A systematic validation procedure for wind farm models in neutral ...
A systematic validation procedure for wind farm models in neutral atmospheric conditions Javier Sanz Rodrigo a, Daniel Cabezón Martínez b, Bibiana García Hevia c a
National Renewable Energy Centre of Spain (CENER), Sarriguren, Spain, [email protected] b CENER, Sarriguren, Spain, [email protected] c CENER, Sarriguren, Spain, [email protected]
1 INTRODUCTION Over the past ten years modelling with Computational Fluid Dynamics (CFD) has boomed in the wind resource assessment community with a large number of commercial and research tools. CFD constitute a clear alternative to traditional linearized/algebraic models especially for complex terrain sites and wind turbine wakes. Yet, the transition from linearized models requires significant training and experience from the user. To overcome user-dependency it is of utmost importance to follow proper model verification and validation on well defined test cases. Even though the number of high quality test cases is still very limited, there are some references for benchmarking. Present paper summarizes these references in order to propose a hierarchical validation procedure. A survey of test cases is presented together with some simulation results based on steady-state RANS modelling in neutral ABL conditions. 2 VERIFICATION/VALIDATION TEST CASES The credibility of a model is built upon two essential principles: verification and validation (V&V), as defined by the AIAA (1998). Verification examines if the model implementation accurately represents the developer’s conceptual description of the model. Validation determines the degree to which the model is an accurate representation of the real world from the perspective of the intended uses of the model. Present paper summarizes a set of test cases, based on field measurements, that has been used by the authors when implementing CFD wind farm models for wind resource assessment (Table 1). In this context, the aim of the models is to predict the annual energy production. The test cases are provided in hierarchical order of complexity. For example, before assessing the flow around hills the model is verified first in flat terrain against atmospheric boundary layer (ABL) theory and horizontally homogeneous ABL experiments. Then, terrain of different complexities is added. Embedded in the ABL model, wind turbine wake models, based on the actuator disk concept, are tested first with a single wind turbine, then with a line and a matrix of them in flat terrain and finally with a matrix of turbines in complex terrain.
Table 1: List of test cases used for validation of wind farm models in wind resource assessment Test Case Description ABL, Flow over hills Monin-Obukhov Theory, Homogeneous and steady-state surface layer in flat terrain flat terrain Homogeneous and steady-state atmospheric boundary layer in flat Leipzig ABL, flat terrain terrain Gentle 126m-high hill with flat upstream conditions. Longitudinal Askervein hill, mild terrain and transversal velocity profiles at ~50x10m met masts. Bolund hill, complex Isolated 12m-high hill with escarpment. Well defined boundary terrain conditions. Flux-profile measurements at 10 met masts Wind Turbine Wakes Sexbierum, Single wake 1x300kW, 30m diameter, 35m hub height, masts at -2.8D, 2.5D, in flat terrain 5D and 8D Wieringermeer Test Wind Farm (ECN) 5x2.5MW Nordex N80, 2x100m + 1x108m met masts Wind turbine raw in flat terrain Horns Rev 80x2MW Vestas V80, 7Dx7D matrix, 1 upwind and 2 downwind (Vattenfall/Dong), masts Offshore Wind Farm UpWind wind farm in 43 turbines, 48.4m diameter, 45&55m hub height, 5 lines complex terrain 11Dx1.5D, 1 met mast
Reference Alinot and Masson (2005) Detering and Etling (1985) Taylor and Teunissen (1987) Bechmann et al. (2009, 2011) Cleijne (1983) Barthelmie et al. (2011), Prospathopoulos et al. (2010) Barthelmie et al. (2011), Hansen et al. (2010) Barthelmie et al. (2011), Politis et al. (2011)
3 ATMOSPHERIC BOUNDARY LAYER MODELING: CFDWIND 3.1 Surface Layer Model: CFDWind 1.0 The modelling of the neutral ABL is typically limited in Computational Wind Engineering (CWE) to the surface boundary layer wherein Monin Obukhov (M-O) similarity theory applies in homogeneous and steady-state conditions, leading to the well known logarithmic velocity profile (U) and a height-independent shear stress, turbulent kinetic energy (k) and wind direction (Coriolis effects are neglected). The turbulent dissipation rate (ε) decays with the inverse of the height above the ground: U=
z ln κ z0
u*
u*2 u*3 ; tke = k = ; tdr = ε = κz Cµ
(1)
where κ=0.41 is the von Karman constant, u* is the friction velocity and z0 is the roughness length. Turbulence closure is achieved using K-theory and RANS turbulence closures, typically of the first-order, as a cost effective alternative to LES-based models. The M-O profiles can be used as solution of the standard k-ε model, ∂k ∂(kui ) ∂ + = ∂t ∂xi ∂x j
ν t ∂k + Gk − ε σ k ∂x j
∂ε ∂(ε ui ) ∂ + = ∂t ∂xi ∂x j
ν t ∂ε ε ε2 + C1ε Gk − C2ε σ ε ∂x j k k
(2)
where νt is the turbulent viscosity and Gk the production of tke by wind shear, to obtain a relationship between the k-ε constants (Richards and Hoxey, 1993):
σ ε Cµ (C2ε − C1ε ) = κ 2
(3)
This model is called by the authors CFDWind 1.0 and is implemented in the commercial CFD solver Fluent 12.0 using modified wall functions to account for the aerodynamic roughness length of the terrain as proposed by Blocken (2007). The model is verified following the approach of Alinot and Masson (2005): a 1 km long 2D empty domain is simulated using M-O profiles as inlet conditions. If the model is in equilibrium with the boundary conditions the profiles should be maintained unaltered throughout the domain as shown in Figure 1 for an offshore roughness length. A sensitivity analysis is presented considering different wall-adjacent-cell heights resulting in minor deviations of tke next to the ground.
