Wind power potential criterion [5].

## Abstract

The use of vertical axis wind turbines (VAWT) in Colombia could tackle the energy distribution difficulties as large parts of the territory are not connected to the electrical grid. The present chapter explains how to design and select an accurate VAWT for a mountain site, (the Chicamocha’s canyon) by characterizing the wind energy potential, selecting the appropriate blade’s airfoil, and design its corresponding blades to obtain an accurate VAWT performance. This methodology can be used to design and allocate a VAWT for residential use, as it tackles the critical point on wind energy design and selection. It is found feasible the use of wind energy at the location where the mean year density power is 485 [W/m2], and the DU06W200 airfoil is suggested as its aerodynamic efficiency (cl/cd) overcomes by 14% the commonly used NACA0018. Finally, straight blades are recommended to overcome the inertial effects of the low wind velocity at the location.

### Keywords

- VAWT
- Colombia
- wind
- energy
- turbine

## 1. Introduction

There is a need of developing wind energy solutions capable to adapt fluctuating flow resources to have a diversified energy portfolio for the energy demand in Colombia [1]. The Chicamocha’s canyon topography does not allow a stable electrical grid, which difficulties the incentives for tourism and commodities at the location, and the local community needs a sustainable source of energy that does not impact the environment. Therefore, this work assembles the feasibility for installing Vertical Axis Wind Turbines (VAWT) along with an optimal design.

The performance of a VAWT relies principally on its airfoil and blades, which generate lift and drag forces that take advantage of the wind kinetic energy to produce torque at the shaft of the turbine. The airfoil design and selection is an important task that depends on three main topics: wind flow conditions, airfoil shape, and modeling. The Darrieus VAWT blades design are based on lift aerodynamic forces and commonly use the commercial NACA0018 airfoil, and its performance varies according to the wind velocities [2]. Claessens [3] developed the DU06W200 airfoil for VAWT turbines, which overcomes the aerodynamic performance of the NACA0018 under high wind velocities than the calculated at Chicamocha’s Canyon nature. Yarusevych and Boutilier [4] analyses a similar Reynolds number but only one angle of attack is analyzed. Therefore, Garcia Rodriguez et al. [1] complements previous studies by increasing the range of Reynolds numbers analyzed for the DU06W200 airfoil, providing further information about the aerodynamic global coefficients and analyzing the performance of both airfoils under different attack angles.

In addition, different geometrical factors related to Power Coefficient

## 2. Chicamocha’s canyon wind energy characterization

The Chicamocha’s canyon national park, known as “PANACHI”, monitor constantly the wind velocity at the canyon to control the cableway safety installed at the location. The administration of the park provided to [1] research the historical data from the year 2009 up to 2012. The wind velocity magnitude is characterized at three different locations: the two highest points of the location (“Mesa de Los Santos” and “PANACHI”) and the river point.

The wind energy potential of the canyon is analyzed by using the mass conservation principle Eq. (1):

where

Manwell et al. [5] establishes how significant the wind energy potential is at a selected location (Table 1).

Poor | |

Good | |

Excellent |

The annual average wind speed and wind power density of the three locations are shown in Table 2. Garcia Rodriguez et al. [1] concludes that the suitable VAWT location is at Chicamocha’s river due to its high wind speed, 6.9

Place | Annual average wind speed [m/s] | Standard deviation | Annual average wind power density [W/ |
---|---|---|---|

“Mesa de los santos” | 5.9 | 0.736 | 306.188 |

Chicamocha’s River | 6.9 | 1.084 | 485.115 |

“PANACHI” | 4.3 | 0.536 | 86.643 |

## 3. VAWT aerodynamics

### 3.1 Aerodynamic airfoil and blades

An airfoil is identified using its aerodynamic parameters [5] as shown in Figure 1. The mean curve line is the focus midway points between the upper and lower surfaces of the airfoil. While the straight line connecting the leading and trailing edges is called the airfoil chord line, and the distance from the leading edge to the trailing edge measured along the chord line is known as the aerodynamic airfoil’s chord (c). Finally, the angle of attack, α, is defined as the angle between the relative wind (U_{rel}) and the chord [6].

