Numerical study of a guide-vane-augmented vertical darrieus tidal-currentturbine *

Zhen Liu , Zhi-meng Wang, Hong-da Shi , Heng-liang Qu

1. Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China, Qingdao 266100,China

2. Department of Ocean Engineering, College of Engineering, Ocean University of China, Qingdao 266100,China

3. Qingdao Municipal Key Laboratory of Ocean Renewable Energy, Ocean University of China, Qingdao 266100,China

Abstract: It is reported that the augmented vertical axis turbine (VAT) has a better operating performance. A guide-vane type augmentation is proposed in this study, with a simpler outline and a better adaptability to various directions of the incident water flow,as compared to the duct-type diffuser. A 2-D numerical model based on the computational fluid dynamics software ANSYS-Fluent is established and validated by experimental data. It is found that the guide vanes could narrow the flow path together with the VAT rotor and increase the flow velocity around the blades. The fluctuation of the instantaneous torque output is significantly reduced by using the guide-vane stator. The numerical results indicate that a four blades setup is suitable for the stator and the chord length of the guide vane should be equal to that of the rotor blade. The gap between the stator and the rotor is suggested to be a quarter of the chord length of the rotor blades. The non-zero pitch angle of the guide vane is found to have negative effects on the torque and the power output. The averaged power and torque coefficients for three non-zero directional angles of the incident flow are approximately 30% lower than those for the zero-directional angle.

Key words: Tidal current energy, vertical axis turbine, augmented rotor, guide vane, numerical simulation

Introduction

Harvesting the sustainable and renewable energy from ocean is a long-term dream for scholars and engineers. The tidal current energy is one of the most promising marine energy resources, predictable and stable for access and conversion. Similar to the wind energy, two types of turbines are always employed to capture the tidal current energy: the horizontal and vertical axis turbines. Comparing to the horizontal type, the vertical axis turbine (VAT) has a better adaptability to the incident flow directions. Excellent self-starting ability makes the VAT available to operate under a lower current velocity condition, as is common at the nearshore areas in North of China. The installed capacity of the VAT prototype device in China has increased to 300 kW[1].

Improving the operating performance of the VAT has always been a research hotspot in the area of the tidal current energy utilization. The optimization of the blade shape is the first focus during the development of the VAT. Twenty symmetric and non-symmetric foil shapes were studied and compared by using the CFD software[2]. It was found that the S-1046 airfoil could increase the power output coefficient by 26.83%. The high-digit symmetrical NACA profile could output a higher power in the low blade speed range than the low-digit one. In contrast,the low-digit profiles could output a higher power in the high blade speed range[3]. The limitations of the fixed pitch Darrieus hydro-turbine were reviewed by Kirke and Lazauskas[4]. It was pointed out that the fixed pitch blades suffered from the poor self-starting torque and the low efficiency. The shaking of the rotor could reduce the service life of the turbines. On the other hand, the variable pitch offered an alternative solution to generate a higher starting torque and achieve a larger efficiency.

Besides the optimization of the blade, the diffuser was another option to improve the dynamic performance of the VAT[5]. Some facilities were employed to increase the flow velocities adjacent to the blades or modify the local flow fields, to improve the fluid forces on the blades and consequently improve the torque generation of the VAT. The Venturi-duct was a simple and efficient facility to improve the local flow speeds around the blades[6].The effects of the duct shape, the position of the turbine, the convergence angle of the duct, and the external shape of the duct were studied by using the computational fluid dynamics (CFD) method[7]. It was observed that all above parameters have an optimum value. A well-designed duct could significantly increase the power output of the VAT[8]. As compared to the case under the free-stream conditions, the maximum power output within the duct has an increase of 74%. In addition, four types of internal duct shapes were compared numerically and the elliptic type duct was found to have a best output of the torque[9].

Another facility was called the “deflector”, which was a deflecting plate right in front of the turbine. The performance of an upstream flat deflector for a two counter-rotating VAT was investigated experimentally[10]. The width and the height of the deflector and the distance between the turbine and the deflector had significant effects on the power output of the turbine. Furthermore, the effects of an upstream deflector on the power output, the torque generation,and the nearby flow fields of the VAT were studied in the water channel[11]. The phase of the torque output and the collision between the blade and the vertical structure were demonstrated. A shortcoming of the deflector was its sensitivity to the direction of the incident flow.