Figure 1: Verification of CFDWind 1.0 in neutrally stratified horizontally homogeneous and steady state surface boundary layer. 1km-long empty domain: outlet velocity (left) and turbulent kinetic energy (right) profiles vs inlet Monin-Obukhov profiles at different first-cell height resolutions
3.2 Atmospheric Boundary Layer Model: CFDWind 2.0 In order to extend the model to the full ABL depth, it is necessary to include Coriolis effects and to limit the growth of turbulence with height, as demonstrated by Detering and Etling (1985) with the simulation of the Leipzig wind profile (1950). This is achieved in the k-ε by adopting the Apsley and Castro (1994) correction on the Cε1 constant:
C ε' 1 = Cε 1 + ( Cε 2 − Cε 1 )
lm lmax
(4)
where lm is the mixing length and lmax=0.00027|Sg|/fc is the maximum mixing length parameterized according to Blackadar (1962) using the magnitude of the geostrophic wind Sg and the Coriolis parameter fc. The limitation in the mixing length does not affect the surface layer, where M-O theory is fulfilled in stationary and horizontally homogeneous conditions. Figure 1 shows the results of the simulation of the Leipzig stationary and neutral wind profile (u*=0.65ms-1, z0=0.3m, Sg=17.5ms-1, fc=1.13e-4 s-1) using the limited-length-scale k-ε model of Apsley and Castro (1994) (so called CFDWind 2.0), compared with the results obtained by the unlimited standard k-ε model (CFDWind 1.0) and a mixing length model which uses a prognostic equation for lm (5) instead of the ε equation.
1 1 1 = + lm κ z lmax
(5)
Figure 2: Verification of horizontally homogeneous and steady state ABL in neutral conditions. Leipzig profile: velocity components (left), turbulent viscosity (right)
The standard k-ε model produces too much mixing in the upper part of the ABL, resulting in a much deeper ABL height. Both the mixing-length and the limited-length-scale k-ε models are able to reproduce the Leipzig wind profile fairly well. The advantage of two-equation turbulence models over one-equation (mixing-length) turbulence models is put in evidence in complex terrain where the mixing length in the lower part of the boundary layer is greatly modified by the terrain topology. 4 FLOW OVER HILLS The Askervein hill project can be considered the cornerstone of boundary layer flow over hills. It is based on two field campaigns conducted in 1982 and 1983 (Taylor and Teunissen, 1987) on a 126 m high smooth hill with flat surroundings in the prevailing wind direction. Over 50 towers were deployed and instrumented for wind speed and turbulence measurements. Many CFD simulations of the Askervein hill test case have been published, for example: Castro et al. (2003) based on RANS modelling and Silva et al. (2007) based on LES. The slopes of the hill are just under the limit for flow detachment and therefore good results can be obtained with linearized models in the windward side and on the hilltop. In the lee side of the hill the flow is highly nonlinear and CFD models are required. Figure 3 shows the results of the 210º wind direction run along the lines A and AA for the 10m mean wind speed and tke. While the mean flow field is correctly reproduced, the tke is underestimated at the hill top and in the wake of the hill. This deficiency is attributed to the limited applicability of isotropic turbulence models in wake flows as much better agreement is found with LES models (Silva et al., 2007). In 2009, a blind comparison of models around the Bolund experiment (2007-08) in complex terrain was organized by Risφ-DTU (Bechmann et al., 2009, 2011). Bolund is a 12m high coastal hill with a sharp escarpment in the prevailing wind directions, making it an ideal case for testing flow models in complex terrain. Ten met masts, equipped with cup and sonic anemometers were deployed. The blind comparison gathered more than 50 model runs including wind tunnel and LES simulations. The scatter of the results was quite significant (Bechmann et al., 2011) and the
best performing models, based on RANS 2-equation approach, had an overall error of 22% in the tke and 10% in the fractional speed-up ratio, defined as: FSRZ =
( S / u*0 )z − ( S0 / u*0 )z (S0 / u*0 )z
(6)
where S is the wind speed magnitude.
