Power output of a wind turbine installed in an already existing viaduct

Renewable and Sustainable Energy Reviews 48 (2015) 287–299

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

Power output of a wind turbine installed in an already existing viaduct Ó. Soto Hernández a, K. Volkov a,n, A.C. Martín Mederos b, J.F. Medina Padrón c, A.E. Feijóo Lorenzo d a

Faculty of Science, Engineering and Computing, Kingston University, Friars Avenue, Roehampton Vale, London SW15 3DW, United Kingdom Zona Eólica Canaria S.A., Veintinueve de Abril, 30 Bajo, Las Palmas 35007, Spain c Instituto Universitario SIANI, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas, Spain d Departamento de Enxeñería Eléctrica, Universidade de Vigo, EEI, Campus de Lagoas-Marcosende, 36310 Vigo, Spain b

art ic l e i nf o

a b s t r a c t

Article history: Received 11 March 2013 Received in revised form 27 October 2014 Accepted 26 March 2015

The maximum power production of a turbine installed beneath an already existing viaduct in Gran Canaria (Spain) is studied based on computational fluid dynamics (CFD) simulation. Porous discs are introduced in order to create a pressure drop, which is traduced into a power production. This method is a contrasted tool that has been largely used in a wide range of studies and gives a good approximation to the potential of a wind turbine in a specific location. Porosity of the disc varies in a wide interval to found the point where power output is maximal. CFD results are used to analyze the effect of incidence of wind flow in a porous disc which simulates the resistance of turbine blades against the wind. Different configurations corresponding to variation of parameters and number of turbines are studied, and conclusions regarding the optimal configuration of wind farm are provided. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Computational fluid dynamics Wind turbine Porous disc Viaduct

Contents 1. 2. 3.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Power production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Configurations of wind farm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Configuration A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Configuration B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Configuration C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Configuration D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Wind direction and speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. CFD model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Results and discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Configuration A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Configuration B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. Configuration C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Configuration D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5. Comparison of different configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

287 290 291 291 291 292 292 292 293 294 294 295 295 296 296 298 298 298

1. Introduction

n

Corresponding author. Tel.: þ 44 20 8547 7948. E-mail address: [email protected] (K. Volkov).

http://dx.doi.org/10.1016/j.rser.2015.03.097 1364-0321/& 2015 Elsevier Ltd. All rights reserved.

Wind energy offers many advantages and it is the fastest-growing renewable energy source in the world. Wind energy is a clean fuel source and does not pollute the air unlike power plants that rely on combustion of fossil fuels. Wind energy is also renewable power

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Nomenclature A Ah c C Cp h k K l p P Q S u v y yþ

Rotor surface, (m2) Averaged horizontal area, (m2) Weibull form factor Weibull scale factor, (m/s) Coefficient of performance Roughness element height facing the wind, (m) Drag coefficient Quadratic resistance coefficient, (kg/m4) Length of porous disc, (m) Pressure, (Pa) Power production, (W) Volume flow rate, (m3/s) Roughness element section facing the wind, (m2) Velocity, (m/s) Wind speed, (m/s) Target height at the inlet boundary, (m) Near-wall non-dimensional coordinate

source, making it one of the lowest-priced renewable energy technologies available today. More recent developments in this technology have allowed wind turbines to be utilized in building design and in design of other civil objects. Wind turbine efficiency remains a critical component of the overall economic justification for a potential wind farm. There is therefore a requirement for prediction methodologies that are capable of addressing the performance of multiple turbine installations within a specific local environment and operating in a range of conditions. In the search of new renewable energies applications and business, ZECSA (Zona Eólica Canaria Sociedad Anónima, www. zecsa.org) has started a new plan which tries to use urban public spaces for power generation. In fact, that energy can come mainly from either solar, wind or biomass. In this case, ZECSA has begun to study different possibilities to produce energy from wind turbines installed in already existing viaducts. Integration of wind turbines in buildings has been studied for many years and is expected to be well developed in the near future [1]. Turbines are located in high points of the building in order to take advantages of higher speeds. It allows minimizing lost regarding to transport and distribution of electricity due to its close position to the consumption point. Wind has a large impact on the design of tall buildings. The wind causes a large build-up of positive pressure on the windward side of the building. Vortex shedding, around the sides and over the top of the building, creates a large pocket of negative pressure on the leeward side of the building. In allowing air to pass through the building, the differential pressure from front to back is reduced and the forces on the building are, in turn, reduced. This approach is sustainable from a structural standpoint in that it allows for a reduction in the quantity of steel and concrete to maintain the building's stability. There are some examples of successfully completed projects regarding the installation of wind turbines in tall buildings [2]. These examples of building-integrated wind turbines were described in the literature [3–20]. The data were taken from [3,4] (also web-pages http://www.skyscrapercenter.com/ and http:// www.norwin.dk/ were used). The Bahrain World Trade Center (WTC) is a building inspired in traditional Arabian Wind Towers, composed by 2 twin towers of 50 storey and 240 m high with three 29 diameter horizontal wind turbines [3]. It was designed by WS Atkins plc (www.atkinsglobal.

z

Height, (m)

Greek symbols

α β ηt ρ

Power law exponent Vertical exponent Wind turbine efficiency Density, (kg/m3)

Subscripts a g h 0 1 2

Short time interval Geometric averaged Height Roughness Upstream Downstream

com) to come with a pioneering project in the world. Design of buildings as elliptical plan and aerofoils permit the wind to be accelerated and create a negative pressure in the wake. Integration of wind turbines in the building was mainly possible due to a similar production on all of them (109% in upper turbine, 100% in middle turbine and 93% in lower turbine) due to a combination of increase of wind speed with height and building shape depending on the airflow (production peak is obtained on the upper turbine, 9% less in the middle turbine and 16% in the lower turbine). The fixed disposition of wind turbines was a problem to be solved in the design due to the probable existence of stresses and blade deflections produced by changes in the wind direction. The building was shaped in order to canalize the incoming flow towards the horizontal axis wind turbine (HAWT). As a result, it was found that the wind stream would acquire an S-shape, which lets allow an attack angle between 285 and 345 degrees. Out of those angles, turbines would stall to avoid the mentioned problems. In fact, wind effect in increased by 30% due to position of the towers. Turbines are fixed to the bridges by means of a specifically designed nacelle. Blades, which are also fixed to the hub, possess a geometry which lets create turbulences at high wind speeds in order to assure a well-balanced behavior of the turbine. Maximum output (225 kW) is achieved at about 20 m/s of wind speed. Bridges had to be carefully designed due to dessert characteristics and load restrictions. An aerodynamic oval shape was adopted and a vibration study had to be done in order to find the natural vibration. Three-turbine system would have a total output of 1100–1300 MWh per year, which permits to cover 11– 15% of energy needs of the building. Strata building, located in Elephant & Castle (London, UK), is the first building which has incorporated cladding-enclosed wind turbines in its structure. It was designed by BFLS (www.bfls-lon don.com) and built by WSP (www.wspgroup.com), completing its construction in 2010. It consists of a 43 storey with 408 apartments which reach 147 m high. Regarding to the group of 3 wind turbines, which are situated on top of the building, possess a 9 m diameter with 5 blades rotor. Each of them is designed according to the Venturi effect which, by means of the integration in tunnel, funnels the wind flow and increases pressure in the blades plane and efficiency. As a consequence, each turbine is capable to achieve 19 kW power output, which is translated into 50 MWh per year in total. Therefore, the given energy covers around 8% of the demanded electricity of the building, roughly enough to run