### 3.2 Lift, drag, and dimensionless parameters

The airflow over an airfoil produces a force distribution on the surface. The flow velocity increases over the convex surface resulting in lower average pressure on the “suction” side of the airfoil compared to its concave “pressure” side. Meanwhile, the viscous friction between the air and the surface of the airfoil slows the airflow to a certain point near the surface [6].

There are three forces of vital importance for aerodynamic analysis as seen in Figure 2, which are:

The lifting force goes in the perpendicular direction to the incident airflow. The lift force is a consequence of the pressure differential generated between the upper and lower surfaces of the airfoil.

Drag force is the tangential component and occurs due to friction forces on the surface of the airfoil

Pitch moment is defined around a perpendicular axis to the cross-section of the airfoil.

Lift and drag coefficients: The lift and drag forces (per unit length of the blade) are usually expressed as a function of two coefficients CL and CD in Eq. (3) and Eq. (4) respectively.

where c is the chord of the blade. The lift and drag coefficients are expressed as a function of the angle of attack (γ). Figure 3 shows the typical coefficients of wind turbine blades. Note that the CL coefficient grows approximately linearly with the angle of attack, while CD remains at a low value. For angles of attack greater than 13°, CL decreases while CD grows rapidly, and the blades go into loss.

The power output is produced through the lift force generated on the airfoil surface. As the turbine rotates, the airfoils encounter an incident wind velocity that is the vector summation of the surrounding flow velocity and the turbine rotation Figure 4 [8].

### 3.3 Reynolds number (Re)

Defines the characteristics of flow conditions Eq. (5):

where μ is the fluid viscosity,

Brusca et al. [9], defined the Reynolds number based on the chord (

where * c*is the chord,

*is the air’s relative velocity to the aerodynamic surface and*w

*is the air’s kinematic viscosity. The*v

*can be expressed as a function of the solidity (σ) of the turbine Eq. (7):*c

where σ is the solidity, * Nb*is the number of blades and

*is the turbine’s radio. Therefore,*R

The Reynolds number strongly influences the power coefficient of a vertical-axis wind turbine. Furthermore, it changes as the main dimensions of the turbine rotor change. Increasing rotor diameter rises the Reynolds number of the blade.

### 3.4 Power coefficient (Cp )

The turbine performance is given by the power coefficient

where * PT*are the total energy, ρ is the air’s density,

*is the velocity of the wind and*V

*is the swept area for the turbine. Hansen et al. [10] express*A

where

### 3.5 Solidity and tip speed ratio

The solidity and Tip Speed Ratio of the turbine are directly related with the

#### 3.5.1 The solidity of the turbine (σ)

The solidity of the turbine (σ) it can see in Eq. (12), is defined as the developed surface area of all blades divided by the swept area [11].

σ has a strong influence on VAWT performance. High solidity machines reach optimum efficiency at a low Tip Speed Ratio (λ) and efficiency drops away quickly on either side of this optimum [12].

A low solidity results in less total blade area, therefore, the blade is lighter. This benefits wind turbine performance as higher rotation speeds can be reached [6].

Paraschivoiu [11] establishes that a maximum

In Figure 5, it can observe when the solidity is increased from 0.05 to 0.2, the static torque coefficient will increase by a factor of approximately 4 for an H-Darrius wind turbine. Therefore, for a high solidity, the turbine has a self-starting capability, because it has a higher static torque coefficient than the low solidity turbines [15].

Increasing

### 3.6 Tip speed ratio (λ or TSR)

The speed ratio (λ) is a ratio between the tip blade speed (ω.R) and the freestream wind velocity, and this ratio is defined as following in Eq. (13):

In Figure 6 it can see a relation between the azimuth angle (ɵ), the angle of attack (α), and the speed ratio (λ), this relation is as follow in Eq. (14):

Zouzou et al. [16] conclude in his investigation that a variable pitch VAWT has a major advantage respectively to fixed pitch VAWT in the case of high solidity rotor where the blade wake is large. That is because the pitch variation of the blade reduces flow separation and as result, the drag forces are lower. Figure 7 shows the relationship between the drag force and the λ and the comparison between the fixed and variable pitch.