The guide vanes surrounding the turbine were also an effective diffuser to the VAT. An omnidirection guide vane was proposed to optimize the performance of the vertical axis wind turbine[12]. In addition, the omni-direction guide vane was found to minimize the negative torque zone and the power coefficient is increased by up to 58% at the tip speed ratio of 2.5[13]. Furthermore, the effects of the guide-vane angles on the performance of the VAT system were analyzed by using the CFD simulations[14]. It was found that the performance could be enhanced by 24.3% with the guide-vanes at the optimized angles. A twin-VAT system with the guide-vanes and the diffuser integrated with the cooling tower was experimentally studied[15]. The torque output is increased by 7-8%. An innovative power augmenter with the complex guide-vanes was proposed to enhance the on-coming flow speed and guide it to an optimum incident angle for the improvement of the performance[16]. An augmented VAT using the airfoil-type guide vanes was compared to an open rotor using the CFD method[17].

With a rapid development of the computer, the numerical simulation becomes a popular desktop tool for the engineers. A 1-D mathematical model based on the blade element momentum method was proposed to evaluate the performance of the VAT with the effects of the diffuser[18]. The adaptive neuro-fuzzy method was used to predict the rotation speed of the turbine system to overcome the inherent variable behavior of the wind speed[19-20]. The transit numerical model based on the Reynolds-averaged Navier-Stokes(RANS) equations was set up to couple with different turbulence models. The RANS equations were solved in the commercial CFD software[21-23], to provide more fluid field information around the rotor and the guide vanes. The 2-D numerical model was recommended to replace the 3-D model to balance the computation cost and the precision in the design stage.

From a literature review, it can be seen that the guide-vane type diffuser is a promising augmentation to improve the performance of the vertical axis Darrieus turbine. It is clear that there is little work published about this type of augmentation for the VAT. An innovative guide-vane type augmentation is proposed in this paper, with a couple of pairs of the NACA-shape hydrofoils, evenly distributed to generate a gradually narrowed flow passage for the rotor. This type of augmentation is more adaptive to the variable directions of the water flow. In this study,the open and augmented rotors are studied and compared with a 2-D numerical model, established based on the CFD software ANSYS-Fluent. The flow fields and the pressure distributions for the augmented and open rotors are compared. The effects of the number of guide vanes, the distance between the rotor and the guide vanes, and the chord length of the guide-vane foils on the performance of the VAT rotor are investigated.

1. The guide-vane augmented vertical axis turbine(GAVAT)

The schematic diagram of a guide-vane augmented vertical axis tidal current turbine is shown in Fig. 1.As shown in Fig. 1(a), the rotor contains three straight blades of diameter (=1.0 m). Each blade is connected to the center shaft of diameter(=0.05 m)by two sets of supporting arms at the upper and lower ends. The cross-section of the blade takes the shape of a symmetrical NACA0018 . The chord length of the cross-section is =0.12 m. The installation point is 0.25Craway from the leading edge, and the pitch angle is set to be zero for all three blades. Figure 1(b)illustrates the outside stator with four guide vanes and two flat covers. The guide vanes are evenly distributed,to concentrate the water flows from different directions to the rotor. The diameter of the stator Dsis defined as the distance between the outer edges of two guide vanes in pair. As seen in Fig. 1(c), the cross-section of the guide vanes at the mid-span takes also the shape of a symmetrical NACA0018. The chord length of the foil is defined as Cs. The gap between the rotor and the stator is defined as G .

Fig. 1 (Color online) Schematic diagram of guide-vane augmented vertical axis turbine

Two dimensionless parameters are employed to represent the hydrodynamic performance of the turbine, including the averaged power coefficient Cpand the averaged torque coefficient Ct. The definitions of the coefficients are as follows[20]:

where ρ,rR are the water density and the rotor radius, respectively, VIis the incident flow velocity from the far field,rA is the rotor swept area, defined as, H is the blade height, Taveis the averaged torque output in one revolution. Accordingly,is the averaged power output in one revolution,which is calculated as, where ω is the angular velocity of the rotor.

2. Numerical model

A 2-D numerical model is established in this study. The continuity equation of incompressible fluids and the unsteady RANS equations are the governing equations. These equations are solved by the general-purpose commercial CFD software ANSYS-Fluent. The finite volume method is used for discretization based on the pressure-based solver. The pressure-velocity coupling is recreated using the SIMPLE scheme. The second-order upwind algorithm is adopted for the convection terms in the spatial discretization.