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the electrical and mechanical services (including three express lifts and automated window-cleaning rigs) as well as the lighting, heating and ventilation of its public spaces, which include an underground car and bicycle park. Construction of Pearl River Tower (Guangzhou, China) building consists in an environmentally friendly building of 310 m high divided into 71 storeys. It was designed by SOM (Skidmore, Owings and Merril LLP, www.som.com) in 2005 and it includes, among other sustainable devices, vertical wind turbines. Due to wind effect on the skyscraper on windward faces, vortex would appear on the sides and over the top, which would also create negative pressures in the leeward of the building. Gaps of 3  4 m2 wide were done in order to decrease forces on structures (decreasing also the amount of steel and concrete used) and, at the same time, it would create a space for wind turbine allocation [4]. Shape of the building allows decreasing drag and increasing wind speed. Vertical wind turbines are used in order to harness wind from two main wind directions with low losses. There have been many studies performed with the aim of predicting the wind yield in certain areas. These studies include investigating wind power potential in Minnesota [5], estimating urban wind resources [6], estimating potential wind yield of small wind turbines in Greater London [7], mapping wind resources over UK cities [8], and estimating wind resources in Dublin [9]. The effect of the separation, the height, and the roof shape of tall buildings on the observed wind speeds between and over said buildings was studied in [10] using CFD. A significant increase in wind speed from the standard input velocity between two identical buildings, which for a separation of 15 m is almost a 100% increase, was observed. Turbulence occurs close to the structures but greatly decreases 10 m above the roof and 6 m from the walls. When looking at the effect of building height on the wind speed increase observed between two identical buildings a little change in the maximum wind speed was found. A difference in the position that this maximum occurs (17 m above the ground for 70 m buildings and 70 m above the ground for 140 m buildings) was identified. The turbulence layer occurring above the roof is thicker for the taller building than the shorter building. In both cases the thickness of the turbulence layer decreases towards the edge of the building. Finally, an investigation into roof shape shows that a roof with a slope facing the wind greatly reduces the turbulence layer, while a roof slopped away from the wind increases the turbulence layer. Potential turbine mounting points on house roofs for different prevailing wind directions were identified in [11]. A method for estimating the energy yield of a building mounted wind turbine was proposed and the energy yield of a hypothetical house in west London was estimated. The CFD work contains good validation against experimental data, consideration of domain dependence, and a mesh convergence study. From their energy yield estimate for a 1.5 kW, 2 m rotor diameter wind turbine positioned first, 3 m above the north gable, and second, with the turbine not above the roof ridge, on a hypothetical house in west London. The predicted capacity factors were 4% and less than 1% respectively. It is necessary for planning permission to be granted for wind turbines above roof height for them to at least have chance of producing an optimal yield. A CFD analysis was performed in [12] to study the flow in a zone over a tall building in an urban environment. A parametric study was performed which included varying the height of building, distance to the upwind building, height of the upwind building, and width of the upwind building. It was found that to achieve the benefits of sitting a wind turbine atop a tall building in an urban environment the height ratio between the building and the upwind building must be a function of the distance between them. The effect of roof shape, wind direction, building height and urban layout on energy yield of wind turbines was investigated in [13] using CFD. When a building is situated in a free stream it

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causes two effects: an acceleration of the flow and an increase in turbulence around the building. A study into the effect of roof shape found a domed roof to give the best all round performance when considering wind from all directions giving increases in wind power of over 40% consistently when measured at a height of 1.3 times the height of the building. Below this height is an area of high turbulence intensity which should be avoided as it is detrimental to the potential yield of a wind turbine. Shapes such as a vaulted or wedged roof may match this for certain wind directions while other shapes such as pyramid and gabled roofs never produce a power increase of more than 30%. Increasing the building height sees a slight increase in the normalized wind velocity. However, these studies were just for the case of one isolated building. A further study, this time with the building surrounded by other buildings suggested that the addition of surrounding buildings slightly reduced the increase in wind velocity when compared to that from an isolated building. Other studies include [14] focusing on CFD analysis of flow over many houses, [15] dealing with high-rise augmented wind turbines, [16] adding a ramp in front of wind turbine on a building roof, [17] computing flow around tall cylinders (buildings). Case studies on building-integrated wind turbines include [18] simulations of flow past a building, [19] giving an overview of research in this area, and [20] on wind power for buildings and multidirectional flow conditions. However, the examples provided above are related to installation of wind turbines in newly-designed tall buildings. There are a number of problems facing wind turbines in general, some of which are of particular issue to an urban location [20]. Depending on the country in question there may be stringent planning laws to abide by which may cause the proposal to be blocked. Wind turbines require uniform laminar flow for optimal performance, so they are generally sited far from urban areas in open spaces. However, for convenience, sometimes wind turbines are placed in urban areas or on buildings. Recently, building integrated wind turbines have been even been developed, where the building has been designed specifically with the installation of wind turbines in mind. Due to turbulence caused by buildings the energy yield of turbines sited on or near buildings is dependent on position. An effective wind turbine in the urban environment would need to be above the average height of the surrounding structures [12]. Mounting the turbine at the top of an existing structure allows the turbine to exploit the increased velocities available higher up the velocity profile. The wind velocity is affected by the presence of buildings, with the zero velocity point increased upwards to a distance above the ground level. The turbulence intensity is substantially higher in the urban environment [14] whilst at the same time the average velocity of the air is lower when compared to flat terrain [21], which both pose problems for the effective performance of a turbine. However, the shape of a building can increase both the average local velocity and the power density. This is known as building augmented wind turbines, where the buildings are used to concentrate and increase the velocity of the air towards the wind turbine [10]. The turbulent boundary layer thickness is dependent on the specific layout of the surrounding surface and any specific application should be studied in order to find the desired mounting locations. In order to ensure the best performance from a wind turbine it would need to project outside of these turbulent zones [10]. Potential turbine mounting points on house roofs for different prevailing wind directions were identified by [1]. Noise emissions often cause opposition to wind turbine, this is of particular issue to an urban area [22]. These emissions are caused by both aerodynamic noise and mechanical noise. Aerodynamic noise is caused by the blades moving through the air, specifically at the tips as this is where the speed is greatest and

