A comprehensive review of the theoretical

Renewable and Sustainable Energy Reviews 51 (2015) 1709–1720

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Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser

A comprehensive review of the theoretical approaches for the airfoil design of lift-type vertical axis wind turbine Jian Chen a,n, Hongxing Yang b, Mo Yang a, Hongtao Xu a, Zuohuan Hu a a b

School of Energy and Power Engineering, University of Shanghai for Science and Technology, China Renewable Energy Research Group (RERG), The Hong Kong Polytechnic University, Kowloon, Hong Kong, China

art ic l e i nf o

a b s t r a c t

Article history: Received 30 April 2014 Received in revised form 14 May 2015 Accepted 11 July 2015

The airfoil researches of the Darrieus wind turbine will not only affect the power coefficient (CP), but also has great impact on the rotor's starting ability. A review on a wide number of different design approaches is conducted in this work to change the current situation in which the airfoil research of Darrieus rotor is not sufficient both in depth and in width. Different from the previous review work, this paper not only gives a comprehensive review of the current Darrieus airfoil's research approaches but also discussed the applicability of their design processes based on research topics, especially for the approaches based on Panel and the CFD method. Two ways of building airfoil database and current progress of the approach based on Momentum, Vortex and Cascade are addressed. In the end, two promising inverse approaches are proposed for the future study of the Darrieus airfoil. Thus, the aim of this paper is to guide relevant readers and experts to find a proper airfoil design approach considering the research purposes, applicability of design approach based on different theoretical methods and adaptability of design approaches' processes. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Darrieus rotor Airfoil Inverse and direct approach Theoretical method Design process

Contents 1. 2.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Review of airfoil research approaches for the Darrieus rotor airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Direct design approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1. Direct design approach based on the Momentum, Vortex and Cascade method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2. Direct design approach based Panel method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3. Direct design approach based on CFD method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Inverse design approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1. Inverse design approach based on Momentum method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2. Proposed inverse design approach based on Panel and CFD method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Summary and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction There are two kinds of vertical axis wind turbines (VAWTs). They are drag-type and lift-type VAWTs. In this paper, we only focus on the lift-type VAWTs, which have a higher power coefficient than that of the drag-type VAWTs. The typical representative

n

Corresponding author. E-mail addresses: [email protected] (J. Chen), [email protected] (H. Yang). http://dx.doi.org/10.1016/j.rser.2015.07.065 1364-0321/& 2015 Elsevier Ltd. All rights reserved.

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of the lift-type VAWTs is the Darrieus rotor patented by a French engineer whose name is George Jeans Mary Darrieus in 1931. The Darreius rotors have several appealing advantages [1], such as taking the wind from any direction [2], low level of noise [3], feasibility of maintenance and simpler construction features [4]. And, recent research of the Darrieus rotor has shown that the Darrieus rotor produces an increased power output in skew flow [5]. The advantages of Darrieus rotor and the ability in skew flow make the Darrieus wind turbine became a promising device to generate the power in the urban environment or building area whose wind condition is more complicated than open areas [6].

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Compared to farms of HAWTs, the VAWT farm has three times the power density at one tenth of the height [2]. Saeidi et al. [7] claimed that a profit of 6 cents per each kWh generated power was gained based on electricity costs in the city of Fadashk in the south Khorasan. Furthermore, a re-emerging interesting has been raised to harness the offshore wind resources using the vertical axis wind turbines [8], several multi-megawatt offshore Darrieus projects are currently under way due to the features of a lower center of gravity, reduced machine complexity and better scalability to very large sizes [9]. However, the previous researches of the Darrieus turbines were less sufficient than that of the horizontal axis wind turbines (HAWTs), especially the airfoil research of the Darrieus turbine. This highly limits the development and utilization of the Darrieus rotor. Generally, there are two topics of the Darreius rotor airfoil researches. They are the investigation of airfoil aerodynamic characters and the study of the airfoil geometric parameters [10]. The aim of the airfoil aerodynamic researches is to understand the aerodynamic mechanics of the Darrieus rotor or to find the suitable pressure and velocity distribution on the airfoil surface, dynamic features, vorticity development [11] and blade weak interaction in a steady flow and unsteady flow condition [12–14]. Moreover, the aim of the investigation of airfoil geometric parameters is to find the right airfoil, which can work well with the complicated aerodynamic conditions of the Darrieus rotor or improve the power coefficient. The goal of these two research topics is the same, which is to guide the airfoil design. In addition, it should be pointed out that the research on the airfoil aerodynamics character is the core of the inverse airfoil design approach of the Darrieus rotor. It was less discussed by other researchers before. The investigation of airfoil geometric parameters relates to the direct airfoil design approach of the Darrieus rotor. With respect to the investigation of aerodynamic mechanics, Claessens [15] in 2006 and Islam [16] carried out a similar research to find the desirable aerodynamic features based on their or previous researchers' work. Their researches were based on a small amount of airfoils and tried to explain the dynamic aerodynamic characteristics with the static aerodynamic characteristics. Some researchers also conducted the PIV or CFD [17–19] investigations of the dynamic aerodynamics phenomenon. Those investigations, largely, studied the vertical structure of the flow field or circulation of shedding vortices caused by the periodic motion of the blades. However, it is hard to find the investigation of the desirable velocity and pressure distribution on the airfoil surface, which is the key of the inverse airfoil design approach. In terms of airfoil geometric investigation, few researchers have been conducted on a small kind of airfoils and their geometrical parameters. Those airfoils are mainly involved in a few numbers of airfoils of the four or six-digit NACA series [15,20–22], Gottingen series [23,24], low-Reynolds number (RN) series [25,26], S-series, A-series and FX series [27]. Types and numbers of airfoils investigated are not adequate for optimization point view. Therefore, the Darrieus rotor airfoil research is far from adequate for the airfoil aerodynamic characters and geometrical parameters from the optimal airfoil design point of view. In 2008, Islam et al. [28] summarized the theoretical methods for the Darreius rotor. He discussed the direct approach based on the Momentum, Vortex and Cascade methods comprehensively. Those direct approaches mentioned above needs static C l (lift coefficient) and C d (drag coefficient) of airfoils at a wide range of the angle of attack (AOA) and RN. This is one of the reasons why the Darrieus rotor airfoil researches conducted before only involved in small types and numbers of airfoils [29]. 2015, Jin et al. [30] reviewed the basic research approach for the Darrieus rotor. They added the