Figure 2 gives a 2-D computational domain and the mesh structures of the guide-vane augmented VAT.A rectangular computational domain of a length of 15rD and a width of 10rD is considered. The velocity inlet boundary is set at the left side of the domain, and the pressure outlet boundary condition is set at the right side. The relative pressure is kept to be 0 Pa, to represent the open condition. The flow direction in all calculations is set to be horizontal from left to right. A non-slip shear option is used for the wall boundary condition at the top and bottom sides.The core domain is 5 Draway from the velocity inlet boundary, to ensure the full development of the incident water flow from the far field and the wake formation in the downstream. The rotor shaft is set at the center on the vertical direction, to reduce the sidewall effects as much as possible.

Fig. 2 (Color online) Computation domain and mesh structures

The computational domain is divided into three parts: the outer and inner stationary sub-domains and the rotational sub-domain. The circular ring domain(the blue part) can rotate together with three blades,and a sliding mesh model is coupled with it. The stationary and rotational sub-domains are connected to each other through the non-conformal interfaces. The mesh motions are prescribed so that the sub-domains are linked at the interfaces and remain in contact with each other (sliding along the interface boundaries) to ensure the accurate exchanges of all numerical flux at the interfaces and a faster computation convergence.The width of the rotational domain cirque is 20 times of the blade foil thickness, to guarantee the boundary layer height to process the near wall flows. It will also not affect the calculated results regardless of the change of the cirque width[17].

In order to reduce the computing time and improve the calculation accuracy, as much as possible,the structured meshes are used in the outer stationary sub-domain. In the rotational sub-domain, the unstructured meshes are employed to fit the complex geometry of the blades. The boundary layer meshes around the blades are refined to deal with the near wall turbulence effects and the wake vortex generation.The wall+y is controlled to be from 20 to 80, as is widely used in the numerical simulations of this type of problems[17].

The selection of the turbulence model, the time step and the mesh number is always a challenge for the CFD software. A number of simulations were carried out by the authors to make proper choices.Based on the validation studies[11], the shear stress transportation (SST) turbulence model, the mesh number of 2×105, and the time step of 0.01 s are used in this study.

In order to further validate the set-up of the numerical model, an open rotor of the Darrieus straight-bladed VAT is considered in the calculation,and the numerical predictions are compared with the corresponding experimental data[24]. The cross-section of the rotor blade is also in the shape of the NACA0018. The incident water flow velocity is 1.0 m/s.The comparisons of the averaged power coefficientversus the tip speed ratio (TSR) between the numerical and experimental results are shown in Fig.3. The TSR is defined as. It can be seen that the numerical predictions agree well with the experimental data, except that the peak value of the numerical curve is at a smaller TSR because of the overestimation of Cpat TSR=2.2. The idealized conditions without mechanical loss and the 2-D simulation may all result in the over-prediction.Generally, the numerical model has shown its capability for unsteady predictions of the VAT hydrodynamic performance under the 2-D condition.

Fig. 3 Validation of 2-D numerical model

3. Results and discussions

3.1 Comparison of flow fields and instantaneous power-outputs

The instantaneous flow fields and torque outputs between the open and augmented rotors are compared.For the augmented rotor, four guide vanes are evenly distributed. Two of them are parallel to the incident flow direction and the other two are vertical to it. The parameters of the augmented rotor are Ds= 1.72 m,and, respectively. The constant incident-velocity of the water flow from the far field is 1.5 m/s. The rotation speed is fixed at 6.6 rad/s and therefore the TSR is 2.2.

The streamlines of the water flow and the contours of the total pressure are shown in Fig. 4. The 0° azimuth angle is defined as the positive direction of Y axis of the coordinate system shown in Fig. 2. The positive rotation direction of the rotor blades is anticlockwise. As shown in Fig. 4(a), the flow velocity inside the open rotor is decreased because of the shelter effects of the rotating blades. The disturbance of the flow field by the blades is weak,and no evident vortexes are observed. Correspondingly,the total pressure is relatively low inside the rotor. A high-pressure zone can be found near the leading edge of all blades at different azimuth angles. In some occasions, the high-pressure zone can also be observed at the trailing edge, caused by the dragging effects of the larger linear-velocities of the blade. On the other hand, the lower pressure zones usually locate at the sheltered side of the foils. As illustrated in Fig.4(b), a pair of guide-vanes parallel to the incident flow direction has little effects on the flow field because of their shape and orientation. On the other hand, two rows of vortexes are shed from a pair of vertical guide-vanes and propagate to the outside region. No obvious vortexes are observed inside the rotor domain.The vortexes shed from the vertical guide vanes have little effects on the flow field inside the rotor domain.When one of the blades rotates to the position near the vertical guide vanes, the flow path inside the stator becomes narrow and the flow velocities around the rotor blades become larger correspondingly. As compared to the open-rotor case, the pressure around the blades consequently becomes larger. It can be imagined that the torques generated by the blades will increase to achieve more power output.

