Feasibility analysis of a Darrieus vertical-axis wind turbine installation in the rooftop of a building

Applied Energy 97 (2012) 921–929

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Feasibility analysis of a Darrieus vertical-axis wind turbine installation in the rooftop of a building Francesco Balduzzi, Alessandro Bianchini, Ennio Antonio Carnevale, Lorenzo Ferrari ⇑, Sandro Magnani ‘‘Sergio Stecco’’ Department of Energy Engineering, University of Florence, Via di Santa Marta 3, 50139 Florence, Italy

a r t i c l e

i n f o

Article history: Available online 28 December 2011 Keywords: Darrieus VAWT Urban context Skewed flow Microeolic turbine

a b s t r a c t The renewed interest that is being paid by architects, project developers and local governments to smallsize wind turbines is mainly connected to the attractive prospects of future applications in the urban environment; the delocalized power production of these systems could indeed provide an effective answer to both the growing demand for renewable energy and the increased attention in buildings with a sustainable and low-energy design. In particular, Darrieus vertical-axis wind turbines (VAWTs) are being considered as one of the most attractive solutions due to their low visual impact, the reduced acoustic emissions and their better response to a turbulent and skewed oncoming flow. The feasibility of this scenario has, however, to be proved yet; in particular, doubts are still connected to the real producibility in a complex terrain like the urban one and to the compatibility of microeolic machines with a densely populated area. On these assumptions, the aim of this work is to critically evaluate the energetic suitability of a Darrieus VAWT installation in the rooftop of a building in a reference European city. With this goal in mind, a numerical CFD analysis was carried out to characterize the flow field in the rooftop area of buildings with different shapes and geometrical proportions: the flow velocity modulus and direction were calculated for different oncoming wind profiles and the results were projected into a net available wind distribution in the rooftop of each building. As a second step, in order to provide a reliable estimation of the real functioning of the turbine in the investigated environment, a specific numerical model has been developed to account for the effects of a skewed flow on the power performance of the Darrieus rotor. The results of these analyses were finally combined and synthesized in an energyoriented study to evaluate the feasibility of a rooftop installation. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Increasing interest is being paid to understand where small-size wind turbines can effectively be exploited to provide delocalized power in the built environment [1]. The main prospects of a similar installation context can be readily understood; in particular, small rotors positioned at the top of a tall building could theoretically exploit a higher zone of the wind profile with respect to that usually exploitable by means of the only turbine tower. Moreover, the energy could be produced directly where it is needed, with a notable contribution to a sustainable design of new buildings in terms of energy consumption. Due to the high roughness length of the terrain and the presence of obstacles characterized by different shapes and permeability along the flowpath, the wind conditions in urban locations are, however, very complex and the real adaptability of wind turbines ⇑ Corresponding author. Tel.: +39 055 4796 570; fax: +39 055 4796 342. E-mail addresses: [email protected]fi.it (F. Balduzzi), [email protected] nifi.it (A. Bianchini), ennio.carnevale@unifi.it (E.A. Carnevale), [email protected] fi.it (L. Ferrari), [email protected]fi.it (S. Magnani). 0306-2619/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2011.12.008

to this environment is not yet tested both in terms of real producibility and of structural compatibility with the buildings. As a result, the wind profile in urban locations is quite different from the classical log-law based profile [1], with the zero-velocity height shifted up to a peculiar value (displacement, d) which is a function of the average height of the surrounding buildings (Fig. 1). Notwithstanding this aspect, some general principles to identify the main requirements of a suitable installation site are provided in technical literature (e.g. [1–4]). In detail, from a theoretical point of view, wind turbines in the urban environment require buildings that are reasonably higher than the average height of the surrounding constructions, in order to take advantage from the local flow deflection and acceleration [1], but only on condition that peculiar geometric proportions between the buildings are fulfilled [5]. Within this context, Darrieus vertical-axis wind turbines (VAWTs) are increasingly appreciated and often considered as the most promising solution in the built environment, due to their very low noise levels and to their reduced sensitivity to a turbulent oncoming wind [5–7]. In addition, recent studies [6,8] put in evidence that some benefits in terms of power increase can be obtained from a Darrieus functioning under skewed flow, mainly

