- Email: [email protected]
Effect of Offshore Wind farm Design on the Vertical Motion of the Ocean
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 80 (2015) 213 – 222
12th Deep Sea Offshore Wind R&D Conference, EERA DeepWind'2015
Effect of Offshore Wind farm Design on the Vertical Motion of the Ocean Ole Henrik Segtnana*, Konstantinos Christakosa a
Polytec R&D Institute, Sørhauggt 128, N-5527 Haugesund, Norway
Abstract In this study the vertical motion of the ocean is studied numerically. A wake model that includes details of the wind farm design, such as the location of the turbines, diameter of rotors and hub height, is used to calculate the change in surface wind speed resulting from potential wind farms in the Havsul area. Using the calculated wind velocities to force a three dimensional ocean model (Regional Ocean Modeling System), the ocean response to two different wind farm designs is estimated. It is found that the wind farm design has a significant effect on the upwelling and downwelling near the wind farm, as the difference in maximum upwelling velocity after 1 day of simulation exceeds 30 m/day. The pronounced changes in vertical velocities are attributed to changes in the horizontal flow over varying topography due to wind stress modifications by the wind farms. © Published by Elsevier Ltd. This © 2015 2015The TheAuthors. Authors. Published by Elsevier Ltd. is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and peer-review under responsibility of SINTEF Energi AS. Peer-review under responsibility of SINTEF Energi AS Keywords: Type your keywords here, separated by semicolons ;
1. Introduction Offshore wind energy is expected to play an important role in future energy supply [1, 2, 3]. Whereas offshore wind farms are advantageous due to the higher wind speeds and their locations away from highly populated areas, potential environmental consequences of installing large wind farms may be pronounced. These include impact of the electric cables on the fish migration [4], collision of endangered birds with the turbines [5] as well as having an effect on the local climate [6, 7]. Recently it has also been shown that offshore wind farms may have an impact on the upper ocean circulation [8, 9]. Changes in the vertical motion of the ocean are likely to be important to the local ecosystems [10], and detailed information about how the wind farm may modify the circulation in its vicinity should be provided prior to installation. Although it has been indicated that wind farms are likely to affect the local ocean circulation, previous studies have focused on idealized model experiments. In particular, details of the wind
1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of SINTEF Energi AS doi:10.1016/j.egypro.2015.11.424
214
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
farm design have not been taken into account when calculating the wake. The objective of the present study is to investigate the effect of wind farm design on the vertical motion in the ocean. Using a wake model that allows for varying wind farm designs, the change in wind velocity will be calculated. We will then perform two experiments with a three dimensional ocean model, forced by the wind velocities calculated by the wake model, and investigate the effect of the wind farm design on the ocean upwelling and downwelling. The study will be performed in the Havsul area, where high wind speed and the potential for offshore wind energy production have been documented [11]. However, the applied method is not restricted to this area and may be applied for any offshore wind farm study. 2. Methods and data 2.1. Wake model In order to estimate the modification of the wind field due to the presence a wind farm, we will in this study apply the wake model described by [12]. The model is based on conservation of momentum and the assumption of linear expansion of the downstream wake [13]. For a single turbine the velocity ܷ௪ at the downwind distance X, is calculated according to 2
Uw
§r · U 0 U 0 ( 1 Ct 1)¨ o ¸ , ©r¹
(1)
where ܷ is the undisturbed wind speed upstream the turbine, ܥ௧ is the thrust coefficient of the turbine and ݎ is the radius of the rotor. It is assumed that the spread of the wake is symmetric in the vertical and lateral directions, and that the radius of the cone, ݎ, at the distance X downstream the wind turbine, is given as
r
ro NX ,
(2)
with κ being the wake decay constant. For a wind farm consisting of multiple turbines, the effects of the individual wakes are combined into one single effect using the methods described in [12]. The wake behind a turbine is then multiplied by a factor, β, defined as
ª§ r · 2 § 'A · º E 1 (1 1 Ct )(¦ «¨¨ o ¸¸ ¨¨ ¸¸ » , i 1 «© ri ¹ © Ao ¹ i » ¬ ¼ N
(3)
where ܣ is the area spanned by the turbine experiencing shadowing (Turbine k), ο ܣis the overlapping area of the upstream wake cone and the area spanned by Turbine k, and ݎ is the radius of the wake cone generated by Turbine i at the same downstream location as Turbine k. In order to retain the undisturbed wind speed downstream the wind farm a layer where ߚ is gradually increased toward 1, is introduced
E
§ Sx · ¸ © 2L ¹
E int (1 E int ) sin¨
if x < L
(4)
if x> L.