Fig. 4 (Color online) Distributions of the pressure and stream lines around the VAT

In order to demonstrate the effects of the guide-vane stator on the performance of the VAT, the instantaneous torque outputs of the open and augmented rotors with respect to the azimuthal angles are shown in Fig. 5. The position relationship among three blades is illustrated in Fig. 5(a). The angle difference between every two blades is 120°. As can be seen in Fig. 5(b), the total-torque curve for the open rotor is close to a sinusoidal shape, with three peaks in a single revolution, contributed sequentially by one of the three blades. The difference between the peak and valley torques is over 110 N·m. On the other hand, the total-torque curve for the augmented rotor is in a pseudo-sinusoidal shape. From the analysis of the torque distribution around the blade at typical positions, it can be found that the driving-rotor pressure generated on the blade surface near the leading edge increases significantly. Although the three peaks are mainly contributed by three blades respectively, due to the increase of the driving-rotor pressure, finally, the difference between the peak and valley torques is reduced to less than 90 N·m. This means that the guide-vane stator can effectively reduce the torque fluctuation of the VAT rotor and subsequently improve the power output.

3.2 Effects of guide-vane stator on the performance of VAT

In order to comprehensively understand the operating mechanism of the guide-vane stator, the effects of its parameters, including the blade number,the chord length of the guide vane Cs, the gap between the guide vane and the rotor blade G , the fixed pitch-angle γ and the incident angle of the flow direction, on the hydrodynamic characteristics and the power output are studied. The above parameters, unless otherwise noted, are set as the four-blade guide vanes,is 2.0 Cr, G is 1.0 Crand γ is 0°. The incident flow velocity is fixed at 1.5 m/s. The rotor is tested over a range of TSR values from 1.0 to 3.0 under the rotation speed varying from 3.0 rad/s, 4.2 rad/s,5.4 rad/s, 6.6 rad/s, 7.8 rad/s to 9.0 rad/s.

The effects of the blade number of the stator on the averaged power and torque coefficients are shown in Fig. 6. Two numbers of 4, 8 are selected for the guide-vanes set-up. The same as the four blades, the eight blades are evenly distributed in the stator and a pair of them are parallel to the direction of the incident water flow. As it can be seen in Fig. 6(a), the curves for Cpin three cases are all in an increasing trend versus the TSR before reaching the peak at 2.2 of the TSR, and then in a decreasing trend as the TSR increases. The 4-blade stator shows a slightly better performance than the 8-blade stator in the entire domain of the TSR. The peak values of Cpfor the 4-blade and 8-blade augmented rotors are 0.38, 0.37,which are 19.8 %, 15.9 % higher than that of the open rotor (=0.31), respectively. The avera- ged value of Cpover the TSR range for these two augmented rotors are 19.2 %, 8.5 % higher than that of the open rotor, respectively. As can be seen in Fig. 6(b), the highest values of Ctfor both 8-blade augmented and open rotors are obtained at TSR=1.8, and the peak value of =0.17for the 4-blade augmented rotor is achieved at TSR =2.2. A better performance of the 4-blade augmented rotor on the improvement ofcan be observed. The highest Ctof the 4-blade augmented rotor is 12% higher than that of the open rotor. The averaged value of Ctof the 4-blade augmented rotor over the TSR range is 19.2% higher than that of the open rotor. It can be found that the operating performance of the VAT can not be improved simply by increasing the number of blades of the stator. The 4-blade augmented rotor has higher values of Cp, Ct. Therefore, four guide vanes are selected, and will be also employed in the subsequent cases.

Fig. 5 Instantaneous torque variation for open and augmented rotors

Fig. 6 Effects of the blade number on the performance of VAT

In view of the effects of the guide vanes on narrowing the flow path between the rotor and the stator, we compare five values of G to find a suitable gap between the stator and the rotor in Fig. 8.As can be seen in Fig. 8(a), the maximum values ofare achieved at 2.2 of the TSR for each G analyzed in this study. The values of Cpat each TSR all increase with the decrease of G from 1.0 Crto 0.25Crindependently. As G decreases to 0.17 Cr, the minimum values of Cpat each TSR are reached. The maximum value of Cpfor G=0.25Cris 0.46, which is 20% higher than the value of Cpwhen. The curves of Ctfor each G follow a same trend over the TSR range in Fig.8(b). Ctincreases with the increase of the TSR until the peak is reached, then Ctdecreases gradually as the TSR increases. The distribution characteristics ofwith respect to G is also the same as that ofThe peak value of Ctat TSR =2.2 for G =0.25 Cris 0.21, and also 20% higher than that when. The averaged values of Cp, Ctforover the TSR range are both 17% higher than those for =1.0rG C . Although the increase of the flow velocity can be realized by reducing the flow path, a threshold of the gap between the stator and the rotor shall be noted. Too small a value of G will impede the flow passing the gap instead of increasing the velocity.

