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An application of the actuator disc model for wind turbine wakes calculations
Applied Energy 101 (2013) 432–440
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
An application of the actuator disc model for wind turbine wakes calculations Francesco Castellani a,⇑, Andrea Vignaroli b,1 a b
University of Perugia, Department of Industrial Engineering, Via G. Duranti 67, 06125 Perugia, Italy VTT – Technical Research Center of Finland, Vuorimiehentie 5, FI-02150 Espoo, Finland
h i g h l i g h t s " In this study a novel technique for wind turbine wakes simulation was implemented. " Production data from a small coastal wind farm in Finland were used for validation. " Results demonstrate an improvement comparing to the traditional analytical models. " Such model can be usefully implemented for large offshore wind farm wakes simulation.
a r t i c l e
i n f o
Article history: Received 19 September 2011 Received in revised form 8 April 2012 Accepted 26 April 2012 Available online 6 June 2012 Keywords: Wakes simulation Wind energy CFD Actuator disc
a b s t r a c t Numerical simulation of wake losses is a fundamental step towards the optimization of the exploitation of the renewable wind energy potential especially in off-shore conditions or in coastal areas. The scientific community is quickly developing new advanced modelling techniques in order to improve the reliability of power losses calculation in many different kinds of environment; analytical models are going to be replaced by new Computational Fluid Dynamics (CFD) codes that seem to be more useful, especially for large offshore wind farms. In the present work an actuator disc model was implemented in order to simulate the wakes of a wind farm; this model was used within the CFD code PHOENICS (the numerical core of the Windsim package) working with an orthogonal Cartesian grid. The model was validated using real production data from a small wind farm operating in the western coastal region of Finland; the numerical wind speed profiles were verified using anemometer data from a mast placed near the turbines. The results demonstrate that, despite its simplicity, the actuator disc model can give very useful information when developing a wind farm in off-shore or coastal areas. This work was carried out within a cooperation between the Department of Industrial Engineering of the University of Perugia and VTT, the technical research centre of Finland. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction During the design process wake losses evaluation is an important aspect of wind park production estimation, especially for offshore wind energy. Existing numerical models to evaluate wake losses can roughly be classified in two types: analytical and physical. In some situations wind turbine wake numerical modelling could represent a fundamental step in the overall design optimization process; the calculation effort is, of course, dependent on the model resolution and reliability.
⇑ Corresponding author. Tel.: +39 075 5853709; fax: +39 075 5853703. 1
E-mail address: [email protected] (F. Castellani). Present address: Windsim – Fjordgaten 15, N-3125 Tønsberg, Norway.
0306-2619/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2012.04.039
Increasing the calculation effort it is possible to use analytical models, actuator disc models, actuator line/surface models or full rotor simulation (Table 1). Initially, simple analytical models were implemented [1]; such models can usually give good results only for simple wind farms in on-shore conditions where power losses due to wakes are lower than the effects of terrain and surface roughness. This kind of model is still in use in many engineering numerical tools for wind energy assessment such as WAsP – the Wind Atlas Analysis and Application Program [2]. When using analytical models, the estimation of wake losses is usually performed downstream the wind climatology calculations; this method does not allow to get a full description of the local wind field nor, in some cases, a good assessment of the energy losses. However, the development of the exploitation of wind energy resources in a wide range of off-shore and coastal sites has
F. Castellani, A. Vignaroli / Applied Energy 101 (2013) 432–440
433
Glossary D Sa CT a P ni DPi Pr
rotor diameter (m) thrust force (N) thrust coefficient axial induction factor power (kW) weight parameter local pressure drop (Pa) local pressure (Pa)
mi q m1 mr A WPD Ei
local wind speed (m/s) air density (kg/m3) free stream velocity at the hub height (m/s) wind speed on the disc (m/s) rotor swept area (m2) average wind power density (kW/m2) energy percentage (%)
Table 1 Wind turbine wakes models. Name
Advantages
Disadvantages
Analytical Actuator disc
Fast and simple calculations Average calculation effort Contextual wind field and wakes simulations Coarse mesh Effects of rotation are considered (able to model wakes vortices) Contextual wind field and wakes simulations Real geometry is modelled
Wake losses calculated downstream the wind field Effects of rotation cannot be simulated Extremely simplified geometry
Actuator line/ surface Full rotor simulation
highlighted some issues when simulating wakes interactions with the main wind flow and multiple wake interactions. The fast development of many offshore and coastal wind projects is pushing the scientific community to study reliable methods for multiple wakes simulation and to reproduce the effect of different boundary layer conditions on wake propagation. For the reasons mentioned above, a great interest is taken in Computational Fluid Dynamics (CFD); this numerical technique is currently successfully applied in the wind energy industry for two main purposes: 1. simulation of the rotor aerodynamics at full scale used when developing a new rotor configuration; 2. simulation of the surface boundary layer used for wind potential assessment studies (especially for complex terrains). In order to study the wakes of a wind farm, both activities should be conducted in a unique domain; unfortunately the grid resolution that is necessary to reproduce the real rotor geometry may be too fine to model the whole wind farm area with a number of cells that could be processed through normal calculation machines. A coarse grid is necessary to model the wind farm area and the boundary layer conditions with a reasonable computation time; but this way, the full rotor simulation is impracticable. A good approximation of the real local wind field can be achieved using the actuator disc model; this model was initially developed to study not only wind turbine rotors but also propellers and helicopter rotors [3]. The actuator disc model disregards fundamental characteristics of wind turbine aerodynamics because it represents any rotor by a distributed action over the flow rather than the complex, vortical structure that a real rotor creates in the flow [4,5]. Despite its simplicity, it is often a useful representation to reproduce wind deficits and wake losses. Recently, the actuator disc model is often used to model multiple wakes in large wind farm; with its possible variations, the model
Finer mesh with high calculations effort Much more parameters for the turbine are necessary Very high calculation effort Knowledge of the geometry and many parameters for the turbine are necessary
can give a reliable description of the far wake [6] and its interaction with the main wind field and of the other wakes. The actuator disc model is very flexible and easy to implement but, especially if used with RANS (Reynolds Average Navier Stokes) solutions and the standard k–e turbulence model, it can give an under prediction of the wake effects that is larger in the near wake region [7–9]. On the contrary it requires a lower calculation effort and, if used on a Cartesian grid, it can be easily integrated with an atmospheric boundary layer simulation [10]. In the near wake region the model reliability can be improved using a different approach for the turbulence closure [11]. A better description of the real flow past the wind rotor can be achieved using the actuator line concept [12]. According to this approach each wind turbine blade is represented as a line or surface acting on the wind [7,13]; a Gaussian distribution can generally be used for the force distribution. With this approach it is possible to model wake vortices so that the implementation of the actuator line model can give a better representation of the aerodynamics of the wakes comparing to the actuator disc. Anyway the finer mesh introduces higher calculation efforts and the simulation of large wind farm can be very hard or impossible. The analysis of the far wake and of the losses within a wind farm is much more feasible using the actuator disc model and the momentum deficit over the rotor surface. In the present work, the actuator disc model is applied to simulate the wakes of a small coastal wind farm; in this test case the wake model can be very useful to investigate the influence of the local conditions of surface roughness and terrain on the mechanisms of wake expansion. The goal of such modelling technique is to develop a fast and reliable method for the estimation of the losses for different layout configurations with a calculation effort compliant with commercial computers. The work is done using the beta version of the commercial code WindSim; the analysis of the test case is used as a benchmark for the application of the actuator disc wakes model.