CFD method and experiment approach. All the research approaches mentioned above are direct approaches. And they discussed less about the process of research approach based on different research topics. Actually, there are two kinds research approaches (direct approach based on panel method and inverse approach based on Momentum method) which have been used and have great potential for the Darrieus airfoil research. Different from the research works of Islam et al. [28] and Jin et al. [30], this paper classified the research approaches based on the two research topics. Those two kinds of research approaches are inverse and direct approaches. We summarized the outline of three direct approaches and one inverse approach. We also presented the different design processes for each research approach, especially for the approaches based on Panel and CFD method. In addition, we discussed the building of the airfoil database carefully and summarized the recent progress of the approach based on Momentum, Vortex and Cascade methods. In the end, we proposed two possible inverse approaches for the future research. Thus, the aim of this paper not only gives a comprehensive review of the airfoil design approaches, but also guides readers to find a proper airfoil design approach through a detailed discussion of the different design approaches, different process of design approach, different theatrical methods and their adaptability, advantage, disadvantage and facing challenges based on the airfoil research topics.

2. Review of airfoil research approaches for the Darrieus rotor airfoil Based on research topics, the research approaches can be classified into two groups. They are the inverse and direct airfoil design approaches. Hence, there are mainly two parts in this section. The first part presents three direct design approaches. They are the approach based on the Momentum, Vortex and Cascade methods summarized by Islam [28], the approach based on Panel method and the approach based on CFD method. The second part presents the inverse design approach. According to the literature review, only one type of theoretical methods (Momentum method) has been used for the inverse airfoil design approach. 2.1. Direct design approach Since the low level of progress in the Darrieus rotor inverse design approach, the Darrieus airfoil research approach, currently, is mainly dominated by the direct design approach. Generally, the direct design approach has two steps. First step is to evaluate the performance of a pre-design Darreius rotor using the geometry parameters gained from some design rules or experience. The second step is to redesign or guess the geometry based on the consideration of the results gained in the first step and some design rules or experience. Above two steps will be executed repeatedly until the target shape is obtained. The basic principle is the same for three direct design approaches based on different theoretical methods. The direct design approach based on the Momentum, Vortex and Cascade method was discussed firstly. 2.1.1. Direct design approach based on the Momentum, Vortex and Cascade method 2.1.1.1. Outline of direct design approach based on Momentum, Vortex and Cascade method. The most widely used theoretical methods for the performance prediction of the VAWT are Momentum [31–34], Vortex [35,36] and Cascade [37,38] models. This approach based on the Momentum, Vortex and Cascade methods is quasisteady approach and is more economical than the Panel method and the CFD method [39]. Thus, the first direct approach, actually,


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Fig. 1. Method used by the Islam source [45].

is based on three models or methods. These three models are evolved into the first direct approach in this paper due to the computational similarity of these three models or methods. In 2008, Islam [28] summarized these robust and fast models for the Darrieus straight-bladed VAWTs and pointed out the advantages and disadvantage of those models. The computational steps of above three models are listed below:

Construction of the pre-stall airfoil characteristics from experi

ments and prediction models at different RN and azimuth angle. Construction of the post-stall airfoil characteristics gained from post-stall models at different RN and azimuth angles. Correction airfoil characteristics considering the finite aspect ratio [40]. Estimation of the local angle of attack and local relative velocities at a whole range of tip speed ratios and azimuth locations. Calculation of the induced velocity ratio and free stream velocity. Calculation of the local normal and tangential forces based on different theories ( Momentum, Vortex and Cascade theory). Dynamic stall consideration [41,42]. Flow curvature model consideration [38,43]. Consideration of the influence of the struts and towers [44]. Wind shear consideration [33].

