Flowdriven rotor simulation of vertical axis tidal turbines: A comparison of helical and straight blades
 DOI : 10.2478/IJNAOE20130177
 Author: Le Tuyen Quang, Lee KwangSoo, Park JinSoon, Ko Jin Hwan
 Organization: Le Tuyen Quang; Lee KwangSoo; Park JinSoon; Ko Jin Hwan
 Publish: International Journal of Naval Architecture and Ocean Engineering Volume 6, Issue2, p257~268, 30 June 2014

ABSTRACT
In this study, flowdriven rotor simulations with a given load are conducted to analyze the operational characteristics of a verticalaxis Darrieus turbine, specifically its selfstarting capability and fluctuations in its torque as well as the RPM. These characteristics are typically observed in experiments, though they cannot be acquired in simulations with a given tip speed ratio (TSR). First, it is shown that a flowdriven rotor simulation with a twodimensional (2D) turbine model obtains power coefficients with curves similar to those obtained in a simulation with a given TSR. 3D flowdriven rotor simulations with an optimal geometry then show that a helicalbladed turbine has the following prominent advantages over a straightbladed turbine of the same size: an improvement of its selfstarting capabilities and reduced fluctuations in its torque and RPM curves as well as an increase in its power coefficient from 33% to 42%. Therefore, it is clear that a flowdriven rotor simulation provides more information for the design of a Darrieus turbine than a simulation with a given TSR before experiments .

KEYWORD
Darrieus turbine , Helicalbladed , Flowdriven rotor simulation , Selfstarting capability , Torque fluctuation , Tidal steam generation