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Present work is done independently from the Windsim development team; the beta version of the actuator disc model is used for calculations while the post-processing is performed using a code that is not included in the commercial software but was developed by the authors. 2. Methodology 2.1. The numerical model The numerical simulation of the wind farm was implemented using the Windsim CFD (Computational Fluid Dynamics) model: a numerical code based on PHOENICS which solves the Reynolds Averaged Navier–Stokes (RANS) equations with a multigrid coupled solver (MIGAL). Windsim was initially developed to simulate the local wind field conditions along the complex Norwegian coastline; it was first applied to reproduce the surface boundary layer induced by orography and roughness singularities in order to estimate the distribution of the wind energy potential within a rectangular domain. After the wind field calculation, it is possible to estimate the power production of a wind farm layout including the effect of the turbine’s wake through the application of an analytical wake model. In the latest versions of the code, turbine wakes are simulated with a simple actuator disc model [14]; the axial force that can be applied on the disc surface depends on the wind speed according to the thrust coefficient curve of the aerogenerator. Since PHOENICS, the numerical CFD core, works on a Cartesian orthogonal grid, the rotor surface can be interpolated only using squared elements. The streamlines passing through the disc are affected by the power extraction and a wind velocity deficit so that the wind speed on the rotor mr is lower than the undisturbed speed m1. The theory represents this mechanism by introducing the axial induction factor:
mr ¼ ð1 aÞ m1
ð1Þ
The thrust coefficient for the whole rotor CT is defined as:
CT ¼ 1
Sa
q m21 A 2
:
ð2Þ
where Sa is the thrust force, q is the air density, m1 is the free stream velocity at the hub height and A is the rotor swept area. In this way it is possible to estimate the force that has to be introduced against the wind on the rotor surface (that is modelled as a group of cells on which the kinetic energy is extracted) for each different wind flow condition. The calculation domain for the simulation of the whole wind farm is divided into a coarse area and a refined area (Fig. 1): the turbines are defined by the cells on which the thrust is applied in the refined area in order to reproduce the turbine wakes. The coarse area is necessary to simulate the main wind field blowing on the wind farm area on a mesoscale; in the refined area, the interaction between the wind field and the turbine wakes can be evaluated on a local scale. In this way, the force on the rotor can be applied and simulated within the CFD-RANS solution so that the real wind distribution and wake extension can be evaluated directly after the numerical CFD iterations. In the Windsim actuator disc model, three different types of force distribution can be used: uniform distribution; parabolic distribution; polynomial distribution.
Fig. 1. The grid architecture.
Since the uniform distribution is the easiest and gives results that can be directly compared with the analytical solution, this configuration was used in the present work to simulate the wakes of a small coastal wind farm in Finland. A matlab post-processing tool was developed for the calculation of the power production from each turbine using two different algorithms: the power curve method and the integral method. With the first method, the power is estimated using the mean wind speed mr calculated for each modelled rotor and then evaluating the undisturbed wind speed with the following formula:
mr
m1 ¼
ð3Þ
ð1 aÞ
The production of each turbine is then estimated from the power curve. Unfortunately the value of the axial induction factor is not provided by the turbine manufacturer and can only be evaluated from the thrust coefficient using the following relationship from the Betz Theory:
C t ¼ 4að1 aÞ
ð4Þ
With the second method, the power for the disc can also be directly estimated using the local wind speed and the maximum pressure drop across the rotor so that from one-dimensional analysis:
P¼
Z
m dP dA ffi
X
ni DPi mi
ð5Þ
A
where ni is a weight parameter used to consider the discretisation related to the chosen grid resolution, DPi is the local pressure drop and mi is the local wind speed. The integral on the rotor swept surface can be approximated with a discrete approach; in this case, the resolution of the interpolation should be consistent with the CFD grid resolution. The value of the specific power obtained in each point inside the rotor should be weighted according to the portion of the area that each point can represent in order to than evaluate the overall value of the power.
F. Castellani, A. Vignaroli / Applied Energy 101 (2013) 432–440 Table 2 CFD model characteristics. Resolution
Actuator cells
Actuator area/rotor area
Overall cells
D/6 D/10 D/12 D/14
32 80 112 156
1.05 0.94 0.92 0.94
904,704 2,775,072 4,149,530 6,243,930
The grid resolution is a key parameter in the overall process: a higher resolution can give more realistic results but can make the calculus very hard because of the higher number of cells (Table 2). However, it is recommended to use a grid resolution in the refined area very near D/16 (where D is the rotor diameter) [14]; this value was obtained from a test simulation that was done on a simple model with a single actuator disc. In the present work, a brief analysis of the influence of the grid resolution was performed on the wind farm model: the wind profiles and the pressure trends upstream and downstream the rotor of the first aerogenerator placed up to the wind were analyzed in order to select the right grid resolution. Fig. 2 shows a great difference both in the trend and in the pressure drop estimation between the results obtained with a resolution
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of D/6 and D/10; even if the minimum grid resolution seems to be D/ 10, the final chosen grid configuration corresponded to a resolution of D/12. This is consistent with the results of the previous study in [14] because of the different rotor dimensions. An observation of the vertical profiles (Fig. 3) downstream the rotor confirms the validity of the results obtained with a minimum grid resolution of D/12; this result seems to be in good agreement with experimental measurements [15]. The core of the wake is well represented only with a good grid resolution: the actuator disc model is not able to give useful results in the near-wake region (less than 2D downstream) but, in order to estimate the power losses in the most reliable way, a very good representation of the wind field in the far wake should be achieved. In this work, the RNG-ke model was used for the turbulence closure; such model ensures a better convergence of the calculus and can give useful results for the estimation of the power extracted by the wind rotor [16]. 2.2. The site In order to validate the numerical method, a wind farm site has been analyzed: wind data and production data were available for a
Fig. 2. Horizontal profiles of normalized pressure
Pr 1=2qm21
for different grid resolutions.
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Fig. 3. Vertical wind profile upstream and downstream the rotor with different grid resolutions.