2.1.1.2. The processes and their capability of the direct design approach based on the Momentum, Vortex and Cascade method. The common process of the direct design approach based on the Momentum, Vortex, and Cascade method is the same as the work conducted by the Islam [45]. This common direct design process used by the Islam is presented in Fig. 1. The computational scheme or theoretical method (Cascade model) in Fig. 1, actually, can be replaced by the CARDAAV (model based on the Double-Multiple Streamtube model) or VDART3 (model based on the Vortex theory). The great disadvantage of these three models is that they need C l (lift coefficient) and C d (drag coefficient) of airfoils at a wide range of the AOA and RN due to a circular motion of the VAWTs [46], especially at low tip speed ratios. Thus, the most critical issue of these models is to build the lift, drag and moment coefficients of airfoils at a wide range of the AOA and RN accurately [45]. 2.1.1.3. Building of the database for the Momentum, Vortex and Cascade methods. Generally, two ways can be used to build the characteristics of airfoils. One is to search the available experimental results. A lot of experiments have been done about the aerodynamic characteristics of the airfoils, but most of those aerodynamic characteristics were focused on the two-dimensional pre-stall and high RN [47,48]. Only few experiments were conducted at the post-stall and lower RN

[49–51], especially for the NACA symmetrical airfoil section. That is reason why most of the Darrieus rotors built by the Sandia National Laboratory [52,53] or other researchers [54] used the NACA symmetrical airfoil sections. Kirke [46] conducted a comprehensive search for the low RN airfoil characteristics and found that no test data are available for the cambered sections through the full 360 AOA and RN below 250,000. According to the statement of McGhee and Walker [55], experimental results of various airfoils also showed large differences at low RN in different wind tunnels. Thus, it is very difficult to find the aerodynamic characteristic (C l and C d ) in the wide range of AOA and RN through the experimental results for the majority of airfoils [46]. Another way is to model the airfoil aerodynamic characteristics using the theory programs. 2D Navier–Stokes solver (EllipSys2D) and potential Panel method codes (XFOIL, PROFIL[56]) are widely utilized for airfoil analysis before the pre-stall by renowned wind turbine research organizations including NREL [57] and Risoe [58]. Raciti Castelli et al. [59] extended the experimental data from Sheldahl and Klimas [49] using the Xfoil. Kumar et al. [60] used a CFD method to predict the lift and drag coefficients in the transition region in a fully turbulent boundary layer. They used the method developed by Basha and Ghaly [61] to predict the lift and drag coefficient at low Reynolds number (1000–160,000). However, the behavior of the airfoil in the post-stall regimes cannot be accurately predicted by the above programs, thus a appropriate post-stall model were needed to extend the characteristics of airfoils to the high AOA [45]. Several researchers [46,62] attempted to use some models to predict the behavior of airfoil in the post-stall regimes, but these models may have some errors when using the static results to predict the dynamic phenomena. A comparison among steady simulation of static aerodynamic characteristics, unsteady simulation of static aerodynamic characteristics and experimental static aerodynamic characteristics showed that the unsteady simulation results are closer to the experiment results than the steady simulation results [63]. The Leishman–Beddoes model for the dynamic stall is questionable up to 301 [64]. Thus, it is also difficult to build the reliable lift, drag coefficient for the entire range of AOA through the theory approaches. Another important issue needed to be stated is that the method based on the Momentum, Vortex and Cascade theory is to predict Darrieus rotor performance with the static airfoil aerodynamic characteristics but rather with dynamic airfoil aerodynamic characteristics. This is the reason why this method is robust and low computation effort [29]. Furthermore, a convergence problem may occur for the Double-Multiple Streamtube model (one of the Momentum model) when this model is used to predict the performance of the Darreius rotor at a higher tip speed ratio [28]. According to the above statements, the Momentum, Vortex and Cascade models are more robust and faster than Panel method or CFD simulation only when the reliability characteristics of airfoils are built well or existent [65]. Thus, this direct approach is difficult to realize the parametric airfoil research, and always limits to a narrow number

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of airfoils [29]. It is suitable for the investigation of the airfoil with extended database at low Reynolds numbers [51] and gives some guidance for the investigation of airfoil aerodynamic mechanism.