(5)
and
E 1
215
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
ߚ୧୬୲ is the interior value of β at the edge of the wind farm, calculated according to Equation (3) and x is the distance downstream the wind farm. In order to obtain the wind speed at the hub height of the turbines, we calculate the wind speed using the logarithmic wind profile for neutral conditions
u* § z ln ¨ k ¨© z o
U ( z)
· ¸¸ , ¹
(6)
where U is the wind speed, כݑthe friction velocity, k the Von Karman constant (0.41) and ݖ the surface roughness. The friction velocity is calculated using the following expression [14]
u*2
U102 (0.8 0.065U102 ) u10 3 ,
(7)
with ܷଵ being the wind speed at 10 m height. We calculate ݖ using the Charnock model [15]
zo
Dc
u*2 g
(8),
where ߙ and g are respectively the Charnocks parameter and the gravity constant. In this study we use ߙ = 0.016, which is within the values recommended by [16]. Input wind data at 10 m height is obtained from the High Resolution Limited Area Model (HIRLAM), operated by the Norwegian Meteorological Institute [17]. 2.2. Regional Ocean Modeling System To calculate the ocean response to anomaly wind forcing caused by a large wind farm we apply the Regional Ocean Modeling System (ROMS) model. ROMS is a free-surface, terrain following model that solves the primitive equations on a staggered Arakawa C-grid [18]. Surface boundary forcing is calculated using the TOGA COARE bulk parameterization [19], whereas vertical mixing is calculated using the k-ϵ generic length scale algorithm [20]. The 3-D fields at the open boundaries are calculated using the adaptive boundary condition algorithm presented by [21], whereas sea surface and 2-D momentum fields are calculated using respectively the Chapman [22] and Flather [23] radiation boundary conditions. For active open boundary conditions we set the nudging time scale equal to 12 hours, whereas for passive boundary conditions it is set equal to 180 days. In the horizontal the applied grid resolution is 500 m, whereas the number of vertical sigma layers is set equal to 20. For surface forcing we use the 6 hourly 12 km meteorological data obtained from the HIRLAM model [17], whereas at the open boundaries data from the Norkyst-800 model is used [24], combined with tidal data from the TPXO tidal model [25], [26]. 3. Case study 3.1 Havsul area The area of focus in the present study is located in the Havsul region off the Møre coast, as shown in Figure 1. The bathymetry is characterized as extremely chaotic with the seabed dominated by bed-rock [27]. The topography is associated with small islands, high coastal mountains and fjords. The offshore wind conditions in the Havsul
216
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
Figure 1: Applied model domain of the Havsul area at the western coast of Norway. The region in red denotes the location of the modeled wind farms. area are considered viable for wind energy installations due to relative high wind speeds [11]. The complex topography causes mesoscale atmospheric phenomena with strong winds along the coastline such as low level coastal jets [28]. Using the NORA 10 dataset [29] the prevailing wind direction is found to be southwest, with a mean value of 217.5 °. The time period considered in this study is from March 11, 2014 to March 13, 2014. During this period the wind speed in the Havsul area was higher than 15 m/s and the wind direction southwest. 3.2 Wind farm design In order to run the wake model described in Section 2.1, information about the wind turbines and the wind farm is required. For the thrust coefficient, ܥ௧ , and the wake decay constant κ, we will in the present study use the values 0.4 and 0.05, respectively. The diameter of the turbine, ݎ , and the height of the turbine are set equal to respectively 120 m and 90 m. In addition to the above mentioned parameters, the geographical coordinates of the turbines are used as input to the model. In this study two different wind farm designs are considered: Wind Farm Design 1 and Wind Farm Design 2. Both are made up by 70 turbines, and arranged to be aligned with the mean wind direction (217.5 °). For Wind Farm Design 1 the turbines are organized in straight rows and columns, whereas for Wind Farm Design 2 the rows are curved. In addition Wind Farm Design 1 has a close to quadratic shape, compared to Wind Farm Design 1 which is made up by 5 rows and 14 columns. The two farms are located at approximately the same location, as illustrated in Figure 2. In Figure 3 we show the wakes at 10 m height generated by Wind Farm Designs 1 and 2, for wind direction equal to 217.5 ° (normal flow), and 10 m wind speed equal to 20 m/s. It is seen that the wind speed is decreasing downwind in both cases and that areas not shadowed by upwind turbines do not experience wind speed reduction. 3.3 Ocean model experiments Using the ocean circulation model and wind wake model described in Section 2, sensitivity experiments of the vertical oceanic motion to wind farm design may be performed. First we calculate the wake induced by the wind farm. The modified wind field obtained from this simulation will be used as input to the ROMS model, which
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
again is used to calculate the vertical oceanic velocity. By varying the wind farm design (Wind Farm Design 1 and 2), we will investigate the change in vertical oceanic velocity due to variations in the wind farm induced wakes. For the time period March 11, 2014 to March 13, 2014 we apply the ROMS model to perform three simulations of the oceanic conditions in the Havsul area: Model run 1, Model run 2 and a control run. The control run is forced by unperturbed wind velocities, i.e. winds not affected by the presence of a wind farm, whereas for Model runs 1 and 2 the model is forced by anomaly wind due to wind farm induced wakes. Input to the wake model that is used to force Model run 1 and Model run 2 are respectively Wind Farm Design 1 and Wind Farm Design 2. For all three model experiments a spin up period of 2 days is applied, where the model is forced by unperturbed wind velocity.