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Nomenclature Acronyms AR Blade Aspect Ratio BEM Blade Element Momentum DMSV Double Multiple Streamtubes with Variable interference factors ESDU Engineering Science Data Units HAWT Horizontal Axis Wind Turbine MS Multiple Streamtubes VAWT vertical axis wind turbine Greeks symbols c skew angle (°) e turbulent kinetic energy dissipation rate (m2/s3) gel electrical efficiency # rotor azimuthal angle (°) j Von Karman constant r turbine solidity u pitch angle of the turbine airfoils (°) v sloping angle of the roof (°) Latin symbols Ah area occupied by the buildings (m2) Aj turbine projected area (m2) turbulence model constant Cl

Fig. 1. Wind profile in the internal boundary layer in a built environment.

connected to the possibility of exploiting an increased swept area (projected perpendicularly to the mainstream direction). In this work, a wide-ranging analysis was performed in order to evaluate the feasibility of a Darrieus turbine installation in the built environment. As a first step, CFD simulations were carried out to outline some general tendencies regarding the influence of the building geometry on the flow conditions in the rooftop area; moving from the numerical results, the net available wind distributions in the rooftop of two study cases were selected. As a second step, a specific correction model to account for the effect of the skewed flow was developed and applied to a numerical code for the evaluation of the performance of H-Darrieus turbines. Finally, the results were combined in an energy-oriented analysis to evaluate the effective energy production over a yearly time horizon of a purposefully designed H-Darrieus turbine as a function of the installation site (in terms of building dimensions and proportions with respect to the surrounding buildings). 2. Numerical analysis The CFD simulations were carried out with the OpenFOAM software package [9]. The modelling approach was a 2-D steady-state

CS D Dt Dtw H ^ H KS Ht N Nr Ns V c d h k tr ts u u yP z0

roughness constant distance between UB and IB (m) turbine diameter (m) tower diameter (m) IB height (m) mean buildings height (m) sand-grain roughness (m) turbine height (m) number of blades number of rods number of struts horizontal wind component (m/s) blade chord (m) displacement (m) UB height (m) Turbulent kinetic energy (m2/s2) rods thickness (m) struts thickness (m) flow velocity (m/s) friction velocity (m/s) height of the ground cells centroid (m) roughness length (m)

Reynolds-Averaged Navier–Stokes (RANS) calculation for incompressible flow without buoyancy effects. From a fluid-dynamic point of view, the assumption of a 2D behaviour of the flux that invests the turbine implies that the streamlines are assumed to follow the same path in each plane perpendicular to the building façade (i.e. parallel to the rotational axis of the VAWT). This reasonable hypothesis, often applied in numerical studies of the built environment (e.g. [5, 14–16]) remarkably simplifies the numerical model, providing a notable reduction of the computational cost as well as enabling a finer in-plane discretization. The pressure–velocity coupling was made with the SIMPLE algorithm and the convergence to the final steady-state was assessed with a maximum amount of 3  103 time steps, which were always sufficient to reach the target final computed residual of 1  105 (see [14–16]). The wall boundary conditions at the bottom of the computational domain were based on the standard wall functions [10] with the sand-grain based roughness modification [11]. The roughness effect was taken into account by imposing suitable values of the sand-grain roughness (KS) and the roughness constant (CS, with CS = 0–1) which can be determined from the roughness length (z0) by Eq. (1) (see [12]):

K s ¼ 9:793

z0 CS

ð1Þ

Within this modelling approach, the near-wall cell size is determined by the condition that its first nodal point must have a distance yP from the wall which satisfies Eq. (2):

yP > K s

ð2Þ

In order to assess the best numerical configuration, the performance of several turbulence models was investigated and validated with experimental wind tunnel measurements of the CEDVAL laboratory [13] by means of a test case based on a single building block (1:200 scale). In particular the standard k–e model, the RNG k–e model and the realizable k–e model were compared:

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Fig. 4. Computational domain. Fig. 2. Vertical velocity profiles along the first test model (125  125  125 mm) [13]: comparison between experimental data and simulations with the Standard k– e turbulence model.