2.1.1.4. Recently progress of the Momentum, Vortex and Cascade method. Recently, some researchers have made some effects to perfect this direct design approach based on Momentum, Vortex and Cascade method. An improvement has been conducted by the Feng-Zhu et al. [66] to predict a more precise RN, especially in high TSR. They presented an algorithm LDWT which adapts the blade RN instead of the free stream wind velocity RN to solve the prediction failure at high tip-speed ratios. Dynamic stall models are included in the Double Multiple Streamtube Model by Dyachuk and Goude [67]. Three dynamics stall models and tower tilting were introduced in DMS model to calculate the aerodynamics of a VAWT which has a titled tower [68]. Antonini et al. [69] proposed an innovative model based on the vortex theory, which includes a second separated wake, to consider the dynamic evolution of the shed vortices and the separation point. The WOMBAT(Weatherly Optimization Method for Blades of Air Turbines) algorithm adopts the multi-objective genetic algorithm based on work of Deb [70]. Bedon et al [65] evaluated the different aerodynamic databases for vertical axis wind turbines, and used the Momentum method and genetic algorithm to provide optimal configurations for different design objectives [59,71]. A 3D free wake vortex model was developed by Fanzhong et al. [72] to predict the aero-elastic behavior of a H-Darrieus rotor.

2.1.2. Direct design approach based Panel method 2.1.2.1. Outline of direct design approach based on Panel method. Panel method, in fact, is not a new method to conduct research of the VAWTs. In 1983, Oler et al. [73] used a doublet Panel method with an integral boundary layer scheme and discrete vortices to predict the lift, drag, pressure distribution of the airfoils and understand the dynamic stall mechanism of the Darrieus rotor. The Panel method was also adopted to predict the performance of the Savonius rotors [74]. Zervos [21] used the surface singularity distributions and vortex particles with finite cores on the wake to study the performance of the five different airfoils. In 2006, Wang et al. [75] conducted a 2D Panel simulation based on singularity elements for a vertical axis tidal turbine. And some researcher [76,77] also applied 3D Panel method to predict the performance of the VAWTs recently. Shi et al. [78] used a 2D vortex type free wake aerodynamic model and solved a Poisson equation for the ‘weak induced’ pressure field to overcome the potential function for the wake vorticity field. A comparison between the Momentum, Vortex and Panel methods has been made by the Ferreira et al. [79] in 2014. He claimed that the streamtube model deviate significantly from the other models, and results showed a good agreement between the Vortex and Panel methods. The general computational steps of the Panel method can be listed below:

Definition of the coordinates frame. Selection of appropriate singularity element distribution on the

surface. Selection of the boundary conditions. Selection of the wake models. Discretization of surface and singularity distributions. Discretization of governing equations (fulfillment of the zero normal flow condition of surface, Kutta condition and Kelvin condition). Calculation of pressure, load, velocity and performance.

2.1.2.2. The processes and their capability of the direct design approach based on Panel method 2.1.2.2.1. The common process of direct approach based on Panel method. The common design process of the Panel method for the Darrieus rotor airfoil is shown in Fig. 2. There are three steps in this common design process. These three steps are the following:

Step 1: Definition and discretization of the airfoil coordinate. Step 2: Power coefficient prediction of the Darrieus turbine by Panel method.

Step 3: To analyze the results. Most researchers [76,78], currently, have used this common process to design the airfoil or get the flow field of the Darrieus rotors. 2.1.2.2.2. The parametrical process of direct approach based on Panel method. However, another process is more powerful than this common process. This process is called parametrical process of direct approach based on Panel method (PPDAPM). And this PPDAPM, especially, is suited for the airfoil geometry design. The reason why the PPDAPM is ready for the airfoil geometry design is that the ordinates of airfoil should be offered in the Panel method firstly [80]. A lot of functions or programs [81,82] for airfoil parameterization can be used to gain the ordinates of airfoil. Thus, the approach based on the Panel method is a promising way for optimal airfoil geometric design of the Darrieus rotor. Unfortunately, there is very little of such researches which has been conducted before. This PPDAPM is presented in Fig. 3. The difference between PPDAPM and common process mainly lies in steps 5 and 6. In step 5, the optimization algorithms for the Panel method can be the design of experiment (DOE) [83], evolutionary algorithm (EA) [59], particle swarm optimization (PSO) [84] or genetic algorithm (GA) [85]. The output of the step 5 is a new airfoil gained from the optimization algorithm. The disadvantage of the Panel method comes from the potential theory which considers the flow without viscous. In the real flow, the effect of the viscous should not be ignored. Although several methods which couple the outer potential flow and inner viscous flow were proposed to introduce the effect of the viscous into the Panel method [78], those coupling methods only can

Panel method Definition and Discretization Airfoil Coordinate

(Singularity element +Kutta condition +Kelvin condition )

Fig. 2. The common design process of the Panel method.


