Review of Experimental Investigations on Wells Turbines for Wave Energy Conversion

Abstract

Wells turbines are one of the most attractive types of rotating machines installed in Oscillating Water Column (OWC) devices, owing to their simplicity of construction and reliability. Their unconventional design, with symmetrical blades staggered orthogonally with respect to the axis of rotation, simultaneously represents one of the main strengths and weaknesses of the turbine, and makes their aerodynamic behavior complex and significantly different from that of other types of machines. The importance of numerical analyses in explaining the physics behind the Wells rotor operation has significantly grown in recent years as proved by the vast available literature. Nevertheless, experimental analyses still hold an important role in modern turbomachinery design, both for the validation of Computational Fluid Dynamics (CFD) models and for verifying the improvements suggested by optimized design in a realistic environment. This review aims to collect and classify published experimental studies on Wells turbines, distinguishing among the types of experimental setups, methodologies adopted, and measurements performed, to identify the current research gaps and guide future experimental research.

1. Introduction

Ocean energy is expected to play an important role in decarbonizing the electricity generation sector [1], given its widespread availability and high energetic content coupled with a better predictability with respect to more commonly exploited renewable energy sources such as solar and wind. These considerations have attracted the attention not only of researchers but also of government grants and private investors [2].

The researchers’ attention for wave energy has produced a number of different Wave Energy Converters (WECs), each exploiting a specific mean of interaction with the waves, hence being more or less suitable for different sites and power densities. Of particular interest are the systems based on the Oscillating Water Column (OWC) principle, given their reliability and applicability to a variety of locations (on- and off-shore) and collector platforms [3]. A WEC based on the OWC principle consists of a chamber (a caisson made of concrete [4] or even a natural cave [5]) open at its bottom and partially submerged under the free water surface as schematically represented in Figure 1. The external sea wave motion is converted into a reciprocating motion of a water column inside the air chamber, which, in turn, induces a similar movement of the air in the upper part of the chamber, where another opening is present. A Power Take-Off (PTO), generally an air turbine, is finally necessary to convert the pneumatic energy of the bidirectional airflow into mechanical energy available for electricity production, by means of a generator.

The peculiarity of the airflow established inside the OWC, i.e., its bidirectional nature, represents the key factor for the selection of an appropriate PTO. Traditional impulse turbines [6] require rectifying systems to be coupled to OWC systems, introducing the need for additional parts. A more convenient choice of PTO is usually represented by self-rectifying turbines.

The Wells turbine, patented in the 1970s by Dr. A. A. Wells [7], is the most studied self-rectifying turbine for wave energy plants since its invention. Its rotor consists of symmetrical blades, originally made of NACA00xx profiles, staggered at 90 degrees with respect to the axis of rotation as sketched in Figure 2.

This simple design results in the aerodynamic forces represented in Figure 2: the tangential force, acting in the direction of rotation, is positive both during the inflow (air is flowing from the atmosphere into the OWC chamber) and the outflow phases (air is pushed out from the chamber), with the exception of very low incidence angle conditions that happen near the flow inversion. The main advantage lies in this simple design that makes the turbine easy to manufacture and reliable. In the last few decades, Wells turbines have been installed in a number of OWC plants for wave energy conversion. These are summarized in Table 1, where the main characteristics of the installed turbines are also reported.

Nevertheless, this simple design comes with some very relevant drawbacks, consisting in a limited operating range due to the aerodynamic stall that occurs at high incidence angles, and a moderate efficiency.

Despite being almost 50 years old, the Wells turbine cannot be considered a consolidated machine, as its aerodynamic behavior, its performance variation as a function of the most relevant geometric parameters, and finally its design procedure have not been completely investigated. Simplified numerical methods can help to understand the rotor behavior: for instance, approaches based on potential flow theory [8,9] can be adopted for an initial selection of the main rotor geometric parameters. Several researchers made use of more sophisticated numerical approaches, often based on Computational Fluid Dynamics (CFD) simulations, to predict the performance of the Wells turbine [10,11,12], also analyzing the features of the local flow near the rotor [13,14,15] and, ultimately, to guide performance optimization processes [16,17,18,19].

Table 1. Wave energy plants equipped with Wells turbines.

Project Name, Site of Installation	Year	Turbine Configuration	Power Output (No. of Turbines × Power)
Sakata Port, Japan [20]	1989	Monoplane with guide vanes	60 kW ($1\times 60$ kW)
Islay, Scotland, UK [21]	1991	Biplane	70 kW ($2\times 35$ kW)
Vizhinjam OWC [22] Trivandrum, India	1991	Monoplane	150 kW ($1\times 150$ kW)
OSPREY [23] Dounreay, Scotland, UK	1995	Contra-rotating	2000 kW ($4\times 500$ kW)
Mighty Whale [24,25] Gokasho Bay Nansei, Japan	1998	Monoplane with guide vanes	≈110 kW (≈3$\times 30$ kW)
Pico power plant [26] Azores, Portugal	1999	Monoplane with guide vanes	400 kW ($1\times 400$ kW)
LIMPET [4] Islay, Scotland, UK	1999	Contra-rotating	500 kW ($2\times 250$ kW)
Mutriku Wave Power plant [27] Mutriku, Basque Country, Spain	2011	Biplane Contra-rotating	296 kW ($16\times 18.5$ kW)
REWEC3 [28] Port of Civitavecchia, Italy	2016	Monoplane	2.2–2.5 MW

Table 1. Wave energy plants equipped with Wells turbines.

