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Numerical Study on Self-Starting Performance of Darrieus Vertical Axis Turbine for Tidal Stream Energy Conversion Zhen Liu 1,2, *, Hengliang Qu 3 and Hongda Shi 1,2 1 2 3

*

Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China, Qingdao 266100, China; [email protected] Qingdao Municiple Key Laboratory of Ocean Renewable Energy, Ocean University of China, Qingdao 266100, China College of Engineering, Ocean University of China, Qingdao 266100, China; [email protected] Correspondence: [email protected]; Tel.: +86-532-6678-1550

Academic Editor: Stephen Nash Received: 10 July 2016; Accepted: 22 September 2016; Published: 29 September 2016

Abstract: Self-starting performance is a key factor in the evaluation of a Darrieus straight-bladed vertical axis turbine. Most traditional studies have analyzed the turbine’s self-starting capability using the experimental and numerical data of the forced rotation. A 2D numerical model based on the computational fluid dynamics (CFD) software ANSYS-Fluent was developed to simulate the self-starting process of the rotor at constant incident water-flow velocities. The vertical-axis turbine (VAT) rotor is driven directly by the resultant torque generated by the water flow and system loads, including the friction and reverse loads of the generator. It is found that the incident flow velocity and the moment of inertia of the rotor have little effect on the averaged values of tip-speed ratios in the equilibrium stage under no-load conditions. In the system load calculations, four modes of the self-starting were found: stable equilibrium mode, unstable equilibrium mode, switch mode and halt mode. The dimensionless power coefficient in the simulations of passive rotation conditions is found to be, on average, 38% higher than those achieved in the simulations of forced rotation conditions. Keywords: tidal stream energy; vertical axis turbine; Darrieus type; self-starting; numerical study

1. Introduction Abundant resources of marine energy make it possible to use the energy in the ocean as an alternative and renewable power source in the future. However, harvesting the marine energy has been a big challenge to the ocean engineers. The tidal stream energy has advantages such as stable energy flux density and high predictability. The devices to capture the tidal stream energy always borrow the idea from the wind energy turbine because of the similarity of these two working fluids. Compared to the more common horizontal-axis turbine, the vertical-axis turbine (VAT) is more adaptable to the direction change of tidal currents. The VAT is also easier to access for maintenance because the electrical generators in the VAT are always installed near or above the water surface. The Darrieus straight-bladed turbine is a typical VAT; it is widely employed for wind and tidal stream energy conversion. The VAT typically suffers from a serious drawback: the blades are stalled or show a poor performance at a low tip-speed-ratio (TSR) owing to the low or even negative (reverse) torque for most azimuth angles [1]. Therefore, the Darrieus turbine was regarded by some scholars to be inherently non self-starting, which can be fixed by utilizing the variable-pitched blades [2,3]. Although the exact definition of self-starting is not consistent throughout the literature, the self-starting performance of the Darrieus VAT has been a main research topic, especially for the small and standalone cases in the field of wind energy [4]. Energies 2016, 9, 789; doi:10.3390/en9100789

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The inability of a Darrieus turbine of low solidity to self-start arises from the existence of a band of TSRs below the operating condition during which the net amount of energy collected by each blade in one revolution is negative [5]. This negative or reverse torque region is called the “dead band”; this was plotted as Cp (dimensionless power coefficient)—λ (TSR) curves in [6]. The corresponding analytical investigations were based on the experimental results of the aerodynamic performance of airfoils [7]. It was reported that the VAT has the lowest self-starting capability with NACA 0012 [8] and a highest capability with NACA 0021, among the various symmetric airfoils investigated [9]. Different blade geometries have been proposed and tested to improve the self-starting capability of the VAT [10–16]. The blade pitch control was also found to be an effective method for the VAT to have a better self-starting capability [17,18]. External auxiliaries, such as the combined Savonius turbine [19] and the ailerons [20], were proposed to improve the self-starting performance of the Darrieus straight-bladed VAT. It was pointed out that inaccurate modeling of the dead band may result in a false prediction due to the effects of dynamic stall and wake interaction being neglected [21]. Therefore, besides experimental studies in the wind tunnel, the computational fluid dynamics (CFD) approach was adopted for the investigations on the self-starting of direct-driven turbine. These studies can reveal the starting characteristics and the related flow fields of a VAT from rest till the operational rotating speed is reached [22–25]. The CFD approach was also adopted in the studies on the self-starting of VATs for tidal stream energy conversion [26,27]. In this study, the definition of self-starting for the Darrieus turbine is introduced in Section 2. In Section 3, a 2D numerical model based on the CFD software ANSYS-Fluent (Canonsburg, PA, USA) is presented and validated. The flow-driven passive rotations of the 2D rotor are simulated numerically. In Section 4, the variations in the flow fields, rotor torques and dimensionless power coefficients are also analyzed. The effects of incident flow velocities, load conditions and moments of inertia on the self-starting characteristics of the VAT are studied. Four self-starting modes of the Darrieus VAT are considered. The main conclusions derived from the results of the 2D numerical simulations and the proposed future work are discussed in Section 5. 2. Self-Starting of Darrieus VAT A Darrieus straight-bladed VAT was employed in this study. The shape of the cross section of the blade is as per the NACA 0018 airfoil. The blade span is taken as 1 m in the 2D calculations of ANSYS-Fluent. The parameters of the turbine rotor are shown in Table 1. The solidity of the rotor is calculated using the equation σ = N ·C/2R. Table 1. Shape parameters of the vertical-axis turbine (VAT) rotor. Description

Value

Number of blades N Blade chord C (m) Blade span S (m) Radius of rotor R (m) Solidity σ Fixed pitch angle β

3 0.12 1.0 0.5 0.36 0◦

One definition of self-starting, given in [6], is that the turbine is considered as self-starting if it can accelerate from rest to the point where a significant power is produced. However, the term “significant power” has not been defined precisely. Another specific definition is that the turbine is deemed to have started if it has accelerated from rest to a condition where the blade operates at a steady speed that exceeds the fluid speed (TSR > 1) [21]. Both of these simple definitions of self-starting, in terms of the load or the TSR, have their drawbacks [28]. The term “self-starting” mentioned in [28] refers to the ability to accelerate from rest to the final operating TSR. For a given VAT rotor, the final operating TSR depends on the incident flow conditions