Figure 3: Askervein hill test case and validation of fractional speed-up ratio and tke along the A (left) and AA lines (right) for the 210º (TU03B)
Figure 4 shows longitudinal profiles at 2 and 5 m heights above ground level along the A (239º) and B (270º) lines of met masts using both versions of CFDWind. Given the small site dimensions it is not expected to find large differences between the two models as the region of interest is within the surface layer. Nevertheless it is interesting to confirm the consistency of CFDWind 2.0 close to the surface. As for the Askervein hill case, the mean flow is reasonably well predicted by both models, especially at the 5m level. At 2m level, the models have difficulties in predicting the flow recirculation area just after the escarpment (M2, M6) and in the wake of the hill (M4, M8). Turbulence is also not well captured in these regions where the flow shows large curvature and anisotropy. The escarpment, almost at 90º with respect to the incoming flow, creates an impingement region where the flow is greatly decelerated. This is a well known situation for
flow around buildings where k-ε models tend to overpredict the production of tke (Murakami et al., 1999). This leads to enhanced mixing and a quicker recovery of the flow in the wake of the obstacle.
Figure 4: Bolund hill test case and validation of fractional speed-up ratio and tke increment along the A (top) and B lines (down) for 239º (case 3) and 270º (case 1) runs
5 WIND FARM WAKES MODELING: CFDWAKE Embedded in the ABL model, a wake model simulates the momentum sink that generates wind power deficit and added turbulence downstream of wind turbines. A review of wind turbine wake models can be found in Crespo et al. (1999). The actuator disk concept, based on the extraction of axial momentum by drag over a rotor disk, is the standard approach due to the limited requirements of input data (only disk geometry and thrust curve). The axial momentum sink Fx extracted at the rotor disk is: 1 Fx = − ρCt U ∞2 A 2
(7)
where ρ is the air density, A is the area of the rotor disk, Ct is the wind turbine thrust coefficient which depends on the incoming freestream velocity at hub height U∞. Inherent with this definition it is the uncertainty related to the thrust coefficient and the definition of the freestream velocity in complex terrain and wake induced flows. A Blade Element Momentum (BEM) approach can be adopted if the drag and lift coefficient data are available. These models reproduce the forces on the single blades and, therefore, are able to introduce both the axial and the rotational forces. Single wake of the Sexbierum experiment in flat terrain is the starting point for wind turbine wake models validation (Cleijne, 1993). The experiment consists on single-wake velocity measurements at axial distances -2.8D, 2.5D, 5.5D and 8D in neutral atmospheric conditions from a 30m diameter wind turbine. The freestream hub-height velocity is 10 ms-1 and the turbulence intensity is 10%. Figure 5 shows the velocity ratio and added turbulence intensity at positions 2.5D and 8D for two versions of CFDWake model (based on CFDWind 1.0). Unfortunately, no information about the variability of the ensemble measurements is available.
Figure 5: Velocity ratio and added turbulence intensity at 2.5 and 8 diameters downwind from the Sexbierum wind turbine for the k-ε and RSM versions of CFDWake model
The actuator disk model is not able to simulate correctly the near wake region, where the aerodynamics of the rotor play a more dominant role. In the far wake (>3D), where wind resource assessment is mostly focussed, the results improve, especially if RSM (Reynolds Stress Model) turbulence model is used. In effect, using RSM modelling seems to be a promising alternative in wake flows, either from wind turbines or terrain, adding anisotropy to the flow physics and still allowing a cost effective solution compared to LES. The next step in complexity would be to simulate the interaction of wind turbine wakes. First, a row of 5 wind turbines in flat terrain separated by 3.8D (ECN test wind farm in the Netherlands; Prospathopoulos et al., 2010) and then Horns Rev 7D by 7D wind farm in offshore conditions (Hansen et al., 2010) have been selected due to the good quality of the available data for validation. In large scale wind farms, the power deficit normalized with the power of the least disturbed wind turbine is selected as validation metric. This approach is the most suitable solution since intermediate met masts are typically not available and the metric is directly related to the intended use of the model, which is to simulate the wake losses for energy yield assessment. Implicit in this validation methodology is the assumption that all the wind turbines have the same response which is characterized solely by the power and thrust curves. This oversimplification constitutes a mayor drawback when analysing validation results since it is very difficult to distinguish between the deficiencies of the flow model and those of the wind turbine themselves. The only way to overcome this difficulty is by monitoring the individual response of the wind turbines and the flow in between the wind turbines. Figure 6 shows some sample results of CFDWake simulations for the ECN and Horns Rev wind farm test cases respectively. The simulations are presented for full-wake conditions, i.e. when the wind turbine rows are aligned with the incoming flow. A narrow wind direction sector of ±2.5º width and a freestream velocity close to the maximum rotor load provide a maximum wake signal. In full wake, the power drops as much as 60% in the second wind turbine and then the deficit is maintained rather uniform in the next turbines downwind. Actuator disk models seem to be able to reproduce the main futures of far wake interaction in flat terrain and neutral conditions.
Figure 6: Power deficit in ECN and Horns Rev wind farms in full wake conditions. Simulation with the k-ε version of CFDWake
Finally, wake coupling with complex terrain constitutes the most challenging case (Politis et al., 2011). In the UpWind project, data from an operational wind farm in complex terrain was used
for validation following the same methodology presented before for ECN and Horns Rev. The wind farm layout consists on a 13D by 1.5D spacing. Figure 7 shows the power deficit at different rows for the k-ε version of CFDWake and for the algebraic model PARK included in the WAsP commercial software.