Project Name, Site of Installation	Year	Turbine Configuration	Power Output (No. of Turbines × Power)
Sakata Port, Japan [20]	1989	Monoplane with guide vanes	60 kW ($1\times 60$ kW)
Islay, Scotland, UK [21]	1991	Biplane	70 kW ($2\times 35$ kW)
Vizhinjam OWC [22] Trivandrum, India	1991	Monoplane	150 kW ($1\times 150$ kW)
OSPREY [23] Dounreay, Scotland, UK	1995	Contra-rotating	2000 kW ($4\times 500$ kW)
Mighty Whale [24,25] Gokasho Bay Nansei, Japan	1998	Monoplane with guide vanes	≈110 kW (≈3$\times 30$ kW)
Pico power plant [26] Azores, Portugal	1999	Monoplane with guide vanes	400 kW ($1\times 400$ kW)
LIMPET [4] Islay, Scotland, UK	1999	Contra-rotating	500 kW ($2\times 250$ kW)
Mutriku Wave Power plant [27] Mutriku, Basque Country, Spain	2011	Biplane Contra-rotating	296 kW ($16\times 18.5$ kW)
REWEC3 [28] Port of Civitavecchia, Italy	2016	Monoplane	2.2–2.5 MW

For a correct description of any fluid dynamic phenomenon, numerical results should be validated against experimental data [29,30]. For the particular case of the Wells turbine, a total number of more than 100 published experimental works can be found in the literature, evenly distributed in time since its invention. Figure 3 reports a timeline of published papers, grouped in periods of 5 years, since the early 1980s until today. This paper aims to provide a systematic classification of all the experimental works on Wells turbines available in literature, focusing on the experimental setup used to test the Wells rotor and on the level of detail of the measurements and analyses conducted, with particular attention given to the final goal of the experimental investigations. Other reviews on Wells turbines can be found in the literature. Raghunathan [8] published complete and extensive reviews in 1995, reporting on the operating principles, expected and measured performance, and alternative Wells turbine configurations, but this work is now dated, given the last 30 years of research. The more recent review written by Shehata et al. [31], collecting a large number (230) of papers, does not focus specifically on experimental works, but it is more centered on numerical approaches, in particular CFD, for analyzing Wells turbine performance.

In the authors’ opinion, the present literature analysis can support researchers interested in existing experimental works on Wells turbines, as it puts together in one single document useful information on the rig used for turbine testing and on the aspects of Wells turbine design and operation investigated so far. It also provides a summary of experimental benchmarks available for validation of future numerical analyses.

The work is organized as follows: Section 2 presents a classification of the experimental rigs built for testing Wells turbines based on the type of flow, i.e., unidirectional or bidirectional. Section 3 presents a classification of the analyses conducted based on whether they aimed at providing only global performance measures or detailed flow analyses. Section 4 presents a summary of the effects of the main geometric parameters and control methods on the performance measures, derived from the available literature. Finally, Section 5 presents some closing remarks together with a few guidelines for future experimental analyses.

2. Experimental Rigs

Different test rigs have been designed and used with the intent of evaluating Wells turbine performance. Linear cascades, traditionally used to investigate the two-dimensional behavior of different profiles in a cascade arrangement [32], have never been used, to the authors’ knowledge, for the characterization of the Wells rotor due to its uncommon blade stagger angle. This peculiar rotor design, together with the relatively small flow angles experienced by symmetrical blade profiles before stall [33], would have resulted in highly skewed linear cascades with challenges that overcome the simplifications provided by this type of experimental test rig.

For this reason, Wells turbine test rigs have always employed the full rotor prototype, both in its traditional and modified configurations (biplane, contra-rotating, with guide vanes). Nevertheless, considering that Wells turbines find their only application in OWC systems, a first classification of test rigs can be made with respect to the possibility of reproducing the bidirectional airflow present in the real system. Unidirectional and bidirectional test rigs are discussed in the following sections.

However, it is important to highlight how, given the low frequencies of the airflow oscillations in an OWC device, no dynamic effects can be observed in the turbine performance as widely discussed in the reference literature on oscillating airfoils [34,35,36] and Wells turbines [37,38,39].

2.1. Unidirectional (Stationary) Flow Rigs

The first experimental characterizations of Wells turbines were conducted in the UK [40,41] using traditional unidirectional-flow test benches. The setup housed at Queen’s University of Belfast, the UK [37], is schematized in Figure 4.

The rig consisted of a suction wind tunnel driven by a centrifugal fan that produced the airflow and provided the pneumatic power for the turbine under test. A calibrated orifice plate was used to measure the flow rate, in accordance with fan testing standards [42], while pressure measurements were used to evaluate the power available to the turbine. Torque and rotational speed measurements allowed to evaluate the output power from the turbine. Only a few years later, Gato et al. [43,44] installed an analogous setup at the Instituto Superior Técnico of Lisbon, Portugal [43,44], initially using an axial-flow and later a centrifugal fan to reproduce the airflow, allowing the installation of turbines with a three times larger diameter (Figure 5).

The advantage of these unidirectional rigs consists in the possibility to perform long experiments under stationary conditions, simplifying the use of aerodynamic probes, such as pressure ones [43] and Hot-Wire Anemometers (HWAs) [45], to perform detailed local flow measurements. As a drawback, characterizing turbomachines performance under stationary operating conditions, i.e., fixing the flow rate delivered by the fan, could result in longer acquisition times given the necessity to analyze a large number of points to describe the performance curve of the machine. In addition, the stall point is not easily identifiable under stationary condition, given the intrinsically unsteady nature of this phenomenon.

Other unidirectional test rigs are the ones built at the University of Tokyo, Japan [46], at the Politecnico of Bari, Italy [47], at the Helwan University at Cairo, Egypt [48], and the Institute of Technology at Madras, India [49]. A list of available experimental rigs, together with a list of the type of turbines tested and their sizes, is given in Table 2.

Table 2. Experimental rigs for testing Wells turbines.