the standard k–e model showed a better fit with the experimental data and was therefore selected as the base scheme for the whole set of simulations. In detail, the numerical approach was validated by means of a comparison between 3D simulations with the numerical code and the experimental data in terms of velocity profiles obtained by [13] on two different buildings’ shapes. The first model (1:200 scale) had a cubic form (H = L = 125 mm and a frontal width of 125 mm), whereas the second model (1:200 scale) was characterized by a height (H) of 125 mm, a length in the wind direction (L) of 100 mm and a frontal width of 150 mm). The comparisons (see Figs. 2 and 3), carried out in terms of vertical velocity profiles, showed constant agreement with the experiments. The main issue in applying the scale factor to the final model was, however, to satisfy the yP constraint both at the ground and on the building walls (e.g. [5,12]); this constraint would lead in fact for z0 values typical of the urban context (z0  1.0 m) to the creation of excessively extended cells at the ground (yP  30 m) with respect to the near-building size (z0 = 3.0  104 m, yP  0.01 m). To overcome this criticality, an explicit modelling of the roughness elements was applied: these elements were considered as squared blocks having the function to virtually reproduce the real roughness effects on the flow. By doing so, the ground roughness of an open-landscape environment can be modelled using a smaller vab must lue of z0 (3.0  102 m). The roughness elements height ( H) be calculated from the average building height of the investigated urban area, whereas the number, width and spacing between the

Fig. 3. Vertical velocity profiles along the second model (125  100  150 mm) [13]: comparison between experimental data and simulations with the Standard k– e turbulence model.

elements are chosen in order to preserve the wind profile which is imposed at the inlet. In this study, two urban schemes were analysed, having different proportions between the investigated buildings. The case studies were selected from a previous work [5], in which a generic urban environment was modelled (Fig. 4): by hypothesizing a wind turbine installation on a specific building (installation building, IB), the oncoming flow on the turbine was calculated as a function of the IB height, the height of its upwind building (UB) and the distance between IB and UB. As suggested by technical literature [14–17], in order to avoid any influence on the final solution, the dimensions of the computational domain must be referred to the tallest building height (H). In this work, however, since two different values of the installation building height were investigated, all the simulations were carried out with fixed dimensions of the boundaries; in further detail, with reference to H = Hmax, the computational domain was obtained extending its boundaries from the IB centre by 15Hmax vertically, 5Hmax upstream and 15Hmax downstream. The mesh discretization was obtained by a hexahedral structured grid with high resolution: the expansion ratio of adjacent cells was kept below 1.15 (a value lower than 1.3 is suggested in [14–16]). In order to ensure the grid-independency of the results, a sensitivity analysis on the cells number was undertaken: five refinement levels of the mesh were tested and compared (see Fig. 5, which reports the calculated mean velocity in a 10 m height zone in the corner of IB). As a result, a number of cells of about 8  104 was selected as the best compromise (the velocity error between the chosen refinement level and the maximum one is lower than 0.1%). As prescribed in [18], the inlet boundary conditions were imposed by the assumption of a constant shear stress with the height

Fig. 5. Sensitivity analysis on the mesh discretization.

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Table 1 Numerical model settings. Algorithm Interpolation schemes Turbulence model Boundary conditions

Simple Always second order Standard k–e Inlet

u u ffiffiffiffiffi p uðzÞ ¼ uj ln ðzdÞ z0 ; eðzÞ ¼ jz ; jðzÞ ¼

Top Outlet Ground Wall

Symmetry plane Zero gradient 3.0  102 m 3.0  104 m



3

2

Cl

Roughness length

(the hypothesis has been also validated by [4, 8–10]). By the assignment of the friction velocity (u), the resulting inlet velocity profile was therefore a logarithmic boundary layer; k and e were imposed by a constant and a hyperbolic function, respectively. The final settings of the numerical model are summarized in (Table 1). 3. Case study The roughness parameters and the wind characteristics exploited in the simulations were extrapolated from a real city data set; in particular, some literature data for London city [19,20] were chosen (Table 2). The displacement value was calculated, following the indications of the ESDU [21], by Eq. (3):