The

For VAWT λ is lower the common range is (λ = 1; λ = 5), this ranges of λ values refer to the Wind Turbine peak (

The

According to Posa [19] there is a relation between λ and the establishment of the flow downstream of a VAWT, this is related to the optimal distance between turbines in wind farm configurations. Establishing the downstream flow of a VAWT to its far-wake behavior takes a shorter distance at higher λ values.

## 4. VAWT design

VAWT design correlates geometrical characteristics of the rotor with the Power Coefficient (22) of the turbine. The influence of the main aerodynamic design parameters is compared with the operation of turbines [20]. This section presents the considerations and parameters necessary for the construction of VAWT turbines. The design procedure taking aerodynamics into account can be expressed as follows:

Application and desired power

Geometrical aspects

Airfoil selection.

### 4.1 Application and desired power

The VAWT turbines have different applications [21] to generate electricity, pump water, purify and/or desalinate water by reverse osmosis, heating, and cooling using vapor compression heat pumps, mixing and aerating bodies of water; and heating water by fluid turbulence. Rathore et al. [22] suggests VAWT use on highways, in which vehicles travel at high speed in both directions producing an acceleration of the surrounding wind that can be used by turbines located in the separators.

To do so, the power (

### 4.2 Geometrical aspects

Among the main aspects of VAWT turbines are the chord length (c), rotor height (H), rotor diameter (D), and aerodynamic airfoil (Figure 10).

#### 4.2.1 Height/diameter ratio (Φ = H/D)

The relation Φ is analyzed from the turbine shape indicating the visual proportions of the turbine. On the other hand, for a fixed sweep area, low Φ values are characteristic of turbines in which optimal flow conditions are obtained in the aerodynamics airfoil, due to large diameters that increase the peripheral speed. On the contrary, high values of Φ can be related to turbines where blade efficiency is preferred [20].

The Darrieus rotor has low aspect ratios to minimize the length of the blade and the center column for a given swept area. If the Φ is increased, then the rotor speed increases (to maintain the same relative wind speed and tip speed ratio), and torque decrease if power is constant [11].

#### 4.2.2 Chord/diameter ratio (ξ = c/D)

High ξ values indicate that chord length is increased to improve the Reynolds number, while low values relate to rotors in which the relative wind speed increases proportionally to the relative wind speed on the aerodynamic airfoil [20].

#### 4.2.3 Rotor swept area (A)

The swept area of the turbine (Figure 10), corresponds to the amount of air that is dragged by the turbine blades. In particular, the larger sweep areas guarantee fewer demanding limits of the turbine radius, therefore a high peripheral speed is obtained leading to a good Reynolds number on the blades.

The energy capture is proportional to the swept area and the cube of wind velocity. It is important to identify an equilibrium between energy capture and the cost of the swept area, a bigger area means more manufacturing cost of the turbine. The parameters Φ and ξ are geometric parameters that allow modifying the swept area of the turbine, they are directly related to the design of VAWT turbines.

#### 4.2.4 Number of blades

According to Paraschivoiu [11] for given solidity, it is structurally advantageous to have fewer blades of a larger chord rather than more blades of a smaller chord. This is due to the bending stresses which are dependent on the square of the chord size whereas the aerodynamics loads are dependent on only the first power of the chord. For these reasons, the VAWT have generally two or three blades, but each design is unique for each application, therefore, it’s important to analyze the relationship between the geometric parameters as the solidity and the

Item | Three blades | Two blades |
---|---|---|

Construction Cost | Higher | Lower |

Assembly Cost | Higher | Lower |

Choice of fabrication techniques | Better | Poorer |

Strength/Weight ratio | Poorer | Better |

Torque ripple | Better | Poorer |

Structural dynamics | Better | Poorer |

### 4.3 Airfoil selection

The VAWT blades’ performance depends largely on the airfoil behavior, which is selected or designed in terms of the wind flow conditions of the feasible location [1].