Experimental Setup	Flow Type/Conditions	Tested Types of Tested Wells Turbines	Diameter of the Test Section [mm]
Queen’s University, Belfast (UK)	Unidirectional/Stationary	Monoplane [40,41], biplane [50]	200
	Bidirectional/Non-stationary	Monoplane [37]	200
University of Limerick, Limerick (IE)	Bidirectional/Stationary, non-stationary	Monoplane [51]	600
University of Tokyo, Tokyo (JP)	Unidirectional/Stationary	Monoplane [46]	304
Istituto Superior écnico, Lisbon (PT)	Unidirectional/Stationary	Monoplane [43], biplane [52], contra-rotating [53], with guide vanes [54]	593
Saga University, Saga (JP)	Bidirectional/Stationary, non-stationary	Monoplane [55], with guide vanes [55]	300
University of Cagliari, Cagliari (IT)	Bidirectional/Quasi-stationary, non-stationary	Monoplane [56]	252
Politecnico di Bari University, Bari (IT)	Unidirectional/Stationary, non-stationary	Monoplane [47]	310
Helwan University, Cairo (EG)	Unidirectional/Stationary	Monoplane [48]	500
University of Siegen, Siegen (DE)	Unidirectional/Stationary	Monoplane [57]	400
	Bidirectional/Stationary	Monoplane [58]
Indian Institue of Technology, Madras (IN)	Unidirectional/Stationary	Monoplane with guide vanes [49]	265
Indian Institue of Technology, Madras (IN)	Bidirectional/Non-stationary	Monoplane with guide vanes [59], biplane [60]	196

Table 2. Experimental rigs for testing Wells turbines.

Experimental Setup	Flow Type/Conditions	Tested Types of Tested Wells Turbines	Diameter of the Test Section [mm]
Queen’s University, Belfast (UK)	Unidirectional/Stationary	Monoplane [40,41], biplane [50]	200
	Bidirectional/Non-stationary	Monoplane [37]	200
University of Limerick, Limerick (IE)	Bidirectional/Stationary, non-stationary	Monoplane [51]	600
University of Tokyo, Tokyo (JP)	Unidirectional/Stationary	Monoplane [46]	304
Istituto Superior écnico, Lisbon (PT)	Unidirectional/Stationary	Monoplane [43], biplane [52], contra-rotating [53], with guide vanes [54]	593
Saga University, Saga (JP)	Bidirectional/Stationary, non-stationary	Monoplane [55], with guide vanes [55]	300
University of Cagliari, Cagliari (IT)	Bidirectional/Quasi-stationary, non-stationary	Monoplane [56]	252
Politecnico di Bari University, Bari (IT)	Unidirectional/Stationary, non-stationary	Monoplane [47]	310
Helwan University, Cairo (EG)	Unidirectional/Stationary	Monoplane [48]	500
University of Siegen, Siegen (DE)	Unidirectional/Stationary	Monoplane [57]	400
	Bidirectional/Stationary	Monoplane [58]
Indian Institue of Technology, Madras (IN)	Unidirectional/Stationary	Monoplane with guide vanes [49]	265
Indian Institue of Technology, Madras (IN)	Bidirectional/Non-stationary	Monoplane with guide vanes [59], biplane [60]	196

2.2. Bidirectional (Non-Stationary) Flow Rigs

With the aim of characterizing the behavior of Wells turbines under conditions as similar as possible to the ones present in an OWC, bidirectional test benches have been designed and built since the early 1980s. These rigs, often referred to as oscillating airflow tests [37] or OWC simulators [61], are typically equipped with a piston running inside a cylindrical chamber, driven by an electric motor [55], an hydraulic actuator [37,62] or a rod and crank mechanism [60], reproducing the water surface motion inside an OWC chamber. Figure 6 shows two schematics for rig configurations of this type: the OWC simulator of the University of Cagliari, Italy, and the reversing airflow test rig of Saga University, Japan.

A similar, recently built test rig is housed at the Indian Institute of Technology of Madras (India) [60], which employs a rod and crank mechanism, driven by a motor, to reproduce the alternate motion of a piston inside a chamber. Both the piston period and stroke length can be varied to simulate different wave motions. The peculiar configuration of these setups does not allow to adopt the defined standards for the measurement of the flow rate (e.g., calibrated orifice plates, conical inlets, and venturi nozzles). The flow rate is therefore calculated based on the piston motion, even though this approach introduces the need for a phase-lag correction to account for the capacitive effect of the chamber volume [39,63]. In addition, the non-stationary flow typically produced within this type of setup complicates detailed flow measurements. As a partial solution, stationary conditions can be produced for a limited time span, fixing a constant piston speed as in [64,65].

An ingenious configuration used to perform bidirectional flow experiments on Wells turbines is the one housed at the University of Limerick, Ireland [51]. It makes use of a directional valve in a traditional suction tunnel as schematized in Figure 7. A similar setup is installed at the University of Siegen, Germany [58]. The most relevant advantage of this particular configuration consists in the possibility to test Wells turbines using standardized airways under reversible flow using the unidirectional flow conditions established with a fan. The price of this configuration is a more complex configuration that typically results in less compact rigs than traditional oscillating ones that make use of pistons.

As seen previously, non-stationary flow conditions are typically reproduced within oscillating flow facilities, given their particular configuration [37]. However, [47] successfully used the unidirectional test rig installed at Politecnico di Bari University [47] to reproduce non-stationary flow conditions, acting on a vector control drive that regulates the suction blower rotational speed, and therefore the flow rate through the tested Wells rotor [66]. With this approach, they were able to reproduce an oscillating flow, although always in one direction.

Table 2 lists the most used experimental setups for the characterization of Wells turbines, including some useful information on their operation, particularly with respect to the flow conditions reproduced (i.e., stationary or non-stationary), the types of turbines tested, and their sizes.

3. Experimental Investigations: Global and Local Performance Analyses

Experimental analyses in turbomachinery can be classified as “global” or “local”. The former type of investigation provides exclusively information related to the performance of the machine, often presented as performance characteristic curves. The latter type provides local analyses of the flow throughout more detailed investigations, using pneumatic multi-hole pressure probes, HWAs, and non-intrusive techniques such as Laser Doppler Anemometry (LDA) and Particle Image Velocimetry (PIV).