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and the load conditions. As pointed out in [29], the final TSR increases with an increase of the incident free velocity and a decrease of the resistive load, and vice versa. If the resistive load is very high, the turbine will fall into the dead band. Based on this information, the turbine can be deemed to be “self-starting” if it meets the following conditions: “The turbine can accelerate from rest to a final tip-speed-ratio to deliver a continuous thrust output, which is an equilibrium point where the fluid dynamic and resistive torques match [29]”. The TSR is defined as: ω·R λ= (1) U∞ where ω is the angular velocity of the rotor and U∞ is the free water flow from the far field. The dimensionless power coefficient Cp can be defined as: Cp =

ω · Tq 3 A 0.5ρU∞ r

(2)

where Tq is the instantaneous torque generated by the turbine, and ρ is the density of water. Ar is the swept area, which can be calculated as: Ar = 2R·S. The averaged dimensionless power coefficient Cp-ave in a revolution is defined as:

C p−ave

1 = T

tZ+ T

C p dt

(3)

t

where T is the period of revolution. 3. Numerical Model 3.1. Numerical Set-up Although the 2D CFD model cannot reflect all the hydrodynamic characteristics of the VAT and will ignore some parasitic drag forces [30], it has been pointed out that the 2D model is suitable for the initial study to save computational cost and time [23]. Considering that the numerical simulation of the self-starting of a VAT is still in a preliminary stage, we decided to use the 2D model in this study. The continuity equation of incompressible fluids and unsteady Reynolds-averaged Navier–Stokes equations are applied as the governing equations. These equations are solved in the general-purpose commercial CFD platform ANSYS-Fluent 12.0. The finite volume method is used for discretization using the pressure-based solver. Spatial and temporal discretizations of second order were used for all the equations and the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) scheme for the solution of the governing equations. The rectangular computational domain is shown in Figure 1. The length and width of the domain are 30 times and 20 times the rotor radius, respectively. The left and right sides are set as the boundaries of the velocity inlet and pressure outlet, respectively. The other two sides are set as symmetry boundaries. The rotor is placed at a distance of 10R from the velocity inlet to ensure the full development of the incident flow from the far field and wake formation in the downstream. The core domain is at a distance of 10R from both the symmetry boundaries to reduce the sidewall effects as much as possible. The incident flow direction and the azimuth angle of 0◦ are also defined in Figure 1. The computational domain is divided into three parts: the circular-ring rotational domain and the outer and inner stationary sub-domains. The circular ring domain (green part) can rotate together with three blades, and a sliding mesh model is coupled with this domain. The stationary and rotational sub-domains are connected to each other through non-conformal interfaces. The mesh motions are prescribed so that the sub-domains linked at the interfaces can remain in contact with each other (sliding along the interface boundaries) to ensure an accurate exchange of all the flux at the interfaces and a faster computational convergence.

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Figure 1. 2D computational domain, boundaries and meshes. Figure 1. 2D computational domain, boundaries and meshes.

To reduce the computation time by accelerating the iteration speeds and to improve the

To reduceinthe computation time bytoaccelerating speedsasand to structured improve the precision precision calculation with respect the reductionthe of iteration possible errors, many meshes in calculation with respect to the reduction of possible errors, as many structured meshes as as possible are used in the outside domain. The rotational and inner stationary sub-domains possible are are used in the outside domain. The rotational innergeometries. stationary The sub-domains are meshed meshed with unstructured elements to fit theand complex boundary layer meshes with around theelements blade foilstoare to capture the near-wall turbulence effects and the wake formations. unstructured fitrefined the complex geometries. The boundary layer meshes around the blade wall y+ istocontrolled from 20 to turbulence 60. The sheareffects stress transportation (SST) turbulenceThe model foils The are refined capture to thebenear-wall and the wake formations. wall y+ 5 meshes and a time step of 0.005 s is employed in this study; this has been with approximately 2 × 10 is controlled to be from 20 to 60. The shear stress transportation (SST) turbulence model with investigated and validated in a previous study by the authors [31]. approximately 2 × 105 meshes and a time step of 0.005 s is employed in this study; this has been The description of the flow-driven passive rotation of the VAT rotor is based on Newton’s investigated and validated in a previous study by the authors [31]. second law, which can be defined as: The description of the flow-driven passive rotation of the VAT rotor is based on Newton’s dω second law, which can be defined as: I  Ts  Tw (4) dωdt I· + Ts = Tw (4) dtand Tw is the hydrodynamic torque generated by the where I is the moment of inertia of the rotor, where I is thewater moment inertia of the rotor, andconsists Tw is the hydrodynamic by the incident flow. of TS is the system load, which of the friction load Tf torque and the generated resistive load of the electric generator Tg. system The friction load is kept constant. permanent synchronous incident water flow. TS is the load, which consists of For theafriction loadmagnetic Tf and the resistive load (PMSG), TgTcan be simplified as: is kept constant. For a permanent magnetic synchronous of thegenerator electric generator friction load g . The generator (PMSG), Tg can be simplified as: TI When the rotor is at rest ; Tg   k  

(

TI

When the rotor is rotating.

(5)

When the rotor is at rest;

Tgtorque = of the generator, and k is a constant-ratio, whose unit is N·ms/rad. where TI is the initial resistive k · ω When the rotor is rotating. From Equation (4), at the time of t + ∆t, the rotation speed of the rotor can be calculated using the following equation:

(5)

where TI is the initial resistive torque of the generator, and k is a constant-ratio, whose unit is N·ms/rad. Tw  Tspeed From Equation (4), at the time of t + ∆t, the rotation of the rotor can be calculated using the st (6) ω  ω  t t   t t following equation: I ( Tw − Ts ) |t ωt+ + θt+∆t at the same ∆t time is updated as: (6) ∆t = ωtangle Furthermore, the instantaneous azimuth I Furthermore, the instantaneous azimuth θ t+∆t attthe same time is updated as: θ angle θ ω t  t

t

t  t

(7)

where θt is the azimuth angle at the time of t. θt+∆t = θt + ωt+∆t · ∆t (7) The new positions of the blades are derived from Equation (7), and cause the flow fields around be updated. After this time step, of thet.torque of the rotor at the new azimuth is then renewed. wherethe θ trotor is thetoazimuth angle at the The coupling of the fluid-structure interaction infrom FluentEquation is achieved a user-defined function The new positions of the blades are derived (7),through and cause the flow fields around

the rotor to be updated. After this step, the torque of the rotor at the new azimuth is then renewed. The coupling of the fluid-structure interaction in Fluent is achieved through a user-defined function (UDF). The torque of the rotor is calculated by the integration of the pressures on each grid of the blade

