: where P: local static pressure, (Pa); P ∞ : free-stream static pressure, (Pa); U ∞ : incoming velocity, (m/s); r: radial distance from hub center to blade section, (m); ρ: fluid density, (kg/m 3 ); and ω: angular velocity, (rad/s).
A comparison of the pressure coefficients of different cross sections of the blades of the three tidal energy turbines with W1, W2, and without winglets is presented in Figure 11.
From Figure 11, it can be seen that, in the cross-section near the tip of the blade (98%, 95%), the pressure coefficients with winglets were significantly larger than those without winglets, and the increase in the pressure coefficients was reflected on the suction side of the blade since the winglets were designed to be oriented towards the suction side.With the intercepted blade section near the root, it can be seen from the figure that the pressure coefficients with and without winglets were almost the same, at 63%, 47%, and 30% of the blade length.It can be seen that the winglets had a positive effect on the increase in the pressure coefficient on the suction surface at the tip of the blade, which meant that the winglets enabled the blade tip to generate more torque.Second, the cant angle of the winglets of W1 was 60 • , while the cant angle of the winglets of W2 was 0 • ; comparing the 98% and 95% of the blade section of W1 and W2, it can be seen that the pressure coefficient of W1 increased more than the pressure coefficient of W2, and the cant angle of the winglets of 60 • had a positive effect on the increase in the pressure coefficient of the blade section.
To further analyze the effect of winglets on the fluid flow at the blade tip, the vorticity iso-surfaces at the tip of the blade without winglets and at the tip of the winglet with W1 under the design tip speed ratio were compared, as shown in Figure 12.A comparison of the pressure coefficients of different cross sections of the blades of the three tidal energy turbines with W1, W2, and without winglets is presented in Figure 11.From Figure 11, it can be seen that, in the cross-section near the tip of the blade (98%, 95%), the pressure coefficients with winglets were significantly larger than those without winglets, and the increase in the pressure coefficients was reflected on the suction side of the blade since the winglets were designed to be oriented towards the suction side.With the intercepted blade section near the root, it can be seen from the figure that the pressure coefficients with and without winglets were almost the same, at 63%, 47%, and 30% of the blade length.It can be seen that the winglets had a positive effect on the increase in the pressure coefficient on the suction surface at the tip of the blade, which meant that the winglets enabled the blade tip to generate more torque.Second, the cant angle of the winglets of W1 was 60°, while the cant angle of the winglets of W2 was 0°; comparing the 98% and 95% of the blade section of W1 and W2, it can be seen that the pressure coefficient of W1 increased more than the pressure coefficient of W2, and the cant angle of the winglets of 60° had a positive effect on the increase in the pressure coefficient of the blade section.
To further analyze the effect of winglets on the fluid flow at the blade tip, the vorticity isosurfaces at the tip of the blade without winglets and at the tip of the winglet with W1 under the design tip speed ratio were compared, as shown in Figure 12.As can be seen in Figure 12, the tip of the turbine blade without winglets generated tip vortices, whereas the tip vortices of the blade of W1 were transferred to the winglet tips, weakening the strength of the tip vortices and suppressing the three-dimensional flow effect in the blade tip region to a certain extent, thereby improving the hydrodynamic performance of the tidal current energy turbine.

Flow Field Characterization of Tidal Current Energy Turbine with Winglets
To investigate the effect of winglets on the wake field characteristics of tidal current energy turbines, firstly, this study compared the downstream mean axial velocities with- As can be seen in Figure 12, the tip of the turbine blade without winglets generated tip vortices, whereas the tip vortices of the blade of W1 were transferred to the winglet tips, weakening the strength of the tip vortices and suppressing the three-dimensional flow effect in the blade tip region to a certain extent, thereby improving the hydrodynamic performance of the tidal current energy turbine.

Flow Field Characterization of Tidal Current Energy Turbine with Winglets
To investigate the effect of winglets on the wake field characteristics of tidal current energy turbines, firstly, this study compared the downstream mean axial velocities without winglets and W1, and the instantaneous axial velocities were processed using the PyTecplot (1.6.0)module in Tecplot (2020 R1) to obtain the mean axial velocities.Figure 13 shows a comparison of the mean axial velocities without winglets and with W1 at different tip speed ratios (4, 5, and 6).
tip vortices, whereas the tip vortices of the blade of W1 were transferred to the wingle tips, weakening the strength of the tip vortices and suppressing the three-dimensiona flow effect in the blade tip region to a certain extent, thereby improving the hydrodynamic performance of the tidal current energy turbine.