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creates a distinctive thumping sound. The different forms of aerodynamic noise are turbulent boundary layer trailing edge noise, separation (stall noise, laminar boundary layer vortex shedding noise, trailing edge bluntness) vortex shedding noise and turbulent inflow noise [23]. Mechanical noise comes from vibrations in the structure, and drives train noises such as bearings and gearboxes. The maximum acoustic emission of a 0.6 MW wind turbine is approximately 104 dB [24]. A comparison between the noise emissions of a wind turbine and that of the background noise over a range of wind speeds shows that at all wind speeds the turbine creates a greater noise than the background noise and that this difference is most apparent at the lower speeds. As the wind speed increases, the difference between them becomes less apparent as the two noise level ranges merge. Wind turbines operate most efficiently in laminar flow conditions. In an urban environment the occurrence of turbulent airflow is increased due to the surrounding buildings, trees and the land features (cliffs, valleys). The materials used in an urban environment also cause larger temperature fluctuations than would normally occur in rural sites, increasing the turbulence due to thermal air flows. Another area of opposition to wind turbines is the on-going debate over the effect that they have on wildlife. It has been put forward that they are hazardous to wildlife, mainly flying animals such as birds and bats which may fatally strike the blades. It may be possible that this problem can be negated using a mesh over the turbine although a slight reduction in airflow could occur. The noise emissions may also affect wildlife as well. The Canary Islands possess optimum conditions for large scale exploitation of renewable energies, especially wind energy. The Canaries are situated in a point where Trade Winds, constant east winds, make these islands an interesting area for developing of wind infrastructures. Along with these general currents, there exist local winds owing to differential warming, sea breeze or vale-mountain flows. In addition, particular orographic conditions of terrains would affect to local winds and create small locations with good conditions for wind power. The chosen infrastructure by ZECSA for this study is the Juncal Viaduct, which is located in the municipality of Gáldar in Gran Canaria (Canary Islands, Spain). This viaduct is part of the dual carriageway which connects the three main populations of Santa María de Guía, Gáldar and Agaete. These three towns are located in the north side of Gran Canaria and form an important population nucleus with a total of 44,443 habitants. The capital of the island (Las Palmas de Gran Canaria) is situated around 31 km from Agaete (the farthest point of the trio of towns). As main city in the island, Las Palmas would attract a potentially important in and outflow of cars in direction to workplaces or in the way back to home. In addition, Guía, Gáldar and Agaete are part of the North Commonwealth of Gran Canaria, which is formed by 10 municipalities, occupying 483 km2 (Mancomunidad del Norte). As alliance of towns, commercial links are incremented in order to encourage economy in the area, so transport flow would be even more increased. As a consequence, traffic jams, delays and even traffic accidents caused by a load of 30,000 cars would increase in the main route across the sea side towns. In addition, Agaete possesses an important port (Puerto de Las Nieves) which serves as connection point with the neighbor island of Tenerife with both passenger and commercial purposes. In fact, the port has turned as a recognized destiny for people who want to have a low time journey between the two islands due to the 1 h journey provided by the actual shipping company. Therefore, in early 1995, the Canary Island Government approved the Insular Plan where one of the principal points was the construction of a dual carriageway which would connect the Guía, Galdar and Agaete, with a new access to Puerto de Las Nieves. The new road would have 9300 m long and cost around 74 million Euros divided into 2 stages (Gobierno de Canarias). In

order to save the Juncal Ravine, situated close to Agaete, at the end of the new carriageway, a viaduct was projected. The designed structure, with direction North-South, had a span of 250 m long and a height of 63 m, with a slope of 0.52%. Its construction, which was finished in April 2000, had several delays due to strong winds present in the area. The Juncal Viaduct has a platform with a total length of 11 m and a camber of 1.42%. It is supported by two doubled pillars of 46.60 m and 33.80 m respectively. The energy production from the wind farm would be not very high due to conditions of the location, characterized by geographical and spacing conditions (www.itccanarias.org/recursoeolico, atlaseolico.idae.es/meteosim). It is not possible to choose an ideal site for the wind turbine as it must be adapted to the existing conditions. The exact geographic coordinates of the viaduct are: latitude is 281 60 56.10″N, and longitude is 15 1410 39.65″O. Wind turbines are characterized by complex, turbulent and unsteady aerodynamic flows, involving dynamic stall and blade-wake interaction. The real 3D flow leads to spanwise effects and to the presence of trailing and tip vortices. However, a quantitative prediction of its aerodynamic performance is still complicated, in particular due to the occurrence of dynamic stall on the blades and 3D flow vortices. Power output of potential wind turbines depends on specific conditions and locations. CFD offers a way to model the complex flow features that occur during the operation of a wind turbine. CFD tools are widely used to investigate wind speed-up through different building configurations and geometries, and to estimate the potential energy yield of a wind turbine installed on/in the buildings. Building a wind farm for wind energy production is a long process and several factors have to be considered for the investment. Given a certain site, the goal is to optimize the investment in a way that safe revenue is guaranteed. This means both maximizing the power output and minimizing the construction and operation costs. Before building a wind farm, detailed information about wind speed distribution (both in terms of direction and intensity) are needed. After those information are gathered, the problem is to optimize the wind farm layout, meaning that the number and the position of the turbines has to be decided. The model proposed is directly derived from a CFD computation of the wind turbine in a real atmospheric boundary layer flow. This model allows removing the most severe assumptions of the analytical model used previously. The paper presents an assessment of the expected power output from a wind turbine placed in existing viaduct, and describes CFD results from a commercial package ANSYS CFX used to model the wind flow through a turbine for a range of resistances of disc representing turbine rotor. The methodology exploits the actuator disc theory and CFD calculations to find the maximum power output of the wind farm. Representing a real turbine with an equivalent actuator disc in a three-dimensional CFD model offers a viable analysis tool for assessing power output of multiple wind turbines in a wind range of conditions and environments. Four different configurations of the wind farm are assessed based on CFD models which use the wind direction and wind speed in the selected area provided by the ITC (Instituto Tecnologico de Canarias). The results obtained are presented and discussed. The influence of loads on the viaduct due to the installation of wind turbines has not been evaluated. Choice of one design or another would depend on the corresponding economic study which will do the balance between investment and incomes produced by the installation.