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(UDF). The torque of the rotor is calculated by the integration of the pressures on each grid of the blade surface. By executing the loop, abovethe loop, the passive of the VAT rotor, including the fluidsurface. By executing the above passive rotationrotation of the VAT rotor, including the fluid-structure structure interaction, can be obtained. interaction, can be obtained. 3.2. Experimental Validation To the capability capabilityofofthe theabove above numerical model, in order to predict the fully passive To validate the numerical model, in order to predict the fully passive selfself-starting performance, the experimental results of the Darrieus straight-bladed VAT rotor should be starting performance, the experimental results of the Darrieus straight-bladed VAT rotor used for comparison. However, valuable experimental data pertaining to the self-starting of the tidal turbine were not available during literature review. review. Therefore, the results of experiments conducted on a prototype prototype wind wind turbine, turbine, reported by Hill et al. al. [7], [7], were were used. used. The blade profile used in the experiments experiments was was that that of of the NACA NACA 0018 0018 airfoil airfoil and and the the blade blade span span was was 0.6 m and the free wind speed was Acomparison comparison of of the the experimental experimental and and numerical numerical results results is is shown shown in in Figure 2. was 66 m/s. m/s. A In Figure is the time when a steady Figure 2, 2, the the dimensionless dimensionless time time t* t* is is defined definedas ast*t*==t/t t/tss,, where tss is rotation the self-starting self-starting process can be divided divided into into three three stages: stages: rotation speed speed is is achieved. achieved. It can be seen that the the linear and equilibrium stages. Untaroiu et al.etsuccessfully predicted the linear linearacceleration, acceleration,plateau plateau and equilibrium stages. Untaroiu al. successfully predicted the acceleration stage and theand angular velocity velocity increasedincreased linearly before reaching equilibrium stage [22]. linear acceleration stage the angular linearly before the reaching the equilibrium However, final steady angular velocity wasvelocity underestimated. The present model showsmodel performance stage [22].the However, the final steady angular was underestimated. The present shows similar to that similar obtained the numerical established by Zhu et al. [24]. by TheZhu linear acceleration performance tousing that obtained usingmodel the numerical model established et al. [24]. The stage underestimated, but the equilibrium stage predicted.stage Compared to thepredicted. previous linearwas acceleration stage was underestimated, butwas thewell equilibrium was well model, the numerical modelmodel, in this the study yields a closer of the acceleration stage connecting Compared to the previous numerical modelprediction in this study yields a closer prediction of the the plateau and equilibrium Moreover, present model predicts the value of final steady acceleration stage connectingstages. the plateau andthe equilibrium stages. Moreover, the present model rotational speed precisely. predicts the value of final steady rotational speed precisely. In addition, The values values of tss calculated in the grid addition, tss in the experiment experiment is is around around 154 154 s.s. The independence study study by Zhu et al. [24] are from 8 s to 15 s, which are approximately ten times smaller than onon ts tin the 3D3D model, which is than that that of of experimental experimentalresult. result.Untaroiu Untaroiuetetal.al.gave gavea abetter betterprediction prediction s in the model, which around 150150 s [22]. TheThe steady angular velocity predicted by using the present model is achieved a littlea is around s [22]. steady angular velocity predicted by using the present model is achieved faster than the experiments, and ts isand around s. The134 inaccurate of angular velocities in little faster than the experiments, ts is134 around s. The predictions inaccurate predictions of angular the plateauinstage and the stage value and of ts the mayvalue be because of the blade andblade the drags created by velocities the plateau of ts may be finite because of height the finite height and the the spokes. Except the time when thethe steady speed is achieved, the present numerical model drags created by the spokes. Except time rotation when the steady rotation speed is achieved, the present shows a better capability predict the entire process than the other numerical models. numerical model shows atobetter capability to self-starting predict the entire self-starting process than the other The comparison indicates that the passive rotation used in thismodel studyused can capture the main numerical models. The comparison indicates that themodel passive rotation in this study can features of the angular velocity during self-starting under the uniform flow capture the main features of the angular velocity during self-starting under theconditions. uniform flow conditions.

Figure 2. 2. Comparison of variations variations in in angular angular velocities velocities for for the the Darrieus Darrieus wind wind turbine. turbine. Figure Comparison of

4. Results 4. Resultsand andDiscussion Discussion 4.1. Calculations without the System Loads In the calculations without the system loads, TSS is is set set as zero. The The VAT VAT rotor is driven by the To demonstrate demonstrate the difference in the results of hydrodynamic torque generated by the incident flow. To the numerical simulations of the traditional forced rotation (under a constant angular velocity) and

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Energies 2016, 9, 789 15 the numerical simulations of the traditional forced rotation (under a constant angular velocity)6 of and the passive motion adopted in this study, a comparison of the velocity contours around a blade at various the passive motion adopted in this study, a comparison of the velocity contours around a blade at azimuth angles is performed, and is shown Figure The incident free velocity for both the the modes various azimuth angles is performed, and isin shown in 3. Figure 3. The incident free velocity for both is setmodes as U∞ = 1.5 m/s. The calculation of the passive rotation was carried out first. Because of the is set as U∞ = 1.5 m/s. The calculation of the passive rotation was carried out first. Because of the existence of the reserve torque, the hydrodynamic torque fluctuated near zero. Instead of continuous existence of the reserve torque, the hydrodynamic torque fluctuated near zero. Instead of continuous acceleration, an an equilibrium wasfound. found.This This averaged angular velocity acceleration, equilibriumstate stateofofthe theangular angular velocity velocity was averaged angular velocity (TSR(TSR = 4.72) waswas then used asasthe thecalculation calculation case of forced rotation. = 4.72) then used thecondition condition for for performing performing the in in thethe case of forced rotation.

◦ ); (b) 90◦ ; Figure 3. Comparisonof ofvelocity velocity contours a blade. Forced rotation: (a) 0°(360°); 90°; Figure 3. Comparison contoursaround around a blade. Forced rotation: (a) 0◦(b) (360 ◦ ◦ ◦ ◦ ◦ ◦ ◦ (c) 180°; (d) 270°; Passive rotation: (e) 0°(360°); (f) 90°; (g) 180°; (h) 270°. (c) 180 ; (d) 270 ; Passive rotation: (e) 0 (360 ); (f) 90 ; (g) 180 ; (h) 270 .