Figure 2: Potential wind farm design at the Havsul area. Number of turbines are 70 in both examples
Figure 3: Wind farm induced for the two wind farm designs described in Section 3.2 (Wind Farm Design 1 and 2) at 10 m height. Wind direction is from southwest (217.5 °). Free slip wind speed at 10 m height is 20 m/s.
217
218
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
4. Results 4.1 Control run In Figure 4 the mean sea surface height and surface currents as well as the mean vertical velocity at low and intermediate depths (sigma layer 3), in the Havsul area are shown for the study time period (March 11, 2014 to March 13, 2014). The surface circulation is seen to be in geostrophic balance, and directed toward northeast. This is partly caused by the surface wind stress piling up water along the Norwegian coastline, resulting in offshore sea surface gradients that are balanced by the Coriolis force. For the vertical velocity both positive and negative values are seen, with values ranging from –250 m/day to 250 m/day.
Figure 4: Mean sea surface height and surface currents (upper) and vertical velocity at sigma layer 3 (lower) in the Havsul area for the time period March 11, 2014 to March 13, 2014. The black regions denote the area intended for wind farm installations. 4.2 Anomaly upwelling/downwelling It is seen from Figure 4 that for the unperturbed flow relatively high vertical velocities occur in the Havsul area during the study period. Therefore, in order to estimate the effect of offshore wind farms on the ocean circulation, we calculate the anomaly vertical velocity. It is defined as the difference between the vertical velocity of the control run and that of the two model experiments (Model run 1 and Model run 2). Results after 6 h, 12 h and 24 h of simulation, for sigma layer 3, corresponding to approximately 20 m depth in the vicinity of the wind farm, are shown in Figure 5. For both model runs the absolute value of the anomaly vertical velocity increases with time, and greatest values are seen west/northwest of the wind farms. However, both the anomaly upwelling and downwelling is more significant for Model run 2, where values exceed 90 m/day after 24 hours of simulation. In comparison, for Model run 1, anomaly vertical velocities are everywhere less than 50 m/day.
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
Figure 5: Anomaly vertical velocity at sigma layer 3, corresponding to approximately 20 m depth in the vicinity of the wind farms for the two model experiments: Model run 1 (left) and Model run 2 (right), after 6 h, 12 h and 24 h of simulation. Units are m/day. Also plotted are the locations of turbines included in the wind farm designs (black dots). Wind direction is from southwest for all cases. 4.3 Anomaly wind stress In Figure 6 the difference in sea surface stress between the control run and Model runs 1and 2 are shown (anomaly wind stress), for the area surrounding the wind farms, after 6 h, 12 h and 24 h of simulation. Due to the wakes generated by the wind farms, the anomaly wind stresses are directed southwestward, in opposite direction of the unperturbed wind. It is further seen that the anomaly wind stresses are relatively constant for the three time instances shown, as the wind direction is stable for this time period. At the boundaries of the wind farm the anomaly wind stress approaches zero, resulting in strong wind stress curl. 4.4 Anomaly currents In Figure 7 the difference in horizontal velocity at sigma layer 3, between the control run and Model runs 1and 2 (anomaly currents) after 6 h, 12 h and 24 h of simulations, are shown. It is seen that the anomaly currents are directed southwestward, opposite to the mean unperturbed currents (Figure 4). Amplitudes are of the order 3 cm/s and approximately constant for all three time instances. However, the anomaly currents west of the wind farms is seen to increase after 12 h and 24 h of simulations, in particular this is the case in Model run 2. 5. Discussion and summary From Figure 5 it was shown that the effect of including wind farms in the model simulations was altered vertical velocity near the wind farm. In studies of the ocean response to idealized wakes in a deep and layered ocean, such vertical motion has been attributed to Ekman pumping caused by the wind stress curl [8, 9]. From Figure 6 it is seen that the wind farms generate strong anomaly shear at its boundaries, and that the curl depends on the design of the wind farm, which may result in different upwelling and downwelling regimes in the case of pronounced Ekman pumping. However, the area surrounding the potential wind farms is relatively shallow, and during strong wind conditions, with intense vertical mixing, the surface Ekman layer reaches down to the sea floor (not shown). The strong vertical mixing results in a highly barotropic ocean and the effect of the earth’s rotation is therefore expected to be insignificant for the horizontal scales under consideration. This indicates that the vertical velocity anomalies seen in Figure 5 are not predominately due to Ekman pumping.