Figure 7: Simulation of power deficit in a complex terrain wind farm using CFDWake and PARK models
In general, linearized models like PARK-WAsP tend to underpredict the power deficit. This is partly corrected by CFD models. The difficulty in these test cases is to separate the influence on the validation results of the flow model and the wake model. Ideally, a validation campaign for complex terrain wind farms would consist of two phases: first without wind turbines to validate the flow over terrain and then with the wind farm to analyse the added uncertainties due to wake modelling. These test cases on wind farm wakes have been intensively simulated with different state-of-theart wake models in the EU funded UpWind project (Barthelmie et al., 2011). 6 CONCLUSIONS The selection of appropriate V&V test cases is a fundamental step of any model development. A survey of test cases for V&V is provided in the context of wind resource assessment. Some test cases are readily available from the literature and some others come from experimental facilities and industrial test cases evaluated in research projects like UpWind. Still, the number of suitable test cases is very limited for a complete validation of all the aspects of the model chain. Essential in the V&V process is the adoption of a model evaluation
procedure that is mutually recognized as standard by model developers and end-users. To this end the IEA Task WAKEBENCH is under way for the definition of an evaluation protocol and best practice guidelines for wind farm models based on intercomparison benchmarks around test cases from wind tunnel experiments to test sites and operational wind farms. The V&V procedures will be largely based on the AIAA (1998) and the COST 732 (2009) guidelines. 7 ACKNOWLEDGEMENTS The authors would like to acknowledge the support from the research institutions and industrial partners that made the validation data available, an essential need of any model development. Most of the wake modeling activity has been funded under the FP6-UpWind EU project (contract number 019945). 8 REFERENCES AIAA, 1998. Guide for the Verification and Validation of Computational Fluid Dynamics Simulations, American Institute of Aeronautics and Astronautics, AIAA-G-077-1998, VA, USA Alinot, C. and Masson, C., 2005. k-ε Model for the Atmospheric Boundary Layer Under Various Thermal Stratifications, Transactions of the ASME 127: 438-443 Apsley, D.D. and Castro, I.P., 1997. A Limited-Length-Scale k-ε Model for the Neutral and Stably-Stratified Atmospheric Boundary Layer, Boundary Layer Meteorol. 83: 75-78 Barthelmie et al., 2011, UPWIND FP8 Final Activity Report, Available at: http://www.upwind.eu/, pp. 47 Bechmann, A., et al., 2009. The Bolund Experiment: Overview and Background. Technical Report RisøR1658(EN), Risø DTU, National Lab., Roskilde, Denmark Bechmann A., et al., 2011, The Bolund Experiment, Part II: Blind Comparison of Microscale Flow Models, Boundary Layer Meteorology, accepted for publication Blocken, B., Stathopoulos, T. and Carmeliet J., 2007, CFD simulation of the atmospheric boundary layer – wall function problems. Atmospheric and Environment 41-2: 238-252. Castro, F.A., Palma, J.M.L.M. and Silva Lopes, A., 2003. Simulation of the Askervein hill flow. Part I: Reynolds Averaged Navier-Stoker equations (k-ε turbulence model), Boundary-Layer Meteorology 107:501-530 Cleijne, J.W., 1993. Results of the Sexbierum Wind Farm: Single Wake Measurements, TNO Report, C19.3, The Netherlands COST 732, 2009, Model evaluation guidance and protocol document, Report of COST Action 732 on Quality assurance and improvement of microscale meteorological models. Available at: http://www.mi.unihamburg.de/COST_732.464.0.html Crespo A., et al., 1999, Survey of modeling methods for wind turbine wakes and wind farms. Wind Energy 2, 1–24 Detering, H.W., Etling D., 1985. Application of the E-ε Turbulence Model to the Atmospheric Boundary Layer, Boundary Layer Meteorology 33: 113-133 Hansen, K.H., et al., 2010, The impact of turbulence intensity and atmospheric stability on power deficits due to wind turbine wakes at Horns Rev wind farm. Submitted to Wind Energy (WE-10-0149). Murakami S., et al., 1999, CFD analysis of wind climate from human scale to urban scale, J. Wind Eng. Ind. Aerodyn. 81: 57-81 Politis, E., et al., 2011. Modelling wake effects in large wind farms in complex terrain: the problem, the methods and the issues. Acepted in Wind Energy (WE-10-0103) Prospathopoulos, J.M., et al., 2010, Evaluation of the effects of turbulence model enhancements on wind turbine wake predictions, Wind Energy, DOI: 10.1002/we.419 Richards, P.J. and Hoxey, R., 1993. Appropriate boundary conditions for computational wind engineering models using the k–ε turbulence model, J. Wind Eng. Ind. Aerodyn. 46-47: 145–153 Silva Lopes, A., et al., 2007. Simulation of the Askervein flow. Part 2: Large-eddy simulations, Boundary-Layer Meteorology 125:85-108 Taylor, P. and Teunissen, H., 1987. The Askervein Hill Project: Overview and Background Data, Boundary-Layer Meteorology 39:15-39
National Renewable Energy Centre of Spain (CENER), Sarriguren, Spain, [email protected] b CENER, Sarriguren, Spain, [email protected] c CENER, Sarriguren, Spain, [email protected]