3.1. Global Performance Analyses

Most of the experimental investigations published since the early 1980s concern the characterization of Wells turbines with different design configurations from a global point view. The term “global” refers to the overall performance of the machine described in terms of the non-dimensional performance parameters typically used for turbomachinery characterization [67]. These are as follows:

• The flow coefficient

  $$\varphi ={\displaystyle \frac{Q}{\Omega r^3}}\propto {\displaystyle \frac{V_z}{\Omega r}}$$

  (1)
• The torque coefficient (or the power coefficient)

  $$T^{*}={\displaystyle \frac{T}{\rho {\Omega }^2{r}^5}}={\displaystyle \frac{P}{\rho {\Omega }^3{r}^5}}$$

  (2)
• The pressure drop coefficient (or, in general, the head coefficient)

  $$p^{*}={\displaystyle \frac{\Delta p}{\rho {\Omega }^2{r}^2}}$$

  (3)
• The efficiency

  $$\eta ={\displaystyle \frac{T\Omega }{\Delta pQ}}\propto {\displaystyle \frac{T^{*}}{p^{*}\varphi }}.$$

  (4)

The above parameters are written in a general form, given that authors have adopted different (although equivalent for their practical implications) formulations. For example, some researchers defined the pressure coefficient $p^{*}$ on the static pressure drop, which can be obtained from wall static pressure measurements [56,68], while others used the total pressure drop through the rotor [51,62]. Given that the exhaust kinetic energy from the Wells turbine is entirely lost [69], a more appropriate definition of the pressure coefficient is the one based on the total-to-static pressure drop, used in [37,68]. Different definitions of efficiency have also been used, depending on the quantity considered to be the available energy [37,51,68,69]. Regardless of the specific definition, global performance parameters in Equations (1)–(4) do not require any local flow measurement but only the flow rate Q (or the axial flow speed at the inlet, $V_z$), the output torque T, the turbine rotational speed $\Omega$, and the pressure drop $\Delta p$ through the rotor.

Several authors adopted global performance characterizations to study the fundamental aspects of Wells turbine operation, e.g., the self-starting behavior [70], or to compare different rotor designs, both in terms of geometric parameters [43,46,71,72,73,74,75,76,77,78,79] and configurations [80,81,82,83]. Wells turbine performance typically shows trends similar to the ones repoorted in Figure 8, which gathers results from both unidirectional [37,80] and bidirectional flow rigs [84].

The non-dimensional pressure drop shows an almost linear dependence on the flow coefficient as initially observed from experiments in unidirectional flow rigs [37,41,57,80,85] and confirmed under oscillating flow conditions [84], while the torque coefficient follows a quadratic law as a function of $\varphi$ until the stall occurs, identified by the steep reduction in both $T^{*}$ and $\eta$ [80,84]. These behaviors are in agreement with the predictions from basic fluid mechanics approaches [8,9], such as the potential flow theory experiments under oscillating flow conditions [56,61,85], providing an important confirmation of these results, except near the flow inversion. In particular, close to the inversion, i.e., where the flow coefficient attains values close to zero, the $p^{*}-\varphi$ curve deviates from the linear trend, due to the very low incidence that the blades operate at and the interaction with the wakes coming from the neighboring blades. Based on Equation (4), an almost constant value of efficiency is expected at every operating condition, except near the inversions, where non-linearities produce very poor values of $\eta$, and for values of $\varphi$ larger than the stall limit. This is essentially confirmed by the experimental analyses shown in Figure 8c, with minor deviations from the expected theoretical trends. Torque coefficient and efficiency suddenly drop after the occurrence of stall due to the flow separation from the blade profile, while only a minor deviation in the slope can be observed for the $p^{*}-\varphi$ behavior in Figure 8a for the same value of the flow coefficient, more visible in stationary flow experiments [80].

An important parameter that can be derived by these typical performance representations is the damping coefficient of the turbine, i.e., the pressure drop through the rotor for a given flow rate [86]. Based on the non-dimensional performance definitions of Equations (1) and (3), a non-dimensional damping coefficient K can be defined as the slope of the curve $\varphi$-$p^{*}$. This parameter is of paramount importance for the correct coupling of a Wells turbine with an OWC chamber, and its variation with rotor geometric parameters should be known for appropriately designing and selecting Wells turbines [43,79].

Less frequently, the torque coefficient and the efficiency are reported as a function of the non-dimensional pressure drop [58,87], considering that in an OWC installation, the turbine is driven by the pneumatic energy imposed by the wave collector to the rotor.

The expected uncertainties for global parameters vary depending on the type of the rig and on the specific characteristics of the rig itself. For unidirectional rigs and tests conducted under stationary flow conditions, the expected uncertainties depend on the instruments used to conduct the experiments [43,44,71,74,83,85], i.e., torque sensors and pressure transducers. Errors on performance parameters can be derived from the sensors’ accuracy specifications by applying the uncertainty propagation method (UPM) [88]. When specified, performance parameters uncertainties are in the order of $\pm 1\%$ [89,90,91], although the maximum uncertainties on efficiency calculations are typically slightly larger than the values for other coefficients, given that $\eta$ is evaluated based on $T^{*}$, $p^{*}$ and $\varphi$, as shown in Equation (4). Other authors [57,58,92] reported values of $\pm 5\%$ for the efficiency, providing detailed uncertainty analyses.

Oscillating flow rigs introduce the need for additional considerations on performance uncertainties, given that they operate under non-stationary conditions. Since the flow is typically periodic and alternate, performance characteristics can be obtained from the measured quantities only after a phase-locked averaging process [56]. Licheri et al. [79] clarified the effect of the number of piston periods acquired on the phase-locked averaged quantities, suggesting a minimum of 5 periods for an acceptable data reduction. Uncertainties are in the order of $\pm 7$–$9\%$ for $T^{*}$, $\pm 1$–$2\%$ for $\varphi$ and $p^{*}$ and $\pm 9$–$10\%$ for $\eta$. Uncertainties in the order of $\pm 3\%$ were declared by Setoguchi et al. [74] for non-stationary measurements, although only minimal information on the averaging process was provided.

3.2. Local Performance Analyses

Limited information on the aerodynamics of the rotor can be drawn from global measurements, and the physics of the flow field near the Wells turbine can be only assumed based on the knowledge of the behavior of similar lifting surfaces. Only a few studies have focused on the “local flow”, i.e., they provided detailed analyses of the flow field inside the turbine using aerodynamic probes, typically multi-hole pressure ones or HWAs. The former are typically used to characterize the mean flow velocity both upstream and downstream of the rotor, typically neglecting the velocity contribution in the radial direction [37,43,46,92] or reconstructing the fully three-dimensional velocity field [56,93]. HWA probes can be important for rotors with relatively high values of the hub-to-tip ratio, where wall proximity effects and leakage flow interaction are expected to affect the flow field distribution. Figure 9 reproduces a representation of the outlet flow in the meridian plane of a Wells turbine [93], where secondary flow structures are observed using a 4-holes aerodynamic pressure probe to reconstruct the mean flow field close to the rotor.