INTRODUCTION
The increasing global economy and limitations of fossil fuel availability have encouraged research on renewable energy. Tidal energy is regular, predictable, and available at higher power densities as compared to other weatherdependent renewable resources. Just as in England or Canada, Korea, a leading country of tidal energy generation, has large the resources of tidal energy and has attempted to extract energy with tidal barrages as well as tidal stream generators. An insitu experiment involving a tidal stream power plant with a helicalbladed Darrieus turbine was carried out at the Uldolmok narrow channel between Jindo islands and Haenam in Korea (Han et al., 2009). However, due to economic and social challenges, the commercialization of hydrokinetic tidal power extraction is not yet realized.
There are several types of tidal stream generators, including drag or lifttype devices as well as horizontal or vertical axis turbines. A Savonius vertical axis turbine is a typical example of a dragtype device, which usually operates at low speeds. The optimal power coefficient normally occurs when the TSR is lower than 1. There have been many attempts to optimize the power coefficient through parameter studies; however, the maximum recorded power coefficient of the Savonius turbine was found to be nearly 20% (Akwa et al., 2012; Menet and Bourabaa, 2004). Meanwhile, the horizontalaxis turbine (HAT) is known as the most efficient tidal stream generator. In a labscale experimental study, the power coefficient achieved was as high as 48% (Batten et al., 2007). In order to achieve high efficiency, the HAT needs to be aligned properly with variable stream lines. In comparison, a Darrieus verticalaxis turbine (VAT) can operate in all flow directions, though it tends to exhibit somewhat lower efficiency than HAT. In an experimental study with a free stream velocity of 1.2m/s, the maximum efficiency was 33% with a straightbladed Darrieus turbine (Shiono et al., 2002). A helicalbladed Darrieus turbine achieved a power coefficient of 41.2% in an optimal design study (Yang and Shu, 2012).
The computational fluid dynamics (CFD) simulation is frequently used as a numerical approach as an alternate to more expensive experimental studies in order to validate the performances of turbines. Additionally, the blade element momentum theory (BEMT) is a theoretical method that is used for the analysis and design of HATs (Batten et al., 2008; Clarke et al., 2007), with the results showing good agreement with those of labscale experiments in terms of the power coefficients. On the other hand, even if the computational cost is high, research using CFD simulations is conducted through threedimensional analyses of HATs (Lee et al., 2012), as this is a viable means of investigating vortex activities over the surfaces or near the tips of the blades in detail. Meanwhile, for the Darrieus VAT, no current theoretical method perfectly captures its actual performance as compared to detailed CFD simulations (Dai et al., 2011; Islam et al., 2008; Jung et al., 2009). BEMT methods with single or multiplestream tube, vortex, and cascades models show improvements in how well they predict the performance of a Darrieus VAT; however, they still exhibits drawbacks. Thus, a CFD simulation becomes a popular tool when used to analyze the performance of a Darrieus VAT (Carrigan et al., 2012; Ghatage and Joshi, 2011; Sabaeifard et al., 2012). Twodimensional CFD with less computation than threedimensional CFD is used in the design of sections of Darrieus VATs instead of a theoretical method. For instance, with help of CFD tools, the cambered airfoil was found to improve the selfstarting capability of a Darrieus VAT (Beri and Yao, 2011). An increase in the number of blades was also proposed to reduce both the torque and RPM fluctuations (Castelli et al., 2012). Among these approaches for performance improvements, a helicalbladed Darrieus turbine is considered to be a strong candidate for overcoming the disadvantages of a straightbladed Darrieus turbine, such as the fluctuation of the torque and the RPM as well as the low selfstarting capability (Shiono et al., 2002). In order to design the helicalbladed turbine and explore threedimensional effects such as tip loss, threedimensional CFD with a high computational cost is mandatory.
The approaches described above involving the use of CFD simulations and the BEMT are typically utilized when the TSR is determined. However, in the actual operating conditions of an experiment, tidal stream turbines begin to rotate from zero angular velocity when the flow speed reaches a sufficient value to rotate them. Afterwards, the TSR of a turbine is determined when a certain load is applied to a turbine in the direction opposite the rotation direction (Bahaj et al., 2007). Although the flow speed is stable under real operating conditions, the TSR as well as the torque are known to fluctuate in Darrieus turbines. Therefore, to capture realistic operational characteristics in an experimental study, a flowdriven rotor simulation, in which the body is driven by the flow, is more appropriate than a simulation with a given TSR. In this work, we introduce a flowdriven rotor simulation using FLUENT with a sixDOF solver to estimate the performance of a Darrieus VAT. First, a threebladed turbine with the NACA 0020 section, as used in a previous study, is studied in order to investigate its basic performance characteristics in 2D CFD simulations. The performance of a helicalbladed turbine is then investigated as compared to a straightbladed turbine by 3D CFD flowdriven rotor simulations to assess the fluctuation and selfstarting capability as well as the power coefficient.