b  4:3z0 ð1  Ah Þ ¼ 13 m d¼H

ð3Þ

b were purposeThree roughness elements of constant height H fully placed before UB and IB, in order to reproduce over UB the correct urban inlet profile in terms of velocity distribution and displacement. Two geometric configurations (Fig. 6) were consequently selected from a previous work [5], in order to achieve at the rooftop of the investigated buildings a lower and a higher available wind distribution with respect to the undisturbed flow, respectively. In detail, the two case studies have a double and quab (following the basic druple IB height than the city average height H requirements proposed by [1]) and the same distance between IB b and UB (D = 0.5 H). In addition, each geometric configuration was simulated with three roof typologies (Table 3): in particular, a flat roof (e.g. tall modern buildings, skyscrapers, etc.) was compared with a sloping roof, with two inclination angles of 8° (roof slope in central Italy) and 18° (average slope of the Italian roofs) respectively, in order to evaluate the flow variations in term of velocity magnitude and skew angle approaching the turbine (e.g. Fig. 7).

b h = 1.5 H; b D = 0.5 H; b (b) H = 4 H; b Fig. 6. Velocity field and streamlines for: (a) H = 2 H; b D = 0.5 H. b h = 2.75 H;

Table 3 Case studies.

Case Case Case Case Case Case

1a 1b 1c 2a 2b 2c

IB height (H)

UB height (h)

Distance between IB and UB (D)

Inclination angle (v)

b 2H

b 1:50 H

b 0:5 H

b 4H

b 2:75 H

b 0:5 H

0° 8° 18° 0° 8° 18°

4. Performance correction model for skewed flow Recent wind tunnel tests ([6,8]) carried out on a low-solidity H-Darrieus wind turbine, have shown that the rotor performance is strongly affected by incidental misalignments of the flow with respect to its main flowpath, which is generally perpendicular to the rotor axis. Surprisingly, VAWTs are characterized by an opposite behaviour in skewed flow than that of the conventional horizontalaxis wind turbines (HAWTs), which are negatively affected by skewed flow conditions [22]: an increase of the power output of

Table 2 London data. b Mean building height ð HÞ Percentage of the total area occupied by buildings Roughness length (z0) Friction velocity (u)

Fig. 7. Examples of the velocity field and streamlines for the same geometric configuration with a flat (a) or a sloping roof (b), respectively. 13.6 m 55% 0.29 m 0.55 m/s

the rotor was in fact noticed for relatively small skew angles. Moving from this evidence, two simplified models have been developed by Mertens et al. [6] and Simão Ferreira et al. [8]. The first model [6]

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consists in a modification of the classical BEM approach, by assuming a reduction of the effective flow velocity as a function of the cosine of the skew angle and a modification of the swept area of the turbine by projecting it perpendicularly to the oncoming flown direction. On the other hand, the second approach [8] is limited to an a posteriori correction of the attended power coefficients on the basis of the flow momentum variation due to the oncoming skewed flow. On these bases, a new aerodynamic model to account for the effects of the skewed flow in an H-Darrieus turbine was specifically developed and embedded in the VARDAR code of the ‘‘Sergio Stecco’’ Department of Energy of the University of Florence (see [23,24]). The VARDAR code makes use of the Double Multiple Streamtubes with Variable interference factor (DMSV, [25]) for the performance estimation of H-Darrieus rotors but the possibility to use a Multiple Streamtubes approach [26] is also provided and adopted whenever very low solidity two-bladed rotors are analysed [6]. Several sub-models to account for the main secondary (e.g. streamtubes expansion, dynamic stall) or parasitic effects (e.g. parasitic torque of the struts and shadowing effect of the central tower) are also embedded [24]. In detail, the theoretical approach that was followed for the proposed skewed-flow model was to improve the original scheme proposed in [6] by providing a more refined description of the flow-blade interaction in the rotor as a function of both the azimuthal position and the span position of the blade itself. With regard to the contribution of the modified velocity, moving from the results of Hoerner [27,28] and Jones and Cohen [29], the lift and drag forces produced by an airfoil in skewed flow conditions are only due to the wind component perpendicular to the blade, whereas no effect is connected to the parallel component. The same assumption was included in the code, where a reduced velocity, connected to the cosine of the skew angle, was considered (see [6]). Focusing on the contribution of the modified area, one can readily understand that the turbine swept area is no longer constant, but experiences a variation as a function of the skew angle [7,8]: in particular, the most correct cross-section which has to be taken into account to model the turbine functioning is the projection of the frontal area (i.e. Aj = Ht  Dt) on a plane normal to the oncoming wind direction. As a consequence of this choice, the projected area increases for relatively small skew angles, due to the contribution of portions of the upper and lower planes of the virtual cylinder swept by the rotor. A limit value to the increment of the projected area, mainly dependent on the turbine geometry, can however be found: beyond this value, part of the flow does not find any blade element on its path (the turbine is seen like a hollow cylinder), thus reducing the effective frontal area. Moving from these assumptions, in order to evaluate the aerodynamic performance of the rotor, the swept volume of the blades was divided into five sectors with slicing planes parallel to the oncoming flow direction, as shown in Fig. 8. Focusing on the aerodynamic implications of this model, the oncoming flow which passes through sectors I and V experiences a single interaction with the blades, whereas the flow passing through sectors II, III and IV, is subjected to a double interaction with the blades (i.e. in the upwind and in the downwind halves of the rotor). As a result of this schematization, the proposed model studies the aerodynamic interactions in sectors II, III and IV with the DMSV approach; sectors I and V are conversely analysed with a modified Multiple Streamtubes (MS) approach, in which the power extraction deriving from only one blade-flow interaction is considered in the calculation of the thrust force of the rotor. In addition, from a perusal of Fig. 8, one can notice that the height of each sector (with the only exception of sector III, which is characterized by a constant height) in the external surface of cyl-