Fig. 4. Map of the site.
meaningful period and were collected by VTT. The site under investigation is located in the archipelago near the city of Pori, in Western Finland. Along a road connecting one of the islands to the mainland, four 1 MW Bonus wind turbines have been in operation since 1999 (Fig. 4). The hub height of the turbine is 62 m and the rotor diameter is 54 m. VTT has been monitoring the wind conditions on the site using a met mast equipped with sensors at hub height ± radius. The site is complex because of the sudden changes of roughness between the sea and the forest covering almost all the islands of the archipelago and the surroundings of the aerogenerators. The grid resolution for the CFD simulations varied with the different models implemented, starting from 3.8 up to 200 m with the refined model and 8.8 up to 302 m with the coarse model. Fig. 5 shows the terrain elevation and the roughness length for the calculation domain: roughness lengths from 0.0001 m (sea surface) up to 1 m (urban-forested areas) were assigned both for CFD and WAsP. Even if a specific forest model is available in WindSim, forested areas were treated as higher roughness area without introducing a porous volume.
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Fig. 5. Terrain elevation (left) and roughness length (right) (m) with the box representing the area from Fig. 4.
2.3. The experimental dataset Failure and production statistics of wind power in Finland are maintained at VTT. Monthly production data and downtime data are thus available for the four turbines under examination. By dividing the monthly production by the availability of the machine it is possible to obtain an estimate of the production of the turbine during the generation time for the entire month. The wind data available on the site have been analyzed in order to find a representative monthly dataset characterized by an energy rose with a prevalent direction such that three of the four wind turbines were producing behind the first one in the row. March 2000 was assumed as a representative month and the energy rose for that month can be seen in Fig. 6 together with the wake-disturbed sectors. The energy rose indicates the percent of total available wind energy as a function of direction and it can be defined as:
Ei ¼ 100
Ni WPDi ð%Þ N WPD
ð6Þ
where Ni is the number of records in direction sector i, N is the total number of records, WPD is the average wind power density defined as:
WPD ¼
N 1 X qV 3j 2N j¼1
where Vj is the wind speed for record j.
ð7Þ
Table 3 Distance of the turbines from the met mast. Distance from met mast (nr. of diameters) T1 T2 T3 T4
2.4 6.6 11 15.7
At the same time WPDi is the average wind power density in direction sector i. Production figures were available only on a monthly basis. Wind statistics measured by the meteorological mast have been used to select which month had wind conditions favorable to maximize wake losses and to minimize the time during which measurements were affected by the wakes from the 4 turbines. Wake disturbed sectors were assessed using the procedure described in IEC 61400-12-1: Annex A [17]. Production statistics were extracted from VTT’s database for the same month. According to the shape of the energy rose, T4 is the turbine less affected by the production losses due to the wake effect (see Figs. 4 and 6), and this is confirmed by measurements. The production of each turbine was divided by the production of T4 in order to quantify of the array efficiency and to be able to compare it with simulations. The meteorological mast is placed 2.4D downstream the turbine nr. 1 in the 270° direction sector (Table 3). 3. Results and discussion
Fig. 6. Energy rose and wake disturbed sectors at the mast position.
Several simulations of the wind blowing from the main direction sectors were performed using a domain of more than 4 millions of cells and the RNG-ke turbulence closure model; the rotors were defined within a grid spaced at 4.5 m (D/12). For the boundary conditions a height of 500 m and a wind speed of 10 m/s above the boundary layer were applied for each modelled direction sector; in this way the free stream conditions at hub height are very near to 6 m/s representing the average value observed in the anemometer dataset. The different energy output for the wind turbines is due only to the wake interactions: disregarding wakes differences in the estimation of the gross energy available calculated for the wind turbines positions are below 1%.
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Fig. 7. Numerical vs experimental wind profiles downstream T1.
Table 4 Results for the power loss estimation. Power % with the integral method 330°
T4 T3 T2 T1
Power % with the power curve method 190°
330°
190°
Rotated
Not rotated
Rotated
Not rotated
Rotated
Not rotated
Rotated
Not rotated
100.00 85.29 75.74 85.56
100.00 71.09 51.78 55.74
96.72 93.04 100.00 87.59
87.17 93.35 100.00 94.97
100.00 98.19 95.04 96.25
100.00 75.69 65.15 69.99
100.00 96.33 97.92 88.71
92.33 93.09 100.00 95.36
Only the main direction sectors affected by wakes were considered to estimate the mean wake effect to be compared with experimental data from the chosen monthly database: 10°, 190°, 330° and 350°. For each sector the power extracted by each rotor was estimated using the post-processing tool and the wakes losses were calculated with respect to the upstream turbine. Results from different sectors were finally weighted according to the energy percentage measured by the anemometer in the monthly database. In this way numerical wake calculations can be compared to the results from the monthly production dataset. Anyway using such procedure some sources of errors were introduced:
1. for orthogonal domains it is possible to have 1 inlet, 1 outlet and 2 frictionless walls; 2. for non-orthogonal domains 2 inlets and 2 outlets are defined. With this grid architecture, it is possible to simulate the actuator discs exactly faced to the wind only for orthogonal sectors; in non-orthogonal situations the axial force is also distributed in a sort of cross surface obtained from two orthogonal rotors: one facing the north–south direction and one facing the east–west direction. Such technique was developed to allow the simulation of all directions [19] also when introducing the effect of the thrust on the rotors; however, the geometry is not well reproduced in the case of non-orthogonal winds.
1. the anemometer dataset can be affected by the wakes (even if the major part of the energy was distributed in undisturbed sectors a meaningful percentage of energy was also observed for blocked sectors); 2. simulations were performed using only one value of the wind speed but wakes can be strongly affected by this parameter due to the thrust coefficient variations; 3. only neutral atmospheric conditions were considered. The anemometer used to validate the numerical model is placed 2.4 diameters downstream the turbine T1 in the 270° sector (Fig. 4). The numerical results from the 270° and 330° sectors were used to compare the numerical and the measured wind speed profiles (Fig. 7); the good agreement found seems to confirm the reliability of the actuator disc model to predict the speed deficit in the far wake. Other sectors were modelled too and the wakes for each direction were characterized evaluating the array efficiency (actual power/max power) in the same way as for the experimental dataset. When the blowing direction changes, Windsim can apply different strategies to manage the boundary conditions [18]:
Fig. 8. Comparison of the wake losses calculated with WAsP and with the actuator disc model.
F. Castellani, A. Vignaroli / Applied Energy 101 (2013) 432–440
439
Fig. 9. Comparison of the wind profile 2.5 diameter downstream calculated with different wake models.
The monthly reference database (March 2000) has two nonorthogonal main directions: 330° and 190°. In the present work, when simulating the non-orthogonal cases, two different calculation methods were compared:
A further improvement of the model will be undertaken through a detailed turbulence analysis: the turbulence induced by the wake can spread up to 15 diameters downstream the turbine [22].