219
220
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
Figure 6: Difference in surface stress between Model run 1 and the control run (left) and Model run 2 and the control run (right) in the vicinity of the wind farms after 6 h, 12 h and 24 h of simulation. Units are N/ଶ . Also plotted are the locations of turbines included in the wind farm designs (red dots). Wind direction is from southwest for all cases.
Figure 7: Difference in horizontal velocity at sigma layer 3 between Model run 1 and the control run (left) and Model run 2 and the control run (right) in the vicinity of the wind farms area after 6 h, 12 h and 24 h of simulation. Units are cm/s. Also plotted are the locations of the turbines included in the wind farm designs (red dots). Wind direction is from southwest for all cases.
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
Figure 8: Model depth [m] in the area near the wind farm (black dots) From Figure 7 it is seen that the oceanic response to reduced wind stress is decreased ocean currents in the flow direction. Due to varying topography in the area of the wind farms modification of the current speed must result in anomaly vertical oceanic motion. After 24 h of simulation strong anomaly vertical velocities west of the wind farm coincides with anomaly currents in the same area (Figures 6 and 7). In this area bathymetry gradients are strong (Figure 8), which indicates that vertical motion is mainly determined by variations in the horizontal flow field, and that this effect is more significant in Model run 2 than it is in Model run 1. In this study it has been shown that vertical oceanic motion may be induced by the presence of large wind farms. Using a wake model that allows for the calculation of the surface wind stress as a function of the wind farm design, it has further been shown that the ocean upwelling/downwelling is influenced by the wind farm design. We have outlined a method of how the ocean response to a specific wind farm design can be calculated, which allows for inclusion of ocean effects in future planning of new offshore wind projects. For the Havsul region it appears that topographic effects play a dominant role in generating vertical velocities, and that Ekman pumping is of less significance. Acknowledgements The authors would like to thank Magnar Reistad at the Norwegian Meteorological Institute, who kindly provided the NORA10 data. References [1] Archer, C.L., Jacobson, M.Z. Spatial and temporal distributions of U.S. winds and wind power at 80 m derived from measurements. J. Geophys.Res. 2003. 108 (D9), 4289. [2] Archer, C.L., Jacobson, M.Z. Evaluation of global wind power. J. Geophys. Res. 2005. 110, D12110. [3] Henderson, A.R., et al. Offshore wind energy in Europe — a review of the state-of-the-art. Wind Energy 6. 2003. p. 35–52. [4] Branover, G.G., Vasilýev, A.S., Gleyzer, S.I., Tsinober, A.B. A study of the behavior of the eel in natural and artificial magnetic fields and an analysis of its reception mechanism. J. Ichthyol. 1971. p. 608–614. [5] Tucker, V.A. A mathematical model of bird collisions with wind turbine rotors. J. Sol. Energy Eng. 1996. p. 253–262. [6] Baidya Roy, S., Pacala, S.W. Can large wind farms affect local meteorology? J. Geophys. Res. 2004. 109, D19101. [7] Rooijmans, P. Impact of a large-scale offshore wind farm on meteorology. Ms Thesis, Utrecht University, Utrecht. 2004. [8] Brostom, G. On the influence of large wind farms on the upper ocean circulation. J. Mar. Sys. 2008. p. 585-591. [9] Paskyabi, M.B., Fer, I. Upper Ocean Response to Large Wind Farm Effect in the Presence of Surface Gravity Waves. Energy Procedia 24. 2013. p. 245-254 [10] Valiela, I. Marine Ecological Processes. Springer-verlag, New York. 1995, 686 pp [11] Christakos K. Characterization of the coastal marine atmospheric boundary layer (MABL) for wind energy applications, Master Thesis, University of Bergen, 2013, URI: http://hdl.handle.net/1956/7186.