NUMERICAL METHODS
> Flow solver
We exploit ANSYS FLUENT, which uses the finite volume method to solve the NavierStokes equation as a flow solver. A pressurebased Reynoldsaveraged NavierStokes (RANS) model is used to compute the flow properties in the unsteady condition. The sliding mesh method is used to transfer fluid media from the inner rotating domain, which contains the turbine, to the outer domain. The shear stress transport (SST)
k ω turbulent model is chosen because it combines the advantage of thek ω model near the wall and thek ε model away from the wall. SSTk ω provides superior results for a flow with a strong adverse gradient and separation in turbine simulations (Dai et al., 2010). A secondorder accurate model and a secondorder upwind model are selected for pressure discretization and momentum, respectively. A secondorder implicit transient formulation is used as well. The residual for the convergence check is set to 104 in order to obtain an accurate solution.> Computational turbine model and problem definition
Twodimensional (2D) computational fluid dynamics (CFD) simulations are frequently used for designing sections of a Darrieus verticalaxis turbine (VAT). Previous work involving 2D CFD simulations (KORDI, 2011) conducted a parametric study of the hydrofoil profile, the number of blades, the solidity, and the diameter. Through this parametric study, an optimal design with three blades was obtained with respect to the power coefficient, fluctuation, and other parameters. The detailed information pertaining to the turbine model is summarized in Table 1. The diameter of the turbine was 3m, the sections used were the NACA 0020 with a chord length of 0.4415
m , and the solidity was 0.1405. A free stream velocity of 3m/s is chosen because most tidal turbines are designed with a range of 2m /s to 4m /s ; this type of turbine was developed for installation into the Uldolmok narrow channel of Korea, which is known to have high flow speeds. The operating speed of the turbine is normally expressed as the tip speed ratio (TSR), which is defined as ωR /V , where ω is the angular velocity,R is the radius of the turbine, andV is the incoming velocity. A sliding mesh is utilized for modeling the rotation of the turbine. In order to use the sliding mesh method, the computation domain is divided into two domains: (1) the outside domain with the inlet velocity, outlet pressure, and symmetry boundary conditions on side surfaces; and (2) the inside domain near the blades with the wall boundary. Between two domains, an interface condition is applied. The domain sizes for 2D and 3D models are shown in Fig. 1. A structural mesh with a viscous length of the mesh expressed asy ^{+} < 5 is recommended around the wall of the blade when thek ω SST turbulent model accounts for the wall function by default. A zoomed view of the mesh near the wall is also included in Fig. 1.The power coefficient of the turbine is estimated through two simulation methods in this study. First, a CFD simulation with the TSR given, similar to methods in other numerical studies, was used. Here, the rotational speed of the turbine axis is specified by user input. Second, a CFD simulation with a given load, that is called a flowdriven rotor simulation, is used. It is similar to an experimental approach, in which the rotational speed of the turbine axis is not fixed, but the turbine is rotated at a certain velocity upon the hydrodynamic moment on the blade, the inertia moment of the blade, and the given counter moment on the rotational axis. The instantaneous power generated by the turbine is equal to the product of the angular velocity (
ω ) of the turbine and the torque (T ) acting on it. The power is not constant because the torque and velocity are not constant in the Darrieus VAT. Hence, the average power per cycle is calculated as the product of the average values of these terms per cycle, as shown belowThe power coefficient (
C _{p} ) is then defined aswhere
A is the frontal area of a turbine, which is equal to the product of the turbine diameter and height in a 3D model or only the turbine diameter in a 2D model;V _{∞} is the free stream velocity; andρ is the fluid density at far field boundary condition.Another quantitative value used to express the performance of a Darrieus VAT is the torque ripple factor (TRF), which is defined as the ratio of the peaktopeak amplitude of the instantaneous torque to the torque averaged in one cycle, as follows:
The numerical result is sensitive to the mesh quality in the boundary layer; hence, additional studies are necessary to check for numerical convergence before conducting further simulations. The dependence of the numerical result on the grid size and time step in a simulation with a TSR of 2.5 is shown in Fig. 2. The torque variation of each blade and the summation of three blades per cycle are respectively shown in Figs. 2(A) and Figs. 2(B), while the dependence of the torque on the mesh size and the number of time steps during a half cycle are presented in Figs. 2(C) and Figs. 2(C)(D), respectively. The degrees of mesh independence are studied with using three levels: coarse (69720 nodes), medium (129450 nodes) and fine (229371 nodes), corresponding to the first layer thickness from the wall, of which the values here are 1.5E4
m , 7.5E5m and 5E5m , with the viscous lengths,y ^{+}, set to 5. Similarly, the independence of the number of time steps on the numerical solutions is investigated by three levels: 200 steps, 300 steps and 400 steps per cycle. The differences between them are ignored. According to the results, 200 time steps and a mediumlevel mesh (129450 nodes) are chosen for the following 2D simulations.> Flowdriven rotor simulation with a given load
In contrast to a simulation with the TSR given, the rotational speed of the blade (
ω ) is not specified in an unsteady flowdriven rotor simulation. In a flowdriven rotor simulation, the turbine blade rotates around its axis at a certain rotational speed by balancing the hydrodynamic moment, the moment of inertia, and the imposed counter moment on the turbine. When the angular position of the turbine blade is notated byθ , the angular velocity and the acceleration of the turbine areθ′ andθ′′ . The rotational motion of the turbine around its axis is determined by the following equationwhere
J is moment of inertia of the turbine,M _{F} is the total hydrodynamic moment acting on the turbine blade andM _{A} is the applied moment on the rotational axis for determining the power of the turbine. Hence, the rotational speed of the blade (ω ) is defined as follows:In the numerical setup, a sixdegreeoffreedom (6DOF) solver (ANSYS, 2010) is utilized through a userdefined function (UDF) to analyze the rigidbody dynamics. The 6DOF solver calculates the hydrodynamic moment by integrating pressure and shear stress on the surface of the turbine blade in other to estimate the motion of a rigid object. Hence, we have to specify the moment of inertia of the turbine blade as well as the constraint of the turbine’s motion in the
x ,y , andz directions in the UDF.RESULTS AND DISCUSSION
> Horizontalaxis turbine (HAT) benchmarking test
First, to benchmark the flowdriven rotor simulation, the experimental data of a HAT with an 80cm diameter in a cavitation tunnel (Batten et al., 2007) are used. These are known as some of the best data measured from experiments with a threeblade HAT. A free stream velocity of 1.73
m /s , a tunnel domain, the NACA 638xx series turbine blade profile with a pitch angle of 20° are used in the experiment as the input conditions in a threedimensional simulation. Fig. 3 shows as well the curves of the torque and the rotational speed of the turbine, which we could predict from an experimental study. The rotational speed of the turbine quickly accelerates from 0 to a high RPM and then gradually decreases in a free load condition. Afterwards, it is significantly reduced to a lower RPM when counter torque is imposed on the turbine axis. A RPM curve with very low fluctuation after the reduction, which is known as one of the main advantages of a HAT, is obtained by a numerical simulation. These characteristics of the RPM curve are different in a VAT, as shown in the next simulation in this study. When comparing the results of the flowdriven rotor simulation with the experimental results, the values ofC _{p} are shown to be close to each other, as shown in Fig. 3, although the positions of the peakC _{p} differ slightly in the two cases. The maximum of the power coefficient, 48%, is achieved when the TSR ranges from 6 to 7.2D simulation
First, a 2D flowdriven rotor simulation of the Darrieus turbine is conducted to ascertain its performances quickly and compare them to those of a simulation with a given TSR. The simulation conditions are summarized in Table 1. The mass and moment of inertia of the turbine which made of aluminum, are utilized in the UDF. The torques and RPMs of the Darrieus turbine are shown in Fig. 4. Briefly, the figure presents the performance of the turbine under three different load conditions: a free load condition and two applied load conditions with counter torques