Flow Field Characterization of Tidal Current Energy Turbine with Winglets
To investigate the effect of winglets on the wake field characteristics of tidal current energy turbines, firstly, this study compared the downstream mean axial velocities without winglets and W1, and the instantaneous axial velocities were processed using the PyTecplot (1.6.0)module in Tecplot (2020 R1) to obtain the mean axial velocities.Figure 13 shows a comparison of the mean axial velocities without winglets and with W1 at different tip speed ratios (4, 5, and 6).From Figure 13, it can be seen that two narrow velocity loss regions appeared behind the blade, and the average axial velocity loss in this region was the largest; as the wake moved backward, the two narrow regions would bend toward the center until they met and finally merge with the outer region and return to the initial flow velocity.This phenomenon was due to the inward radial velocities caused by the clogging effect, which has also been reported in other studies [26,27].As the tip speed ratio increased, the location of the intersection of the two narrow regions moved closer to the turbine, which meant that wake velocity recovery was accelerated in the far-wake region.Comparing the cloud From Figure 13, it can be seen that two narrow velocity loss regions appeared behind the blade, and the average axial velocity loss in this region was the largest; as the wake moved backward, the two narrow regions would bend toward the center until they met, and finally merge with the outer region and return to the initial flow velocity.This phenomenon was due to the inward radial velocities caused by the clogging effect, which has also been reported in other studies [26,27].As the tip speed ratio increased, the location of the intersection of the two narrow regions moved closer to the turbine, which meant that wake velocity recovery was accelerated in the far-wake region.Comparing the cloud diagrams under the same tip speed ratio, the winglets could accelerate the intersection of these two narrow regions downstream of the turbine, and at a tip speed ratio of 5, the intersection of the two narrow regions without winglets was at z/D = 12, while the position of W1 was at z/D = 7.To gain a more comprehensive understanding of the downstream wake recovery trend of the tidal energy turbine with and without winglets, the average axial velocities of different sections in the axial direction were intercepted, and Figure 14 shows a comparison of the average axial velocity recovery of different sections of the wake for W1 and the turbine without winglets at the designed tip speed ratio (TSR = 5).From Figure 14, it can be seen that the average axial velocity recovery of W1 in the near-wake region (<4 D) was slower than that without winglets; having winglets made the axial velocity deficit in the near-wake region of the turbine larger.However, as the axial distance (>8 D) increased, the mean axial velocity recovery of the wake was faster in W1 than without winglets.To further analyze the influence of winglets on the characteristics of the wake flow field, the structure of the wake vortex without winglets and W1 is given in this study, as shown in Figures 15 and 16.
Figure 14, it can be seen that the average axial velocity recovery of W1 in the near-wake region (<4 D) was slower than that without winglets; having winglets made the axial velocity deficit in the near-wake region of the turbine larger.However, as the axial distance (>8 D) increased, the mean axial velocity recovery of the wake was faster in W1 than without winglets.To further analyze the influence of winglets on the characteristics of the wake flow field, the structure of the wake vortex without winglets and W1 is given in this study, as shown in Figures 15 and 16. Figure 15 shows the equivalent surfaces of the turbine without winglets for Q = 1 at different tip speed ratios (4, 5, and 6) and the x/D = 0 plane, and Figure 16 shows the equivalent surfaces of W1 for Q = 1 at different tip speed ratios (4, 5, and 6) and the x/D = 0 plane.The Q = 1 iso-surfaces in Figures 15 and 16 show that the tip vortex and root vortex were present in all tip speed ratio ranges, while the root vortex was present for a longer time at lower tip speed ratios.The root vortex would merge with the hub vortex in the far-wake region, and at lower tip speed ratios, the long vortex formed by the fusion of the root vortex and the hub vortex underwent meandering and finally broke up.The tip vortex showed a clockwise inclination in the x/D = 0 plane and the inclination of the tip vortex decreased with the increase in the tip speed ratio, as can be seen from the x/D = 0 plane in Figures 15 and 16, which shows that the tip vortex underwent vortex pairing and then broke up and finally became a small-scale structure.As the tip speed ratio increased, the tip vortex pairing was more forward, and at a tip speed ratio of 4, the tip vortex pairing without winglets occurred at z/D = 4, while at tip speed ratios of 5 and 6, the vortex pairing was at z/D = 2 and z/D = 1, respectively.W1 had the vortex pairing of the tip vortex at z/D = 3 at a tip speed ratio of 4, and at tip speed ratios of 5 and 6, the vortex pairing was at z/D = 1 and z/D = 0-1, respectively.It can be seen that W1 had the vortex pairing occurring further forward in the tip vortex than the blade without winglets at the same tip speed ratio.Also, comparing Figures 15 and 16  breakup was closer forward with increasing tip speed ratio, but at the same tip speed ratio, the tip vortex breakup of W1 was faster, and at a tip speed ratio of 5, the tip vortex without winglets was prone to breaking up at about z/D = 8, while the tip vortex breakup of W1 occurred at about z/D = 5.The trailing edge of the blade created a vortex sheet, which was weak at low tip speed ratios and not captured by the Q values used for the iso-surfaces.