221
222
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222 [12] González-Longatt, F., Wall P., Terzija V. Wake effect in Wind Farm Performance: Steady-State and Dynamic Behaviour. Renewable Energy, 2011, p. 329-338 [13] Jensen, N.O. A note on wind turbine interaction. Risø-M-2411. Risoe National Laboratory, Roskilde, Denmark, 1983. 16 pp [14] Wu, J. Wind-Stress coe cients over Sea surface near Neutral Conditions-A Revisit. Journal of Physical Oceanography. 1980. p. 727-740. [15] Charnock, H. Wind stress over a water surface. Quart J Roy Meteorol Soc. 1955 p. 639–640 [16] Kraus, E.B. Atmosphere-Ocean interaction. Oxford University Press, London. 1972. 275 pp [17] Unden et al. HIRLAM-5 Scientific Documentation, HIRLAM-5 Project, SMHI, Norkoping, Sweden. 2002. 146 pp [18] Shchepetkin, A.F., McWilliams J.C. The Regional Ocean Modeling System: A split-explicit, free-surface, topography following coordinates ocean model, Ocean Modelling, 2005, 9, p. 347-404. [19] Fairrall, C.W., Bradley, E.F., Rogers, D.P, Edson, J.B., Young, G.S. Bulk parameterization of air-sea fluxes for tropical Ocean global atmosphere Coupled-Ocean Atmosphere Response Experiment. Journal of Geophysical Research. 1996. P. 3747-3764 [20] Rodi, W. Examples of calculation methods for flow and mixing in stratified fluids. Journal of Geophysical Research. 1987, (C5) p. 53055328 [21] Marchesiello, P., McWilliams J.C., Shchepetkin A.F., Open boundary conditions for longterm integration of regional oceanic models. Ocean Modeling. 2001, p. 1-20 [22] Flather, R.A. A tidal model of the northwest european continental shelf. Memoires de la Société Royale de Sciences de Liège. 1976. p. 141–164 [23] Chapman, D.C. Numerical treatment of cross-shelf open boundaries in a barotropic coastal ocean model. Journal of Physical Oceanography. 1985, p. 1060–1075 [24] Albretsen, J., Sperrevik, A.K., Staalstrøm, A., Sandvik, A.D., Vikebø, F., Asplin, L.. Norkyst-800 report no. 1. User manual and technical descriptions. Report 2; Institute of Marine Research; Nordnesgaten 50, P.O.Box 1870 Nordnes 5817 BERGEN; 2011. [25] Egbert, G.D, Bennet A.F., Foreman M.G.G. TOPEX/POSEIDON tides estimated using a global inverse model, Journal of Geophysical Research.1994, .p.821-24,852 [26] Egbert G.D., Erofeeva S.Y. Efficient Inverse Modeling of Barotropic Ocean Tides. J. Atmos. Ocean. Tech. 2002 p.183-204. [27] Frøysa, K.G (editor), NORCOWE Annual Report. 2010 43 pp [28] Konstantinos Christakos, George Varlas, Joachim Reuder, Petros Katsafados, Anastasios Papadopoulos, Analysis of a Low-level Coastal Jet off the Western Coast of Norway, Energy Procedia, Volume 53, 2014, Pages 162-172, ISSN 1876-6102, http://dx.doi.org/10.1016/j.egypro.2014.07.225. [29] Reistad, M., Breivik, Ø., Haakenstad, H., Aarnes, O.J., Furevik, B.R., Bidlot, J.R.. A high resolution hindcast of wind and waves for the North Sea, the Norwegian Sea, and the Barents Sea. Journal of Geophysical Research. 2011. 116:C05019, doi:10.1029/2010JC006402
ScienceDirect Energy Procedia 80 (2015) 213 – 222
12th Deep Sea Offshore Wind R&D Conference, EERA DeepWind'2015
Effect of Offshore Wind farm Design on the Vertical Motion of the Ocean Ole Henrik Segtnana*, Konstantinos Christakosa a
Polytec R&D Institute, Sørhauggt 128, N-5527 Haugesund, Norway
Abstract In this study the vertical motion of the ocean is studied numerically. A wake model that includes details of the wind farm design, such as the location of the turbines, diameter of rotors and hub height, is used to calculate the change in surface wind speed resulting from potential wind farms in the Havsul area. Using the calculated wind velocities to force a three dimensional ocean model (Regional Ocean Modeling System), the ocean response to two different wind farm designs is estimated. It is found that the wind farm design has a significant effect on the upwelling and downwelling near the wind farm, as the difference in maximum upwelling velocity after 1 day of simulation exceeds 30 m/day. The pronounced changes in vertical velocities are attributed to changes in the horizontal flow over varying topography due to wind stress modifications by the wind farms. © Published by Elsevier Ltd. This © 2015 2015The TheAuthors. Authors. Published by Elsevier Ltd. is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and peer-review under responsibility of SINTEF Energi AS. Peer-review under responsibility of SINTEF Energi AS Keywords: Type your keywords here, separated by semicolons ;