1. using the conventional domain geometry and distributing the axial force on the cross surface (usually used by Windsim); 2. rotating the terrain and roughness model so that the calculations can be performed referring to orthogonal cases and all the rotors can be represented exactly facing the wind.
4. Conclusions
The results of Table 4 demonstrate that the model is very sensible to the boundary conditions and that the method used to calculate the turbine power can slightly change the results. For the actuator disc, the most reliable results were obtained using a rotated domain and the integral method for the power estimation; the results obtained with this technique are presented hereafter. An estimation of the overall array efficiency was obtained using the results for each sector and the energy rose distribution; these results were also compared in Fig. 8 with the estimations made with the analytical wake model of WAsP. The default standard settings for the WAsP wind flow model (version 8.4) were used for the simulation; the results were calculated under neutral boundary layer conditions and using the default wake decay constants in the PARK wake model. A very good agreement with the experimental data was found. The improvement of the results by comparing them to the analytical model should be addressed mainly to the possibility for the CFD actuator model to reproduce the wind field at the beginning of the far wake in a reliable way. The numerical wind profile 2.4 diameters downstream calculated through CFD is clearly more realistic than the profile considered in the Park Wake model used by WAsP (Fig. 9). The boundary of transition between the near wake and the far wake region was discussed by many authors [4,5,7]; a reliable definition of such boundary measured in number of turbine diameters cannot really be defined because of its general dependence on the atmospheric flow conditions. The near wake extends from the disc to two or three diameter downstream [4,5,15,20] but it can even reach a distance up to 5 diameters [21]. The energy exchanges between the wakes and the main stream can only be modelled in a reliable way using a realistic description of the wind field within the wake area; this would allow a better prediction of wakes propagation in the whole wind farm.
In the present work, the application of the actuator disc model for the simulation of wind turbine wakes within a CFD code was experimented on a test case of a small coastal wind farm. Results demonstrate that such technique can indeed be very useful to simulate the wind turbine wakes and their interaction with the main wind field. The accuracy of the proposed model was found to be higher than the one of traditional analytical wake models. The model is not proposed for an exhaustive wake simulation but for an estimation of the power losses of a wind farm through a reliable prediction of the far wake characteristics. The proposed model is suited to simulate wake–wake interaction and effects in different shear conditions [23,24]. A key feature for this technique should be the possibility to obtain good results in a very fast way in order to be attractive for industrial applications, even for large offshore wind farms; this could be very useful to investigate the shadow effects between different layouts of a wind turbine park [25,26]. However, the post-processing downstream the CFD calculus was found to be a fundamental part of the model. Many improvements can still be added to the model, such as: introducing different kinds of thrust force distribution in order to reproduce some known effects like the edge interaction; developing the simulation of turbulence using different models; introducing rotational effects. The post-processing phase could also be improved by developing the weighting algorithm and by using higher resolutions. The actuator disc model can be very useful to perform a comprehensive simulation of a wind farm wake but it is intrinsically affected by errors in the near wake region; this is due not only to the lack of geometric representation of the rotor, but also to the inability of the model to reproduce the physics of the problem [27]. References [1] Katic I, Højstrup J, Jensen NO. A simple model for cluster efficiency. In: EWEC proceedings, 7–9 – October 1986, Rome, Italy; 1986. [2] WAsP – The wind atlas analysis and application program.
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[3] Van Kuik GAM. On the limitations of Froude’s actuator disc concept. PhD Thesis, Technical University of Eindhoven Doctoral Thesis; 1991. [4] Vermeer LJ, Sørensen JA, Crespo A. Wind turbine wake aerodynamics. Prog Aerospace Sci 2003;39:467–510. [5] Sanderse B. Aerodynamics of wind turbine wakes – Literature review. Energy research centre of the Netherlands.. [6] Réthoré PE, Sørensen NN, Zahle F. Validation of an actuator disc model. In: European wind energy conference & exhibition proceedings – Tuesday 20– Friday 23 April 2010, Warsaw, Poland. [7] Réthoré PE. Wind turbine wake in atmospheric turbulence. PhD Thesis. Aalborg University, Department of Civil Engineering; 2009. ISSN 1901-729. [8] Rados KG, Prospathopoulos JM, Stefanatos NCh, Politis ES, Chaviaropoulos PK, Zervos A. CFD modeling issues of wind turbine wakes under stable atmospheric conditions. In: European wind energy conference & exhibition proceedings, Parc Chanot, Marseille, France, 16–19 March 2009. [9] Cabezón D, Sanz J, Martí I, Crespo A. CFD modelling of the interaction between the Surface Boundary Layer and rotor wake. Comparison of results obtained with different turbulence models and mesh strategies. In: European wind energy conference & exhibition proceedings, Parc Chanot, Marseille, France, 16–19 March 2009. [10] Mikkelsen R. Actuator disc methods applied to wind turbines. PhD thesis, Technical University of Denmark, Mek dept.; 2003. [11] El Kasmi A, Masson C. An extended k–e model for turbulent flow through horizontal-axis wind turbine. J Wind Eng Indus Aerodyn 2008;96: 103–22. [12] Von Karman T. Aerodynamics. Mc Graw-Hill; 1963. [13] Troldborg N. Actuator line modeling of wind turbine wakes. PhD thesis, DTUMEK, Denmark; 2008. [14] Crasto G, Gravdahl AR. CFD wake modeling using a porous disc. In: European wind energy conference & exhibition proceedings, Brussels Expo, Belgium, 31 March–3 April 2008. [15] Schepers JG. ENDOW: Validation and improvement of ECN’s wake model. Technical Report ECN-C-03-034, Energy research Centre of the Netherlands; 2003.
[16] Mansour K, Yahyazade M. Effects of turbulence model in computational fluid dynamics of horizontal axis wind turbine aerodynamic. WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANIC 2011;6(3). ISSN: 1991-8747. [17] IEC 61400-12 WIND TURBINES – Part 12-1: power performance of electricity producing wind turbines; 2006. [18] Castellani F, Vignaroli A, Gravdahl AR. Wind simulation on complex terrain: about the dependencies on inlet flow orthogonality. In: European wind energy conference & exhibition proceedings – Athens, Greece, 27 February–2 March 2006. [19] Castellani F. Grid control for CFD wakes simulation in complex terrains. In: European Wind Energy Conference & Exhibition Proceedings – Parc Chanot, Marseille, France, 16–19 March 2009. [20] Manwell JF, McGowan JG, Rogers AL. Wind energy explained: theory, design and application. John Wiley & Sons, Ltd.; 2002. [21] Zahle F, Sørensen NN. On the influence of far-wake resolution on wind turbine flow simulations. Sci Making Torque Wind – J Phys: Conf Series 2007;75: 012042. [22] Højstrup J. Spectral coherence in wind turbine wakes. J Wind Eng Indus Aerodyn 1999;80:137–46. [23] Crasto G, Castellani F, Gravdahl AR, Piccioni E. Offshore wind energy prediction through CFD simulation and the actuator disc model. In: European wind energy conference & exhibition proceedings – Brussels Expo, Belgium, 14–17 March 2011. [24] Castellani F, Crasto G, Gravdahl AR. Actuator disc wind turbine wakes simulation: about the dependences on the wind shear conditions. 1° Convegno Nazionale di Ingegneria del Vento – INVENTO 2010 – Spoleto 30 Giugno-3 Luglio; 2010. ISBN: 978-88-6074-330-5. [25] Frandsen S, et al. The shadow effect of large wind farms: measurements, data analysis and modelling. Report from RisøNational Laboratory for Sustainable Energy – Risø-R1615(EN); 2007. [26] Barthelmie RJ et al. Flow and wakes in large wind farms: Final report for UpWind WP8. Report from RisøNational Laboratory for Sustainable Energy – Risø-R1765(EN); 2011. [27] Réthoré P-E, Sørensen NN, Bechmann A. Modelling issues with wind turbine wake and atmospheric turbulence. Sci Making Torque Wind 2010.