The vortex sheet could be seen in the Q = 1 iso-surface plots of Figures 15c and 16c with a tip speed ratio of 6.At a tip speed ratio of 6, the vortex formed by the vortex drained from the trailing-edge vortex vane rotating with the tip vortex is called the trailing-edge vortex, and the trailing-edge vortex does not directly interact with the tip vortex.It can be seen from the figure that the trailing-edge vortex of W1 was stronger than that of the trailingedge vortex without winglets.Figure 15 shows the equivalent surfaces of the turbine without winglets for Q = 1 at different tip speed ratios (4, 5, and 6) and the x/D = 0 plane, and Figure 16 shows the equivalent surfaces of W1 for Q = 1 at different tip speed ratios (4, 5, and 6) and the x/D = 0 plane.The Q = 1 iso-surfaces in Figures 15 and 16 show that the tip vortex and root vortex were present in all tip speed ratio ranges, while the root vortex was present for a longer time at lower tip speed ratios.The root vortex would merge with the hub vortex in the far-wake region, and at lower tip speed ratios, the long vortex formed by the fusion of the root vortex and the hub vortex underwent meandering and finally broke up.The tip vortex showed a clockwise inclination in the x/D = 0 plane and the inclination of the tip vortex decreased with the increase in the tip speed ratio, as can be seen from the x/D = 0 plane in Figures 15 and 16, which shows that the tip vortex underwent vortex pairing and then broke up and finally became a small-scale structure.As the tip speed ratio increased, the tip vortex pairing was more forward, and at a tip speed ratio of 4, the tip vortex pairing without winglets occurred at z/D = 4, while at tip speed ratios of 5 and 6, the vortex pairing was at z/D = 2 and z/D = 1, respectively.W1 had the vortex pairing of the tip vortex at z/D = 3 at a tip speed ratio of 4, and at tip speed ratios of 5 and 6, the vortex pairing was at z/D = 1 and z/D = 0-1, respectively.It can be seen that W1 had the vortex pairing occurring further forward in the tip vortex than the blade without winglets at the same tip speed ratio.Also, comparing Figures 15 and 16, it can be seen that the location of tip vortex breakup was closer forward with increasing tip speed ratio, but at the same tip speed ratio, the tip vortex breakup of W1 was faster, and at a tip speed ratio of 5, the tip vortex without winglets was prone to breaking up at about z/D = 8, while the tip vortex breakup of W1 occurred at about z/D = 5.The trailing edge of the blade created a vortex sheet, which was weak at low tip speed ratios and not captured by the Q values used for the iso-surfaces.The vortex sheet could be seen in the Q = 1 iso-surface plots of Figures 15c and 16c with a tip speed ratio of 6.At a tip speed ratio of 6, the vortex formed by the vortex drained from the trailing-edge vortex vane rotating with the tip vortex is called the trailing-edge vortex, and the trailing-edge vortex does not directly interact with the tip vortex.It can be seen from the figure that the trailing-edge vortex of W1 was stronger than that of the trailing-edge vortex without winglets.As shown in Figure 17, the instantaneous turbulent kinetic energy changes were compared between the turbulent kinetic energy (TKE) without winglets and W1 at different tip speed ratios.As can be seen in the figure, TKE developed and increased from behind the blade, and at a tip speed ratio of 5, TKE without winglets developed smoothly at z/D < 2 D, and increased and spiraled between z/D = 4 D and z/D = 7 D. Combined with the phenomenon in Figure 15, it is can be seen that the TKE showed a spiral shape due to the vortex synthesized by the tip vortex after undergoing vortex matching, and the gradual increase in TKE after z/D > 8 D was due to the breaking of the tip vortex.It spread toward the centerline as the TKE developed and became faster toward the centerline as the tip speed ratio increased.Comparing the TKE of W1 at the same tip speed ratio, it can be seen that the increase and spread of TKE to the centerline of W1 was significantly larger than that without winglets.Larger TKE values occurred between z/D = 1 D and z/D = 2 D behind the hub of the turbine for W1 and without winglets, which was due to the fragmentation of the root vortex.As shown in Figure 17, the instantaneous turbulent kinetic energy changes were compared between the turbulent kinetic energy (TKE) without winglets and W1 at different tip speed ratios.As can be seen in the figure, TKE developed and increased from behind the blade, and at a tip speed ratio of 5, TKE without winglets developed smoothly at z/D < 2 D, and increased and spiraled between z/D = 4 D and z/D = 7 D. Combined with the phenomenon in Figure 15, it is can be seen that the TKE showed a spiral shape due to the vortex synthesized by the tip vortex after undergoing vortex matching, and the gradual increase in TKE after z/D > 8 D was due to the breaking of the tip vortex.It spread toward the centerline as the TKE developed and became faster toward the centerline as the tip speed ratio increased.Comparing the TKE of W1 at the same tip speed ratio, it can be seen that the increase and spread of TKE to the centerline of W1 was significantly larger than that without winglets.Larger TKE values occurred between z/D = 1 D and z/D = 2 D behind the hub of the turbine for W1 and without winglets, which was due to the fragmentation of the root vortex.