1 INTRODUCTION Over the past ten years modelling with Computational Fluid Dynamics (CFD) has boomed in the wind resource assessment community with a large number of commercial and research tools. CFD constitute a clear alternative to traditional linearized/algebraic models especially for complex terrain sites and wind turbine wakes. Yet, the transition from linearized models requires significant training and experience from the user. To overcome user-dependency it is of utmost importance to follow proper model verification and validation on well defined test cases. Even though the number of high quality test cases is still very limited, there are some references for benchmarking. Present paper summarizes these references in order to propose a hierarchical validation procedure. A survey of test cases is presented together with some simulation results based on steady-state RANS modelling in neutral ABL conditions. 2 VERIFICATION/VALIDATION TEST CASES The credibility of a model is built upon two essential principles: verification and validation (V&V), as defined by the AIAA (1998). Verification examines if the model implementation accurately represents the developer’s conceptual description of the model. Validation determines the degree to which the model is an accurate representation of the real world from the perspective of the intended uses of the model. Present paper summarizes a set of test cases, based on field measurements, that has been used by the authors when implementing CFD wind farm models for wind resource assessment (Table 1). In this context, the aim of the models is to predict the annual energy production. The test cases are provided in hierarchical order of complexity. For example, before assessing the flow around hills the model is verified first in flat terrain against atmospheric boundary layer (ABL) theory and horizontally homogeneous ABL experiments. Then, terrain of different complexities is added. Embedded in the ABL model, wind turbine wake models, based on the actuator disk concept, are tested first with a single wind turbine, then with a line and a matrix of them in flat terrain and finally with a matrix of turbines in complex terrain.
Table 1: List of test cases used for validation of wind farm models in wind resource assessment Test Case Description ABL, Flow over hills Monin-Obukhov Theory, Homogeneous and steady-state surface layer in flat terrain flat terrain Homogeneous and steady-state atmospheric boundary layer in flat Leipzig ABL, flat terrain terrain Gentle 126m-high hill with flat upstream conditions. Longitudinal Askervein hill, mild terrain and transversal velocity profiles at ~50x10m met masts. Bolund hill, complex Isolated 12m-high hill with escarpment. Well defined boundary terrain conditions. Flux-profile measurements at 10 met masts Wind Turbine Wakes Sexbierum, Single wake 1x300kW, 30m diameter, 35m hub height, masts at -2.8D, 2.5D, in flat terrain 5D and 8D Wieringermeer Test Wind Farm (ECN) 5x2.5MW Nordex N80, 2x100m + 1x108m met masts Wind turbine raw in flat terrain Horns Rev 80x2MW Vestas V80, 7Dx7D matrix, 1 upwind and 2 downwind (Vattenfall/Dong), masts Offshore Wind Farm UpWind wind farm in 43 turbines, 48.4m diameter, 45&55m hub height, 5 lines complex terrain 11Dx1.5D, 1 met mast
Reference Alinot and Masson (2005) Detering and Etling (1985) Taylor and Teunissen (1987) Bechmann et al. (2009, 2011) Cleijne (1983) Barthelmie et al. (2011), Prospathopoulos et al. (2010) Barthelmie et al. (2011), Hansen et al. (2010) Barthelmie et al. (2011), Politis et al. (2011)
3 ATMOSPHERIC BOUNDARY LAYER MODELING: CFDWIND 3.1 Surface Layer Model: CFDWind 1.0 The modelling of the neutral ABL is typically limited in Computational Wind Engineering (CWE) to the surface boundary layer wherein Monin Obukhov (M-O) similarity theory applies in homogeneous and steady-state conditions, leading to the well known logarithmic velocity profile (U) and a height-independent shear stress, turbulent kinetic energy (k) and wind direction (Coriolis effects are neglected). The turbulent dissipation rate (ε) decays with the inverse of the height above the ground: U=
z ln κ z0
u*
u*2 u*3 ; tke = k = ; tdr = ε = κz Cµ
(1)
where κ=0.41 is the von Karman constant, u* is the friction velocity and z0 is the roughness length. Turbulence closure is achieved using K-theory and RANS turbulence closures, typically of the first-order, as a cost effective alternative to LES-based models. The M-O profiles can be used as solution of the standard k-ε model, ∂k ∂(kui ) ∂ + = ∂t ∂xi ∂x j
ν t ∂k + Gk − ε σ k ∂x j
∂ε ∂(ε ui ) ∂ + = ∂t ∂xi ∂x j
ν t ∂ε ε ε2 + C1ε Gk − C2ε σ ε ∂x j k k
(2)
where νt is the turbulent viscosity and Gk the production of tke by wind shear, to obtain a relationship between the k-ε constants (Richards and Hoxey, 1993):
σ ε Cµ (C2ε − C1ε ) = κ 2
(3)
This model is called by the authors CFDWind 1.0 and is implemented in the commercial CFD solver Fluent 12.0 using modified wall functions to account for the aerodynamic roughness length of the terrain as proposed by Blocken (2007). The model is verified following the approach of Alinot and Masson (2005): a 1 km long 2D empty domain is simulated using M-O profiles as inlet conditions. If the model is in equilibrium with the boundary conditions the profiles should be maintained unaltered throughout the domain as shown in Figure 1 for an offshore roughness length. A sensitivity analysis is presented considering different wall-adjacent-cell heights resulting in minor deviations of tke next to the ground.