HWA probes are characterized by a very high response frequency coupled to a limited intrusiveness [94,95], allowing very detailed measurements, including the turbulence intensity of the inlet flow as in [45,65]. In particular, Raghunathan et al. [45] evaluated the effect of turbulence intensity on the performance of both a monoplane and biplane Wells turbine, under constant flow rate conditions. They observed that increasing the inlet turbulence intensity generally results in a higher turbine efficiency while delaying the occurrence of stall. This is explained considering that Wells turbine prototypes typically operate at relatively low Reynolds’ numbers, which cause a laminar separation bubble to form near the leading edge of the blade, inducing complete separation on the suction surface. Higher inlet turbulence levels may facilitate the laminar bubble reattachment, promoting transition to a turbulent boundary layer. Nevertheless, the gain in efficiency associated to the larger inlet turbulence is small, due to the fact that the blade speed is typically about 3–5 times larger than the inlet absolute velocity that determines the turbulence intensity.

Licheri et al. [65] employed a slanted HWA probe to reconstruct the flow field inside the blade pitch of a Wells rotor, using the multi-rotation technique to evaluate the fully three-dimensional flow field downstream of the rotor. They characterized the flow distortion associated to (a) the constant-chord design of the rotor, (b) the leakage flow through the tip gap, and (c) the obstruction at the blade root. They used this information to locate the least performing regions inside the blade pitch. A representation of the outlet axial velocity component in two adjacent blade vanes for a Wells rotor prototype is shown in Figure 10, where the regions affected by the leakage flow are clearly highlighted at larger radii by low, and even negative, values of $W_{z,2}$, thus altering the flow field distribution.

Another interesting local flow analysis, despite being only qualitative, was performed by Suzuki and Arakawa [96] to visualize the flow patterns on the blade surface of differently shaped rotors inside a circulating-water tunnel with the oil-film method.

4. The Effects of Geometric Parameters and Control Methods

With the aim to better understand how the simple design of the Wells turbine impacts on its performance, a survey into the aspects of Wells turbine design and operation investigated in experimental studies is reported in the following paragraphs. Figure 11 highlights the most relevant geometric parameters for a Wells rotor: the tip clearance size t, the tip and hub radii $r_{tip}$ and $r_{hub}$, respectively, the blade chord c, the blade height h, the number of blades z, the blade sweep angle $\epsilon$, and offset g, and the blade profile.

Following the standard similarity practices, non-dimensional geometric parameters can be defined and used for the evaluation of their impact on the performance of a rotor:

• The hub-to-tip ratio

  $$\nu ={\displaystyle \frac{r_{hub}}{r_{tip}}}$$

  (5)
• The rotor solidity, which is a measure of the flow obstruction on the annulus area of the rotor, due to the presence of the blades

  $$\sigma ={\displaystyle \frac{A_{blade}}{A_{rotor}}}={\displaystyle \frac{hcz}{\pi r_{tip}^2(1-{\nu }^2)}}$$

  (6)
• The non-dimensional tip gap, with respect to the chord or the blade height

  $$t_c={\displaystyle \frac{t}{c}}\mathrm{or}{t}_h={\displaystyle \frac{t}{h}}$$

  (7)
• The blade aspect ratio

  $$AR={\displaystyle \frac{h}{c}}$$

  (8)
• The sweep ratio, or blade offset,

  $$g_c={\displaystyle \frac{g}{c}}$$

  (9)
• The blade shape.

All the effects associated to the above geometric parameters have been experimentally investigated since the early 1980s. A review of these experimental results before 1995 was published by Raghunathan [8], clarifying that a complete separation of the effects due to the geometric parameters listed above is not always easy to be obtained, in particular with experimental analyses. Most of the investigations have been focused on the effects of solidity [37,43,46,51,57,64,71,72,74,78] and blade profile [51,64,71,72,73,74,75,76,77,97,98,99,100,101] on global performance, in particular on the rotor efficiency and on the occurrence of stall [8]. In addition, some studies have considered the effects of these geometric parameters on the starting characteristic of the Wells rotor [46,71] (of great importance in years when AC/AC power converters were not used but less important at the time of writing) and on the so-called “hysteretic effect” of turbine performance under unsteady operating conditions [72,74], a phenomenon that was later proved to be caused by the OWC and not by the turbine [63]. Figure 12 shows a classification of the experimental studies on Wells turbines with respect to the most significant aspects analyzed. It highlights how a large number of experimental articles on the geometry effects in monoplane turbines focus on solidity and blade profile. The bin named “others” includes all the remaining geometric effects studied in the last 50 years, such as sweep ratio [64,102], skew (or sweep angle) [91,103,104], blade aspect ratio [72,74,79,105], and other geometry modifications such as end plates [59,106,107], porous fences [108], cut trailing edge [109], and suction slots [110].

4.1. The Rotor Solidity

The fundamental importance of this parameter in determining the rotor characteristic curves, in particular the damping coefficient, presented in Section 3.1, and the turbine self-starting behavior, justifies the large number of investigations dedicated to this aspect [37,43,46,51,57,64,71,74,78]. Raghunathan and Tan [71] compared different rotor solidities under stationary flow conditions, indicating 0.6 as the optimal value to obtain a reasonable compromise between the starting behavior [111] and global efficiency. Gato and Fãlcao [43] compared the global performance of three rotors with different solidities under stationary flow conditions against the performance predictions obtained with simplified numerical methods (i.e., actuator disk theory), finding a general good agreement between numerical and experimental results. Moreover, they reconstructed the local mean flows along the blade span downstream of each rotor configuration, under the assumption of two-dimensional flow in the axial-tangential surface, i.e., neglecting radial flow components. Apart from the expected discrepancies observed between measured velocities and numerical predictions in the wall regions, they highlighted the effects associated to (a) the leakage flow in the tip region, and (b) the lower solidity at higher radial positions. In particular, see Figure 13, it can be observed that for higher rotor solidities, the axial velocity contribution $C_z/V_{flow}$ (non-dimensionalized with respect to the mean flow velocity) along the blade span is even more unbalanced from hub to tip, where it reaches higher values due to the increasingly high blockage at the hub induced by the constant chord design used in traditional monoplane rotors.