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
An application of the actuator disc model for wind turbine wakes calculations Francesco Castellani a,⇑, Andrea Vignaroli b,1 a b
University of Perugia, Department of Industrial Engineering, Via G. Duranti 67, 06125 Perugia, Italy VTT – Technical Research Center of Finland, Vuorimiehentie 5, FI-02150 Espoo, Finland
h i g h l i g h t s " In this study a novel technique for wind turbine wakes simulation was implemented. " Production data from a small coastal wind farm in Finland were used for validation. " Results demonstrate an improvement comparing to the traditional analytical models. " Such model can be usefully implemented for large offshore wind farm wakes simulation.
a r t i c l e
i n f o
Article history: Received 19 September 2011 Received in revised form 8 April 2012 Accepted 26 April 2012 Available online 6 June 2012 Keywords: Wakes simulation Wind energy CFD Actuator disc
a b s t r a c t Numerical simulation of wake losses is a fundamental step towards the optimization of the exploitation of the renewable wind energy potential especially in off-shore conditions or in coastal areas. The scientific community is quickly developing new advanced modelling techniques in order to improve the reliability of power losses calculation in many different kinds of environment; analytical models are going to be replaced by new Computational Fluid Dynamics (CFD) codes that seem to be more useful, especially for large offshore wind farms. In the present work an actuator disc model was implemented in order to simulate the wakes of a wind farm; this model was used within the CFD code PHOENICS (the numerical core of the Windsim package) working with an orthogonal Cartesian grid. The model was validated using real production data from a small wind farm operating in the western coastal region of Finland; the numerical wind speed profiles were verified using anemometer data from a mast placed near the turbines. The results demonstrate that, despite its simplicity, the actuator disc model can give very useful information when developing a wind farm in off-shore or coastal areas. This work was carried out within a cooperation between the Department of Industrial Engineering of the University of Perugia and VTT, the technical research centre of Finland. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction During the design process wake losses evaluation is an important aspect of wind park production estimation, especially for offshore wind energy. Existing numerical models to evaluate wake losses can roughly be classified in two types: analytical and physical. In some situations wind turbine wake numerical modelling could represent a fundamental step in the overall design optimization process; the calculation effort is, of course, dependent on the model resolution and reliability.
⇑ Corresponding author. Tel.: +39 075 5853709; fax: +39 075 5853703. 1
E-mail address: [email protected] (F. Castellani). Present address: Windsim – Fjordgaten 15, N-3125 Tønsberg, Norway.
0306-2619/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2012.04.039
Increasing the calculation effort it is possible to use analytical models, actuator disc models, actuator line/surface models or full rotor simulation (Table 1). Initially, simple analytical models were implemented [1]; such models can usually give good results only for simple wind farms in on-shore conditions where power losses due to wakes are lower than the effects of terrain and surface roughness. This kind of model is still in use in many engineering numerical tools for wind energy assessment such as WAsP – the Wind Atlas Analysis and Application Program [2]. When using analytical models, the estimation of wake losses is usually performed downstream the wind climatology calculations; this method does not allow to get a full description of the local wind field nor, in some cases, a good assessment of the energy losses. However, the development of the exploitation of wind energy resources in a wide range of off-shore and coastal sites has
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Glossary D Sa CT a P ni DPi Pr
rotor diameter (m) thrust force (N) thrust coefficient axial induction factor power (kW) weight parameter local pressure drop (Pa) local pressure (Pa)
mi q m1 mr A WPD Ei
local wind speed (m/s) air density (kg/m3) free stream velocity at the hub height (m/s) wind speed on the disc (m/s) rotor swept area (m2) average wind power density (kW/m2) energy percentage (%)
Table 1 Wind turbine wakes models. Name
Advantages
Disadvantages
Analytical Actuator disc
Fast and simple calculations Average calculation effort Contextual wind field and wakes simulations Coarse mesh Effects of rotation are considered (able to model wakes vortices) Contextual wind field and wakes simulations Real geometry is modelled
Wake losses calculated downstream the wind field Effects of rotation cannot be simulated Extremely simplified geometry
Actuator line/ surface Full rotor simulation
highlighted some issues when simulating wakes interactions with the main wind flow and multiple wake interactions. The fast development of many offshore and coastal wind projects is pushing the scientific community to study reliable methods for multiple wakes simulation and to reproduce the effect of different boundary layer conditions on wake propagation. For the reasons mentioned above, a great interest is taken in Computational Fluid Dynamics (CFD); this numerical technique is currently successfully applied in the wind energy industry for two main purposes: 1. simulation of the rotor aerodynamics at full scale used when developing a new rotor configuration; 2. simulation of the surface boundary layer used for wind potential assessment studies (especially for complex terrains). In order to study the wakes of a wind farm, both activities should be conducted in a unique domain; unfortunately the grid resolution that is necessary to reproduce the real rotor geometry may be too fine to model the whole wind farm area with a number of cells that could be processed through normal calculation machines. A coarse grid is necessary to model the wind farm area and the boundary layer conditions with a reasonable computation time; but this way, the full rotor simulation is impracticable. A good approximation of the real local wind field can be achieved using the actuator disc model; this model was initially developed to study not only wind turbine rotors but also propellers and helicopter rotors [3]. The actuator disc model disregards fundamental characteristics of wind turbine aerodynamics because it represents any rotor by a distributed action over the flow rather than the complex, vortical structure that a real rotor creates in the flow [4,5]. Despite its simplicity, it is often a useful representation to reproduce wind deficits and wake losses. Recently, the actuator disc model is often used to model multiple wakes in large wind farm; with its possible variations, the model
Finer mesh with high calculations effort Much more parameters for the turbine are necessary Very high calculation effort Knowledge of the geometry and many parameters for the turbine are necessary
can give a reliable description of the far wake [6] and its interaction with the main wind field and of the other wakes. The actuator disc model is very flexible and easy to implement but, especially if used with RANS (Reynolds Average Navier Stokes) solutions and the standard k–e turbulence model, it can give an under prediction of the wake effects that is larger in the near wake region [7–9]. On the contrary it requires a lower calculation effort and, if used on a Cartesian grid, it can be easily integrated with an atmospheric boundary layer simulation [10]. In the near wake region the model reliability can be improved using a different approach for the turbulence closure [11]. A better description of the real flow past the wind rotor can be achieved using the actuator line concept [12]. According to this approach each wind turbine blade is represented as a line or surface acting on the wind [7,13]; a Gaussian distribution can generally be used for the force distribution. With this approach it is possible to model wake vortices so that the implementation of the actuator line model can give a better representation of the aerodynamics of the wakes comparing to the actuator disc. Anyway the finer mesh introduces higher calculation efforts and the simulation of large wind farm can be very hard or impossible. The analysis of the far wake and of the losses within a wind farm is much more feasible using the actuator disc model and the momentum deficit over the rotor surface. In the present work, the actuator disc model is applied to simulate the wakes of a small coastal wind farm; in this test case the wake model can be very useful to investigate the influence of the local conditions of surface roughness and terrain on the mechanisms of wake expansion. The goal of such modelling technique is to develop a fast and reliable method for the estimation of the losses for different layout configurations with a calculation effort compliant with commercial computers. The work is done using the beta version of the commercial code WindSim; the analysis of the test case is used as a benchmark for the application of the actuator disc wakes model.