Conclusions
This study compared and analyzed the influence of winglets on the hydrodynamic performance of tidal current energy turbines through numerical simulation to study the reason why winglets affect the hydrodynamic performance; compared the average velocity recovery trend of the wake field of the tidal current energy turbine with and without winglets, as well as the evolution of the wake vortex; analyzed the influence law of the winglets on the turbine s flow field characteristics; and obtained the following conclusions: (1) The hydrodynamic experimental results and PIV flow field test results of the turbine without winglets were compared with the numerical simulation results, which fully verified the accuracy of the numerical simulation method adopted in this paper in calculating the hydrodynamic performance of the turbine and flow field characteristics.
(2) The tip region of the turbine blade without winglets produced a significant threedimensional effect that reduced the energy conversion efficiency of the turbine.

Conclusions
This study compared and analyzed the influence of winglets on the hydrodynamic performance of tidal current energy turbines through numerical simulation to study the reason why winglets affect the hydrodynamic performance; compared the average velocity recovery trend of the wake field of the tidal current energy turbine with and without winglets, as well as the evolution of the wake vortex; analyzed the influence law of the winglets on the turbine's flow field characteristics; and obtained the following conclusions: (1) The hydrodynamic experimental results and PIV flow field test results of the turbine without winglets were compared with the numerical simulation results, which fully verified the accuracy of the numerical simulation method adopted in this paper in calculating the hydrodynamic performance of the turbine and flow field characteristics.(2) The tip region of the turbine blade without winglets produced a significant threedimensional effect that reduced the energy conversion efficiency of the turbine.Compared with the energy conversion efficiency of the turbine without winglets, the energy conversion efficiencies of the W1 and W2 turbines with winglets were improved at all tip speed ratios, and the energy conversion efficiencies of W1 and W2 were improved by 25.78% and 19%, respectively, at the designed tip speed ratio of 5.By increasing the pressure coefficient of the cross-section in the blade tip region, the winglets caused the blade tip to generate more torque and transfer the blade tip vortex to the wingtip of the winglets, weakening the strength of the tip vortex and suppressing the three-dimensional effect in the tip region to a certain extent, thus improving the energy conversion efficiency of the turbine.(3) Two narrow velocity loss regions appeared behind the turbine blades, and as the tip speed ratio increased, the location where the two narrow regions intersected moved forward, while the winglets accelerated the intersection of these two regions at the same tip speed ratio.At a tip speed ratio of 5, the mean axial velocity recovery in the wake of the W1 turbine with winglets was slower than that of the turbine without winglets in the near-wake region (<4 D), but as z/D increased (>8 D), the mean axial velocity recovery in the wake of W1 turbine with winglets was faster than that of the turbine without winglets.At the same tip speed ratio, the winglets could accelerate the vortex pairing of the tip vortices, as well as the breaking of the tip vortices, and this change was reflected in the change in TKE.

JFigure 1 .
Figure 1.(a) Distribution of chord length and torsion angle along the radius of tidal energy turbine blade; (b) three-dimensional modeling of tidal turbine.
distribution/°F igure 1.(a) Distribution of chord length and torsion angle along the radius of tidal energy turbine blade; (b) three-dimensional modeling of tidal turbine.

Figure 1 .
Figure 1.(a) Distribution of chord length and torsion angle along the radius of tidal energy turbine blade; (b) three-dimensional modeling of tidal turbine.