Figure 13 reports, in addition to the measurements from [43], also the traverse measurements made with a similar probe by Licheri et al. [61], for a rotor with a larger solidity, showing an analogous trend, even more exacerbated by the higher solidity that produces a higher hub blockage. Moreover, the effect associated to a larger tip clearance size ($t_c=1$% in [43] while $t_c=2.78$% in [61]) appears at larger radial positions, showing like a “jet flow” of higher velocity.

A way to obtain a more uniform axial flow at the turbine outlet consists of using constant solidity rotors as investigated by Suzuki et al. [46]. In this work, the performance of four rotors with different solidities, kept constant (for each machine) along the blade radius, was evaluated both from a global and a local point of view under stationary flow conditions. The authors used a bidimensional pressure probe to reconstruct axial and tangential velocity components downstream of the so-called “fan-shape” (i.e., with a radially increasing blade chord), with the aim of evaluating local efficiencies and aerodynamic coefficients. They found the best efficiency rotor to have a value of solidity of 0.6, while they predicted that a value of 0.8 would be necessary to have a self-starting turbine. A comparison of flow structures between constant-chord and constant-solidity blades was presented by the same authors [96], using the oil-film method to visualize the near-wall flow on the blade surface for different blade configurations. Starzmann and Carolus [112] investigated the impact of the so-called “fan-shaped” blades, i.e., with a positive radial variation in blade chord length, comparing rotors with different values of solidity and hub-to-tip ratios under stationary conditions. They evaluated the effect of design parameters not only with reference to turbines performance but by additionally measuring acoustic emissions, a truly important characteristic for real OWC–Wells turbine installations.

4.2. The Blade Profile

Several authors studied the influence of the blade profile on the aerodynamics of the Wells rotor, mostly from a global point view [51,64,71,72,73,74,75,76,77,97,98,100,101]. With the aim of evaluating the “hysteresis” in performance under oscillating flow conditions, Setoguchi et al. [74] conducted an interesting experimental investigation of the local flow by measuring the pressure distribution along the blade surface at midspan. A slip ring unit, represented in Figure 14, was adopted to connect the rotating pressure taps to the non-rotating pressure transducers. With this arrangement, the authors of [74] reconstructed the pressure distribution on one of the most common blade profiles used in the Wells turbine, i.e., the NACA 0015, at different incidence angles and for rotors with a different number of blades. In the same work [74], the authors compared NACA 00xx series profiles with different thickness ratios, while other authors investigated Wells turbine performance with CA9 and HSIM15 profiles [51,64,100], and modified NACA 0015 and Eppler 472 profiles [77]. As a general result, thicker symmetric profiles have shown better performance together with a more effective starting characteristic [8].

4.3. The Hub-to-Tip Ratio

The hub-to-tip ratio $\nu$ has a significant effect Wells turbine performance, given its relevant influence on the tip leakage flow and the evolution of secondary flows at the blade root [8,71], both associated with the stall occurrence. In addition, the hub-to-tip ratio plays a role on the self-starting behavior of the turbine, although the value of $\nu$ to obtain this feature depends on the value of the rotor solidity [113]. Nevertheless, these effects have not yet been analyzed with local flow investigations which can better clarify the expected influence of this parameter on the local flow. On the other hand, small size experimental rigs make it difficult to perform similar detailed analyses, and the minimum achievable value of $\nu$ is often limited by the dimension of the measuring section [71,79]. Raghunathan’s considerations on the design of the Wells turbine recommend values of $\nu <0.6$ [114], although a more recently experimental and numerical analysis from [78,112] pointed out that sensibly lower values of the hub-to-tip ratio are preferable for aerodynamic and acoustic performance, considering that the self-starting issue has now lost its importance.

4.4. The Tip Clearance Size

Several works have investigated the relevance of the tip gap size on the rotor performance [72,74,77,79,105], all focused on global performance. They observed that increasing the size of the tip clearance, typically reported in non-dimensional form with respect to the blade chord [72,74], determines a wider stable operating range for the turbine, while the cycle-averaged efficiency of the rotor reduces [8]. Torresi et al. [12] provided an explanation of these effects using numerical investigations, showing how a larger tip leakage can energize the boundary layer near the suction side of the blade, effectively delaying stall. Even though no detailed experimental analyses to characterize the tip leakage flow in a Wells turbine are available at the present time, the loss quantification recently proposed by Licheri et al. [79] confirms the general explanation of the tip clearance effects proposed by Torresi et al. [12]. Figure 15 shows the influence of the tip gap-to-height ratio $t_h$ on the efficiency and flow coefficient at stall. This figure reports the cycle-averaged efficiency $\overline{\eta }$, evaluated based on loss contributions defined by the same authors in [68], under non-stationary operating conditions representative of a regular wave motion. Larger tip clearance sizes, non-dimensionalized with respect to the blade height, result in lower rotor efficiencies due to the larger amount of fluid flowing through the tip gap, i.e., not producing work. On the other hand, the stall point is effectively delayed with larger tip clearance size, due to the energizing effect on the suction side of the boundary layer [12].

Takao et al. [107] investigated the effects of end plates at the tip of a monoplane Wells rotor with the aim of improving the initial performance while delaying the stall occurrence. They tested different sizes and positions of end plates using the Saga University bidirectional rig [55], comparing these experimental results with numerical simulations. The presence of end plates modifies the interaction between the leakage flow and the flow on the suction surface, resulting in a more efficient Wells rotor with a larger stable operating range.