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Present work is done independently from the Windsim development team; the beta version of the actuator disc model is used for calculations while the post-processing is performed using a code that is not included in the commercial software but was developed by the authors. 2. Methodology 2.1. The numerical model The numerical simulation of the wind farm was implemented using the Windsim CFD (Computational Fluid Dynamics) model: a numerical code based on PHOENICS which solves the Reynolds Averaged Navier–Stokes (RANS) equations with a multigrid coupled solver (MIGAL). Windsim was initially developed to simulate the local wind field conditions along the complex Norwegian coastline; it was first applied to reproduce the surface boundary layer induced by orography and roughness singularities in order to estimate the distribution of the wind energy potential within a rectangular domain. After the wind field calculation, it is possible to estimate the power production of a wind farm layout including the effect of the turbine’s wake through the application of an analytical wake model. In the latest versions of the code, turbine wakes are simulated with a simple actuator disc model [14]; the axial force that can be applied on the disc surface depends on the wind speed according to the thrust coefficient curve of the aerogenerator. Since PHOENICS, the numerical CFD core, works on a Cartesian orthogonal grid, the rotor surface can be interpolated only using squared elements. The streamlines passing through the disc are affected by the power extraction and a wind velocity deficit so that the wind speed on the rotor mr is lower than the undisturbed speed m1. The theory represents this mechanism by introducing the axial induction factor:
mr ¼ ð1 aÞ m1
ð1Þ
The thrust coefficient for the whole rotor CT is defined as:
CT ¼ 1
Sa
q m21 A 2
:
ð2Þ
where Sa is the thrust force, q is the air density, m1 is the free stream velocity at the hub height and A is the rotor swept area. In this way it is possible to estimate the force that has to be introduced against the wind on the rotor surface (that is modelled as a group of cells on which the kinetic energy is extracted) for each different wind flow condition. The calculation domain for the simulation of the whole wind farm is divided into a coarse area and a refined area (Fig. 1): the turbines are defined by the cells on which the thrust is applied in the refined area in order to reproduce the turbine wakes. The coarse area is necessary to simulate the main wind field blowing on the wind farm area on a mesoscale; in the refined area, the interaction between the wind field and the turbine wakes can be evaluated on a local scale. In this way, the force on the rotor can be applied and simulated within the CFD-RANS solution so that the real wind distribution and wake extension can be evaluated directly after the numerical CFD iterations. In the Windsim actuator disc model, three different types of force distribution can be used: uniform distribution; parabolic distribution; polynomial distribution.
Fig. 1. The grid architecture.
Since the uniform distribution is the easiest and gives results that can be directly compared with the analytical solution, this configuration was used in the present work to simulate the wakes of a small coastal wind farm in Finland. A matlab post-processing tool was developed for the calculation of the power production from each turbine using two different algorithms: the power curve method and the integral method. With the first method, the power is estimated using the mean wind speed mr calculated for each modelled rotor and then evaluating the undisturbed wind speed with the following formula:
mr
m1 ¼
ð3Þ
ð1 aÞ
The production of each turbine is then estimated from the power curve. Unfortunately the value of the axial induction factor is not provided by the turbine manufacturer and can only be evaluated from the thrust coefficient using the following relationship from the Betz Theory:
C t ¼ 4að1 aÞ
ð4Þ
With the second method, the power for the disc can also be directly estimated using the local wind speed and the maximum pressure drop across the rotor so that from one-dimensional analysis:
P¼
Z
m dP dA ffi
X
ni DPi mi
ð5Þ
A
where ni is a weight parameter used to consider the discretisation related to the chosen grid resolution, DPi is the local pressure drop and mi is the local wind speed. The integral on the rotor swept surface can be approximated with a discrete approach; in this case, the resolution of the interpolation should be consistent with the CFD grid resolution. The value of the specific power obtained in each point inside the rotor should be weighted according to the portion of the area that each point can represent in order to than evaluate the overall value of the power.
F. Castellani, A. Vignaroli / Applied Energy 101 (2013) 432–440 Table 2 CFD model characteristics. Resolution
Actuator cells
Actuator area/rotor area
Overall cells
D/6 D/10 D/12 D/14
32 80 112 156
1.05 0.94 0.92 0.94
904,704 2,775,072 4,149,530 6,243,930
The grid resolution is a key parameter in the overall process: a higher resolution can give more realistic results but can make the calculus very hard because of the higher number of cells (Table 2). However, it is recommended to use a grid resolution in the refined area very near D/16 (where D is the rotor diameter) [14]; this value was obtained from a test simulation that was done on a simple model with a single actuator disc. In the present work, a brief analysis of the influence of the grid resolution was performed on the wind farm model: the wind profiles and the pressure trends upstream and downstream the rotor of the first aerogenerator placed up to the wind were analyzed in order to select the right grid resolution. Fig. 2 shows a great difference both in the trend and in the pressure drop estimation between the results obtained with a resolution
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of D/6 and D/10; even if the minimum grid resolution seems to be D/ 10, the final chosen grid configuration corresponded to a resolution of D/12. This is consistent with the results of the previous study in [14] because of the different rotor dimensions. An observation of the vertical profiles (Fig. 3) downstream the rotor confirms the validity of the results obtained with a minimum grid resolution of D/12; this result seems to be in good agreement with experimental measurements [15]. The core of the wake is well represented only with a good grid resolution: the actuator disc model is not able to give useful results in the near-wake region (less than 2D downstream) but, in order to estimate the power losses in the most reliable way, a very good representation of the wind field in the far wake should be achieved. In this work, the RNG-ke model was used for the turbulence closure; such model ensures a better convergence of the calculus and can give useful results for the estimation of the power extracted by the wind rotor [16]. 2.2. The site In order to validate the numerical method, a wind farm site has been analyzed: wind data and production data were available for a
Fig. 2. Horizontal profiles of normalized pressure
Pr 1=2qm21
for different grid resolutions.