T of 3.5kN ⋅m andT of 4.75kN ⋅m per unit length. The free load condition initially is a case in which no counter torque is applied to the turbine axis and where the turbine accelerates to around 125 RPM under hydrodynamic moment from the flow and then decelerates to about 90 RPM, fromt = 0.0s to 4.56s . Low selfstarting capability due to the need to overcome the inertia of a large turbine is well known as one of the main disadvantages of a straightbladed turbine (Shiono et al., 2002), which is also demonstrated by slow acceleration in the beginning of the RPM curve. From the initial state, the turbine accelerates slowly fromt = 0.0 to 0.6s and the rotational speed then increases from 0 RPM to 15 RPM. Afterwards, it accelerates rapidly, with the rotational speed finally reaching a maximum value of 125 RPM att = 1.5s . Subsequently, the rotational speed gradually reduces to a convergent value, 90 RPM, with low fluctuation. When counter torque of 3.5kN ⋅m is applied to the turbine axis att = 4.56s , the rotational speed decreases significantly and then gradually increases to a new convergent value of 52 RPM. By multiplying the counter torque and the rotational speed, the corresponding power coefficient is 0.48. As shown in the torque curve, high fluctuation of the torque on the axis of the turbine is observed. This is also another main drawback of a Darrieus VAT. If a high counter torque such as 4.75kN ⋅m is applied, the rotational speed of the turbine is dramatically reduced and the turbine starts to rotate in the opposite direction in what is known as an overloading condition. This is shown in the lower subfigure in Fig. 4.The power coefficient of the Darrieus turbine predicted by the 2D flowdriven rotor simulation is depicted when counter torque is imposed with different values, as shown in Fig. 5. For a comparison, the power coefficient predicted from a simulation with the TSR given is also plotted. The results from both simulations are in good agreement; the maximum power coefficient is nearly 0.535 when the TSR is around 2. There is a small gap between the TSRs when using these two approaches. The power coefficient cannot be predicted when the TSR is less than 2 in the flowdriven rotor simulation, which is considered as an overloading condition, for example, with counter torque of 4750
N ⋅m , as shown in Fig. 4. It is speculated that the overloading condition arrives at a somewhat small value of the imposed torque due to the 2D assumption.3D simulation
3D tip effect on power coefficient
Here, the performance of the Darrieus turbine is investigated through two configurations with the same height: a straightbladed and a helicalbladed turbine. Additional information is also shown in Table 1. The height of the turbine is 7.2
m and the heighttodiameter ratio of both turbines is 2.4. The inclination angle of the helicalbladed turbine is defined aswhere
n ,h , andd are number of blades, the span of the rotor blade and the diameter of the rotor (Shiono et al., 2002), respectively. Our helicalbladed turbine has an inclination angle of 66.4°; hence, its blades cover 360° from a top view. The ratio and inclination angle were sourced from a previous study (KORDI, 2011). The domain of the 3D simulation is shown in Fig. 1, and 1,512,783 nodes are used after the grid convergence is checked. As in the 2D simulation, the 3D flowdriven rotor simulation requires the moment of inertia of the aluminum turbine for the sixDOF solver, which is connected via UDF to the flow solver. Fig. 6 shows a comparison of the power coefficients of both turbines along with the 2D turbine. The maximum power coefficients of the helicalbladed and straightbladed are were respectively 0.42 and 0.33 at a TSR of approximately 2.2, which are 22% and 38% lower than that of the 2D turbine, respectively. These results indicate that 3D tip effect is significant and that the helical blades enable the turbine to extract more power from the tidal flow due to the inclination angle. Previous studies also showed that the power coefficients from the 3D simulation and the experiment were nearly half of those from a 2D CFD estimation (Mohamed, 2012; Raciti et al., 2011).Fig. 7 presents the pressure distribution in the crosssections of planes 1, 2, 3, 4, and 5 from the middle to the tip positions along the vertical axis corresponding to
z /0.5H values of 0%, 50%, 75%, 90%, and 99%. The 3D tip effect is clearly shown in the straightbladed turbine according to the decrease in the pressure difference near the blades when the crosssection moves toward the blade's tip. More specifically, it can be seen that the difference in the positive and negative pressure levels shows a slight reduction from planes 1 to 2, after which they sharply decrease from planes 2 to 4. Moreover, the difference of the pressure levels is nearly nonexistent on plane 5. The pressure distribution on plane 1 is similar to that in the 2D CFD simulation; therefore, the difference between these planes can explain a major gap in the power coefficients between the 2D and 3D models shown in Fig. 6.For the helicalbladed turbine, the azimuth blade angle along the vertical axis is different in each section. Thus, the characteristics of the pressure contours are clearly different from those in the straightbladed turbine. The 3D tip effect is only apparent between the pressure