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around thethe blade at As shown in Figure Figure 3a–c,e,f, 3a–c,e–f,the thegeneral generalcharacteristics characteristicsofofthe theflow flowstructures structures around blade ◦ , 90◦ and 180◦ for the two rotation modes are similar. The high speed area at the azimuth angles of 0 at the azimuth angles of 0°, 90° and 180° for the two rotation modes are similar. The high speed area both leading and trailing edges of the blade in the casecase of passive rotation is larger thanthan that that in the at both leading and trailing edges of the blade in the of passive rotation is larger incase the of theofforced rotation. Moreover, the low area near sides the blade, the case of passive case the forced rotation. Moreover, thespeed low speed areathe near theofsides of the in blade, in the case of rotation,rotation, is smaller thatthan in the case of forced passive is than smaller that in the case ofrotation. forced rotation. 270◦ , the the blade blade is is forced forced to to rotate rotate in in a relatively relatively As shown in Figure 3d, at the azimuth angle of 270°, low speed area, which is in the the wake wake area area of of the the rotor. rotor. The The flow flow velocities velocities around around the blade blade are are higher higher at at thethe leading andand trailing edges of the the forcing effect than those those in inthe theother otherareas. areas.Especially Especially leading trailing edges ofblade, the blade, the forcing is evident. On theOn other shown Figure the flow velocities outside the rotor the are relatively effect is evident. thehand, otheras hand, as in shown in3h, Figure 3h, the flow velocities outside rotor are high for the passive rotation. vortex can also becan observed the trailing edge in theedge casein ofthe passive relatively high for the passiveArotation. A vortex also be at observed at the trailing case rotation. the difference the flowin structure thebetween passive the andpassive forced rotations is of passiveTherefore, rotation. Therefore, the in difference the flowbetween structure and forced observed is mainly in the wake in area the rotor. Compared the flow dragged by the forcedby blade, rotations observed mainly theofwake area of the rotor.toCompared to the flow dragged the the flow pushes drags the and bladedrags morethe significantly insignificantly the passive mode themode blade when rotatesthe to forced blade, theand flow pushes blade more in thewhen passive the wake of the rotor. blade rotates to the wake of the rotor. A time history of the instantaneous torques under no-load condition condition in the starting process is and the the moment of inertial kg·m m22.. shown in Figure Figure 4. 4. The The incident incidentfree freevelocity velocityisisUU∞∞ == 1.5 m/s m/s and inertial is is II == 10 kg· that thethe torques of theofindividual blades blades are disordered before t =before 4.0 s during acceleration. It can canbebeseen seen that torques the individual are disordered t = 4.0 s during After that moment, the equilibrium state is predicted for both the individual and total torques. acceleration. After that moment, the equilibrium state is predicted for both the individual and total The positive peak of peak the total is reduced to 42% that of anofindividual blade because of torques. The positive of thetorque total torque is reduced to of 42% of that an individual blade because thethe reverse torques from thethe other two blades. of reverse torques from other two blades.

Figure 4. Time history of the instantaneous torques during the starting process. Figure 4. Time history of the instantaneous torques during the starting process.

The effect of the incident flow velocity on the rotation speed of the rotor is shown in Figure 5. The effect of the incident flow velocity on the rotation speed of the rotor is shown in Figure 5. Even without any external resistance, the rotor fails to self-start at the flow velocity U∞ = 0.5 m/s, and Even without any external resistance, the rotor fails to self-start at the flow velocity U∞ = 0.5 m/s, keeps switching between “the start and stop” states. As shown in Figure 5a, the equilibrium state is and keeps switching between “the start and stop” states. As shown in Figure 5a, the equilibrium state predicted earlier when the incident velocity is higher. The equilibrium RPM (revolution per minute), is predicted earlier when the incident velocity is higher. The equilibrium RPM (revolution per minute), which varies from 90 to 217, also increases as the incident velocity increases. As shown in Figure 5b, which varies from 90 to 217, also increases as the incident velocity increases. As shown in Figure 5b, except the velocity condition of 0.5 m/s, the equilibrium TSRs at different incident velocities tend to except the velocity condition of 0.5 m/s, the equilibrium TSRs at different incident velocities tend to be close (varying from 4.53 to 4.72). The fluctuation ratios of the rotation speeds in these cases are all be close (varying from 4.53 to 4.72). The fluctuation ratios of the rotation speeds in these cases are all less than 1%. This indicates that the incident flow velocity has only a small effect on the TSR of the less than 1%. This indicates that the incident flow velocity has only a small effect on the TSR of the Darrieus turbine’s rotor under no-load condition if the turbine can self-start. Darrieus turbine’s rotor under no-load condition if the turbine can self-start. The hydrodynamic performance analysis is shown in Figure 6; only three incident–velocity The hydrodynamic performance analysis is shown in Figure 6; only three incident–velocity values values are shown in the figure to illustrate the comparison clearly. As shown in Figure 6a, the total are shown in the figure to illustrate the comparison clearly. As shown in Figure 6a, the total torque can torque can increase up to 610 N·m and 263 N·m at the incident velocities of 2.5 m/s and 1.5 m/s, respectively, in the acceleration stage. In the equilibrium stage, the positive peak-values of the total torque at the above two velocities are 111 N·m and 43 N·m, respectively. The time averaged values

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increase up to 610 N·m and 263 N·m at the incident velocities of 2.5 m/s and 1.5 m/s, respectively, in the acceleration stage. In the equilibrium stage, the positive peak-values of the total torque at the 2016, 9, 789 are 111 N·m and 43 N·m, respectively. The time averaged values of the total 8 of 15 aboveEnergies two velocities torque Energies 2016, 9, 789 8 of 15 converge to zero. Moreover, the total torque at U∞ = 0.5 m/s keeps fluctuating near zero throughout of the total torque converge to zero. Moreover, the total torque at U∞ = 0.5 m/s keeps fluctuating near the time domain. It can be seentoinzero. Figure 6b that thetotal peak valueatof Ckeeps for U m/s in the p of ∞ = 1.5 of the total torque converge torque U∞positive =peak 0.5 m/s fluctuating zero throughout the time domain. It Moreover, can be seenthe in Figure 6b that the value positive Cp fornear U∞ equilibrium stages isthe 0.36, which is slightly larger than thatlarger Uthan 2.5 m/s = 0.31). These ∞ throughout time domain. can be seenisin Figure 6bfor that the= peak value positive Uresults ∞ =zero 1.5 m/s in the equilibrium stages isIt0.36, which slightly that for U(C ∞ of =p 2.5 m/s (CC p p=for 0.31). indicate that the passive model used in this study can accurately simulate the rotor motion under = 1.5 m/s in theindicate equilibrium is 0.36,model whichused is slightly for U∞ =simulate 2.5 m/s (Cthe p = rotor 0.31). These results that stages the passive in thislarger studythan canthat accurately no-load conditions. These results that the passive model used in this study can accurately simulate the rotor motion under indicate no-load conditions. motion under no-load conditions.