4.5. The Blade Aspect Ratio

Suzuki et al. [105] investigated the effects on global performance and stall onset induced by different values of the blade aspect ratio $AR$. A reduction in the turbine efficiency as well as in the operating range was observed and confirmed by a comparison with other existing experimental results. Nevertheless, in his review, Raghunatan [8] noticed that the variation of the $AR$ in the existing works was obtained by simply varying the blade chord, at the price of conducting tests under different values of the Reynolds’ number. Following this important consideration and taking into account the low values of the Reynolds’ number (in the transitional range) typical of Wells turbine prototypes, Licheri et al. [79] investigated the effects of $AR$, paying particular attention to reproduce similar flow regimes for all tested geometries, confirming the results obtained in [105] and explaining how the performance variation is caused by a change in the effective Reynolds’ number and not by a direct effect of the $AR$. Figure 15 clearly shows the very limited influence of $AR$ on both the loss contributions and operating range, for the values considered in [79].

4.6. The Blade Sweep

The sweep ratio $g_c$ represents the distance of the blade staking line from the leading edge line (g), non-dimensionalized with the chord c as shown in Figure 11. The value of this parameter plays a role on the mechanism of flow separation from the blade surface as highlighted by Raghunathan in [8]. More specifically, for a constant chord blade design with a $g_c<0.5$ (backward-swept blades), the stall is postponed with also a limited gain in the peak efficiency of the turbine. Setoguchi et al. presented more extended comparisons for this parameter [64], confirming the previous results for a NACA0020 blade profile but showing an opposite trend in the stall occurrence for CA9 and HSIM15 profiles. Unfortunately, the authors could not find any local flow analyses available in the literature evaluating the flow modifications due to this parameter, and the explanation of these differences is not completely clear and only based on numerical studies [115].

Also the blade sweep angle, represented in Figure 11 with the symbol $\epsilon$, and often referred to as the blade skew [104], plays a role both on the stall occurrence and on the rotor efficiency [116]. Simply backward or forward swept blades have shown to reduce both the operating range and the rotor efficiency [73,96], although the stall is less abrupt than for unswept blades [73]. Optimized combinations of backward (at the hub) and forward sweep [104] can provide improvements both in terms of the operating range and efficiency, although the increment of the latter is only marginal.

4.7. Other Wells Rotors Configurations

In order to allow a Wells turbine to operate with higher pressure drops, for a given flow rate, without introducing transonic effects due to high rotational speeds at the blade tip (see Equation (3)), multiplane turbines can be adopted [50]. Only configurations with two blade rows have been reported in the literature, and the resulting arrangement is named the biplane Wells turbine. Figure 16 sketches the velocity triangles in this machine, assuming a fully axial inlet flow.

The performance of a biplane Wells turbine was initially investigated by Raghunathan [50] under stationary flow conditions, in order to understand the effect of the inter-row distance G (typically non-dimensionalized with the blade chord c) on the global performance, finding a less abrupt stall with respect to a monoplane Well turbine. Gato and Curran [52] extended these analyses, testing different turbine solidities and values of $G/c$ and investigating the effect of the relative blade stagger angle (blade clocking) between the two planes on the overall turbine performance. Setoguchi et al. [117] performed similar investigations on different biplane Wells turbine configurations, comparing their performance and suggesting some guidelines for their design. Morais et al. [118] presented a more detailed investigation on biplane Wells turbines, comparing a high solidity biplane rotor with other similar machines, including a local flow characterization using a bidimensional pressure probe downstream of each row. Moreover, this study evaluates the effect of introducing a row of guide vanes between the two rotors, both analyzing the global performance and comparing the local 2D flow field, extending the analyses proposed by Alves et al. [92] on the same turbine configurations and in the same test rig. Carrelhas et al. [83] extended the previous work, focusing on biplane rotors with different solidities, with and without intermediate guide vanes and comparing these configurations also with respect to their acoustic emissions. The biplane turbine with intermediate guide vanes produced the highest peak efficiency, although with the smallest operating range due to stall, while acoustic emissions in the free-stall operating range were almost the same for all the tested turbines, given that the turbulent boundary layer at the trailing edge is the primary noise source. Das et al. [60] evaluated the operation of a small biplane Wells turbine, characterizing its performance under different load conditions as well as its starting behavior under oscillating flow.

Gato et al. [43,69] observed how the exit kinetic energy represents a considerable, although not the most relevant [68], loss contribution in the conversion process provided by a Wells turbine. In order to recover this exit kinetic energy, they proposed the addition of stator blades, placed both at the inlet and outlet of the rotor (given the bidirectional flow). Stator blades, typically referred as guide vanes, represent a relatively simple solution that allows to obtain a fully axial outlet flow. Unfortunately, the bidirectional nature of the flow in Wells turbine operation requires the use of a double row of guide vanes [54], with a modification of the inlet flow to the turbine. Experimental studies on such a configuration were conducted in unidirectional and stationary setups [54], confirming the expected modifications in turbine global performance with an increase, of about 5%, in the peak efficiency for the tested rotor geometry. Takao et al. [119] presented similar analyses, while Govardhan and Dhanasekaran [120] compared the radial distributions of velocity components at the exit of the inlet guide vane row, also referred as inlet guide vanes (IGVs), for Wells rotors with constant chord and constant solidity blade, explaining the reasons behind the performance improvements produced by the presence of IGVs. Setoguchi et al. [121] proposed an improvement, introducing a radial shape variation instead of the simpler configuration obtained, maintaining a fixed blade profile along the blade span.

Exit kinetic energy recovery can be achieved also using two contra-rotating Wells rotors [8], at the price of introducing an additional generator (or a gear box) to reverse the direction of rotation of one rotor and, finally, resulting in a more complex and expensive configuration than monoplane and biplane Wells turbines. Unidirectional stationary investigations conducted on small scale turbines [53,122] confirmed the expected performance of this particular turbine configuration, although bidirectional analyses conducted on a full-scale turbine by Folley et al. [123] showed significant differences from the predictions, suggesting the inadequacy of stationary experiments for reproducing the unsteady behavior of contra-rotating Wells rotors.