contours in planes 4 and 5, while the other planes show different characteristics due to their different azimuth angles. In detail, from planes 1 to 3, the NACA section of blade 1 moves from 0° toward 90° in terms of the azimuth blade angle; therefore, the difference in the negative and positive pressure zones near blade 1 becomes greater. The pressure contours near blades 2 and 3 also depend on their azimuth blade angles. Regarding the straightbladed turbine, the position of the NACA section was identical in all planes; therefore, the pressure contours in all sections show similar pressure differences. In addition, the pressure contours in the circular area inside the three blades present different characteristics of the flow in the helicalbladed and straightbladed turbines; the green color shown is dominant in the case of the helicalbladed turbine; thus, its pressure is lower than that of the straightbladed turbine. Subsequently, the helicalbladed turbine could absorb more energy from the tidal flow than the straightbladed turbine due to the large difference between the inside and outside pressure levels.
Fig. 8 shows the flow velocity vectors over the two turbines, demonstrating how the helical geometry affects the streamlines. The flow has strong mutual interaction with the three blades before it moves downstream. Thus, the streamlines are strongly deformed in terms of their direction when they pass through the helicalbladed turbine, whereas only small deflections are observed in the case of the straightbladed turbine. The differences in the streamlines between the two 3D turbines mainly cause the differences in the pressure distribution of each section and in their power coefficients.
> Selfstarting capability and fluctuation
The helicalbladed turbine is known to have advantages over the straightbladed turbine in terms of its selfstarting capability and the reduced fluctuation of its torque curve, as visually exhibited by the 3D flowdriven rotor simulation shown in Fig. 9. Fig. 9(A) shows the hydrodynamic torque on the rotational axis of the turbines with the RPM in the free load condition. In the beginning, both of the turbines were forced to rotate under high hydrodynamic torque, 32
kN ⋅m , with the RPM increasing from 0. Next, the torque continues to increase from 32kN ⋅m to 65kN ⋅m untilt = 0.45sec , and the RPM increases sharply to its maximum value of 105 at t = 0.9sec in the helicalbladed turbine. In contrast, the torque is reduced from 32kN ⋅m to 0kN ⋅m until t = 0.5sec in the straightbladed turbine. Meanwhile, the RPM increases from 0 to 20 untilt = 0.3sec , becoming nearly constant between 0.3sec and 0.6sec in the straightbladed turbine. Afterwards, the torque on the straight blades increases rapidly from 0kN ⋅m to 57kN ⋅m between 0.5sec and 0.9sec , and the RPM reaches its maximum value of 95 att = 1.5sec . After reaching the maximum value, both the RPM and the torque decrease to their convergent values in both turbines. Due to the high fluctuation of the torque, the acceleration in the early stage of the straightbladed turbine is delayed compared to that of the helicalbladed turbine; thus, the helicalbladed turbine shows greater selfstarting capability than the straightbladed turbine. In other words, the selfstarting capability is improved by the helical blade because the duration required to reach the maximum rotation speed for the helicalbladed turbine is shorter (0.9sec ) than that of the straightbladed turbine (1.5sec ).Fig. 9(A) shows the hydrodynamic torque on the rotational axis of the turbines and the RPM when the maximum power coefficients of the helicalbladed and straightbladed turbines are 0.42 and 0.33, respectively. The average TSR was approximately 2.2 when the corresponding counter torque levels are 26.8
kN ⋅m and 20kN ⋅m on the helicalbladed and straightbladed turbines, respectively. Clearly, the torque curves present another advantage of the helicalbladed turbine over the straightbladed turbine in the form of the low fluctuation of the torque. In detail, the torque ripple factors (TRF) are 0.065 and 1.675 in the helicalbladed and straightbladed turbines, respectively. The RPM curves also show high fluctuation in the straightbladed turbine. Using similar definitions of TRF, the RPM ripple factors are 0.0057 and 0.077 in the helicalbladed and straightbladed turbines, respectively. In sum, the torque and RPM curves of the helicalbladed turbine are much smoother than those of the straightbladed turbine.As noted above, the main advantage of the Darrieus VAT is its ability to generate power from the flow in any direction without any yawing control as compared horizontalaxis turbine which is mainly used in tidal steam generators (Beri and Yao, 2011). A straightbladed Darrieus VAT is advantageous given its simple manufacturing process and assembly stages. However, researchers should consider how to overcome the two main drawbacks of the straightbladed Darrieus turbine: its low selfstarting capability and the high fluctuation of the torque on its turbine axis. There are