(a) (b) (a) (b) Figure 5. Effects of the incident flow velocity on the rotation speed (No-load condition): (a) Revolution Figure 5. Effects of the incident flow velocity on the rotation speed (No-load condition): (a) Revolution Figure 5. Effects of the flow velocity per minute (RPM); (b) incident Tip-speed-ratio (TSR).on the rotation speed (No-load condition): (a) Revolution per minute (RPM); (b) Tip-speed-ratio (TSR). per minute (RPM); (b) Tip-speed-ratio (TSR).

(a) (b) (a) (b) Figure 6. Effects of the incident free velocity on the hydrodynamic performance (No-load condition): Figure 6. Effects (a) Torque; (b) Cpof . the incident free velocity on the hydrodynamic performance (No-load condition): Figure 6. Effects of the incident free velocity on the hydrodynamic performance (No-load condition): (a) Torque; (b) Cp.

(a) Torque; (b) Cp . The effect of moment of inertia on the hydrodynamic performance of the VAT rotor is shown in The of moment inertiaisonset theashydrodynamic performance of the VAT rotor is shown of in Figure 7. effect The incident free of velocity 1.5 m/s. As expected, the rotor with a lower moment Figure 7. The incident free velocity is the setearlier as 1.5(Figure m/s. As7a). expected, the rotor aVAT lower moment of in inertia finishes the self-starting process The averaged peak values of the torques The effect of moment of inertia on hydrodynamic performance ofwith the rotor is shown inertia finishes thestage self-starting process earlier (Figure 7a). The averaged peak values of the torques in theThe equilibrium the three values of moment ofexpected, inertia arethe veryrotor close.with The a averaged-value Figure 7. incident free for velocity is set as 1.5 m/s. As lower moment of 2 is slightly infinishes the peak equilibrium stage three values moment of inertia are close. The averaged-value of the torque for I =for 1.0 the kg· m lower than those the very otherpeak two values ofofmoment of inertia the self-starting process earlierof (Figure 7a). Thefor averaged values the torques in of the peak torqueinfor I = 1.07b, kg· m2time-averaged is slightly lower thaninthose for the other twofor values of moment of inertia. As shown Figure the TSRs the equilibrium stage different moment the equilibrium stage for the three values of moment of inertia are very close. The averaged-value of inertia. Asare shown Figure the time-averaged TSRs stage for different of inertia also in close. The7b, fluctuation in the TSR for Iin=the 1.0 equilibrium kg·m2 is much larger than thatmoment for the the peak torque for I = 1.0 kg·m2 is slightly lower than those for the other two values of moment of 2 is much larger than that for the of inertia arebecause also close. in the TSR for = 1.0 kg· other cases, the The rotorfluctuation with a lower moment of Iinertia is m more sensitive to variations in the inertia. As shown in Figure 7b, the time-averaged TSRs in the equilibrium stagetofor different moment other cases, becausealso theindicate rotor with lower moment of inertiamoment is more of sensitive variations in the torque. The results thatathe rotors with different inertia values will achieve 2 is much larger than that for the of inertia are also close. The fluctuation in the TSR for I = 1.0 kg · m results also under indicate that the rotors with different moment of inertia values will achieve atorque. similarThe rotation speed no-load conditions. otheracases, rotor with a lower moment of inertia is more sensitive to variations in the similarbecause rotation the speed under no-load conditions. 4.2.The Calculations System that Loadsthe rotors with different moment of inertia values will achieve torque. results with alsothe indicate 4.2. Calculations with the System Loads conditions. a similar rotation speed under no-load

generator are mainly determined by the internal configurations and connections [33]. The generators with different installed capacities (from 1 kW to 10 kW) considered in this study have the same outline shape and internal configurations and connections [32], and the bearings and connecting components are all assumed to be same. Thus, the friction loads from the driven train are set as 10 N·m for all the generators. Three values of moment of inertia (1 kg·m2, 10 kg·m2 and 20 kg·m2) and Energies 2016, 789 three9,incident free velocities (1.0 m/s, 1.5 m/s and 2.5 m/s) were employed. Hence, there was a total of 36 cases in the calculations with system loads.

(a)

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(b)

Figure 7. Effects of the moment of inertia on the hydrodynamic performance (No-load condition):

Figure 7. Effects of the moment of inertia on the hydrodynamic performance (No-load condition): (a) Torque; (b) TSR. (a) Torque; (b) TSR. Table 2. Calculating parameters for different generators.

4.2. Calculations with the System LoadsRated Rotation Installed Capacity

Initial Torque Constant Ratio k G (kW) Speed (RPM) (N· m) (N· m· s/rad) In the calculation cases with the system loads, not all the entire drive train was considered and 1 200 1.5 2.6 only the electric generator with necessary connectors (the bearing and clutch) were used to provide the 2 200 2.0 6.0 resistance loads. A typical widely employed 5 series of PMSG,250 4.5 for wind energy 13.6and tidal stream energy utilization in China [32],10 were used to provide have a linear relationship 150 the input system 13.0 loads, which40.8

