Effect of Blade Profiles on the performance of Bidirectional Wave Energy Turbine

To fulfill the ever growing demands of world energy consumption, the wave energy should be extracted economically. The oscillating water column is most commonly used to extract energy from waves. It consists of a chamber in which waves drives the entrapped air column to rotate the Wells turbine. The Wells turbine is a self-rectifying low-pressure axial reaction turbine with 90 stagger angle. These turbines consist of symmetrical airfoil profile to achieve unidirectional rotation for the bi-directional airflow. The turbine performance predominantly depends on the aerodynamic characteristics of the airfoil profile used. In this study, the performance of Wells turbine with various symmetrical airfoil profiles was analysed using ANSYS CFX 14.5. The CFD analysis was performed by solving three dimensional steady Reynolds averaged Navier-Stokes equation with k-ω SST turbulence closure model. The reference geometry has NACA0015 as blade profile and the CFD results were compared with the experimental values. The performance characteristics of the new airfoil profiles were compared with the reference case to analyse the suitability of airfoils in wave energy extraction. The NACA0021 airfoil profile showed better performance in the post-stall regime compared to the NACA0015 and the S1046 airfoil profiles.


Introduction
The Wells turbine is used to extract the energy from the bidirectional airflow inside the oscillating water column (OWC).It consists of a symmetrical airfoil with 90 o stagger angle.It provides unidirectional torque for the oscillating flow without any guidevanes, which makes the power take-off system simple [1].On the contrary, the Wells turbine has limitations such as narrow operating range, noisy operation, and poor starting characteristics.The performance of the turbomachines primarily depends on the airfoil profile used.There were many studies done on the effect of different symmetrical and non-symmetrical airfoil profiles on the performance of Wells turbine.The airfoils with thicker profiles improve starting characteristics and performance of the Wells turbine [2,3].The stall characteristics of Wells turbine can be improved by optimization of airfoil profile.Webster et al. [4] optimized the NACA0015 airfoil profile and reported better stall characteristics.Setoguchi et al. [5] investigated the performance characteristics of four different airfoil profiles and concluded that NACA four-digit airfoil profiles with 20% thickness ratio are suitable for better performance of Wells turbine.Takao et al. [6] compared the performance characteristics of airfoils with sweep.They studied the following airfoil profiles NACA0015, NACA0020, CA9, and HSIM 15-262123-1576 and reported that NACA0015 is the desirable airfoil profile to achieve better performance.The airfoil profile CA9 with solidity 0.64 is suitable to achieve better performance in the real sea conditions [7].Takao et al. [8] investigated airfoil profiles NACA0015, NACA0020 and modified Eppler472 and reported that modified Eppler472 airfoil profile is superior to the other profiles analysed.Mohamed et al. [9] proposed the use of nonsymmetrical airfoil profiles in the Wells turbine.The optimization of airfoil profile in Wells turbine is also investigated by many researchers [9][10][11].From the above studies, it is evident that the performance of Wells turbine is highly influenced by the nature of airfoil profile used.To analyse the influence of airfoil profiles on the Wells turbine performance three airfoil profiles are used in this study.Based on the previous studies airfoils NACA0015 and NACA0021 are chosen as the suitable candidates for the blade profile.Mohamed [12] evaluated the effects of various symmetrical and nonsymmetrical airfoil profiles on the performance of Darrieus turbine.

Description of rotor geometry
The Wells turbine geometry used in the work of Torresi et al. [13] is taken as the reference case for this study.It consists of NACA0015 as the blade profile.The specifications of the reference geometry are provided in Table 1.

Numerical formulation
The computational domain for numerical analyses is shown in Fig 3 .To minimize the computational time, a single blade with rotational periodicity is chosen as the computational domain.The upstream and the downstream length is fixed as 4C and 6C respectively.The computational domain was discretized with unstructured tetrahedral elements using ICEM CFD.To capture the near wall flow physics, 20 layers of prism elements were generated around the blades with a stretching ratio of 1.2.
The surface mesh of the computational domain is presented in  Where T is the torque, ρ is the density of air, ω is the angular velocity of the turbine, R tip is the tip radius, Δp o is the stagnation pressure drop, Q is the discharge, U ∞ is the free stream inlet velocity and U tip is the blade tip velocity.The performance characteristics of the Wells turbine is obtained by plotting the above nondimensional parameters against the flow coefficient (FC) U*.

Grid independence study
The grid independence study is performed to select the mesh with optimum resolution.It is essential to perform this study as the computational time will increase with an increase in a number of grid elements.To perform this study meshes with three resolutions such as coarse, medium and fine is selected and the efficiency is compared for the entire flow range.The results of all grids are almost same and the maximum deviation between the medium and fine grid is 6.8% which is acceptable.Hence the medium grid with 3 million elements is retained for numerical simulations throughout this study.The plot of grid independency study is shown in Fig 5.