1

2

3

Definition and

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Panel method

Initial Airfoil

Discretization

(Singularity element

Parameters

Airfoil Coordinate

+Kutta condition +Kelvin condition)

6

5

4

Optimization

New airfoil

Strategies (DOE,

Parameters

GA, PSO)

Object 7

Final airfoil

Fig. 3. A parametrical process of direct approach based on the Panel method.

handle the cases of ‘mild’ separation, for the cases with massive separation additional modeling efforts or the solution of the full NavierσStokes equations is required [80]. It should be mentioned that the Panel method needs well depicted dynamic stall models. Wang [75] stated that his Panel model only a fully theoretical tool which can be the basis for a more sophisticated future model which includes theoretical stall. The same as the Wang, Simão Ferreira, [76] have used 2D and 3D Panel methods to view the near weak of VAWTs in 2009. He applied the CFD method to simulate the dynamic stall phenomenon.

2.1.3. Direct design approach based on CFD method 2.1.3.1. The outline of direct design approach based on the CFD method. The reason why the CFD investigation of the VAWTs has become more and more popular is that the development of computer and appealing ability of the CFD compared to the Momentum, Vortex, Cascade and Panel method. The greatest advantage of the CFD method is that the effects of dynamic stall, viscosity, flow curvature and parasitic drag, which needed to be modeled in the method based on the Momentum, Vortex and Cascade theory and Panel method, can be easily considered in CFD simulations. But, the greatest disadvantage of the CFD method is relatively higher computational consumption. Many researchers have conducted the CFD simulation on the VAWTs recently [4,86]. Table 1 presents a brief review of CFD researches [26,54,76,87,88] which were compared with the experimental results. From this table, it is found that different authors used different simulation strategies. The simulation strategies are mainly concerned about two aspects, discretion of the computational domain and solving strategies for computational domain [89]. Items related to the discretion of computational domain can be the total mesh number, the size of the computational domain, the height of the first boundary-layer and so on. And the terms related to the solving strategies can be the turbulence model, wall function, interpolating scheme, boundary conditions and so on.

Generally, research topics or established practice for a specific class of problem determine the requirements of computational time, accuracy and cost resources [90]. And the requirements of computational time and accuracy decide the adoption of CFD simulation strategies [86]. The research topics of the airfoil design can be airfoil aerodynamic research and the effect of airfoil geometry on the performance. And the CFD has a great advantage in the study of airfoil aerodynamic [30]. In general, less computational time and acceptable accuracy are needed for the geometric design of the airfoil, especially for parametrical design of airfoil. While higher computational time and accuracy are needed to understand the aerodynamic mechanics of the airfoil. Less computational time and accuracy mean smaller computational domain, fewer total mesh number, larger time steps for the unsteady simulation and so on. Simão Ferreira [76] discussed the CFD strategies for the Darrieus rotor in 2009. Almohammadi et al. [26] compared the effect of different mesh independency techniques on the CFD simulation results. A brief summary in Table 1 also gives some reference for selection of the CFD strategies. However, in this paper, we mainly focus on the CFD design process and the capability of those CFD design process.

2.1.3.2. The processes and their capability of the direct design approach based on CFD method 2.1.3.2.1. The common process of direct approach based on CFD method. According to the Raciti et al. [29], the main steps of the common CFD design process are pre-procedure, simulation step and post-procedure presented in Fig. 4. The purpose of the pre-procedure is to generate the geometry of the computational domain and discrete the computational domain with high quality meshes or grids [88]. Thus, there are two steps for the pre-procedure. The first step is to create the geometry of the computational domain according to the purpose of study. A certain degree of geometric simplification, in most cases, are conducted due to the high computational cost and time [90]. However, authors must

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Table 1 CFD investigation on the Darreius rotor. Author

Simao Ferreira [76]

Howell et al. [54]

McLaren [89]

Almohammadi et al. [26]

Rosario et al. (2014)

Wekesa [87]

Dimension 2D Blade NACA 0015 profile

2D,3D NACA 0022

2D Tailed NACA0021&0015

2D NACA0015

2D NACA 0015 NACA4518

2D

Diameter Chord length Mesh number Nodes on blades Height (first layer) Mesh type

0.4 m 0.05 m

0.3 mm 0.1 m

2.5 m 0.4 m&0.42 m

2.5 m 0.4 m

2.5 m&0.6 m 0.4 m&0.1 m

2D 1.6 million n

2D&3D/1.3 million n

2D 7.2n10e4–5.67n10e5 989

2.38n104 2.16n106 400–7552

2D 7n105 n

n

0.02%c

n

n

0.752 mm

n

n

Quadrilateral

Tetrahedron Unstructured

Unstructured

Structured

RN or velocity Domain size Time-step or degree Turbulence model yþ Algorithm Interpolating scheme Inlet