Employing CFD modeling, Garcia Rodriguez [1] found that the DU06W200 airfoil aerodynamics performance is larger than NACA0018 under the Chicamocha’s canyon wind energy conditions. Table 4 summarizes the calculated aerodynamic coefficients of the most feasible point, proving the advantage of considering the DU06W200 airfoil [1].

Airfoil | Cl | Cd |
---|---|---|

0.707 | 0.0801 | |

0.876 | 0.0853 |

## 5. VAWT types and selection

According to Liu et al. [24] the VAWTs are categorized as drag or lift-based devices. The first ones utilize wind drag on the blades to rotate and the last one utilizes the lift on the blades. In Figure 11 it can observe these categories.

### 5.1 Drag-based turbines

The Drag-based turbines have the advantage of self-starting ability, and they are commonly found as small-sized turbines in urban and remote areas with relatively low wind speed. These turbines generally are not preferred due to high solidity, heavier weight, and low efficiency. One example of this turbine is the Savonius turbine [24], Figure 12 shows characteristic parameters of a Savonius wind turbine with two semicircular airfoil blades.

The Savonius turbine produces high torque at low tip-speed ratios (

According to Zemamou et al. [25] the number of blades has an important impact on the turbine performance. For obtaining the highest value of the

### 5.2 Lift-based turbines

The lift-type turbine consists of airfoil sections that capture the wind energy using the lift force. This lift force produces torque on a shaft, which can then be connected to a generator to produce electricity as power output [15]. The advantage of this configuration is their simple and extruded blades, hence lower manufacturing costs [24]. The straight type, Troposkien type, and helicoidal type are examples of this configuration.

#### 5.2.1 Straight type

These blades usually are used in small-scale, fixed pitch, rooftop designs are commercially available for domestic and other applications. The straight blades have a high value of

According to Ali and Sattar Aljabair [27] this configuration is better than the type helicoidal at low wind velocity, also, the power coefficient values for DWTs straight model with 2 blades are higher than other models as can see in Table 5. The Straight blades present a higher value of

DWT type | Number of blades | Wind velocity self-starting (m/s) | ||||||
---|---|---|---|---|---|---|---|---|

3 | 4 | 4.5 | 4.85 | 5.15 | 6.45 | 7.65 | ||

Straight | 2 | 0.2495 | 0.2506 | 0.2635 | 0.275 | 0.2895 | 0.3076 | — |

3 | 0.2407 | 0.2494 | 0.2606 | 0.2678 | 0.2846 | 0.3065 | — | |

Twisted 70° | 2 | 0 | 0 | 0 | 0 | 0.0372 | 0.0757 | 0.1216 |

3 | 0 | 0 | 0 | 0.0195 | 0.0597 | 0.1008 | 0.1323 | |

Helical 120° | 2 | 0 | 0 | 0 | 0 | 0.0449 | 0.0690 | 0.0889 |

3 | 0 | 0 | 0 | 0.0427 | 0.0789 | 0.1332 | 0.1465 |

#### 5.2.2 Troposkien

The Troposkien architecture is characterized by hub-to-hub blades, this configuration offers a lower aerodynamic drag (compared to the H-shaped one), which minimizes the bending stress in the blades [28]. In Figure 16 it can see the Troposkien type.

According to Battisti et al. [28] the Troposkien type is more efficient than the H-shaped configuration (two straight blades) at high values of TSR as can see in Figure 17. On other hand, for low values of TSR, the Troposkien present a lower

Quite similar behavior is registered for low wind velocities and a cut-in wind speed of 6–6.5 m/s is observed. For high values of wind velocity, the Troposkien is capable to generate significantly more power than the H-shaped configuration as shown in Figure 18. This quite different behavior could relate to the higher blade Reynolds number, which promotes an improved aerodynamic efficiency, in the investigation of [28], the radius of the Troposkien type is bigger than the H-shaped type to maintain the same rotor swept area. For this reason, the Troposkien type have a bigger

#### 5.2.3 Helical type

Helical H-rotor distributes the blade airfoil along the rotor perimeter uniformly, thus making the swept area as well as the blade sections constant to the wind in all cases of turbine rotation [29]. In Figure 19 it can observe the Helical type.

