Improved Wells Turbine using a Concave Sectional Profile

The current need to develop sustainable power sources has led to the development of ocean-based conversion systems. Wells turbine is a widely used converter in such systems which suffers from a lack of operational range and power production capacity under operational conditions. The profile named IFS which is concave in the post-mid-chord region, can produce significantly larger lift forces and show better separation behavior than the NACA profiles. In the present study, we tested this profile for the first time in a Wells turbine. The performance of six different blade designs with IFS and NACA profiles were evaluated and compared using a validated computational fluid dynamic model. Although the substitution of the NACA profile with the IFS profile in all cases increased the torque generated, the most efficient power generation and the largest efficient range were achieved in the design with varying thickness from the hub with a 0.15 thickness ratio reaching to the ratio of 0.2 at the tip. The operational span of this design with the IFS profile was 24.1% greater and the maximum torque generation was 71% higher than the case with the NACA profile. Therefore, the use of the IFS profile is suggested for further study and practical trials.


Introduction
The world's need for energy is increasing and the devastating effects of fossil fuel consumption has made humankind to seek every extractable and sustainable form of energy. One such source of energy is the sea. The power density of ocean-based generation is higher than wind and solar-based techniques. Furthermore, many populated societies live close to coastlines, which reduces the need for electricity distribution infrastructure from costal sources. Many of the countries with large coastal areas such as the UK, India, Australia, and the USA are the leading countries in developing ocean-based power systems [1,2]. One of the most significant sources of energy from the ocean is from waves as they reach the shore. In 2000, the incident waves of the Pacific Ocean produced nearly as much energy as the entire world's electrical power consumption [3]. The kinetic energy of the waves must be converted into electricity. One candidate conversion system is the oscillating water column (OWC) which is demonstrated in Fig. 1. This system is amongst the most developed techniques and is already deployed. However, the most important component of the system is a self-rectifying air turbine, which is not yet effective in real sea conditions since such turbines have inferior operational range and power production than other candidate systems [4][5][6]. The OWC consists of a capture chamber that contains a fixed amount of air which is connected to a duct containing the turbine as shown in Fig. 1. Fluctuation of the water surface changes the pressure level in the chamber and consequently induces reversible bi-directional flow which acts as the working fluid for the self-rectifying turbine [7-11]. The Wells turbine is a practical and inexpensive axial self-rectifying turbine. It is often used for low flow velocities such as those produced by oceanic incident waves [13][14][15]. The Wells turbine rotor as shown in Fig. 2 has several blades with symmetrical profiles as their sectional profile which are radially installed around the hub and with a stagger angle of 90 o . Considering an air profile in a free stream with the relative velocity, W , and relative angle of attack to the chord,  , the lift and drag forces are produced on the airfoil. For a Wells turbine blade with an airfoil section, the incident flow attacks with the absolute velocity V  on a cascade with the angular velocity of Ur  = . The resulting velocity is a relative velocity with an angle of attack The tangent of this angle of attack is the non-dimensional flow coefficient as defined in Eq. 1. The angles of attack and relative velocities over sectional profile result in lift and drag forces which can be resolved into tangential (Eq. 2) and axial (Eq. 3) forces on the blade as shown in Fig. 3. The blade section of a Wells turbine is symmetrical and so the tangential force generates torque always in the same direction regardless of the direction of air flow. The Wells turbine produces a positive time-averaged power due to the low frequencies of wave motion [16-19].
Wells turbines suffer from narrow operational range due to suction side stalling and a low tangential component of the lift force, which leads to low torque and, therefore, low power generation [8,20]. Waves change randomly in power and frequency and so the reversing flow may experience sudden changes which stall the turbine. Employing the profiles with greater stall angle and high lift generation is an effective solution to resolve this issue. Many attempts have been made to improve performance through geometrical modification. In the current study, the blade profile is considered. The effects of sectional profile thickness of the blade on the performance of both starting and running regimes have been investigated experimentally [18]. Thicker profiles enabled the turbine to have better efficiency and wider efficient range because of the onset of stalling was more gradual. In a fixed pressure drop state, the increase of thickness led to the increase of torque generation and better starting behavior [16,[21][22][23]. The performance of a small-scale Wells turbine with four different profiles and two sweep ratios of 0.5 and 0.35 has also been investigated [24]. A sweep ratio of 0.35 and the thickness ratio of 20% were found to be optimum. Studies into the effect of sweep ratio on the operational range of the Wells turbine have shown that a sweep ratio of 0.35 is most efficient [24][25][26]. As far as the scale is concerned, studies of the profile thickness showed that 20% thickness is favorable for smaller scales while 15% is better for large scales [26][27][28]. A mathematical multi-objective optimization algorithm coupled with computational fluid dynamics (CFD) was used to investigate swept designs [29,30]. The torque coefficient and the stall margin were increased substantially for forward-swept turbines. A study of blades with constant thickness and variable thickness was investigated using CFD and experiments, showing that variable thickness has greater performance [31]. Variable thickness blades also generate less entropy [20]. Another study used two-dimensional CFD to optimize the geometry called "NACA 0021" for application in the Wells turbine and was able to increase the tangential force by 8.8% and an insignificant increase of 0.2% in the efficiency [32]. An improved profile with a 5% better efficiency was obtained from an initial airfoil design from the wind turbine industry named "S809M" using a similar CFD procedure [32,33]. Using the "S1046" profile in the Wells turbine improved torque generation by 3% in a water environment compared to the "NACA 0015" profile [34]. A numerical optimization of the NACA0015 profile produced a new profile with a surface that was almost linear after the mid-chord point and a slightly concave profile near the trailing edge. This design generated 14% more torque in three-dimensional simulations [35]. Mathematical optimization algorithms have allowed such geometries to be discovered but such methods require a large number of simulation cases to achieve reasonable results. This significantly increases the project time and costs. Most modified geometries mentioned in this review have not yet been validated experimentally.
In addition to the modifications reviewed above, there is a turbine profile from the marine sector that yet has not been considered for use in Wells turbines, even though it is known that it generates more lift than the NACA series: IFS (Institute Fur Schiffbau). IFS profiles were designed experimentally [36,39]. They have a very high lift to drag ratio, optimized for best functionality in rudders. The IFS profile series have a steep lift curve before the stall and capability to postpone the separation bubbles formation [36,37]. The higher lift generation of the IFS profile enables the turbine to work over a broader range of flow coefficients. This is advantageous for OWC applications in variable sea conditions. It is also useful to compare aerodynamic properties of the IFS and NACA profiles. Table 1 and Fig. 4 help us to better characterize the two profiles performance based on aerodynamic parameters which are the well-known Reynolds number, CL as the Lift coefficient and is the αs angle of attack at the onset of a stall. Evidently from Table 1 we see that in contrast with the NACA series, the lift production of the IFS series increases substantially with thickness. This feature is beneficial in the Wells turbine application since the thicker profiles are better in terms of working range and torque generation [29]. The thicker versions of IFS profile produce more lift and hence more tangential force than thick NACA profiles. Therefore, such profiles can be an effective solution for the main gap of the Wells turbine which is narrow operational range and weak power generation. The current study, we aimed to test and analyze using of IFS profile in the application of the Wells turbine for the first time via a three-dimensional CFD setup.  Figure 4. The lift coefficient trend of the IFS and NACA profile compared for a three dimensional hydrofoil against incidence angle. Defining the profile curve with an approximate polynomial function based on Eq. 4, where t is the thicknessto-chord ratio leads us to fixed coefficients for NACA and IFS series as brought in Table 2. Shape of the IFS profile is shown in Fig. 5a for a thickness ratio of 20%. four blade designs were generated with variable (VTBt) and constant (CTBt) thickness ratios where t is the thickness ratio. Two other designs are the backwards-swept and (BSBt) and forwards-swept blade (FSBt) with sweep ratio of 35%. These designs are illustrated in Fig. 5b.