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Fig. 3. Vertical wind profile upstream and downstream the rotor with different grid resolutions.
Fig. 4. Map of the site.
meaningful period and were collected by VTT. The site under investigation is located in the archipelago near the city of Pori, in Western Finland. Along a road connecting one of the islands to the mainland, four 1 MW Bonus wind turbines have been in operation since 1999 (Fig. 4). The hub height of the turbine is 62 m and the rotor diameter is 54 m. VTT has been monitoring the wind conditions on the site using a met mast equipped with sensors at hub height ± radius. The site is complex because of the sudden changes of roughness between the sea and the forest covering almost all the islands of the archipelago and the surroundings of the aerogenerators. The grid resolution for the CFD simulations varied with the different models implemented, starting from 3.8 up to 200 m with the refined model and 8.8 up to 302 m with the coarse model. Fig. 5 shows the terrain elevation and the roughness length for the calculation domain: roughness lengths from 0.0001 m (sea surface) up to 1 m (urban-forested areas) were assigned both for CFD and WAsP. Even if a specific forest model is available in WindSim, forested areas were treated as higher roughness area without introducing a porous volume.
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Fig. 5. Terrain elevation (left) and roughness length (right) (m) with the box representing the area from Fig. 4.
2.3. The experimental dataset Failure and production statistics of wind power in Finland are maintained at VTT. Monthly production data and downtime data are thus available for the four turbines under examination. By dividing the monthly production by the availability of the machine it is possible to obtain an estimate of the production of the turbine during the generation time for the entire month. The wind data available on the site have been analyzed in order to find a representative monthly dataset characterized by an energy rose with a prevalent direction such that three of the four wind turbines were producing behind the first one in the row. March 2000 was assumed as a representative month and the energy rose for that month can be seen in Fig. 6 together with the wake-disturbed sectors. The energy rose indicates the percent of total available wind energy as a function of direction and it can be defined as:
Ei ¼ 100
Ni WPDi ð%Þ N WPD
ð6Þ
where Ni is the number of records in direction sector i, N is the total number of records, WPD is the average wind power density defined as:
WPD ¼
N 1 X qV 3j 2N j¼1
where Vj is the wind speed for record j.
ð7Þ
Table 3 Distance of the turbines from the met mast. Distance from met mast (nr. of diameters) T1 T2 T3 T4
2.4 6.6 11 15.7
At the same time WPDi is the average wind power density in direction sector i. Production figures were available only on a monthly basis. Wind statistics measured by the meteorological mast have been used to select which month had wind conditions favorable to maximize wake losses and to minimize the time during which measurements were affected by the wakes from the 4 turbines. Wake disturbed sectors were assessed using the procedure described in IEC 61400-12-1: Annex A [17]. Production statistics were extracted from VTT’s database for the same month. According to the shape of the energy rose, T4 is the turbine less affected by the production losses due to the wake effect (see Figs. 4 and 6), and this is confirmed by measurements. The production of each turbine was divided by the production of T4 in order to quantify of the array efficiency and to be able to compare it with simulations. The meteorological mast is placed 2.4D downstream the turbine nr. 1 in the 270° direction sector (Table 3). 3. Results and discussion
Fig. 6. Energy rose and wake disturbed sectors at the mast position.
Several simulations of the wind blowing from the main direction sectors were performed using a domain of more than 4 millions of cells and the RNG-ke turbulence closure model; the rotors were defined within a grid spaced at 4.5 m (D/12). For the boundary conditions a height of 500 m and a wind speed of 10 m/s above the boundary layer were applied for each modelled direction sector; in this way the free stream conditions at hub height are very near to 6 m/s representing the average value observed in the anemometer dataset. The different energy output for the wind turbines is due only to the wake interactions: disregarding wakes differences in the estimation of the gross energy available calculated for the wind turbines positions are below 1%.
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Fig. 7. Numerical vs experimental wind profiles downstream T1.
Table 4 Results for the power loss estimation. Power % with the integral method 330°
T4 T3 T2 T1
Power % with the power curve method 190°
330°
190°
Rotated
Not rotated
Rotated
Not rotated
Rotated
Not rotated
Rotated
Not rotated
100.00 85.29 75.74 85.56
100.00 71.09 51.78 55.74
96.72 93.04 100.00 87.59
87.17 93.35 100.00 94.97
100.00 98.19 95.04 96.25
100.00 75.69 65.15 69.99
100.00 96.33 97.92 88.71
92.33 93.09 100.00 95.36
Only the main direction sectors affected by wakes were considered to estimate the mean wake effect to be compared with experimental data from the chosen monthly database: 10°, 190°, 330° and 350°. For each sector the power extracted by each rotor was estimated using the post-processing tool and the wakes losses were calculated with respect to the upstream turbine. Results from different sectors were finally weighted according to the energy percentage measured by the anemometer in the monthly database. In this way numerical wake calculations can be compared to the results from the monthly production dataset. Anyway using such procedure some sources of errors were introduced:
1. for orthogonal domains it is possible to have 1 inlet, 1 outlet and 2 frictionless walls; 2. for non-orthogonal domains 2 inlets and 2 outlets are defined. With this grid architecture, it is possible to simulate the actuator discs exactly faced to the wind only for orthogonal sectors; in non-orthogonal situations the axial force is also distributed in a sort of cross surface obtained from two orthogonal rotors: one facing the north–south direction and one facing the east–west direction. Such technique was developed to allow the simulation of all directions [19] also when introducing the effect of the thrust on the rotors; however, the geometry is not well reproduced in the case of non-orthogonal winds.
1. the anemometer dataset can be affected by the wakes (even if the major part of the energy was distributed in undisturbed sectors a meaningful percentage of energy was also observed for blocked sectors); 2. simulations were performed using only one value of the wind speed but wakes can be strongly affected by this parameter due to the thrust coefficient variations; 3. only neutral atmospheric conditions were considered. The anemometer used to validate the numerical model is placed 2.4 diameters downstream the turbine T1 in the 270° sector (Fig. 4). The numerical results from the 270° and 330° sectors were used to compare the numerical and the measured wind speed profiles (Fig. 7); the good agreement found seems to confirm the reliability of the actuator disc model to predict the speed deficit in the far wake. Other sectors were modelled too and the wakes for each direction were characterized evaluating the array efficiency (actual power/max power) in the same way as for the experimental dataset. When the blowing direction changes, Windsim can apply different strategies to manage the boundary conditions [18]:
Fig. 8. Comparison of the wake losses calculated with WAsP and with the actuator disc model.