2. Power production The methodology is based on the application of actuator disc theory. It consists on the introduction of a porous disc which

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would simulate the performance of a wind turbine. More specifically, a porous disc would produce a pressure drop on wind flow in a wake. Measuring the pressure difference up and downstream the disc, along with the volume flow rate through the disc area would result in the energy extraction rate of the simulated wind turbine. Despite the actuator disc does not directly take specific technical specification from real turbines but dimensions, it has been proved to be a satisfactory method in order to study wind turbines power production [25,26]. This methodology was used in [27] in order to study the performance of a building-mounted ducted cross flow wind turbine. A resistance coefficient was applied to the turbine in order to perform one-dimensional calculations and furthermore a CFD simulation. Actuator disc model is used as a simple method for simulating horizontal axis tidal turbines, both in CFD calculations [28–30] and wind tunnel experiments [31]. Actuator disc produces a similar far wake to a real turbine, but eliminates some of the scaling issues which occur in experiments, and reduces the mesh resolution required in CFD simulations. In fact, it says that as air is isentropic up and downstream from the turbine, the Bernoulli equation can be applied. A jump of pressure will appear just before and after passing the actuator disc (turbine). Pressure will drop suddenly leading flow to diffuse to increase its area in order to achieve the initial pressure in the downstream [32]. The model proposed in [33] considers non-uniform pressure distribution and curvilinear flow across the turbine plane (the effects not included in the Betz approach). The porous loss model takes into account the pressure gradient, Δp/l, through the porous region using a user-defined quadratic loss coefficient, K. The material is defined as having a drag coefficient, k, which relates the pressure drop across the disc with the velocity at the disc location. The resistance coefficient of the turbine to the flow is introduced as follows:
2 p1  p2 k¼ ; ρu 2 where p1 and p2 the static pressures immediately upstream and downstream of the rotor, respectively, u is the one-dimensional wind speed immediately upstream of the rotor, and ρ is the air density. This equation gives output power as function of resistance coefficient
P ¼ ηt p1  p2 uA ¼ 12 ηt kρu3 A; where ηt is the efficiency of the turbine, and A is the flow area. Disc porosity, which is represented by their quadratic resistance coefficient, K, varies in order to embrace a range of simulated disc resistance which goes from 0 (which is equivalent to a solid wall) up to 8 kg/m4. This approach allows finding the point of maximum power output from the actuator disc. In fact, power output would increase from K ¼ 0 up to a certain value and then, it experiences and steady decreases. Calculation of pressure drop must be done based on a chosen reference velocity. There are two options for this. The first one is the superficial velocity, which is the velocity which would exist if the porosity K ¼1, and the second option is the true velocity, which is the actual velocity in the porous region flow passages. The superficial velocity is used in this study. In two most favorable cases, wind speed at the inlet is studied in a wider range in order to compare the computed results.

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configurations are presented in the Table 1. Each configuration is designed by placing a certain number of turbines in the same plane as the main body of the viaduct, which is included between the two supporting pillars. Dimension restrictions due to the presence of the irregular terrain, pillars and viaduct platform are taken into account. Distance between pillars is 119.25 m, while maximum height between the ground and bottom surface of the viaduct is 60.90 m. Altogether makes a total available surface of approximately 5900 m2. However, due to the geometric characteristics of wind turbines, not all the surface available would be occupied. 3.1. Configuration A The configuration A is shown in the Fig. 1. A single porous disc simulating a wind turbine is placed under the viaduct. This design is based on the model WTN 600 manufactured by Wind Technik Nord (www.windtechniknord.de). In fact, the chosen upwind wind turbine has a nominal output power of 600 kW at a rated wind speed of 12 m/s with a cut-in speed of 3 m/s and a cut-out wind speed of 25 m/s. The chosen diameter of the disc is 46 m which would occupy around 76% of total height from the ground to the bottom of the platform. A centre point of the disc is located in the vertical of maximum clear height. Distance from ground to the centre point is 29 m, while separation of the disc from the nearest pillar is set to 17.1 m. The distance of the lowest point of the disc to the terrain is fixed at 6 m, while the separation from the highest point of the turbine to the viaduct is 8.62 m. The swept area of the disc comprises 1661.9 m2 and length of the porous disc is set to 3 m long, which is enough to simulate the blades influence. 3.2. Configuration B The second design of the wind turbine (simulated by porous discs), configuration B, includes two discs of different diameters as shown in the Fig. 2. In fact, it is an expansion of the configuration A as a new disc has been added to the 46 m diameter rotor. In this case, a new disc of 30 m of diameter fills the available space left for the configuration A. This smaller disc is based on another existing wind turbine developed by Wind Technik Nord, namely WTN 250. This turbine has a nominal output power of 250 kW at a rated wind speed of 14 m/s with 4 m/s and 14 m/s for cut-in and cut-out speeds respectively. The swept area is 706.86 m2, while the length of the porous disc is also 3 m long.

Table 1 Configurations used in calculations. Configuration Number of Discs

Diameter of Disc 1 (m)

Diameter of Disc 2 (m)

A B C D

46 46 26 6.1

– 30 26 –

1 2 2 24

3. Configurations of wind farm Four different configurations of the wind turbine (simulated by porous discs) have been designed and used in calculations in order to study a wider range of options. Brief characteristics of these

Fig. 1. Configuration A with one porous disc.

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Fig. 2. Configuration B with two discs of different diameters.

Fig. 3. Configuration C with two discs of the same diameters.

Distance between two disc centers is 51 m, which lets having a space of 12.4 m from the closest point of the nearest pillar. A free space in the top side of the disc is 7.25 m. In total, the small disc uses about 70% of the total height available. Therefore, by adding both porous discs, the total swept surface available to extract wind power is 2368.75 m2, representing this area an approximately 40% of available free space. Taking the original wind turbines used as references, the potential output power would be 850 kW at nominal wind speeds. However, these figures must not be taken seriously, as conditions in the location are highly different from the standards. 3.3. Configuration C In configuration C, shown in the Fig. 3, a scheme of two wind turbines (simulated by porous discs) has been maintained. However, the diameter of first porous disc has been decreased up to the same dimension of the small rotor and equals 26 m. Therefore, a pair of identical discs of 530.9 m2 each gives a total swept area of 1061.8 m2. The centre of the first turbine is located in a higher point respecting to the previous place and equals 39 m. Nevertheless, as a consequence of the shorter diameter, the distance between the edge of the disc and the pillar is increased up to 22.6 m. Distance from the bottom of the viaduct structure to the ground is changed to 8.6 m and 26 m respectively. 3.4. Configuration D The last studied layout, configuration D, breaks with the three previous designs. In this case, a much larger number of turbines have been evaluated. Thus, 24 small wind turbines (simulated by porous discs) are placed instead of the 2 medium discs. As a reference for these discs, the model Enair 160, manufactured by Enair (www.enair.es), is chosen. This machine is described as a 6.1 m diameter rotor which would be able to generate 160 kW as nominal power at 12 m/s. The blades start to rotate at 2 m/s and it is cut-out at 14 m/s. The swept area by the rotor is established in 29.22 m2 which brings a total of 701.4 m2 of absorbing surface. The 24 porous discs shown in the Fig. 4 are distributed in three rows of 8 turbines in each, forming a grid where distances between circumference centers are 10 m in both vertical and horizontal directions. The group is centered in the available space, having a distance of 21.5 m from each pillar, with a minimum space from the viaduct platform of 7.5 m, while the smallest extent to the ground is set to 6.65 m. In addition, a free space from the ravine axis to the first row of disc has been increased up to 26.1 m.