Materials and Methods
The frequency, f , of the reversible air flows inside a wave energy system is minimal ( 0.1Hz  ), and so it is common to assume a quasi-steady-state flow for the simulation. This has been validated for simulations of Wells turbine [2, 9-11, 16, 20, 21, [41][42][43][44][45]. This approach greatly reduces the computational expense of simulations and simplifies post-processing. In the quasi-steady-state approach, the turbine is tested only in one direction of the flow field since the dynamic effects of the low frequency flow on the performance of the turbine is negligible [2, 9-11, 16, 20, 21, [41][42][43][44][45]]. In the current study, validation of the CFD set up was made based on the results of a previous study, for which the blade geometry is presented in Table 3 [13]. In the current case, the length downstream of the blade is more important than the length to the inlet because the numerical results are mostly affected by suction side phenomena. The outlet was placed far enough from the blade to ensure that the far-field wakes are attenuated. In this study, the sizing of the simulation domain is set to be 5 times the chord length upstream and 10 chords downstream (Fig. 6), respectively whereas in various studies, the sizing of the domain is less than our domain [2, 16, 20, 29-35, 42-45]. The efficiency of the turbine was calculated for five different numbers of grid cells in the flow coefficient, 0.10. The variation in efficiency stops above 1.8 million cells (Fig. 7). Therefore, this number of cells was selected for the rest of the calculations. The use of commercial softwares is common for simulation of turbomachinery systems such as the Wells turbine. ANSYS software was used in previous works for the three-dimensional simulation of the Wells turbine. Studies show that turbulence modelling based on the RANS Equations provides reliable results however choosing the right turbulence model is crucial to get a more accurate prediction of the turbine's performance specially near stall regime. Different solvers and turbulence models were used before and among them the K  − SST model is more common. Table 4 summarizes the information of the simulation techniques employed by recent studies.
Turbulence modelling based on the RANS Equations cannot predict complex flow behaviour in the stall state of the Wells turbine accurately. This problem can be noticed in the studies presented in Table 4 and is intensified in one study, in which the torque amounts after the stall point rose, contradicting experimental observations [42].
K  − SST is the best choice of turbulence model since it is more powerful than K  − model in predicting the onset and number of flow separation events with adverse pressure gradient such as the suction side of the Wells turbine [41][42][43][44][45][46][47]. In the proposed methodology we used this model. The domain was meshed using a structured high-quality hybrid O-H type of grid which is shown in Fig. 8. O-H type means there is a circular region around the sectional profile in which the density of mesh is greater and smartly increases near the blade. The far from blade the domain is divided by half H type regions to generate a structured mesh from inlet to O region and from O region to outlet. This mesh type is optimized for the meshing around the turbomachine blades with boundary layer consideration. This type allows to reach a very fine mesh around walls for better boundary layer simulation but not so dense mesh far from the walls to keep the total number of cells optimized. The concentration of the mesh around the walls is generated with the size of 5 m  for the first cells to guarantee the Y + around one which is the optimum condition for K  − SST turbulence modelling.  The Wells turbine's rotor has symmetry around the rotational axis. Hence, a moving reference frame can be used to avoid the high computational cost of simulating the whole rotor. This technique leads to the solution of the flow field around one blade by rotating the reference flow domain instead of the blade with the same rotational velocity as the rotor. This methodology is common in turbomachinery studies and provides accurate results while reduces the complexity of all CFD stages [2, 10, 20, 29, 30, 41-45]. The angular velocity of the rotor was fixed to be 2000RPM for all the simulations and it was equal to the velocity set in previous experiments [13]. Air at 25 o C was selected as the fluid, and the reference pressure was set 1 atm. The selected turbulence model was K  − SST solved along with the Reynolds Averaged Navier-Stokes Equations using the finite volume discretization method and high-order upwind schemes for all the flow components. The turbulence intensity was set to be 10%. Normal fixed velocity speed was set at the inlet, average static pressure was used for the outlet with a relative pressure of 0 atm. Periodic boundaries were defined along the meridional surfaces. All other boundaries were defined to be walls with a no slip condition, including the blade, shroud and the hub.