several experimental and numerical approaches that seek to overcome these drawbacks. These include a cambered foil to enhance the selfstarting capability and an increase in the number of blades to reduce the fluctuation of the torque (Castelli et al., 2012; Hwang et al., 2009). Thus far, the utilization of helical blades is one of the most promising solutions to accomplish these goals. Recently, throughout insitu experiments, a helicalbladed turbine has been proven to offer continuous high performance in South Korea (Han et al., 2013). Our work is among the first to present a quantitative assessment of the performance of the helicalbladed Darrieus turbine using a flowdriven rotor simulation, which provides operational characteristics close to those of an actual experiment as compared to a simulation with a given TSR. The advantages of the helicalbladed turbine are demonstrated through a direct comparison with the straightbladed turbine of the same size. First, the helicalbladed turbine shows an improvement in the selfstarting capability with higher torque levels and with less time required to reach the maximum RPM as compared to a straightbladed turbine. Next, the fluctuation of the torque acting on the rotational axis during the power extraction stage is significantly reduced; that is, the TRF is reduced from 1.675 to 0.065 while the RPM remains nearly constant. The power coefficient also is improved from 33% to 42% in the given conditions of the Darrieus turbine. Consequently, an improvement of the selfstarting capability and a reduction of the fluctuation by the helicalbladed turbine are clearly demonstrated as compared to a straightbladed turbine in flowdriven rotor simulations. The improvement of the power coefficient by the helicalbladed turbine may be dependent on the operating conditions or on blade characteristics such as the pitch control, which is known to improve the power coefficient of Darrieus turbines (Hwang et al., 2009; Schönborn and Chantzidakis, 2007). An improvement of the power coefficient of Darrieus turbines is the subject of our future study.
CONCLUSION
In this study, flowdriven rotor simulations are conducted in an effort to investigate the operational characteristics of a Darrieus turbine which can be captured in an actual experiment instead of a simulation with a given tip speed ratio (TSR). Specifically, the selfstarting capability, fluctuation of the torque and the RPM characteristics while also considering an overloading condition are clearly demonstrated in a flowdriven rotor simulation. Twodimensional (2D) computational fluid dynamics (CFD) simulations initially show that the power coefficient predicted from a flowdriven rotor simulation is in very good agreement with the prediction from a simulation with a given TSR. Next, the threedimensional (3D) effect on the power coefficient of Darrieus turbines is explored in detail by comparing the results from 2D and 3D simulations. Finally, through 3D CFD simulations for an optimal design, the helicalbladed turbine shows prominent advantages over a straightbladed turbine of the same size, including an improvement in its selfstarting capability and the minimization of the fluctuation of the torque levels and RPM while extracting power as well as an increase of its power coefficient from 33% to 42% under the given operating conditions. Eventually, in the design stage of a Darrieus turbine, it is certain that a flowdriven rotor simulation can provide more information than a simulation with a given TSR before expensive experimental work.

[Fig. 1] 2D and 3D computational models of a Darrieus turbine and problem definition.

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[Fig. 2] Dependencies of numerical solutions on mesh size and the number of time steps in 2D simulation with a given TSR. A: torques of each blade, B: torques summed by 3 blades, C: torques with the first layer thickness varied, D: toques with the number of time steps varied.

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[Fig. 3] Benchmarking test of a flowdriven rotor simulation with the experimental study of a horizontal axis turbine. A: Torque and RPM curves from the present simulation, B: comparison of power coefficients.

[Fig. 4] The torque and RPM curves of threeblade Darrieus turbine from the 2D flowdriven rotor simulation.

[Fig. 5] Power coefficients predicted from the 2D different simulations.

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[Table 1] Detail information of the targeted turbine and flow condition.

[Fig. 6] Power coefficients of a 2D model and 3D models predicted by the flowdriven rotor simulations.

[Fig. 7] Pressure distributions in sections of different heights of the straightbladed and helicalbladed turbines.

[Fig. 8] Streamlines of the straightbladed and helicalbladed turbines.

[Fig. 9] (A) Torque and RPM curves in the free loading condition for demonstrating the self starting capability and (B) those in a given loading condition for comparing the fluctuations of darrieus turbines with different shape blades.