Fig. 4. Configuration D with mini-discs.

This configuration would have the advantage of its reduced weight, which would permit to have a lighter, and, therefore, cheaper supporting structure. In addition, these kind of small wind turbines are usually provided by a design which allows the turbine to rotate in order to face the wind flow by means of a drawbar. Noise produced by rotation of rotor is lower than larger wind turbines, a fact which would help the wind farm to be accepted by population in the surroundings of the installation. Porous plugs are inserted as a frozen body in order to create a separate element from the existing bodies. A multi-body is created, which permits each solid to be meshed independently but the node connectivity across each of the interfaces matches. It must be noted that in the inlet and outlet interfaces there are not just one surface but two. In fact, one surface belongs to the fluids domain and other surface, which is coincident with it, belongs to the porous domain.

4. Wind direction and speed An importance of characterizing the wind shear at the given site is needed for both the turbine design and an accurate prediction of its power output. The most commonly used methods of estimating wind shear are known as the log law and the power law. The log law is based on principles of boundary layer flow. A variation of the log law is the modified log law, which takes into account the effective ground level at a site, and it is often used to account for the effect of tree canopies on wind shear. A weakness of the log law is that it cannot to be used to represent the wind shear for all conditions (the log law is mathematically undefined for time periods where the wind speeds at two different heights are the same). The power law is developed empirically to represent wind shear. Gran Canaria is a territory with some area dominated by strong winds, especially in the south-east and north-west part of the island. The most favorable southeaster zone is located in a flat extensive terrain close to the sea side, where roughness promotes the presence of high speed winds. The northwest area of the island, where the Juncal Viaduct is located, is also a source of strong winds with the only inconvenience of the irregular land, with the predominant presence of mountains and ravines. Wind data are provided by both ITC (Instituto Tecnológico de Canarias, www.itccanarias.org/recursoeolico) and IDAE (Instituto para la Diversificación y Ahorro de Energía, atlaseolico.idae.es/meteosim). In order to get the wind map and find the best location of the wind farm, the wind speed at each point is obtained by measuring the wind speed at 10 m high, extrapolating data to 40, 60 and 80 m high and extending horizontally by points separated by 100 m. Despite the location of the Juncal Viaduct in UTM coordinates is (431802.3, 3110201.04), it is necessary to use the wind data at the point of flow input in the later simulation (the coordinate UTM Z is based on the ellipsoid WGS84). As it will be explained later in this report, input surface is 480 m away from the viaduct in NE direction, which is the main wind direction in the area according to data provided by the ITC. Therefore, the location corresponding to the input wind data has been assumed to be represented in the point (432363, 3110359), which is the centre point of the inlet surface. However, this point does not

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appear in the tables calculated by the ITC, so the nearest point has been taken as representative input data for wind: (432350, 3110350). The formula, which is widely used to calculate the wind frequency distribution if graphic information about wind behavior is not available, was proposed in [34]. Wind frequency is calculated by the equation [34]  c  v K  1  c  f¼ exp  v ; C C C

Table 2 ITC wind data.

where v is the wind speed, c is the form factor and C is the scale factor. To calculate the wind height variation in short term period (minutes and hours) the model proposed in [35] is used  α vh z ¼ h ; va za

Table 3 IDAE wind data.

z, (m) v, (m/s) c

293

40 6.250 2.271

z, (m) v, (m/s) C c

30 5.57 6.05 2.271

60 6.680 2.285

60 6.34 6.91 2.285

80 6.990 2.276

80 6.69 7.29 2.276

100 6.91 7.56 2.246

where vh is the averaged speed at short time intervals at height zh, and va is the averaged speed at short time intervals at height za. The vertical exponent, α, is given by   1 0:0881 v
ln a ;
 α¼ 6 ln zg =z0 1 0:0881 ln za =10 where zg is the geometric averaged height between both heights to be extrapolated, zg ¼(za zh)1/2, and z0 is the estimated roughness length. The roughness length is calculated as z0 ¼(S h)/(2Ah), where S is the roughness element section facing the wind, h is the roughness element height facing the wind, and Ah is the averaged horizontal area. The power law exponent is a function of wind speed and surface roughness length (type of terrain), and it varies for different types of terrain [36]. The surface roughness length is a parameter used to characterize shear and is also the height above ground level where the wind speed is zero. The surface roughness length varies according to the terrain of the site. The chosen roughness length is fixed at 0.1 m, as the assessed area due to the absence of woods and the only presence of few trees and crops [37]. The wind height variation (monthly averaged speed) is calculated as follows:  β v z ¼ ; za va where v is the averaged wind speed (annual or monthly) at height za, va is the averaged wind speed (annual or monthly) at height z. The vertical exponent is calculated by

β¼

0:37  0:08 ln va
: 1 0:088 ln za =10

Wind data were obtained from 2 official agencies, one at state level (IDAE) and other one is the Canary Island research body (ITC). Table 2 (wind direction is fixed at NE) and Table 3 provide some information about wind speed at different heights. Wind data provided by IDAE is more complete as Weibull constant, C, has been added which is useful for calculation of wind resource at different speeds. Using data given by ITC, the Weibull distribution for the wind inlet at 40 m high is calculated. The wind probability distribution, presented in the Fig. 5 for the wind inlet location, has a maximum at wind speed of 5 m/s. Wind direction, shown in the Fig. 6, is provided by IDAE data at 80 m high in the closest point (432450, 3109650), which shows that the most frequent direction of wind is NE with more than 30% of probability per year. However, it is followed very close by ENE, which has a probability of 25.59%. Knowing predominant wind direction is important as it determines the section of land to be modeled. The turbulence intensity is fixed at 5%. The wind turbulence has a relatively constant averaged value for periods of time of one hour

Fig. 5. Wind probability distribution at 40 m high.

N NNW NW WNW W

35 30 25 20 15 10 5 0

NNE NE ENE E

WSW

Frequency (%) Wind Speed (m/s)

ESE SW

SE SSW

SSE S Fig. 6. Wind rose at 80 m.

or more, but during a shorter period it can be highly variable. This chaotic variation can decrease the output power production of a given wind turbine and cause overloads in its components.