2.1.
Validation of the setup The Wells turbine performance is evaluated with three main variables: torque coefficient, pressure drop coefficient and efficiency which are defined by Eq. s 5 to 7 respectively. The curve line for these three parameters is sketched in Figs. 9a, b, and c based on the flow coefficient variable which is the non-dimensional blade's velocity as shown in Eq. 1. This variable is introduced as the tangent of angle of incidence for the relative velocity at the tip's section in some literatures. The performance variables graphed in Fig. 9 show the satisfactory agreement with the experimental data [13]. The reason is the simulation data regarding the operational zone where the turbine is working in no stall region is predicted with even less relative error than CFD results of the benchmark [2]. The current results illustrate the right physical behavior of the flow around the Wells turbine's blade. However, in the stall and post-stall regions, the results are not accurate with respect to the experimental results. The reason is that, as discussed, the classic turbulence models based on RANS equations fail to accurately simulate the highly turbulent flow formed in the wake of the Wells turbine rotor. Nevertheless, the aim of this study was to provide reliable data for the flow coefficients before the stall regime where the use of the turbine is practical, and this goal is achieved by the present setup.  Fig. 10 a shows that the CTB20IFS has a larger stall margin which enables the turbine to generate more power to a wider operational range. The drop in the torque values of CTB20NACA occurs in the flow coefficient of 0.24, while for CTB20IFS torque values continued to rise up-to the flow coefficient of nearly 0.3. In this point, the torque coefficient of the CTB20IFS is nearly 90% more than that of the CTB20NACA. The maximum torque coefficient and the operational zone of the rotor with IFS profile have been increased by is nearly 38% and 25% by order. Fig. 10b indicates that the CTB25IFS shows a slight increase in the torque generation in comparison with the CTB25NACA and both designs have similar torque coefficient maxima. In Fig. 10c, the torque coefficient of BSB20IFS reached a significantly higher value than that of the BSB20NACA and the range of torque generation has been widened by 31%. Fig. 10d provides the torque coefficient data of FSB20 rotor. The FSB20NACA rotor does not exhibit a stall point. This is due to the flaw occurred in the RANS turbulence modelling as discussed for highly turbulent stall region in this blade. However, for the before stall points the torque production of IFS profile is more than NACA and because of the less turbulent flow at its suction surface the model captures the stall onset and the increasing trend stops at a flow coefficient of 0.3. Fig. 10 e displays the torque coefficient of VTB20 rotor. The maximum torque coefficient of VTB20IFS profile occurs at a flow coefficient of 0.32, which is 21% higher than the flow coefficient at the maximum torque coefficient of VTB20NACA. The amount of this maximum for VTB20IFS is 71% greater than for VTB20NACA. Finally, fig. 10 f shows the torque values of VTB25 blade. As seen the IFS profile exhibits 47% larger maximum torque and an 11% increase in the operational range compared with the NACA profile. Fig. 10. The torque coefficient diagram for different simulated blades with the NACA and IFS profiles as their sectional profile.