16D n

3.2Dn5.6D–9.6Dn16.8D 0.5–101

3.9n10

10 m/s

50cn87.5c 8.975979n10 5 s

2.5Dn9D 5n10-4 s

60cn120c 1n10 5 s

Transition SST and SST SST κ ω yþ o 1 PISO Second-order upwind

Velocity inlet Pressure outlet

Transition SST SST κ ω yþ o 1 SIMPLE Secondorder upwind Velocity inlet Pressure outlet Transition SST is appropriate for VAWT simulations

RNG κ ε

SST κ ω

yþ o10 n Second-order

Average 1.3 n n

Velocity inlet

Velocity inlet

Velocity inlet

Transition SST RNG κ ε yþ close to 1 SIMPLE Single-order & second-order upwind Velocity inlet

Outflow

Outflow

Pressure outlet

The results gained from the DES model is most closely matched the experiments

3D simulations were shown to be in reasonably good agreement with the experimental measurements

(1) SST model is the most suitable model for the simulation of VAWT (2) A over prediction of CP was found at high TSR

2D

10 m/s

10Dn14D 1/161, 1/81 1/41, 1/21 LES, DES one-equation SpallartAlmaras RNG k-model yþ close to 1 n n

Outlet Results

2.7n10e5

Structured & unstructured 10 m/s

4

NACA 0022 0.35 m 0.04 m

(1) (1)Transition SST is better than the RNG κ ε model. (2) (2) A over prediction of CP was found at high TSR

Transition SST is very close to experimental results

Fig. 4. The common design process of the CFD method.

consider the effect of these simplifications for the realistic and logical conclusions. Hence, Siddiqui et al. [90] studied the various levels of simplifications or approximations from two-dimensional to threedimensional geometry to quantify the effect of these simplifications. Then, meshes or grids, in the second step, will discrete the computational domain through different mesh generation strategies. The mesh quality is one of the most important issues in this step [91]. Almohammadi et al. [26] investigated mesh refinement, General Richardson Extrapolation (GRE), Grid Convergence Index (GCI) and

the fitting method to gain a mesh independent solution for a straight blade Darreius rotor. The simulation procedure includes the input of the boundary condition, selection of the solving strategies and output of the simulation results for analysis. Different simulation strategies [89] will affect the results significantly. The Courant–Friedrichs– Lewy (CFL) criterion was investigated by Trivellato and Castelli [92] to ensure the stability and trustable simulation results of a 2D VAWT. Four different turbulence models were used by


Ferreira et al. [93] to verify the model sensitivity to the grid refinement (space and time). A three dimensional numerical simulations was conducted using the large eddy simulation (LES) with dynamic smagorinsky subgrid scale (SGS) model [94]. The performance of VWT was predicted accurately. The postprocedure is to analyze the output of the monitoring flow properties [95] or flow field [86]. The analyzed results offer guidance for the further optimization of the geometry. Most of the CFD researches in Table 1 were carried out through this common CFD design process. This process is the widely used at present. Each step of this process is operated manually. Thus, this process, most of the time, is used for cases which have complicated geometry [96] or were not aimed at the parametrical study [86]. The greatest disadvantage of this common process is that users need to modify the geometry, generate the mesh, choose the simulation settings and analyze the results manually when design parameters are changed. Generally speaking, this common process is suited for the researches of either the

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geometry design [97,98] or the investigation of aerodynamic mechanism [86,96]. 2.1.3.2.2. An automatic analysis process of direct approach based on CFD method. In fact, the mouse clicks of the common process can be replaced by an automatic CFD analysis process based on the researches of Hilbert et al. [99] and Mohamed et al. [100–102]. This automatic CFD analysis process uses the system command function of the programming language (C, Matlab or Fortran) to carry out all the steps of the common process automatically. This automatic process is presented in Fig. 5. In this figure, Matlab is the presenter of a programming language in this automatic CFD analysis process and arranges the sequence of the CFD common process. A similar process has been presented by Mariano et al. [103] to update the rotor angular velocity and export this value to the CFD code using the Matlab program. This process is much more efficient than the common design process mentioned above. It eliminates the manual operation in the common process. But, additional measures may be needed for

Geometry generation

Journal file Mesh

Journal file Simulation

Post Analysis

Performance

Fig. 5. An automatic analysis process of direct approach based on the CFD method.