5. CFD model Similar to the concept of a porous disc for experimental studies, a momentum loss across a disc area in a CFD simulation also has a number of advantages. While the scaling issues do not apply to CFD (since the model may be specified at any dimensions) there are significant computational benefits in approximating the turbine as a disc rather than modeling its geometry in full. A full model of the turbine blades requires mesh resolution at the surface to be sufficient to capture the boundary layer and separation around the turbine

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(y þ ¼10–100 for the wall functions), whilst also capturing the development of the wake up to 30 of rotor diameters downstream. This requires a large number of mesh elements and subsequently significant computational efforts. The computational domain was made large enough so that the walls of the domain did not influence the flow close to the viaduct. The computational domain includes an area of 960 m long and 440 m width where the origin is situated in the maximum height point between the viaduct and the bottom of the ravine. Two domains have been included, porous domain and fluid domain. The first domain is formed by the porous discs which simulate the wind turbine rotors, while the second domain simulates the air flow surrounding the rotors, the viaduct and the ground. The method represents the swept volume of the wind turbine blades as a porous medium, and by adjusting the resistance of the porous medium the balance between the energy extraction and the bypass flow can be optimized. In order to simulate the porous plug resistance, the solution set up needs to be changed by editing the porous domain settings. To do this, the porous plug domain is given certain porosity. This is a value between 0 and 1 which represents the available open flow area. The value of 0.9 means that the porous medium creates a 10% reduction in flow area or a 10% increase in local flow velocity. This reduction in flow area can be thought of as representing the flow area which would be occupied by the actual blades and hub of a wind turbine rotor. Within the viaduct, a sub-domain of a cylindrical volume shape was created to represent a cross-flow wind turbine rotor. It was impractical to model the aerodynamic effect of the rotor blades, so momentum extraction was simulated by giving the cylindrical volume resistance to the flow in the form of a thrust term. Porous domain corresponds to the discs which simulate the wind turbine rotors. Characteristics were equally set for each configuration. The loss model is defined by two loss coefficients, linear and quadratic resistance coefficients. The quadratic resistance coefficient varies from 0 to 8 kg/m4 in order to simulate different types of rotor characteristics regarding to its absorption of wind power by means of a pressure drop. Numerical calculations were based on full steady-state threedimensional Reynolds-averaged Navier–Stokes (RANS) equations. The flow is viscous and incompressible. The numerical model uses the Shear Stree Transport (SST) turbulence model [38] in order to blend the robust and accurate formulation of the k–ω model in the near-wall region with the free-stream independence of the k–ε model in the far field. The calculations were based on commercial finite volume unstructured CFD code ANSYS CFX 13.0. Hexahedral and prismatic elements are used to capture velocity gradients through the boundary layer adjacent to a surface. At the same time, hybrid meshes incorporate pyramid and tetrahedral cells in the freestream regions to provide greater flexibility to represent complex geometry. ANSYS CFX is based on a coupled solver for mass and momentum and uses an algebraic multigrid algorithm for convergence acceleration. The numerical scheme is a co-located pressure based method for all Mach numbers. The second order finite difference schemes are used to discretize the governing equations and equations of turbulence model. Convergence to a steady state is accelerated by the use of algebraic multigrid techniques, and by the application of low-Mach preconditioning. Preconditioning improves the rate at which information propagates through the flow domain during the solution iterations. Due to the impracticality of modeling the turbulent structure close to the ground, wall functions are used to model the mean wind profile and turbulent kinetic energy. In the fluid domain, the air flow sets on the inlet boundary, while it leaves the enclosure through the outlet. The viaduct and

ground surface are set as solid walls. No-slip and no-penetration boundary conditions are applied to the walls (viaduct, wind turbine and ground). Roughness factor is fixed at 0.2 m. A free slip boundary condition was implemented at the top and side walls of the domain. A vertical profile of wind speed was set entering the inlet with constant static pressure at the outlet of the domain. Uniform velocity distribution (u¼ 4 m/s, v ¼w ¼0) is used as initial conditions. The power law is used to specify the wind speed profile on the inlet boundary where wind enters the computational domain [37]. Data provided by ITC gives a wind speed of 6.25 m/s at 40 m high (reference wind speed at the reference height). The reference height is set at 107 m (it means 40 m above the lowest point on the inlet boundary). The power law exponent depends on the ground roughness which is minimum for flat sea or smooth, hard ground and maximum in a buildings environment. It is chosen to be 0.16 m due to the existing ground characteristics [37]. The turbulence intensity is 5% on the inlet boundary. In calculations, the turbulence level at the inlet boundary was defined in terms of the turbulent kinetic energy and its dissipation rate, which were calculated from the measured turbulence intensity and velocity. The calculations were launched on unstructured meshes generated for each configuration. Number of nodes and cells for each mesh used in calculations are provided in the Table 4. An unstructured tetrahedral mesh was used with the finest resolution (down to 2 mm) close to regions where the greatest changes in wind speed and pressure gradient were expected, i.e. at the viaduct edges and within the porous region, and with a coarser resolution at the outer walls of the domain (up to a few meters). Close to the ground, the mesh was extruded as an inflation layer to more accurately model the flow which would be parallel to the surfaces.

6. Results and discussion A number of CFD simulations were carried out for several simulated rotor resistances. The extracted wind power depends on the coefficient describing momentum losses and the flow though the porous disc which depends also on the rotor surface. For larger surface, the amount of power delivered is higher than smaller turbines. However, the concentration of watts per square meter is not the same and that is a key factor in the decision for a wind farm installation. 6.1. Configuration A The configuration A includes just one porous disc of 46 m of diameter and a disc length of 3 m. This scenario is developed in order to have a first impression of how wind flow would behave and what alternative solutions could be proposed. The model is used with quadratic resistance coefficient going from 0 to 8 kg/m4 (for these values the mass flow rate changes from 7378 kg/s to 1463 kg/s). Dependence of the power output on quadratic resistance coefficient is shown in the Fig. 7. The power output is around 16,000 W for K¼0.1 kg/m4 and it is increased up to 27,269 W, which represents 70% more. At this point, the power starts a stable progression with a peak of Table 4 Number of nodes and cells for different meshes. Configuration

Number of nodes

Number of cells

A B C D

610,297 610,297 463,533 393,147

2,538,106 2,538,106 2,004,715 2,227,382

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295

Fig. 8. Power output for configuration B.

Fig. 7. Power output for configuration A.

power on K¼0.5 kg/m4 with P¼29,129 W. Then, it slightly decreases with small changes for K¼0.7 kg/m4 and 0.9 kg/m4, where there is a decrease of 0.4% and 2.6% respectively, respecting to the peak point. From this situation, the power extraction from the porous disc decreases steadily. However, there is a sudden low for K¼1.1 kg/m4, where power decreases by 27% and then it is increased by 25%. Despite this simulation is repeatedly carried, the result remains in the same figures. This result would likely be due to simulation issues (using higher calculation potency this result would not appear). Regarding to the last K value (K¼8 kg/m4), the power production would be 14,795 W. Fig. 9. Power output for configuration C.