with the rotation speed. Considering the output torque of the rotor in the forced and passive rotation Four self-starting modes were chosen: found in the calculations system a) Stable Equilibrium cases, four installed capacities G were 1 kW, 2 kW, 5 with kW and 10 loads: kW. The values of initial torque Mode (SEM); (b) Unstable Equilibrium Mode (UEM); (c) Switch Mode (SM); (d) Halt Mode (HM). The and constant ratio k for each G are listed in Table 2. The friction loads of the generator are mainly typical curves for these four modes are plotted in Figure 8. For the SEM (Condition: U∞ = 1.0 m/s, I = 1 determined internal and connections [33]. generators with adifferent 2, G the kg·mby = 2 kW), after configurations a quick increase during the initial stage, theThe rotation speed follows sinusoidalinstalled capacities (from 1 kW to 10 kW) considered in this study have the same outline shape and shape curve and reaches a stable equilibrium state; For the UEM (Condition: U∞ = 1.5 m/s, I = 20 kg· m2,internal configurations connections [32], and is the and components are speed all assumed G = 1 kW),and the rotation speed of the rotor farbearings less than that forconnecting the SEM. Furthermore, the rotor still shows periodic variationloads characteristics after 12 s; Fortrain the SM (Condition: ∞ =·m 1.5 for m/s,all I = 20 kg· m2, to be same. Thus, the friction from the driven are set as 10UN the generators. G = 5 kW), the rotation variation shows the start and stop 2 , 10that Three values of moment of speed inertia (1 kg·m kg·the m2rotor andkeeps 20 kgswitching ·m2 ) andbetween three incident free velocities states and fails to self-start; For the HM (Condition: U∞ = 1.0 m/s, I = 20 kg·m2, G = 2 kW), the rotor tries (1.0 m/s, 1.5 m/s and 2.5 m/s) were employed. Hence, there was a total of 36 cases in the calculations to rotate at the initial stage, then quickly halts, and finally fails to restart again. with system loads. Table 2. Calculating parameters for different generators. Installed Capacity G (kW)

Rated Rotation Speed (RPM)

Initial Torque (N·m)

Constant Ratio k (N·m·s/rad)

1 2 5 10

200 200 250 150

1.5 2.0 4.5 13.0

2.6 6.0 13.6 40.8

Four self-starting modes were found in the calculations with system loads: (a) Stable Equilibrium Mode (SEM); (b) Unstable Equilibrium Mode (UEM); (c) Switch Mode (SM); (d) Halt Mode (HM). The typical curves for these four modes are plotted in Figure 8. For the SEM (Condition: U∞ = 1.0 m/s, I = 1 kg·m2 , G = 2 kW), after a quick increase during the initial stage, the rotation speed follows a sinusoidal shape curve and reaches a stable equilibrium state; For the UEM (Condition: U∞ = 1.5 m/s, I = 20 kg·m2 , G = 1 kW), the rotation speed of the rotor is far less than that for the SEM. Furthermore, the rotor speed still shows periodic variation characteristics after 12 s; For the SM (Condition: U∞ = 1.5 m/s, I = 20 kg·m2 , G = 5 kW), the rotation speed variation shows that the rotor keeps switching between the start and stop states and fails to self-start; For the HM (Condition: U∞ = 1.0 m/s,

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I = 20 kg·m2 , G = 2 kW), the rotor tries to rotate at the initial stage, then quickly halts, and finally fails to restart again. Energies 2016, 9, 789 10 of 15

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Figure 8. Four typical modes of self-starting processes under the load conditions.

Figure 8. Four typical modes of self-starting processes under the load conditions. The time histories of the torques corresponding to the four modes during the self-starting process shown inofFigure 9. Figure 9a shows that after to the the acceleration during during the initialthe stage, the The time are histories the torques corresponding four modes self-starting hydrodynamic torque and the system load show a sinusoidal shape in the equilibrium state. The total process are shown in Figure 9. Figure 9a shows that after the acceleration during the initial torque also fluctuates near zero to enable the rotor to rotate stably. In Figure 9b, periodic variations stage, the hydrodynamic torque andmodes the of system load showunder a sinusoidal shape in the equilibrium Figure 8. Four typical self-starting processes the load conditions. of the hydrodynamic torque, system load, and total torque can be observed, which cause the rotor to state. The total also fluctuates zero enable rotor to rotate stably. Inlow. Figure 9b, rotate inThe antorque unstable equilibrium state.near Forcorresponding the SM to in Figure 9c,the the hydrodynamic is very time histories of the torques to the four modes during torque the self-starting periodicAlthough variations of the hydrodynamic torque, system load, and total torque can be observed, a relatively stable total-torque can be generated, the rotation speed is low, and this causes process are shown in Figure 9. Figure 9a shows that after the acceleration during the initial stage, the which cause rotor to rotate in an unstable equilibrium state. For the SM in Figure 9c, thehydrodynamic rotorthe to switch between the start and stop states. Since there is no increase in the net torque, the torque and the system load show a sinusoidal shape in the equilibrium state. The total rotor cannot be made to accelerate anymore. As shown in Figure 9d, the hydrodynamic torque torque also torque fluctuates to enable the rotor to rotate stably. In Figure 9b, periodic the hydrodynamic isnear veryzero low. Although a relatively stable total-torque canvariations be generated, the quickly andthis causes the net torque totodecrease tobetween a negative value. After the rotor halts,toSince the there of the is hydrodynamic torque, system load, and total torque can be observed, which the rotor rotationdecreases speed low, and causes the rotor switch the start andcause stop states. system be theequilibrium sum of thestate. friction initial torques, andhydrodynamic the hydrodynamic during rotateload in anwill unstable For and the SM in Figure 9c, the torquetorque is very low. is no increase in thea net torque, the rotor cannot be made tothe accelerate anymore. As shown in Figure 9d, relatively stable total-torque can torque be generated, rotation speed is low,again. and this causes theAlthough resting state fails to generate positive net and restarts the rotor rotation the hydrodynamic decreases quickly andstates. causes thethere netistorque to decrease a negative value. the rotor totorque switch between the start and stop Since no increase in the net to torque, the made to accelerate anymore. As shown in the Figure 9d, the and hydrodynamic torque and the After the rotor rotorcannot halts,bethe system load will be the sum of friction initial torques, decreases quickly and causes net torque to fails decrease a negativepositive value. After rotor halts, hydrodynamic torque during thethe resting state to to generate netthetorque andthe restarts the system load will be the sum of the friction and initial torques, and the hydrodynamic torque during rotor rotation again. the resting state fails to generate positive net torque and restarts the rotor rotation again.

(a)

(a)

(c)

(b)

(b)

(d)

Figure 9. Time histories of torques during self-starting under the load conditions: (a) Stable Equilibrium Mode (SEM); (b) Unstable Equilibrium Mode (UEM); (c) Switch Mode (SM); (d) Halt Mode (HM). (c)

(d)

Figure 9. Time histories of torques during self-starting under the load conditions: (a) Stable Equilibrium

Figure 9. Time of torques during Mode self-starting under load conditions: (a)(HM). Stable Equilibrium Mode histories (SEM); (b) Unstable Equilibrium (UEM); (c) Switchthe Mode (SM); (d) Halt Mode Mode (SEM); (b) Unstable Equilibrium Mode (UEM); (c) Switch Mode (SM); (d) Halt Mode (HM).