Tjiu et al. [29] made a comparison was made between the helical, straight, and Troposkien types. The comparison was made using 3 blades using the NACA 0015 airfoil with a TSR of 5. The behavior can be seen in Figure 20 where it can be observed that the Troposkien typology obtained the highest fluctuation with a Cp value of approximately 0.3, the straight blades typology had a fluctuation in the Cp of 0.2 and the lowest fluctuation was obtained by the helicoidal rotor with a variation of approximately 0.03 Cp. However, despite the benefits obtained, the helical blades are more expensive to manufacture, so depending on the desired application and the available budget, a middle point must be chosen for the selection of the different types of rotors.

### 5.3 VAWT selection

A critical factor in the feasibility of power generation with VAWT turbines is the self-starting of the turbine, according to Ali and Sattar Aljabair [27], at a wind speed of 3 m/s, the VAWT with airfoil DU06W200 has the capability of self-starting as seen in Table 6. The straight blade type has better performance because the turbine can self-start at lower wind velocity than the others turbines.

DWT type | Number of blades | Wind velocity self-starting (m/s) |
---|---|---|

Straight | 2 | 3 |

3 | 3 | |

Twisted 70° | 2 | 5.75 |

3 | 5 | |

Helical 120° | 2 | 6.5 |

3 | 6 |

The straight blade configuration offers the flexibility to adjust the swept area. Rotor height and diameter can be independently adjusted to suit each design. In addition, this configuration is usually mounted on a tower, which provides higher stability, lower bending, and torsional stresses on the blades compared to the Troposkien topology. Similarly, the gravity-induced bending stress is lower in the straight-bladed configuration as they are stiffer with the same chord length and thickness as the blades of a Troposkien rotor. In addition, they are vertically positioned and suspended by supports, so they are not subjected to constant bending stress due to gravity [31].

In his investigation Meana-Fernández et al. [13] proposes an optimized design for medium and low wind speed which presents a maximum 𝐶𝑝 of 0.5798 and 0.5996 respectively, as observed in Table 7.

Wind speed | Medium | Low |
---|---|---|

Number of blades N | 3 | 3 |

Rotor radius R | 1 m | 3 m |

Rotor height H | 3 m | 5 m |

Blade chord c | 111 mm | 333 mm |

Rotor solidity | 1/3 | 1/3 |

Airfoil | DU-06-W-200 | DU-06-W-200 |

Nominal Wind speed | 9 m/s | 4.5 m/s |

Rated power | 1.5 kW | 1 kW |

Maximum power coefficient | 0.5798 | 0.5996 |

The type of blades used by [13] were straight blades, it is observed that the proposed design presents a good performance for both medium and low wind speed. It should be noted that for low speeds, as described throughout this section, straight blades perform well without the complexity of construction and high manufacturing cost of the helical type for example, or the instability and torsional stress produced by the Troposkien type.

## 6. Conclusions

The current literature review analyzes a full VAWT design and installation facility by considering the site wind energy potential, the airfoil performance analysis, and the 3D blade type selection. Experimental and theoretical formulations are referenced to validate the proposed method, leading to an optimal VAWT design. It is found that Chicamocha canyon’s large wind energy potential is found at its river, and the critical point is found at one of its boundaries locations (“Mesa de Los Santos”). This wind velocity is taken as a baseline point to select the airfoil and blade designs, as is the minimum value to overcome inertial effects to start VAWT rotation. Literature found that using DU06W200 airfoil, improves by 23% the aerodynamic performance of the VAWT airfoil blades, the reason why is selected to move on at the current design. Finally, the literature review shows that considering 3 straight blades on the VAWT design, complements the airfoil design and selection, as these blades have shown experimentally an accurate performance under the analyzed critical wind flow conditions. The future work will design the size of the VAWT blades and optimized the current proposes, to reach a feasible domain to be used in local facilities.