Figure 3 .
Figure 3. Schematic design parameters of the winglets.

Figure 3 .
Figure 3. Schematic design parameters of the winglets.

Figure 3 .
Figure 3. Schematic design parameters of the winglets.

Figure 5 .
Figure 5. Schematic diagram of boundary condition settings for the computational domain.

Figure 5 .
Figure 5. Schematic diagram of boundary condition settings for the computational domain.

Figure 7 .
Figure 7. Hydrodynamic performance of the tidal current turbine at an inflow velocity of 1.5 m/s.

Figure 7 .
Figure 7. Hydrodynamic performance of the tidal current turbine at an inflow velocity of 1.5 m/s.

Figure 7 .
Figure 7. Hydrodynamic performance of the tidal current turbine at an inflow velocity of 1

Figure 8 .
Figure 8. Streamline distribution near the blade at a flow velocity of 1.5 m/s.

Figure 8 .
Figure 8. Streamline distribution near the blade at a flow velocity of 1.5 m/s.

Figure 9 .
Figure 9.Comparison of velocity in the near field of the turbine between numerical simulation results and experimental results at the designed tip speed ratio.

Figure 9 .
Figure 9.Comparison of velocity in the near field of the turbine between numerical simulation results and experimental results at the designed tip speed ratio.

Figure 10 .
Figure 10.Comparison of energy conversion efficiencies and drag coefficients of turbines without and with winglets.

Figure 10 .
Figure 10.Comparison of energy conversion efficiencies and drag coefficients of turbines without and with winglets.

J 18 Figure 11 .
Figure 11.Comparison of pressure coefficients for different sections of the blade without and with winglets.

Figure 11 .Figure 12 .
Figure 11.Comparison of pressure coefficients for different sections of the blade without and with winglets.J. Mar.Sci.Eng.2023, 11, x FOR PEER REVIEW 13 of 18

Figure 12 .
Figure 12.(a) View of the tip vorticities without winglets; (b) view of the tip vorticities of W1.

Figure 13 .
Figure 13.Comparison of average axial velocity of the turbine without winglets and W1.

Figure 13 .
Figure 13.Comparison of average axial velocity of the turbine without winglets and W1.

Figure 14 .
Figure 14.Comparison of the average axial flow velocity between the turbine without winglets and W1 at the designed tip speed ratio.

Figure 14 .
Figure15shows the equivalent surfaces of the turbine without winglets for Q = 1 at different tip speed ratios (4, 5, and 6) and the x/D = 0 plane, and Figure16shows the equivalent surfaces of W1 for Q = 1 at different tip speed ratios (4, 5, and 6) and the x/D = 0 plane.The Q = 1 iso-surfaces in Figures15 and 16show that the tip vortex and root vortex were present in all tip speed ratio ranges, while the root vortex was present for a longer time at lower tip speed ratios.The root vortex would merge with the hub vortex in the far-wake region, and at lower tip speed ratios, the long vortex formed by the fusion of the root vortex and the hub vortex underwent meandering and finally broke up.The tip vortex showed a clockwise inclination in the x/D = 0 plane and the inclination of the tip vortex decreased with the increase in the tip speed ratio, as can be seen from the x/D = 0 plane in Figures15 and 16, which shows that the tip vortex underwent vortex pairing and then broke up and finally became a small-scale structure.As the tip speed ratio increased, the tip vortex pairing was more forward, and at a tip speed ratio of 4, the tip vortex pairing without winglets occurred at z/D = 4, while at tip speed ratios of 5 and 6, the vortex pairing was at z/D = 2 and z/D = 1, respectively.W1 had the vortex pairing of the tip vortex at z/D = 3 at a tip speed ratio of 4, and at tip speed ratios of 5 and 6, the vortex pairing was at z/D = 1 and z/D = 0-1, respectively.It can be seen that W1 had the vortex pairing occurring further forward in the tip vortex than the blade without winglets at the same tip speed ratio.Also, comparing Figures15 and 16, it can be seen that the location of tip vortex

Figure 17 .
Figure 17.Comparison of instantaneous turbulent kinetic energy without winglets and W1 at different tip speed ratios.

Figure 17 .
Figure 17.Comparison of instantaneous turbulent kinetic energy without winglets and W1 at different tip speed ratios.

Table 1 .
Main particulars of the designed turbine.

Table 1 .
Main particulars of the designed turbine.

Table 1 .
Main particulars of the designed turbine.

Table 2 .
Design parameters for winglets.

Table 2 .
Design parameters for winglets.

Table 2 .
Design parameters for winglets.