6.2. Configuration B In this design, apart from the already existing disc (disc 1), an additional porous disc with a diameter of 30 m (disc 2) is inserted on the same plane as the first disc. The reason for this option is to have the chance to compare the influence of a new turbine in the surroundings and how it would affect to the extraction of power. Also, having a larger surface available, the power output is increased considerably. Dependence of the power output on quadratic resistance coefficient is shown in the Fig. 8 for disc 1 and disc 2. The mass flow rate through disc 1 changes from 7393 kg/s if K ¼ 0 to 1479 kg/s if K¼ 8 kg/m4, and the mass flow rate through disc 2 changes from 2844 kg/s if K ¼ 0 to 805 kg/s if K ¼8 kg/m4. The power production for disc 1 is similar to those computed for configuration A. It increases until it reaches a peak on K ¼0.5 kg/m4 with a power output of 29,220 W. For values of K ¼0.7 kg/m4 and 0.9 kg/m4 the power computed is almost at the same level as the peak, with 29,133 W and 28,485 W respectively. Regarding to disc 2, increase in power is not as the case for disc 1. In fact, the peak is reached for K ¼1.5 kg/m4, where P ¼18,577 W. In this case, increase in power from low values to the peak is done more steadily than the larger disc. The difference between the power output for K ¼1.5 kg/m4 and K ¼ 0.5 kg/m4 is about 15% with a less sharped decrease for highest values. The power production is just 11% between the two installed porous discs for K ¼ 8 kg/m4. Therefore, as total extracted power from the simulated turbines, the peak figure corresponds to K ¼0.7 kg/m4, where both productions balances their values in order to achieve a maximum power of 46,707 W. As before, there is a zone ranging from K ¼0.5 kg/m4 to K ¼1.5 kg/m4 where changes in total power output does not change dramatically. The difference between the maximum and minimum values represents just about 4%.

6.3. Configuration C The configuration C keeps two discs layout with the center located in the similar places. However, both discs have a smaller diameter of 26 m, which allows to avoid turbulence created close to the ground level, which would penalize the production of power. Dependence of the power output on quadratic resistance coefficient is shown in the Fig. 9 for disc 1 and disc 2. The mass flow rate through disc 1 changes from 2370 kg/s if K ¼0 to 456 kg/s if K ¼8 kg/m4, and the mass flow rate through disc 2 changes from 2148 kg/s if K ¼0 to 545 kg/s if K ¼8 kg/m4. The flow through two equal porous discs is close to each other. The power output follows a similar trend as in earlier cases with a sharped increase on low K values, reaching of power peak and steady smooth decrease. The only difference to be pointed in the disc 2, is a small step on K ¼0.5 kg/m4 which, as for configuration B, could be due to simulations issues as it does not seem to be any special turbulence crated by any obstacle. A high difference on extracted power is due to a small change on volume flow rate through the porous discs. In fact, flow rates differences of about 200 or 300 kg/s is translated as power outputs differences in a range of 2000 or 3000 W. Therefore, the maximum power produced for disc 1 corresponds to K ¼0.5 kg/m4 (P ¼9386 W), while a power of 12,311 W is produced by disc 2 with K ¼0.9 kg/m4. The maximum total power output produced by both discs is brought by K ¼ 0.7 kg/m4, which delivers the power output of 21,587 W. That amount of power is similar to the production with a configuration of K ¼0.9 kg/m4 where it would be 21,271 W, a small difference in terms of absolute values.

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Fig. 10. Power output for configuration D.

Fig. 12. Evolution of power flux density for different configurations.

Fig. 11. Power production for different configurations.

6.4. Configuration D The configuration D is divided in rows (lower, middle and upper rows) in order to analyze the flow separately depending on the height of the porous discs arrays. Dependence of the power output on quadratic resistance coefficient is shown in the Fig. 10 for lower, middle and upper discs. The mass flow rate through lower disc changes from 996 kg/s if K¼0 to 397 kg/s if K¼8 kg/m4, the mass flow rate through middle disc changes from 1018 kg/s if K¼0 to 410 kg/s if K¼ 8 kg/m4, and the mass flow rate through upper disc changes from 1046 kg/s if K¼0 to 416 kg/s if K¼ 8 kg/m4. In this configuration, the maximum power production was reached with K value of 4 kg/m4, where the power output for lower, middle and upper rows of discs were 5458 W, 5929 W and 6236 W respectively. Therefore, the total extracted power from the wind farm formed by 24 simulated turbines would be 17,624 W.

6.5. Comparison of different configurations Power production for different configurations studied is presented in the Fig. 11. The output power for configuration B is higher compared to other three designs. The value of the quadratic resistance coefficient at which the peak of power production is reached for each configuration varies. In fact, for the first three configurations the peak is reached for the values between 0.5 and 0.9 kg/m4 with a major importance of 0.7 kg/m4.

Fig. 13. Dependence of power production on inlet wind speed for configurations B and D.

Fig. 12 shows the evolution of the power flux density (concentration of watts per squared meter) where it can be noted how in the configuration D it is highly improved for the values higher than 0.9 kg/m4. There is a similar concentration of watts per squared meter for configurations B and C, while for the configuration A, formed by just one rotor, the production of power per square meter is significantly lower. Regarding to the wind flow, it was found that it is canalized along the ravine and faces the porous disc surface in a small attack angle. However, the wind speed at the rotor location drops dramatically to almost half of the inlet wind speed. It significantly affects the extraction of wind power by the porous discs. Wider simulations were carried out for configurations B and D in order to analyze the wind at the rotors for inlet wind speed range from 1 to 25 m/s. As can be seen in the Fig. 12, the power flux density increases exponentially and starts to have more interesting values from v ¼12 m/s. The power production achieves good figures from that wind speed value as presented in the Fig. 13. Velocity contours are shown in the Fig. 14 (wind direction is x axis). Respecting to the wind flow, it has been found that wind speed at the disc porous location decreases dramatically up to 50% of inlet

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297

Fig. 14. Velocity contours in xz plane at y ¼80 m.