Figure 1: Verification of CFDWind 1.0 in neutrally stratified horizontally homogeneous and steady state surface boundary layer. 1km-long empty domain: outlet velocity (left) and turbulent kinetic energy (right) profiles vs inlet Monin-Obukhov profiles at different first-cell height resolutions
3.2 Atmospheric Boundary Layer Model: CFDWind 2.0 In order to extend the model to the full ABL depth, it is necessary to include Coriolis effects and to limit the growth of turbulence with height, as demonstrated by Detering and Etling (1985) with the simulation of the Leipzig wind profile (1950). This is achieved in the k-ε by adopting the Apsley and Castro (1994) correction on the Cε1 constant:
C ε' 1 = Cε 1 + ( Cε 2 − Cε 1 )
lm lmax
(4)
where lm is the mixing length and lmax=0.00027|Sg|/fc is the maximum mixing length parameterized according to Blackadar (1962) using the magnitude of the geostrophic wind Sg and the Coriolis parameter fc. The limitation in the mixing length does not affect the surface layer, where M-O theory is fulfilled in stationary and horizontally homogeneous conditions. Figure 1 shows the results of the simulation of the Leipzig stationary and neutral wind profile (u*=0.65ms-1, z0=0.3m, Sg=17.5ms-1, fc=1.13e-4 s-1) using the limited-length-scale k-ε model of Apsley and Castro (1994) (so called CFDWind 2.0), compared with the results obtained by the unlimited standard k-ε model (CFDWind 1.0) and a mixing length model which uses a prognostic equation for lm (5) instead of the ε equation.
1 1 1 = + lm κ z lmax
(5)
Figure 2: Verification of horizontally homogeneous and steady state ABL in neutral conditions. Leipzig profile: velocity components (left), turbulent viscosity (right)
The standard k-ε model produces too much mixing in the upper part of the ABL, resulting in a much deeper ABL height. Both the mixing-length and the limited-length-scale k-ε models are able to reproduce the Leipzig wind profile fairly well. The advantage of two-equation turbulence models over one-equation (mixing-length) turbulence models is put in evidence in complex terrain where the mixing length in the lower part of the boundary layer is greatly modified by the terrain topology. 4 FLOW OVER HILLS The Askervein hill project can be considered the cornerstone of boundary layer flow over hills. It is based on two field campaigns conducted in 1982 and 1983 (Taylor and Teunissen, 1987) on a 126 m high smooth hill with flat surroundings in the prevailing wind direction. Over 50 towers were deployed and instrumented for wind speed and turbulence measurements. Many CFD simulations of the Askervein hill test case have been published, for example: Castro et al. (2003) based on RANS modelling and Silva et al. (2007) based on LES. The slopes of the hill are just under the limit for flow detachment and therefore good results can be obtained with linearized models in the windward side and on the hilltop. In the lee side of the hill the flow is highly nonlinear and CFD models are required. Figure 3 shows the results of the 210º wind direction run along the lines A and AA for the 10m mean wind speed and tke. While the mean flow field is correctly reproduced, the tke is underestimated at the hill top and in the wake of the hill. This deficiency is attributed to the limited applicability of isotropic turbulence models in wake flows as much better agreement is found with LES models (Silva et al., 2007). In 2009, a blind comparison of models around the Bolund experiment (2007-08) in complex terrain was organized by Risφ-DTU (Bechmann et al., 2009, 2011). Bolund is a 12m high coastal hill with a sharp escarpment in the prevailing wind directions, making it an ideal case for testing flow models in complex terrain. Ten met masts, equipped with cup and sonic anemometers were deployed. The blind comparison gathered more than 50 model runs including wind tunnel and LES simulations. The scatter of the results was quite significant (Bechmann et al., 2011) and the
best performing models, based on RANS 2-equation approach, had an overall error of 22% in the tke and 10% in the fractional speed-up ratio, defined as: FSRZ =
( S / u*0 )z − ( S0 / u*0 )z (S0 / u*0 )z
(6)
where S is the wind speed magnitude.