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The of the the VAT VAT rotor The operating operating performance performance of rotor is is given given in in Figure Figure 10. 10. Only Only the the SEM SEM results results are are shown to demonstrate the rotor performance under the stable equilibrium state after self-starting. shown to demonstrate the rotor performance under the stable equilibrium state after self-starting. The at at thethe stable equilibrium stage are are shown in Figure 10a and The time-averaged time-averagedvalues valuesofofoutput outputtorque torque stable equilibrium stage shown in Figure 10a are used to calculate the output power in Figure 10b. It can be seen that the rotor linked to a generator and are used to calculate the output power in Figure 10b. It can be seen that the rotor linked to a with a smaller has a higherhas speed and delivers lower torque and power. For apower. given generator withinstalled a smallercapacity installed capacity a higher speed and delivers lower torque and generator, larger TSR will enable theenable rotor to more power. highest output-power For a givenagenerator, a larger TSR will thegenerate rotor to generate more The power. The highest output2 , and G = 10 kW. predicted in this study is 3.37 kW under the condition: U = 2.5 m/s, I = 1 kg · m 2 ∞ power predicted in this study is 3.37 kW under the condition: U∞ = 2.5 m/s, I = 1 kg·m , and G = 10 kW.

(a)

(b)

Figure rotor: (a) (a) Output Output Torque; Torque; (b) (b) Output Output Power. Power. Figure 10. 10. Operating Operating performance performance of of the the VAT VAT rotor:

A typical comparison of the pressure and hysteresis loop of vertical torques around a blade in A typical comparison of the pressure and hysteresis loop of vertical torques around a blade in the forced and passive rotation cases is shown in Figure 11. The calculation conditions are as follows: the forced and passive rotation cases is shown in Figure 11. The calculation conditions are as follows: U∞ = 1.5 m/s, I = 1 kg·m2,2and G = 5 kW. The averaged TSR for passive rotation is 2.36, which is used U∞ = 1.5 m/s, I = 1 kg·m , and G = 5 kW. The averaged TSR for passive rotation is 2.36, which is used as the fixed TSR for forced rotation. The instantaneous azimuth angle of the blade is 90°. The contours as the fixed TSR for forced rotation. The instantaneous azimuth angle of the blade is 90◦ . The contours of pressure distribution around the blade airfoil are illustrated in Figure 11a. It can be seen that the of pressure distribution around the blade airfoil are illustrated in Figure 11a. It can be seen that the general distribution of the pressure around the airfoil is similar. The main difference can be found in general distribution of the pressure around the airfoil is similar. The main difference can be found in the domain of negative pressure at the left side of the blade. the domain of negative pressure at the left side of the blade. The hysteresis loop of vertical torques generated on the blade at the azimuth angle of 90° for two The hysteresis loop of vertical torques generated on the blade at the azimuth angle of 90◦ for rotation conditions are compared in Figure 11b. The downward direction is defined as the positive two rotation conditions are compared in Figure 11b. The downward direction is defined as the positive direction of the vertical torques. The direction of the hysteresis loop is anticlockwise. The torque direction of the vertical torques. The direction of the hysteresis loop is anticlockwise. The torque distribution characteristics for the forced and passive rotation conditions are similar. A peak can be distribution characteristics for the forced and passive rotation conditions are similar. A peak can be found at the leading edge in the negative pressure domain. Except a small section of the leading edge found at the leading edge in the negative pressure domain. Except a small section of the leading edge in the positive pressure domain, most torques generated on the blade cells in the vertical direction in in the positive pressure domain, most torques generated on the blade cells in the vertical direction in the passive rotation case are slightly higher than those for the forced rotation condition. In this case, the passive rotation case are slightly higher than those for the forced rotation condition. In this case, the resultant torque in the vertical direction for passive rotation is 43 N·m higher than that for the the resultant torque in the vertical direction for passive rotation is 43 N·m higher than that for the forced rotation condition. forced rotation condition. A comparison of the predicted values of Cp-ave for the passive and forced rotation conditions is A comparison of the predicted values of Cp-ave for the passive and forced rotation conditions is shown in Figure 12. As in the case of Figure 10, only the results of the simulations for passive rotation shown in Figure 12. As in the case of Figure 10, only the results of the simulations for passive rotation for the SEM are shown. It can be seen that the curve of Cp-ave in the passive rotation condition has a for the SEM are shown. It can be seen that the curve of Cp-ave in the passive rotation condition has varying trend similar to that in the case of the forced rotation. A peak value of Cp-ave is predicted as 0.47 a varying trend similar to that in the case of the forced rotation. A peak value of Cp-ave is predicted under the condition of U∞ = 1.5 m/s, I = 1 kg·m2, and G = 5 kW. The TSR in the equilibrium state is 2.36. as 0.47 under the condition of U∞ = 1.5 m/s, I = 1 kg·m2 , and G = 5 kW. The TSR in the equilibrium state Overall, the Cp-ave in the passive simulation is, on average, 38% higher than those calculated in the forced is 2.36. Overall, the Cp-ave in the passive simulation is, on average, 38% higher than those calculated in rotation cases, as can be seen in Figure 11, which is caused by a higher torque generated by the blade. the forced rotation cases, as can be seen in Figure 11, which is caused by a higher torque generated by The results indicate that the previous studies that used the methodology of a given rotation speed have the blade. The results indicate that the previous studies that used the methodology of a given rotation underestimated the real operating performance of the VAT rotor without any controls. speed have underestimated the real operating performance of the VAT rotor without any controls. On the other hand, it should be pointed out that the 2D numerical model has an inevitable disadvantage in ignoring some realistic frictions, parasitic drags and other 3D effects. Therefore, not the absolute values but the relative values of the power coefficient in Figure 12 may provide more reference value to the comparison of the numerical simulations for the passive and forced rotation

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On the other hand, it should be pointed out that the 2D numerical model has an inevitable disadvantage in ignoring some realistic frictions, parasitic drags and other 3D effects. Therefore, not the2016, absolute Energies 9, 789 values but the relative values of the power coefficient in Figure 12 may provide12more of 15 Energies 2016, 9, 789 12 of 15 reference value to the comparison of the numerical simulations for the passive and forced rotation stable rotation speed of conditions in this study. study. Moreover, Moreover,aausable usableelectricity electricityoutput outputneeds needsa arelative relative stable rotation speed conditions in this study. Moreover, a usable electricity output needs a relative stable rotation speed thethe rotor and thethe generator. of rotor and generator.It Itmeans meansthat thatthe thebig bigvariation variationshown shownin inFigure Figure 99 should should be controlled of the rotor and the generator. It means that the big variation shown in Figure 9 should be controlled artificially to match the need of the electricity generation and output. artificially to match the need of the electricity generation and output.