925

Fig. 8. Schematic view of the turbine model divided in 5 sectors.

inder changes with #; as a result, the torque output of a blade at a certain azimuthal angle is determined by a different combination of blade portions working in accordance with a DMSV or a MS model. The calculation scheme of the proposed model can be summarized as follows:  The aerodynamic performance of sectors II, III and IV are calculated with a Double Multiple Streamtubes approach with the VARDAR code;  The performance of sectors I and V are defined by a modified Multiple Streamtubes approach which considers only one interaction between the flow and the blades;  The torque value of the machine at each azimuthal angle (#) is calculated with an averaged mean on the basis of the height ratio between the sectors and the final performance of the turbine is finally computed. The validity of the new model has been verified by means of the only experimental data available in the technical literature [8], referred to a low-solidity two-bladed H-Darrieus turbine. The comparison between simulations and wind tunnel measurements has shown a notable agreement (Fig. 9), with a remarkable improvement in the trend description if compared to the previous theoretical model [8]. On this basis, although a new experimental campaign has been already planned by the authors to achieve a more extensive validation of the proposed approach, the model

Fig. 9. Comparison between simulated and experimental data.

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has been here applied to the calculation of the performance of an H-Darrieus turbine in the built environment.

5. Feasibility analysis The CFD results and the developed model to account for the performance variation due to the skewed flow were combined in order to perform a feasibility analysis of an H-Darrieus installation in the rooftop of a building in the built environment. As a first step, a study turbine was designed, whose main features are reported in Table 4: the H-Darrieus scheme was adopted (Fig. 10) and structural and dimensional constraints, which could be compatible with a rooftop installation, were taken into account in designing the machine (see [23]); in particular, due to the high rotational speeds of these rotors, thick supporting struts and auxiliary tie-rods have been included in the model in order to resist the centrifugal loads acting on the blades. The CFD simulations for the selected buildings geometries (see Table 3) were hence analysed. A 2 m height zone over the corner of IB was taken into account as the reference section for the turbine functioning [5]. Within this zone, the mean velocity variation DU (%), with respect to the undisturbed wind profile at the same height, and the skew angle of the wind flow were calculated on the hypothesis that the turbine slightly affects the oncoming flow field. In the averaging process, a maximum mean square error of 3% on the velocity modulus and of 7% on the skew angle were noticed. In the present analysis, turbulence effects were neglected and they may require further evaluations in the next future. The main results of the analysis are summarized in Fig. 11. Upon examination of Fig. 11, it is worth noticing that the geometric proportions between the UB and the IB have a remarkable influence on the velocity variation at the rooftop of IB; Case 1 configurations (with or without the sloped roof) show indeed a constant decrease of the flow velocity with respect to the undisturbed wind profile, whereas Case 2 configurations constantly offer a positive velocity variation, which is however maximized by the application

Fig. 10. Scheme of the designed H-Darrieus turbine.