CFD Validation
To ensure the numerical accuracy of the simulations performed the present numerical results are validated with the experimental results of Curran and Gato [16] and the numerical results of [13,17,18,19].The CFD validation of the numerical results is presented in Fig 6.
The performance characteristics of the Wells turbine for the entire flow range is plotted and verified.From the figure, it is evident the present numerical results follow the same trend as the existing CFD results except for the work of Shaaban and Abdel Hafiz [18].In their work, they reported that the steady RANS model failed to predict the stall phenomenon of the Wells turbine.

Effect of Airfoil Profiles
The present work investigates the effect of three different airfoil profiles on the performance of Wells turbine.The study has been done for the entire flow From Fig. 7a, it is evident that the maximum torque coefficient is obtained for NACA0015 profile followed by S1046 and NACA0021.The NACA0021 airfoil profile performs better in the post-stall regime and the drop in torque and efficiency is not severe as compared to the other airfoil profiles.The pressure drop of the NACA0021 airfoil profiles is lower than the NACA0015 and S1046 airfoil profiles (Fig. 7b).The peak efficiency is obtained for the S1046 airfoil profile at U*=0.125, however, the difference between the maximum efficiency of S1046 and NACA0015 is not sign9ificant.At low FC (U*=0.075), it can be noticed that the efficiency of S1046 is significantly higher than the other airfoil profiles.The efficiency of NACA0021 is better in the post-stall regime compared to the S1046 and NACA0015 airfoil profiles.
The static pressure distribution on the blade suction surface of the different airfoil profiles is presented in Fig 8 .At U*=0.075, the pressure distribution is almost same for all the airfoil profiles.With the increase in FC, the incidence is also increased.At U*=0.225, the suction pressure is minimum at the leading edge (LE) for all the cases.This pressure difference between the suction and the pressure side creates the lift force.At FC U*=0.225, the peak torque is obtained for all the cases (Fig 7a).At U*=0.275, a large low-pressure region is noticed on the on the suction side (SS) of the blade.This can be attributed to the high incidence of the flow at high FCs.The low-pressure region on the blade SS implicates adverse pressure gradient and it leads to flow separation.This can be corroborated by a sudden drop in torque and efficiency in Fig 7a and 7c.In order to analyse the stall phenomenon in detail, the surface streamlines on the blade suction surface are presented in Fig 9.

Conclusion
In this numerical study, the performance of Wells turbine with different airfoil profiles was investigated.Three symmetrical airfoil profiles such as NACA0015, NACA0021 and S1046 was selected for this study.The prominent conclusions drawn from this study were listed below.
 The performance of Wells turbine predominantly depends on the airfoil profile used. The maximum peak efficiency was achieved in the case of S1046 airfoil whereas the maximum peak torque was obtained in case of the NACA0015 airfoil. The NACA0021 airfoil showed better performance in the post-stall regime. Furthermore, optimization of these airfoil profiles is recommended to obtain an optimized airfoil profile with improved performance characteristics.

Fig 4 .
The numerical analyses were done by solving incompressible steady three dimensional Reynolds averaged Navier-Stokes (RANS) equation using coupled solver ANSYS CFX 14.5.It solves the aerodynamic equations for (u,v,w,p) as a single system[14].The rotation of turbine is realized by implementing the rotating reference method.The boundary conditions are applied in CFX-Pre.Air at 25 o C is taken as the working fluid and the compressibility effects are neglected.Uniform velocity and zero pressure gradient boundary conditions are given on the inlet and outlet respectively.The blade and hub are imposed with no-slip boundary condition whereas the shroud is kept as counter-rotating no-slip wall.The lateral faces of the computational domain is taken as periodic faces to account for the rotational periodicity.The turbulence intensity at the inlet is fixed as 5% (medium intensity) and k-ω SST with automatic wall function is chosen as the turbulence closure model.It is suitable for flows with severe adverse pressure gradient and separation[15].It activates k-ε model away from the wall and k-ω model closer to the wall, thereby incorporating the merits of both turbulence models.A high-resolution advection scheme is employed for spatial discretization to ensure second-order accuracy.The numerical simulations are run up to 2000 iterations and the residual convergence criteria value is set to 1e-5 to ensure convergence.

Table 1 .
Reference geometry specifications The description of the airfoil profiles used in this study is provided in Table 2 and the comparison of airfoil profiles used is shown in Fig 2.

Table 2 .
Details of airfoil profiles