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a large complex three-dimensional case using millions of elements and involving complex physics [104]. In the end, this process is also a foundation of the parametric optimization process which will be discussed in the following section. 2.1.3.2.3. The parametric optimization process of direct approach based on CFD method. Two processes mentioned above can be adopted for the airfoil geometry design and the investigation of the airfoil aerodynamic mechanism. However, the parametric optimization process is a process designed for the parametric design. This design process is very popular in the aeronautics and space industry [105] and was firstly used by Mohamed in 2010 [106] to optimal design the obstacle shielding of the Savonius rotor. In 2011, Mohamed [102] again used this method to optimal design of the blade profile of a Savonius rotor which is presented in Fig. 6. Generally, this parametric optimization process presented in Fig. 6 includes five parts [104]. They are initial case, automatic CFD analysis, optimization algorithm, new case and final case. In the initial case, the parametric of the models is chosen in the literature or pervious works [104]. Then, the automatic CFD analysis module will conduct the simulation of the initial models. After that, the optimization algorithm will generate a new case based on some of the approach of selection. And the new case will be simulated repeatedly until the final case meets the design aims. The core parts of this parametric optimization process are the automatic CFD analysis and the optimization algorithm. The optimization algorithm can be the single-point algorithms, DOE algorithms and evolutionary algorithms and so on. These five parts were arranged by command function of the programming language [100]. Based on the statement Dominique and Janiga the geometry simplification of simulated cases or proper selection of the CFD strategies should be fulfilled to realize this parametric process [104]. The geometry of the Darrieus rotor, under certain assumptions, is not very complicated, especially for the H-Darrieus when the effect of struts and shaft is ignored. The geometry may be even simpler when the rotor has a higher aspect ratio. The aspect ratio of H-Darrius is defined as the ratio of the length of the blade to the chord length of the airfoil. It was verified that the effect of the aspect ratio can be left out of account if the aspect ratio is larger than 10 [107]. Hence, three dimensional (3D) airfoil geometry can be degraded into two dimensional (2D) geometry. In 2012, Carrigan [108] used this process to optimize the 2D airfoil profile of Darrieus rotor. He used three variable parameters and four variable parameters evolutionary algorithms at a fixed tip speed ratio to get the maximum torque for the NACA four digital airfoil families. In the same time, a lot of functions [109] and mathematical tools [81,82] have been established to describe the geometry of

the airfoils with the development of aviation and the turbo machinery industry. This makes the parameterization of airfoil possible. By using these functions and tools, the section of the airfoils can be generated through the programming language. The files which represent the geometry information can be imported into the meshing program. Then the above automatic CFD analysis process can be run without manual interruption. It should be pointed that the EA and PSO strategies are always hampered by high evaluation cost and slow convergence [110] or swarm stagnation [84]. Consequently, it will cost a lot of computational resources to conduct the optimal design using CFD method and EA or PSO algorithms. Different from the EA and PSO algorithms, however, orthogonal method is an experimental strategy to find the solutions with minimum effort. This method has been widely used for the optimal design in the industry. A comparison made by Tanaka [111] between the orthogonal method and genetic algorithms shows that the orthogonal method can find the solutions to the same problems as GA effectively. Thus, the efficiency of design of experiment method may be higher than the EA and the PSO method. A similar research was conducted by Bourguet et al. [112], they used a parametric design of experiments (DOE)/response surface models (RSMs) method and an automatic CFD method to optimize the blade profile.

2.2. Inverse design approach 2.2.1. Inverse design approach based on Momentum method 2.2.1.1. Outline of the inverse design approach based on Momentum method. The inverse design approach, in general, means that airfoil profile is gained from specifying a desirable velocity or pressure distribution according to the boundary-layer development and performance considerations. The inverse design approach is always regarded as a powerful design approach superior to the direct approach [85]. Modern inverse airfoil design has been evolved into an approach, which can consider the multipoint design not just the pressure and velocity distributions. Those multipoint designs can be the boundarylayer shape factor, a segment of the airfoil geometry and airfoil global parameters etc. [113]. The inverse airfoil design approach has been widely used in the area of aeronautics and space industry, but has been introduced in the design of the Darrieus rotor recently, especially the design of the small Darrieus rotor, which operates at high angles of attack and low RN. Henriques et al. and Saeed et al. [114,115] used the inverse design approach for the airfoil design of the Darrieus rotor, the method used to predict the CP of the Darrieus rotor is the

Fig. 6. Blade profile optimal design conducted by Mohamed in 2011 [102].


Momentum method. The calculation steps of the Momentum will be described in the direct design approach. The design process of this inverse approach will be presented in the following paragraphs.

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Advanced optimal algorithms or shape parameterization meth-

ods [81,116] can be used for the inverse design of the airfoil. Advanced optimal algorithms can be the DOE, EA, GA or PSO etc. Prediction reliability of the airfoil aerodynamic characteristic at low RN and high AOA is needed to be further validated [18].