Table 4 Main features of the study turbine. Parameter Turbine main features Turbine diameter Turbine height Swept area Blades’ number Blades’ type Blades’ chord Aspect ratio of the blades Solidity

Symbol

Unit

Value

Dt Ht A N

(m) (m) (m2)

c AR

(m)

2.0 2.0 4.0 3 Straight 0.3 6.7 0.45

r

Aerodynamic design of the blades Airfoil Thickness Maximum thickness location Camber line type Pitch angle

t

(% of c) (% of c)

u

(°)

Resistant elements Struts’ number Struts’ thickness Tie-rods’ number Tie-rods’ thickness Diameter of the central tower

Ns ts Nr tr Dtw

Power and efficiency parameters Electrical efficiency Nominal wind speed Rated power @ unom Cut-in speed Cut-out speed

(m) (m)

6 0.030 3 0.003 0.060

(m/s) (W) (m/s) (m/s)

0.8 16.0 1730 3.0 20.0

(m)

gel unom P ucut-in ucut-out

NACA0018 18% 25% Straight 0

Fig. 11. Mean velocity variations (a) and skew angles (b) in the analysis section at the rooftop of the investigated buildings.

of the 8° sloped roof. Moreover, in Case 1 configurations a more pronounced dependence from the inclination angle of the roof was found both in terms of velocity variation and of skew angle; in Case 2 configurations, conversely, a lower dependence from the roof slope can be appreciated and almost the same skew angle was found with sloping roofs with either v = 8° or v = 18°.

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Moving from the results of Fig. 11, the attended performance of the Darrieus turbine was calculated using the developed model embedded in the VARDAR code. The turbine characteristic curves were calculated for all the wind velocities in the range between 0 and 20 m/s (selected cutout velocity) and for the skew angles highlighted by the analysis of Fig. 11b. Then, the new curves were matched with the inverter load curve, which was determined as the envelop of the best operating points of the turbine in aligned flow [30]: as a result, the expected power that is extracted by the rotor in each flow condition was calculated. It is worth pointing out, however, that, the original load curve is not optimized anymore in case of an oncoming skewed flow, due to the shape modification of the characteristic curve at each wind velocity. In order to overcome the potential power losses connected to this problem, a real-time adaptation of the load request could be provided as a function of the skew angle: this solution seems, however, to be very complex and was not taken into account here. As an example, the power curve for the aligned-flow condition is compared to that at c = 33° (Case 2a) in Fig. 12. Upon examination of Fig. 12, a power increase in skewed conditions up to 6% can be appreciated; in addition, one can also notice that the performance improvement due to the effects of the skewed flow can also lead to a reduction of the minimum cut-in speed, thus extending the operating range of the rotor and increasing the energy harvesting for the low-wind conditions. Finally, in order to perform a yearly calculation of the available power production, some assumptions were introduced:  A prevailing wind direction was considered, in which all the oncoming wind during the year was supposed to blow. This assumption is often verified in urban applications, in which the installation building is often chosen to ensure a façade perpendicular to the prevailing wind.  The wind in that direction was assumed to have a Rayleigh velocity distribution [5], with the scale factor to match the attended mean velocity of 6 m/s at Href. These assumptions are in fact needed to get some general tendencies, but it is readily noticeable that they impose a heavy simplification of the real urban environment, whose precise description can be ensured only by 3D simulations of the peculiar analysed case. On these hypotheses, the net available wind distributions in the investigated zone in the rooftop of IB were finally calculated for the considered buildings geometries (Fig. 13). Upon examination of Fig. 13, one may notice that different installation choices can lead to a remarkable modification of the

Fig. 13. Available wind distributions for plan roof cases (a) and sloped roof cases [v = 8° – (b) and v = 18° – (c)].