Fig. 7 Effects of Cs on the performance of VAT

Fig. 8 Effects of G on the performance of VAT

Fig. 9 Pitch angles of guide-vane blades

Fig. 10 Effects of γ on the performance of VAT

Inspired by the onmi-direction-guide-vane for the wind turbine, we set a pitch angle γ of the guidevane blades in the stator, as shown in Fig. 9 for a better guidance to the incident flow cooperating with the rotation of the rotor. The clockwise and anticlockwise rotation angles are defined as 30°, -30°,respectively.

The effects of the pitch angle of the guide vanes on the averaged power and torque coefficients of the augmented rotor are shown in Fig. 10. As can be seen in Fig. 10(a), for both directions of the angle, it causes a significant decrease of Cpespecially at the large TSR part. The negative angle has a slightly better performance than the positive one. The peak values offor the guide vane with non-zero pitch angles are also reached at TSR =2.2. The highest Cpfor the negative and positive pitch-angles are 0.31, 0.28,which are 29%, 36% lower than those of the zero-pitch blades, respectively. As can be seen in Fig.10(b), the peak values of Ctfor the non-zero pitch angles are reached at TSR=1.8. The highest Ctwhen γ is 30°, -30° are 0.13, 0.15, which are 35%,21% lower than that of the zero-pitch stator. It can be concluded that the current pitch-angle sets for four guide-vanes can not improve the performance of the augmented rotor.

Fig. 11 Directional angles of the incident water flow

Fig. 12 Effects of the incident direction of water flow on the performance of VAT

Since the incident flow direction is fixed in the numerical model, the stator rotates to an angle α varying from 0° to 67.5° to represent four directional angles of the incident water flow, as shown in Fig. 11.The effects of the incident flow-direction on the averaged power and torque coefficients are shown in Fig. 12. It is clearly shown in Fig. 12(a) that the overall Cpfor all non-zero directional angles of the incident water flow are reduced. The highest Cpwhen α is 22.5°, 45° and 67.5° is 0.30, 0.31 and 0.30 at TSR=1.8, which is 30%, 31% and 30%lower than that in the zero angle case, respectively. As can be seen in Fig. 12(b), the peak values of Ctwhen α is 22.5°, 45° are both 0.15 at TSR = 1.8. For 67.5°, the highest Ctis 0.14 at TSR = 2.2. The averaged values of Cpand Ctfor 22.5°, 45° and 67.5° over the range of the TSR are 28%, 34% and 33%lower than those in the zero-directional angle case.

4. Conclusions and future work

In this study, an augmented tidal current turbine is proposed, including a guide-vane type stator and a Darrieus type vertical axis rotor. A 2-D unsteady numerical model is built to investigate the operating performance of the augmented turbine. The numerical model is validated by experimental data to be a reliable desktop tool for further studies.

The streamlines of the flow-fields and the contours of the total pressure indicate that the guide vanes of the stator can narrow the flow path and increase the flow velocity and the pressure when the rotor blades rotate to the position near the guide-vanes.It also can be seen from the instantaneous torque output curves that the guide vanes can reduce the fluctuation of the total torque-output, to have better averaged power and torque coefficients.

It is found that the operating performance of the augmented rotor can not be significantly improved simply by increasing the blade number and the chord length of the guide-vanes. Although reducing the gap between the stator and the rotor can increase the torque and the power output, too small a gap will clearly make the coefficients decrease. The optimized value of the above parameters should be the blade number is four, Csis 1.0 Cr, G is 0.25Cr. The pitch angle of the guide vanes is also found to have negative effects on the rotor performance. The averaged coefficients Cp, Ctfor three non-zero directional angles of the incident flow are approximately 30% lower than those in the zero-directional angle case.

In the future, a more complex design of the omni-directional guide-vane augmented VAT will be made for a better performance under the actual sea conditions. A fully passive flow-drive numerical model will also be developed for the possible improvement of self-starting characteristics of the augmented VAT. The present work will be extended to the 3-D model for more details of the flow fields and the optimization of the design.

Acknowledgements

This work was supported by the Qingdao Livelihood S&T Project (Grant No. 17-6-3-25-gx), the Program of Introducing Talents of Discipline to Universities (111 Project, B14028).