Table 5 Comparison of power flux density (W/m2) for configurations B, C and D. K

0 0.1 0.3 0.5 0.7 0.9 1.1 1.5 2 4 8

Configuration B

C

D

0 9.56 17.09 19.17 19.72 19.71 19.49 18.83 17.95 15.16 12.21

0 9.49 17.37 17.75 20.33 20.03 19.68 18.78 17.68 14.45 11.19

0 4.12 10.41 14.83 17.96 20.12 21.80 23.77 24.92 25.13 23.08

wind speed. This means that for the mean direction and wind speed in the area, the wind under the viaduct is around 3 m/s. It leads to a lower extraction of power from wind as wind turbine starts to work properly from 6 or 7 m/s. However, the wind flow is conducted through the ravine, arriving to the discs in an almost perpendicular direction. This effect is an interesting point as it can be seen how local wind flow is modified respecting to the prevailing wind in the area in order to face the rotor surfaces. Adding a new smaller porous disc to the previous large turbine did not affect to the mass flow through the rotor surface of disc 1. In fact, power production of the large turbine is practically the same. As it is natural, the power extraction is considerably increased due to increase of available swept surface. Therefore, the power output at the peak point is increased by 60%. Having a look to the stream flow in the vertical plane though the large disc 1, it can be seen how the upstream flow does not utilize the entire surface of the simulated rotor. This effect occurs in both configurations A and B, and could be produced by the effect of the ground in the wind flow due to the boundary layer which decelerates the wind near the terrain surface. Configuration C with two smaller porous discs would be more effective as now there is a larger gap between the ground and the rotor. The results obtained show that power production in this design is considerably decreased as available extraction surface is also highly

decreased by 55%. However, the wind stream occupies the entire surface available, which results in a better exploitation of available rotor. This effect leads to a higher power flux density (concentration of watts per meter squared) for both porous discs. The amount of power flux density for configuration B at the peak power point is 19.72 while in the next design with smaller rotors that figure was raised up to 20.33 W/m2 as can be seen in the Table 5. It is not a large increase but it gives a clue about how smaller turbines would take more advantage of the disposable swept area. The configuration D, formed by 24 porous discs with diameter of 6.1 m each, possess a larger amount of power flux density compared to three previous designs. In comparison with configuration C, power flux density is increased by 24% with 25.13 W/m2. The amount of energy extracted by each surface unit is higher for smaller porous disc. This fact could be useful regarding to economics calculations which would result in more affordable designs for smaller turbines rather than large high weighted rotor that would compromise an installation to be more expensive due to more complex designs and higher quality materials. Configurations B and D are more deeply studied by means of simulation for a wider range of wind velocities at the inlet boundary. In fact, wind speeds from 1 to 25 m/s are simulated in order to equate the power production with the Weibull distribution at the location. Thereby, a more realistic vision of the possible power production over a year could be estimated. Configuration B contributes to the highest amount of net power compared to configuration D while the multi-disc wind farm has the better concentration of watts per square meter, so those are the best options for this comparison. The Table 6 shows the data regarding to the power extraction at different wind speeds. Power flux density is higher in the 24 small wind turbines design (configuration D). However, the difference is not really important until high wind speeds (about 19 m/s). In addition, power production is increased exponentially with the wind, achieving reasonable values for inlet wind speeds of 12–13 m/s, which would mean around 6 m/s at the wind turbines location. For these velocities, the porous disc behaves in a similar way as the turbines taken as models, having a power production of 160 and 420 kW for configurations B and D respectively. However, it must be taken into account that these values would also depend on the wind turbine efficiency and coefficient of performance, which would lead the figures to decrease.

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Table 6 Exploded data of power extraction from configurations B (K ¼0.7) and D (K¼ 4). v, (m/s) Configuration D PLower

PMid

Configuration B PUpper

PTotal

P1

P2

modeling approach. The CFD model used in calculations offers a potentially economical methodology for simulating complete multiple wind turbines within a specific environment.

PTotal

Acknowledgments 3 4 6 8 10 13 17 20

603 657 691 1952 3687 2158 5845 1430 1557 1640 4628 21,004 1080 22,084 5022 5450 5735 16,209 26,237 13,991 40,229 11,525 12,589 13,269 37,384 66,746 20,028 86,774 22,348 24,369 25,681 72,399 118,981 72,521 191,503 48,928 53,569 56,513 159,011 260,963 158,184 419,148 109,599 119,627 126,046 355,273 584,391 350,169 934,560 178,827 194,522 204,780 578,130 955,981 576,397 1,532,378

This project was developed in collaboration with ZECSA (Zona Eolica Canaria Sociedad Anónima). ZECSA is a renewable energy sector-oriented research company, focused on innovation and development of technology-based projects in the natural environment. This work pretends to be the beginning of expansion of use of renewable energies in public spaces. This is the Plan for Exploitation of Public Infrastructures for Renewable Energies (PAINPER in Spanish initials).

7. Conclusions CFD is an efficient tool in order to do the first approximation to the search of a solution for the installation of wind turbines in existing viaducts by means of simulated porous discs. In fact, it can be used to compare different locations and then to choose the most favorable resolution. Then, it would be time to introduce the wind measurement devices in the chosen location in order to assess the local conditions as prior step for installing the wind farm. Four different configurations of the wind turbines integrated to the existing viaduct were compared and power output for each configuration was predicted from CFD calculations. The CFD simulations provide insight into the patterns of flow and possible reasons for the change in performance of the wind turbine in different configurations. Except for the lack of high wind speeds, the configurations B and D should be the most suitable to be installed in the specific location. The first would provide a large amount of power due to its extensive swept surface. However, not all the surface will be exploited due to its proximity to the ground. Also, large turbines would need sophisticated supporting structures which would have to deal with high weights and higher vibrations which will concur in bigger investments. The latter design formed by 24 small turbines will have around 25% more of power flux density. Due to the light weight of these kinds of turbines, the supporting structure would not be loaded with forces and momentums as high as the configuration A. Also vibrations would tend to be smaller. In addition, these turbines possess a design which allows the rotor to rotate according to the wind flow direction. On the other hand, despite the higher amount of watts per square meter, the gross power output will be around half than the configuration B. The calculations showed that wind flow is canalized and reaches the wind turbines almost perpendicularly. Therefore, despite the prevailing wind in the area has a not suitable angle of attack, and power extraction would be incremented due to the ravine effect in the wind flow. On the other hand, on the contrary as it was firstly thought, the wind speed at the site of the porous disc under the viaduct decreases to about half of the inlet speed. This makes the power output to be low as the averaged wind speed is about 3–4 m/s depending on the height. This effect can be explained by the influence of roughness or orography of the terrain, as the viaduct is located in an irregular ravine. The relationship between height and width of the ravine are not enough to produce a tunnel effect that would increase the wind speed. The present approach has several advantages compared to classical analytical wake models. It is derived from a CFD model where several physical issues are taken into account (real atmospheric profiles, the presence of the ground, an appropriate turbulence model). Finally, the model can take advantage from further developments of the CFD model, for instance if non-neutral atmospheric profiles have to be taken into account. The results computed support the use of actuator disc methodology based on a normal fidelity CFD

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