Fig. 12. Turbine power curve modification in skewed flow.

wind statistical distributions, which are shifted in terms of both the average velocity and the characteristic frequencies; conversely, the distributions are slightly affected by the roof slope when a small inclination angle is chosen, whereas an high inclination angle can substantially modify the wind conditions in the rooftop, especially in the case of a short building. Under these assumptions, the variation of the yearly energy production of the turbine with respect to a hypothetic installation in the undisturbed wind at Href = 36 m (Case 0 with null skew angle) are presented in Fig. 14; in detail, the energy production of each configuration was calculated either with or without accounting for the skew angle effects (thus with the modified cut-in speed and power curve). From a perusal of Fig. 14, it is worth noticing that:

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Fig. 14. Energy yield variation with respect to Case 0 for the investigated study cases.

 The right choice of an urban installation site, i.e. a geometric condition which enables the turbine to exploit the acceleration induced by the upwind building (Case 2 geometries), can indeed provide a remarkable increase of the turbine production, whereas a constant detriment of the available power can be suffered when a wrong installation site is chosen (Case 1 geometries).  The sloping angle of the roof has a relevant impact on the attended performance of a Darrieus turbine installed in the rooftop area. In the case of tall buildings, a sloping roof is deemed to ensure an improvement of the flow conditions in the investigated area; in addition, small inclination angles (approximately 8–10°) seems to guarantee the best combination between velocity increases and skew angles. On the other hand, in the case of an unfavourable buildings geometry, small inclination angles are supposed to improve the flow conditions in the rooftop, whereas steep sloping roofs could even worsen the oncoming flow.  The opportunity of exploiting a skewed flow with Darrieus wind turbines is deemed to represent a very important opportunity, due to the sensible increase provided in the yearly power yield of these machines. This effect could be further increased with a more sophisticated logic of control, although a similar solution would increase the complexity of the electrical systems and the control apparatus. Finally, although proper economic and cost analyses cannot be carried out in this context, due to the fact that the contributions of all the others wind directions are here neglected in the energy yield evaluation, some interesting remarks can be done by critically analysing the attended variation of the capacity factor (relative to the main wind direction considered) of the turbine in the

investigated installations schemes (Table 5) with respect to the hypothetic one in Case 0. It is readily noticeable how the relatively low velocity and skew angle variations discussed in Fig. 11 have a remarkable impact on the potential yearly production of the machine, mainly due to the performance benefits induced at low wind velocities (which are, however, the most frequent conditions in a long-time horizon). Furthermore, on the basis of the consideration that the convenience of a turbine installation is proportional to the capacity factor [31], Table 5 clearly indicates that a microeolic installation in the built environment could indeed represent a profitable solution, but only on condition that a suitable installation site is chosen; in detail, buildings reasonably higher that the surrounding constructions can take advantage from the flow acceleration over their façade induced by the interaction with the upwind building, with a notable increase of the potential energy available for the turbine. Moreover, the application of Darrieus VAWTs to this environment is deemed to represent a promising solution thanks to the performance improvement connected to the effects of a skewed flow. On the other hand, a wrong choice of the installation building, i.e. a condition in which a detriment of the rooftop flow conditions is induced by the surrounding buildings, could dramatically compromise the energy production and the convenience of the investment, as well. Finally, in order to get an idea of the electricity saving potentially obtainable with the energy yield of the turbine, statistical indicators for the energy consumptions of residential and office buildings were considered; in detail, a daily amount of 25 Wh/m3 was assumed as the reference electricity consumption of this buildings’ typology [32,33]. On this basis, the energy harvesting of the single turbine investigated in this work is assumed to provide a total energy saving per year for the considered buildings in the range between 1.4% in Case 1a without skew effects and 2.5% in Case 2c with skew effects. Although the global amount appears small for a single rotor, one can consider that multiple turbines are generally placed in the rooftop: e.g. four turbines could provide up to 10% of the global electricity demand in Case 2c, which could be sufficient, for example, to satisfy the common energy consumptions of the building (e.g. lighting of the shared spaces, etc.). 6. Conclusions A wide-ranging analysis was carried out to evaluate the energetic suitability of a Darrieus VAWT installation in the rooftop of a building in a reference European city. With this goal in mind, the first step of the analysis consisted on a numerical CFD analysis to characterize the flow field in the rooftop area of two buildings with different proportions with respect to both the average surrounding buildings height and their upwind building; in addition, the application of either a plan or a sloping roof was considered. The flow velocity modulus and direction (skew angle) were calculated for different oncoming wind profiles and compared to their