2.2.1.2. The processes and their applicability of the inverse design approach based momentum method. The design process of the inverse approach proposed by Saeed [115] is depicted in Fig. 7. This design process has seven steps which are described below:

In addition, there are also several concerns which are needed to be pointed out:

Step 1: Specification of the velocity, pressure distribution,

A desirable pressure/velocity distribution may not yield a

boundary-layer development or single design parameters over different segments of airfoil surface. Step 2: Generation of the airfoil geometry according to the multipoint constriction on the airfoil surface using the multipoint inverse design program PROFILE based on the Panel method. Step 3: Calculation of the aerodynamic characteristic (C l and C d ) using the XFOIL program. Step 4: Prediction of the rotor CP using the aerodynamic characteristic gained in the third step. Step 5: Comparison is made between the power coefficient and certain criterion. If this airfoil evaluated in the above procedures can meet the object, then output the final design. Step 6: If this airfoil cannot meet the design object, a new velocity distribution will be generated in the sixth step to repeat the steps from 2 to 6 until the design object is met.

In fact, this inverse design approach has several unsettled questions, and there is still a large room of improvement for the inverse airfoil design approach. Those questions are listed below:

Velocity, pressure distribution, boundary-layer development or single design parameters are the important issues of a modern inverse design approach [113]. However, the author has only given a little discussion about this issue.

1

closed airfoil [19].

Based on the author's statement, the power coefficient is only

predicted at one design point whose rotational speed is 30 rad/ s. In fact, variation of the airfoil geometry and series may change the optimal rotational speed [27]. And the algorithm to generate the new velocity and pressure is not well depicted.

Moreover, the CP prediction model used by Saeed is the Double-multiple Streamtube model which may suffer the converge problem [28,117] and needs airfoils aerodynamic characters in a wide range of the AOA and RN.

2.2.2. Proposed inverse design approach based on Panel and CFD method It should be noted that the pure inverse design can be implemented by conformal mappings, streamline coordinatebased transformations, boundary integral formulations and Panel method [118]. Thus, it may be better to integrate the Panel method into the inverse airfoil design, especially for the CP prediction of the Darreius rotor [119]. And the CFD design method can also be used for the inverse airfoil design. Jahangirian and Shahrokhi [85] used the inverse design approach and the CFD method to design a transonic airfoil.

2

3

5

4

Velocity Distribution

6

Computer code

New velocity

CARDAAV

Distribution

DMSV model

Object 7

Final airfoil

Fig. 7. The design process used by Saeed.

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Based on the Momentum,Vortex and Cascade

Inverse approach

Based on Panel method Based on CFD method

Design approaches for Darrieus rotor airfoil

Based on the Momentum, Vortex and Cascade Direct approach

Based on Panel method Based on CFD method

Fig. 8. Summary of the design method for Darrieus rotor's airfoil.

3. Summary and conclusion This work presents a review on the three direct and one inverse approaches available in the literature. The outline of different theoretical methods and the design process of different approaches were discussed in detail to find a suitable design approach for the airfoil researches. Based on the literature review, this work also proposed two new inverse approaches. Fig. 8 presents these six approaches which can be classified into inverse and direct approaches. Furthermore, following conclusions can be drawn from the present review.

4) The Momentum method is the sole method used for the inverse approach. Thus, there is enormous and untapped potential in the inverse approach. The CFD method can be used in the inverse design to predict the CP of the Darrieus rotor. The Panel method is suitable for the inverse approach due to the fact that the pure inverse can be implemented by the Panel method. Hence, we proposed two new kinds of inverse approaches based on the Panel and CFD methods for further research. Some suggestions were given to improve the inverse approach.

Acknowledgments 1) The direct approach based on the Momentum, Vortex and Cascade methods is quasi-steady approach and needs C l and C d of airfoils at a wide range of the AOA and RN. Generally, there are two kinds of methods which can be used for the building of the C l and C d database. Hence, the Momentum, Vortex and Cascade methods are more robust and faster than the Panel method or CFD simulation only when the reliability characteristics of airfoils are built well or existent. Thus, the approach based on Momentum, vortex and Cascade methods is always used of the commend design process and seldom used in the parametrical design of the airfoils. 2) The computational cost of the direct approach based on the Panel method is higher than the direct approach based on the Momentum methods, but Panel method is more accurate and simpler than the Vortex method and the CFD method. The common process is currently the most popular process for the direct approach based on the Panel method. We proposed a new and promising PPDAPM process for the airfoil geometry design due to the fact that the ordinates of airfoil should be offered in the Panel method firstly. More efforts should be conducted to couple the outer potential flow and inner viscous flow were proposed and to introduce the effect of the viscous into the Panel method. 3) The direct approach based on the CFD method is currently the most popular approach. The computational cost of the approach based on the CFD method is highest among three direct approaches. It cannot only predict the CP but also present the detailed flow information. There are mainly three design processes for this approach. At present, the common process is widely used. The automatic analysis process and parametric optimization process have gained in popularity due to the development of the computer industry and a lot of optimization algorithms (EA, GA, DOE, RAM and PSO algorithms).

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