Pressure drop coefficient curves
1 Figure 11 demonstrates almost linear proportion between the pressure drop coefficient and the 2 flow coefficient. This is expected for Wells turbines, based on previous studies and is ideal for an 3 OWC system [1][2][3][4]16]. However, the gradient of the line between the pressure drop coefficient and 4 the flow coefficient undergoes a disorder due to stalling. In some cases, a nonlinearity occured in the 5 flow above the flow coefficient at which stalling occurred. Figure 11 shows that the loss of the static 6 pressure in the rotors with IFS profile is nearly 20% larger than NACA with the CTB20IFS and 7 VTB20IFS experience the lowest increase in the pressure loss among other blades. Correspondingly, 8 they produced the largest torque values that offset the greater pressure loss in comparison with 9 NACA. Therefore, their efficiency would not be affected significantly.

11
The IFS profile generates more pressure drop than the NACA profile (Fig. 11a, 11b). While this  located after the stall point of its corresponding NACA profile. In the BSB20 case as shown in Fig.   41 12c, the IFS geometry has a significantly lower peak efficiency than the NACA geometry. For the 42 FSB20 blade in fig. 12d we can see, the IFS profile also has a lower peak efficiency than the NACA 43 profile. In fig. 12e, for VTB20IFS blade, the maximum efficiency is approximately 6% greater than the 44 equivalent NACA blade and the efficiency range is enlarged by 24% more than any other blade with 45 the IFS profile. For example, for a flow coefficient of 0.36, the 2VTB20NACA is nearly zero efficient,

46
while the VTB20IFS has an efficiency of 34%. Finally, results indicate that VTB20IFS is significantly 47 effective in addressing the problem of narrow operational range and sudden stall of the Wells turbine,

48
which was the primary goal stated in the introduction section. For CTB25, VTB25, BSB20 and FSB20 49 as shown in Figs. 12 b, 12f, 12c and 12d the IFS profile is predicted to have a peak efficiency that is 50 significantly lower than the NACA equivalent. This is due to the excessive increase in the static 51 pressure loss over the blades. They have comparatively weaker performance than the same blades 52 with the NACA profiles. Therefore, the only IFS case that satisfies the performance gaps of the Wells 53 turbine to a great extent is VTB20. High torque generation and smaller losses enabled the VTB20IFS 54 turbine to have a considerable increase in the operating range with good efficiency.

57
To conclude, Table 5 summarizes the key results of the above data for different blades tested with 58 IFS profile.

96
In Fig. 14, The circumferential velocity is contoured on the three meridional planes near the 97 leading edge, mid-chord and the trailing edge of the VTB20 blade. Fig. 14a illustrates that the flow 98 field behind VTB20IFS is much stronger than VTB20NACA and tends to remain attached. Based on 99 Fig. 14b and 14c, on the tip of the IFS blade, the separation zone formed by the interaction of the low-    found to be superior to the NACA geometry in torque generation and, particularly, improving the 169 total performance of VTB20 blade. The obtained results can be summarized as follows:

170
• The IFS profile was capable of producing much higher torque amounts and generating more 171 power as a result.

172
• The VTB20IFS profile demonstrated 71% increase for the maximum torque coefficient and 24.1% 173 increase for the efficiency range respectively.

174
• The efficiency results indicated that the VTB20IFS profile is the best shape since it produced the 175 highest efficiency and the widest operational range among others.

176
• The SS streamline contours demonstrated a smaller separation area for VTB20IFS hence better 177 performance results.

180
This study aimed to introduce and test a new reference profile for application in the Wells turbine 181 by replacing the NACA profile which has a sudden stall and low torque generation. The IFS profile