Figure 3: Askervein hill test case and validation of fractional speed-up ratio and tke along the A (left) and AA lines (right) for the 210º (TU03B)
Figure 4 shows longitudinal profiles at 2 and 5 m heights above ground level along the A (239º) and B (270º) lines of met masts using both versions of CFDWind. Given the small site dimensions it is not expected to find large differences between the two models as the region of interest is within the surface layer. Nevertheless it is interesting to confirm the consistency of CFDWind 2.0 close to the surface. As for the Askervein hill case, the mean flow is reasonably well predicted by both models, especially at the 5m level. At 2m level, the models have difficulties in predicting the flow recirculation area just after the escarpment (M2, M6) and in the wake of the hill (M4, M8). Turbulence is also not well captured in these regions where the flow shows large curvature and anisotropy. The escarpment, almost at 90º with respect to the incoming flow, creates an impingement region where the flow is greatly decelerated. This is a well known situation for
flow around buildings where k-ε models tend to overpredict the production of tke (Murakami et al., 1999). This leads to enhanced mixing and a quicker recovery of the flow in the wake of the obstacle.
Figure 4: Bolund hill test case and validation of fractional speed-up ratio and tke increment along the A (top) and B lines (down) for 239º (case 3) and 270º (case 1) runs
5 WIND FARM WAKES MODELING: CFDWAKE Embedded in the ABL model, a wake model simulates the momentum sink that generates wind power deficit and added turbulence downstream of wind turbines. A review of wind turbine wake models can be found in Crespo et al. (1999). The actuator disk concept, based on the extraction of axial momentum by drag over a rotor disk, is the standard approach due to the limited requirements of input data (only disk geometry and thrust curve). The axial momentum sink Fx extracted at the rotor disk is: 1 Fx = − ρCt U ∞2 A 2
(7)
where ρ is the air density, A is the area of the rotor disk, Ct is the wind turbine thrust coefficient which depends on the incoming freestream velocity at hub height U∞. Inherent with this definition it is the uncertainty related to the thrust coefficient and the definition of the freestream velocity in complex terrain and wake induced flows. A Blade Element Momentum (BEM) approach can be adopted if the drag and lift coefficient data are available. These models reproduce the forces on the single blades and, therefore, are able to introduce both the axial and the rotational forces. Single wake of the Sexbierum experiment in flat terrain is the starting point for wind turbine wake models validation (Cleijne, 1993). The experiment consists on single-wake velocity measurements at axial distances -2.8D, 2.5D, 5.5D and 8D in neutral atmospheric conditions from a 30m diameter wind turbine. The freestream hub-height velocity is 10 ms-1 and the turbulence intensity is 10%. Figure 5 shows the velocity ratio and added turbulence intensity at positions 2.5D and 8D for two versions of CFDWake model (based on CFDWind 1.0). Unfortunately, no information about the variability of the ensemble measurements is available.
Figure 5: Velocity ratio and added turbulence intensity at 2.5 and 8 diameters downwind from the Sexbierum wind turbine for the k-ε and RSM versions of CFDWake model
The actuator disk model is not able to simulate correctly the near wake region, where the aerodynamics of the rotor play a more dominant role. In the far wake (>3D), where wind resource assessment is mostly focussed, the results improve, especially if RSM (Reynolds Stress Model) turbulence model is used. In effect, using RSM modelling seems to be a promising alternative in wake flows, either from wind turbines or terrain, adding anisotropy to the flow physics and still allowing a cost effective solution compared to LES. The next step in complexity would be to simulate the interaction of wind turbine wakes. First, a row of 5 wind turbines in flat terrain separated by 3.8D (ECN test wind farm in the Netherlands; Prospathopoulos et al., 2010) and then Horns Rev 7D by 7D wind farm in offshore conditions (Hansen et al., 2010) have been selected due to the good quality of the available data for validation. In large scale wind farms, the power deficit normalized with the power of the least disturbed wind turbine is selected as validation metric. This approach is the most suitable solution since intermediate met masts are typically not available and the metric is directly related to the intended use of the model, which is to simulate the wake losses for energy yield assessment. Implicit in this validation methodology is the assumption that all the wind turbines have the same response which is characterized solely by the power and thrust curves. This oversimplification constitutes a mayor drawback when analysing validation results since it is very difficult to distinguish between the deficiencies of the flow model and those of the wind turbine themselves. The only way to overcome this difficulty is by monitoring the individual response of the wind turbines and the flow in between the wind turbines. Figure 6 shows some sample results of CFDWake simulations for the ECN and Horns Rev wind farm test cases respectively. The simulations are presented for full-wake conditions, i.e. when the wind turbine rows are aligned with the incoming flow. A narrow wind direction sector of ±2.5º width and a freestream velocity close to the maximum rotor load provide a maximum wake signal. In full wake, the power drops as much as 60% in the second wind turbine and then the deficit is maintained rather uniform in the next turbines downwind. Actuator disk models seem to be able to reproduce the main futures of far wake interaction in flat terrain and neutral conditions.
Figure 6: Power deficit in ECN and Horns Rev wind farms in full wake conditions. Simulation with the k-ε version of CFDWake
Finally, wake coupling with complex terrain constitutes the most challenging case (Politis et al., 2011). In the UpWind project, data from an operational wind farm in complex terrain was used
for validation following the same methodology presented before for ECN and Horns Rev. The wind farm layout consists on a 13D by 1.5D spacing. Figure 7 shows the power deficit at different rows for the k-ε version of CFDWake and for the algebraic model PARK included in the WAsP commercial software.