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Fig. 9. Comparison of the wind profile 2.5 diameter downstream calculated with different wake models.
The monthly reference database (March 2000) has two nonorthogonal main directions: 330° and 190°. In the present work, when simulating the non-orthogonal cases, two different calculation methods were compared:
A further improvement of the model will be undertaken through a detailed turbulence analysis: the turbulence induced by the wake can spread up to 15 diameters downstream the turbine [22].
1. using the conventional domain geometry and distributing the axial force on the cross surface (usually used by Windsim); 2. rotating the terrain and roughness model so that the calculations can be performed referring to orthogonal cases and all the rotors can be represented exactly facing the wind.
4. Conclusions
The results of Table 4 demonstrate that the model is very sensible to the boundary conditions and that the method used to calculate the turbine power can slightly change the results. For the actuator disc, the most reliable results were obtained using a rotated domain and the integral method for the power estimation; the results obtained with this technique are presented hereafter. An estimation of the overall array efficiency was obtained using the results for each sector and the energy rose distribution; these results were also compared in Fig. 8 with the estimations made with the analytical wake model of WAsP. The default standard settings for the WAsP wind flow model (version 8.4) were used for the simulation; the results were calculated under neutral boundary layer conditions and using the default wake decay constants in the PARK wake model. A very good agreement with the experimental data was found. The improvement of the results by comparing them to the analytical model should be addressed mainly to the possibility for the CFD actuator model to reproduce the wind field at the beginning of the far wake in a reliable way. The numerical wind profile 2.4 diameters downstream calculated through CFD is clearly more realistic than the profile considered in the Park Wake model used by WAsP (Fig. 9). The boundary of transition between the near wake and the far wake region was discussed by many authors [4,5,7]; a reliable definition of such boundary measured in number of turbine diameters cannot really be defined because of its general dependence on the atmospheric flow conditions. The near wake extends from the disc to two or three diameter downstream [4,5,15,20] but it can even reach a distance up to 5 diameters [21]. The energy exchanges between the wakes and the main stream can only be modelled in a reliable way using a realistic description of the wind field within the wake area; this would allow a better prediction of wakes propagation in the whole wind farm.
In the present work, the application of the actuator disc model for the simulation of wind turbine wakes within a CFD code was experimented on a test case of a small coastal wind farm. Results demonstrate that such technique can indeed be very useful to simulate the wind turbine wakes and their interaction with the main wind field. The accuracy of the proposed model was found to be higher than the one of traditional analytical wake models. The model is not proposed for an exhaustive wake simulation but for an estimation of the power losses of a wind farm through a reliable prediction of the far wake characteristics. The proposed model is suited to simulate wake–wake interaction and effects in different shear conditions [23,24]. A key feature for this technique should be the possibility to obtain good results in a very fast way in order to be attractive for industrial applications, even for large offshore wind farms; this could be very useful to investigate the shadow effects between different layouts of a wind turbine park [25,26]. However, the post-processing downstream the CFD calculus was found to be a fundamental part of the model. Many improvements can still be added to the model, such as: introducing different kinds of thrust force distribution in order to reproduce some known effects like the edge interaction; developing the simulation of turbulence using different models; introducing rotational effects. The post-processing phase could also be improved by developing the weighting algorithm and by using higher resolutions. The actuator disc model can be very useful to perform a comprehensive simulation of a wind farm wake but it is intrinsically affected by errors in the near wake region; this is due not only to the lack of geometric representation of the rotor, but also to the inability of the model to reproduce the physics of the problem [27]. References [1] Katic I, Højstrup J, Jensen NO. A simple model for cluster efficiency. In: EWEC proceedings, 7–9 – October 1986, Rome, Italy; 1986. [2] WAsP – The wind atlas analysis and application program.
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[3] Van Kuik GAM. On the limitations of Froude’s actuator disc concept. PhD Thesis, Technical University of Eindhoven Doctoral Thesis; 1991. [4] Vermeer LJ, Sørensen JA, Crespo A. Wind turbine wake aerodynamics. Prog Aerospace Sci 2003;39:467–510. [5] Sanderse B. Aerodynamics of wind turbine wakes – Literature review. Energy research centre of the Netherlands.
[16] Mansour K, Yahyazade M. Effects of turbulence model in computational fluid dynamics of horizontal axis wind turbine aerodynamic. WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANIC 2011;6(3). ISSN: 1991-8747. [17] IEC 61400-12 WIND TURBINES – Part 12-1: power performance of electricity producing wind turbines; 2006. [18] Castellani F, Vignaroli A, Gravdahl AR. Wind simulation on complex terrain: about the dependencies on inlet flow orthogonality. In: European wind energy conference & exhibition proceedings – Athens, Greece, 27 February–2 March 2006. [19] Castellani F. Grid control for CFD wakes simulation in complex terrains. In: European Wind Energy Conference & Exhibition Proceedings – Parc Chanot, Marseille, France, 16–19 March 2009. [20] Manwell JF, McGowan JG, Rogers AL. Wind energy explained: theory, design and application. John Wiley & Sons, Ltd.; 2002. [21] Zahle F, Sørensen NN. On the influence of far-wake resolution on wind turbine flow simulations. Sci Making Torque Wind – J Phys: Conf Series 2007;75: 012042. [22] Højstrup J. Spectral coherence in wind turbine wakes. J Wind Eng Indus Aerodyn 1999;80:137–46. [23] Crasto G, Castellani F, Gravdahl AR, Piccioni E. Offshore wind energy prediction through CFD simulation and the actuator disc model. In: European wind energy conference & exhibition proceedings – Brussels Expo, Belgium, 14–17 March 2011. [24] Castellani F, Crasto G, Gravdahl AR. Actuator disc wind turbine wakes simulation: about the dependences on the wind shear conditions. 1° Convegno Nazionale di Ingegneria del Vento – INVENTO 2010 – Spoleto 30 Giugno-3 Luglio; 2010. ISBN: 978-88-6074-330-5. [25] Frandsen S, et al. The shadow effect of large wind farms: measurements, data analysis and modelling. Report from RisøNational Laboratory for Sustainable Energy – Risø-R1615(EN); 2007. [26] Barthelmie RJ et al. Flow and wakes in large wind farms: Final report for UpWind WP8. Report from RisøNational Laboratory for Sustainable Energy – Risø-R1765(EN); 2011. [27] Réthoré P-E, Sørensen NN, Bechmann A. Modelling issues with wind turbine wake and atmospheric turbulence. Sci Making Torque Wind 2010.