Curran and Gato [80] summarized and compared the global performance of different Wells turbine configurations, including monoplane turbines with and without guide vanes, biplane, and contra-rotating turbines. They also reported local analyses, with the aim of comparing exit flow angles for a monoplane rotor with and without guide vanes and for biplane and contra-rotating turbines.

4.8. Control Methods for Wells Turbine Operation

One of the most important limitations of the Wells turbine design is the stall occurrence at relatively small incidence angles, which leads to a limited stable operating range. Two control strategies, already used in other turbomachinery applications [124], have been suggested to control the operating conditions of a Wells monoplane turbine [8], without the need to introduce any other components into the system: the variable rotational speed and the variable pitch blades. Velocity triangles in Figure 17, drawn under the assumption of a fully axial inlet flow, help to visualize how the flow incidence angle i can be controlled using these two control strategies.

Lekube et al. [125] investigated, using numerical approaches, the possibility of regulating the turbine rotational speed, evaluating the possibility to avoid stall under real sea states. Starting from experimental measurements of acoustic emissions for a laboratory scale Wells turbine, Starzmann et al. [87] used a numerical approach to reproduce the effect of this control strategy on the noise of Wells turbine installations, showing the potentiality of a rotational speed regulation to reduce acoustic emissions. Licheri et al. [84,126] conducted an experimental analysis on a variable speed Wells rotor prototype at the University of Cagliari under oscillating flow conditions reproduced within an OWC simulator. They demonstrated, through investigations based only on global performance quantification, the effectiveness of a rotational speed control to obtain the desired turbine operating condition, maximizing the cycle operating efficiency with respect to the constant speed rotor.

Gato et al. conducted experimental analyses on Wells rotors with variable pitch blades in the late 1980s [127], with the aim of characterizing the aerodynamic performance of a Wells rotor with staggered blades. Gato and Fãlcao [127,128] characterized the stationary performance of a Wells rotor for several fixed values of the stagger angle, showing an improved efficiency and, as expected, the actual extension of the stable operating range. Inoue et al. [129,130] conducted tests in rotors with a fixed blade pitch angle under under stationary conditions, evaluating the self-starting behavior. At the present time, the only work that analyzed the performance of a Wells rotor with continuously varying pitch angle is that of Tease [131]. In this experimental investigation, a mechanism was capable of regulating the blade pitch angle under pulsating conditions, with the aim to limit the maximum flow angle achieved during operation. Setoguchi et al. [132] proposed a Wells rotor with self-pitch-controlled blades, focusing their investigations on its starting behavior of such a rotor and showing the benefits of this passive control strategy. Very recently, Licheri et al. [133] evaluated the performance of a Wells turbine prototype, equipped with variable pitch blades and installed in an OWC simulator, reconstructing its global and local performance under oscillating operating conditions for several constant values (during a test) of the the blade stagger angle. The results are in agreement with the previous literature and also with two-dimensional CFD simulations [134], showing the potential of less expensive calculations to define control laws for the performance maximization of variable pitch Wells rotors.

5. Discussion

5.1. Current Limitations of Available Studies

Despite the large number of analyses published in the last 40 years on Wells turbines, conducted both using numerical and experimental approaches, existing correlations between the performance and geometric parameters are still not exhaustive, and further studies are needed. This lack of information translates into the scarcity of usable rules for the design of a Wells turbine optimized for a specific site or for coupling it to an existing OWC. Raghunathan [114] provided important guidelines for designing a Wells turbine, but these do not include all geometric parameters and are based on requirements that are not longer relevant (e.g., the need for self-starting capabilities). In addition, many researchers were unable to obtain a complete separation of the effects due to different geometric parameters due to practical experiments limitations. Although still of general validity, the correlations provided in [114] should be reviewed in light of more recent research and integrated with more detailed and rigorous analysis.

The systematic study of the effect of geometric parameters on the Wells turbine performance is nowadays strongly based on numerical simulations, in particular on CFD analyses, but experimental investigations still play a fundamental role for (a) providing an adequate database for the validation of numerical predictions and (b) the verification of optimized solution from numerical simulations under operating conditions representative of the real ones.

However, the size of existing test rigs does not allow to always reproduce the real operating conditions of the Wells turbine, particularly in terms of the Reynolds’ number, which is typically lower due to the reduced size used in prototypes. Only a few investigations [71,79,99] have analyzed the Reynolds’ number effect on the performance of a Wells turbine, and in particular on the efficiency, essentially confirming the general behavior of isolated profiles. Takao et al. [99] found the critical Reynolds’ numbers for Wells turbines to be of the order of $4.0 \times {10}^5$: for larger values, the peak and mean efficiency (obtained under stationary and oscillating operating conditions, respectively) are almost constant. They obtained this result using the rig available at the University of Limerick [51], which is at the time of writing the largest experimental setup built for Wells turbine testing (see Table 2).

5.2. Further Investigations Needed

In order to satisfy these requirements, experimental analyses conducted only from a global point of view are not sufficient, and detailed local flow analyses are necessary to provide more thorough information and explanations of the rotor aerodynamics. Moreover, the characterization of secondary flow losses in Wells turbines can be used to define or to adapt existing turbomachinery loss models to such an unusually staggered rotor. With this in mind, Wells turbine test rigs, that always employ the full rotating components of the machine, still represent an effective solution for investigating and characterizing cascade effects. These analyses should also be extended even in innovative configurations, for instance in rotors with the control of the blade stagger angle [133].

During the last decade, a number of novel geometric configurations have been proposed and evaluated by numerical analyses. These new configurations promise to overcome some limitations of traditional Wells turbine designs, i.e., the relatively low aerodynamic efficiency and the limited operating range. Fences, end-plates, casing treatments, slats, gurney flaps and many other solutions have been analyzed, but never tested experimentally. It is the authors’ opinion that experimental tests continue to have a fundamental importance in analyzing the proposed solutions and, in general, validating the numerical result in terms of global and local quantities. Laboratory test rigs, and particularly oscillating rigs, are therefore of fundamental importance to guide the search for better performing and more stable machines.