Figure 7: Simulation of power deficit in a complex terrain wind farm using CFDWake and PARK models
In general, linearized models like PARK-WAsP tend to underpredict the power deficit. This is partly corrected by CFD models. The difficulty in these test cases is to separate the influence on the validation results of the flow model and the wake model. Ideally, a validation campaign for complex terrain wind farms would consist of two phases: first without wind turbines to validate the flow over terrain and then with the wind farm to analyse the added uncertainties due to wake modelling. These test cases on wind farm wakes have been intensively simulated with different state-of-theart wake models in the EU funded UpWind project (Barthelmie et al., 2011). 6 CONCLUSIONS The selection of appropriate V&V test cases is a fundamental step of any model development. A survey of test cases for V&V is provided in the context of wind resource assessment. Some test cases are readily available from the literature and some others come from experimental facilities and industrial test cases evaluated in research projects like UpWind. Still, the number of suitable test cases is very limited for a complete validation of all the aspects of the model chain. Essential in the V&V process is the adoption of a model evaluation
procedure that is mutually recognized as standard by model developers and end-users. To this end the IEA Task WAKEBENCH is under way for the definition of an evaluation protocol and best practice guidelines for wind farm models based on intercomparison benchmarks around test cases from wind tunnel experiments to test sites and operational wind farms. The V&V procedures will be largely based on the AIAA (1998) and the COST 732 (2009) guidelines. 7 ACKNOWLEDGEMENTS The authors would like to acknowledge the support from the research institutions and industrial partners that made the validation data available, an essential need of any model development. Most of the wake modeling activity has been funded under the FP6-UpWind EU project (contract number 019945). 8 REFERENCES AIAA, 1998. Guide for the Verification and Validation of Computational Fluid Dynamics Simulations, American Institute of Aeronautics and Astronautics, AIAA-G-077-1998, VA, USA Alinot, C. and Masson, C., 2005. k-ε Model for the Atmospheric Boundary Layer Under Various Thermal Stratifications, Transactions of the ASME 127: 438-443 Apsley, D.D. and Castro, I.P., 1997. A Limited-Length-Scale k-ε Model for the Neutral and Stably-Stratified Atmospheric Boundary Layer, Boundary Layer Meteorol. 83: 75-78 Barthelmie et al., 2011, UPWIND FP8 Final Activity Report, Available at: http://www.upwind.eu/, pp. 47 Bechmann, A., et al., 2009. The Bolund Experiment: Overview and Background. Technical Report RisøR1658(EN), Risø DTU, National Lab., Roskilde, Denmark Bechmann A., et al., 2011, The Bolund Experiment, Part II: Blind Comparison of Microscale Flow Models, Boundary Layer Meteorology, accepted for publication Blocken, B., Stathopoulos, T. and Carmeliet J., 2007, CFD simulation of the atmospheric boundary layer – wall function problems. Atmospheric and Environment 41-2: 238-252. Castro, F.A., Palma, J.M.L.M. and Silva Lopes, A., 2003. Simulation of the Askervein hill flow. Part I: Reynolds Averaged Navier-Stoker equations (k-ε turbulence model), Boundary-Layer Meteorology 107:501-530 Cleijne, J.W., 1993. Results of the Sexbierum Wind Farm: Single Wake Measurements, TNO Report, C19.3, The Netherlands COST 732, 2009, Model evaluation guidance and protocol document, Report of COST Action 732 on Quality assurance and improvement of microscale meteorological models. Available at: http://www.mi.unihamburg.de/COST_732.464.0.html Crespo A., et al., 1999, Survey of modeling methods for wind turbine wakes and wind farms. Wind Energy 2, 1–24 Detering, H.W., Etling D., 1985. Application of the E-ε Turbulence Model to the Atmospheric Boundary Layer, Boundary Layer Meteorology 33: 113-133 Hansen, K.H., et al., 2010, The impact of turbulence intensity and atmospheric stability on power deficits due to wind turbine wakes at Horns Rev wind farm. Submitted to Wind Energy (WE-10-0149). Murakami S., et al., 1999, CFD analysis of wind climate from human scale to urban scale, J. Wind Eng. Ind. Aerodyn. 81: 57-81 Politis, E., et al., 2011. Modelling wake effects in large wind farms in complex terrain: the problem, the methods and the issues. Acepted in Wind Energy (WE-10-0103) Prospathopoulos, J.M., et al., 2010, Evaluation of the effects of turbulence model enhancements on wind turbine wake predictions, Wind Energy, DOI: 10.1002/we.419 Richards, P.J. and Hoxey, R., 1993. Appropriate boundary conditions for computational wind engineering models using the k–ε turbulence model, J. Wind Eng. Ind. Aerodyn. 46-47: 145–153 Silva Lopes, A., et al., 2007. Simulation of the Askervein flow. Part 2: Large-eddy simulations, Boundary-Layer Meteorology 125:85-108 Taylor, P. and Teunissen, H., 1987. The Askervein Hill Project: Overview and Background Data, Boundary-Layer Meteorology 39:15-39