Table 5 Attended variation of the capacity factors as a function of the installation site. Test case

Case 1a

ˆ – IB = 2.00H ˆ UB = 1.50H Roof slope Theoretical approach Capacity factor variation (%)

0° No skew 37.2%

Case 1b

Skew 34.2%

Case 2a ˆ – IB = 4.00H ˆ UB = 2.75H Roof slope Theoretical approach Capacity factor variation (%)

0° No skew +71.3%

8° No skew 35.5%

Case 1c

Skew 32.4%

Case 2b

Skew +74.4%

8° No skew +84.7%

18° No skew 47.4%

Skew 44.5%

Case 2c

Skew +95.9%

18° No skew +81.3%

Skew +93.0%

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level in the undisturbed wind. Under the assumption of Rayleigh distribution of the blowing wind, the results were projected into net available wind distributions in the rooftop of each building. As a second step, a numerical model was developed to account for the effects of the skew angle of the flow on the power performance of the H-Darrieus turbine: the modified turbine power curves were hence evaluated with the developed model with the flow conditions previously calculated for the study configurations. Finally, the results of the CFD simulations and the new turbine model were combined in a comparative feasibility analysis of a medium-size H-Darrieus turbine in the built environment. The analysis showed that notable increments (up to 70%) of the attended capacity factor in the rooftop area of an installation building in the urban environment can be achieved whenever a building reasonably higher than the average of the surrounding constructions is selected and suitable geometric proportions of the building itself with respect to its upwind building are fulfilled; otherwise, a constant detriment of the energy potential was noticed. In addition, a positive influence on the velocity increment in the rooftop area of the sloping angle of the roof was appreciated; this effect was maximized by the application of a sloping roof with an inclination angle of 8°, which was deemed to guarantee the more effective guidance to the flow which overcomes the building. Focusing on the application of a Darrieus turbine, it is also worth noticing that the skew angles attended in the rooftop of a building in a urban environment (15–35°), seem to ensure a further increase (up to 12%) of the attended energy harvesting thanks to the improved behaviour of these machines in skewed-flow conditions; on the basis of a specific model that was developed to account for this effect in the performance estimations of Darrieus VAWTs, this contribution is deemed to be maximized whenever a skew angle of approximately 25° is achieved. References [1] Mertens S. Wind energy in the built environment. Brentwood (UK): MultiScience; 2006. [2] Dayan E. Wind energy in buildings: power generation from wind in the urban environment – where it is needed most. Refocus 2006;7(2):33–8. [3] Banks D, Cochran B, Denoon R, Wood G. Harvesting wind power from tall buildings. In: Proceedings of the CTBUH 8th world congress; 2008 March 3–5; Dubai (UAE), Chicago: Council on Tall Buildings and Urban Habitat; 2008. p. 320–7. [4] Beller C. Urban Wind Energy – State of the Art 2009. Roskilde (Denmark): Risø Laboratory - DTU; 2009 Report No.: Risø-R-1668(EN). [5] Balduzzi F, Bianchini A, Carnevale EA, Chesi A, Ferrari L. Influence of the building geometry on microeolic installations in the urban context. In: Proceedings of world renewable energy congress XI; September 25–30, 2010; Abu Dhabi (UAE); 2010. [6] Mertens S, van Kuik G, van Bussel G. Performance of an H-Darrieus in the skewed flow on a roof. J Solar Energy Eng 2003;125:433–40. [7] Mertens S. The energy yield of roof mounted wind turbines. Wind Eng 2003;27(6):507–17. [8] Simão Ferreira CJ, van Bussel G, van Kuik G, An analytical method to predict the variation in performance of an H-Darrieus in skewed flow and its experimental validation. In: Proceedings of the european wind energy conference 2006; 2006 February 27–March 2, Athens (Greece); 2006. [9] OpenCFD Ltd. website: .

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