(a) (b) (a) (b) Figure 11. Comparison of hydrodynamics between the forced and passive rotations: rotations: (a) Figure 11. Comparison of hydrodynamics between the forced and passive (a) Pressure Pressure Figure 11. Comparison of hydrodynamics between the forced and passive rotations: (a) Pressure Contour; (b) Hysteresis loop of torques. Contour; (b) Hysteresis loop of torques. Contour; (b) Hysteresis loop of torques.

Figure 12. Comparison of Cp-ave under passive and forced rotation conditions. Figure 12. 12. Comparison Comparison of of C Cp-ave under passive and forced rotation conditions. Figure p-ave under passive and forced rotation conditions.

The self-starting modes for all the calculation cases are listed in Table 3. When the moment of The self-starting modes for all the calculation cases are listed in Table 3. When the moment of inertia is self-starting low, the rotormodes can drive thethe generator withcases smaller G. For large the value of G, the The for all calculation are values listed inofTable 3. aWhen moment of inertia is low, the rotor can drive the generator with smaller values of G. For a large value of G, the mode from HM SM the or SEM as thewith incident velocity a medium moment of inertiachanges is low, the rotor cantodrive generator smaller valuesincreases; of G. For aFor large value of G, the mode mode changes from HM to SM or SEM as the incident velocity increases; For a medium moment of inertia (I from = 10 kg· m22to ), the cannot drive any generator at U∞ = 1.0For m/s.aIn addition, the self-starting changes HM SMrotor or SEM as the incident velocity increases; medium moment of inertia inertia (I = 102 kg·m ), the rotor cannot drive any generator at U∞ = 1.0 m/s. In addition, the self-starting mode at Urotor ∞ = 1.5 m/s. The rotor drive theatgenerators at U∞ =In2.5 m/s except one with (I = 10iskgthe ·mSM ), the cannot drive anycan generator U∞ = 1.0 m/s. addition, the the self-starting mode is the SM at U∞ = 1.5 m/s. The rotor can drive the2 generators at U∞ = 2.5 m/s except the one with G = 10 is kW; large of inertia (I = 20 kg· m ), the fails toatdrive any when mode theFor SMa at U moment = 1.5 m/s. The rotor can drive the rotor generators U∞ = 2.5generators m/s except the G = 10 kW; For a large∞ moment of inertia (I = 20 kg·m2), the rotor fails to drive any generators when the ∞ =a1.0 m/s) and can a small installed (G = 1 one velocity with G =is10low kW;(U For large moment of drive inertiathe (I =generator 20 kg·m2 ),with the rotor fails to drivecapacity any generators the velocity is low (U∞ = 1.0 m/s) and can drive the generator with a small installed capacity (G = 1 kW, 2 kW) whenisthe is higher. whenorthe velocity lowvelocity (U∞ = 1.0 m/s) and can drive the generator with a small installed capacity kW, or 2 kW) when the velocity is higher. (G = 1 kW, or 2 kW) when the velocity is higher.

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Table 3. Summary of self-starting modes. Free Velocity (m/s)

1

1.5

2.5

1

1.5

2.5

1

1.5

2.5

Moment of Inertia (kg·m2 )

Installed Capacity (kW)

Mode of Self-Starting

1

1 2 5 10

SEM SEM HM HM

1

1 2 5 10

SEM SEM SEM SM

1

1 2 5 10

SEM SEM SEM SEM

10

1 2 5 10

HM HM HM HM

10

1 2 5 10

SM SM SM SM

10

1 2 5 10

SEM SEM SEM SM

20

1 2 5 10

HM HM HM HM

20

1 2 5 10

UEM UEM SM SM

20

1 2 5 10

SEM SEM UEM UEM

5. Conclusions In this study, a 2D numerical model based on the CFD software ANSYS-Fluent was established to investigate the self-starting performance of the Darrieus straight-bladed VAT rotor. The passive rotation driven directly by the incident flow could be simulated numerically. The system loads, including the friction torque, initial torque and reverse torque during the rotation of the generator were also considered in the numerical model. The model was validated by the experimental data of the self-starting process of the Darrieus wind turbine. A comparison of the flow structures indicates that the blades were pushed by the flow more significantly in the wake area of the rotor in the simulations of the passive rotation condition. Under no-load condition, the free velocity and the moment of inertia of the rotor were found to have little effect on the TSR. Under system load conditions, there were four modes of self-starting: SEM, UEM, SM and HM. The highest power predicted in this study is 3.37 kW. A larger negative pressure domain was observed around a blade at the azimuth angle of 90◦ for the passive rotation case. This will cause the generation of a higher working torque at the leading edge, especially in the negative pressure domain for passive rotation. Consequently, the averaged dimensionless power coefficient in

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the passive simulation was, on average, 38% higher than those derived from the simulation of forced rotation with the same TSR. A rotor with a lower inertia can be expected to deliver more torque and power for tidal stream conversion. It should be pointed out that the 2D numerical model has ignored some important 3D effects, including the parasitic drags and frictions. We believe that this yielded an overestimation on the prediction of the power coefficient. In the future work, this numerical methodology on the flow-driven self-starting of VAT should be applied in the 3D model to recruit for a more precise prediction on the passive rotation of the Darrieus turbine. The experimental study on the self-starting of VAT needs to be conducted in the water flow tank to provide more reliable data. Acknowledgments: The authors are grateful for the financial support fully provided by the National Natural Science Foundation of China (51279190 and 51311140259), partly provided by Shandong Natural Science Funds for Distinguished Young Scholar (JQ201314) and Innovation Project (2014ZZCX06105), Qingdao Municipal Science & Technology Program (14-2-4-20-jch and 14-9-1-5-hy), Huangdao District S&T Program (2014-4-15) and the Program of Introducing Talents of Discipline to Universities (111 Project, B14028). Author Contributions: Zhen Liu and Hongda Shi conceived and designed the numerical simulation; Hengliang Qu performed the numerical simulations; Zhen Liu and Hengliang Qu analyzed the data; Zhen Liu prepared the paper. Conflicts of Interest: The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

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