1. Introduction Offshore wind energy is expected to play an important role in future energy supply [1, 2, 3]. Whereas offshore wind farms are advantageous due to the higher wind speeds and their locations away from highly populated areas, potential environmental consequences of installing large wind farms may be pronounced. These include impact of the electric cables on the fish migration [4], collision of endangered birds with the turbines [5] as well as having an effect on the local climate [6, 7]. Recently it has also been shown that offshore wind farms may have an impact on the upper ocean circulation [8, 9]. Changes in the vertical motion of the ocean are likely to be important to the local ecosystems [10], and detailed information about how the wind farm may modify the circulation in its vicinity should be provided prior to installation. Although it has been indicated that wind farms are likely to affect the local ocean circulation, previous studies have focused on idealized model experiments. In particular, details of the wind
1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of SINTEF Energi AS doi:10.1016/j.egypro.2015.11.424
214
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
farm design have not been taken into account when calculating the wake. The objective of the present study is to investigate the effect of wind farm design on the vertical motion in the ocean. Using a wake model that allows for varying wind farm designs, the change in wind velocity will be calculated. We will then perform two experiments with a three dimensional ocean model, forced by the wind velocities calculated by the wake model, and investigate the effect of the wind farm design on the ocean upwelling and downwelling. The study will be performed in the Havsul area, where high wind speed and the potential for offshore wind energy production have been documented [11]. However, the applied method is not restricted to this area and may be applied for any offshore wind farm study. 2. Methods and data 2.1. Wake model In order to estimate the modification of the wind field due to the presence a wind farm, we will in this study apply the wake model described by [12]. The model is based on conservation of momentum and the assumption of linear expansion of the downstream wake [13]. For a single turbine the velocity ܷ௪ at the downwind distance X, is calculated according to 2
Uw
§r · U 0 U 0 ( 1 Ct 1)¨ o ¸ , ©r¹
(1)
where ܷ is the undisturbed wind speed upstream the turbine, ܥ௧ is the thrust coefficient of the turbine and ݎ is the radius of the rotor. It is assumed that the spread of the wake is symmetric in the vertical and lateral directions, and that the radius of the cone, ݎ, at the distance X downstream the wind turbine, is given as
r
ro NX ,
(2)
with κ being the wake decay constant. For a wind farm consisting of multiple turbines, the effects of the individual wakes are combined into one single effect using the methods described in [12]. The wake behind a turbine is then multiplied by a factor, β, defined as
ª§ r · 2 § 'A · º E 1 (1 1 Ct )(¦ «¨¨ o ¸¸ ¨¨ ¸¸ » , i 1 «© ri ¹ © Ao ¹ i » ¬ ¼ N
(3)
where ܣ is the area spanned by the turbine experiencing shadowing (Turbine k), ο ܣis the overlapping area of the upstream wake cone and the area spanned by Turbine k, and ݎ is the radius of the wake cone generated by Turbine i at the same downstream location as Turbine k. In order to retain the undisturbed wind speed downstream the wind farm a layer where ߚ is gradually increased toward 1, is introduced
E
§ Sx · ¸ © 2L ¹
E int (1 E int ) sin¨
if x < L
(4)
if x> L.
(5)
and
E 1
215
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
ߚ୧୬୲ is the interior value of β at the edge of the wind farm, calculated according to Equation (3) and x is the distance downstream the wind farm. In order to obtain the wind speed at the hub height of the turbines, we calculate the wind speed using the logarithmic wind profile for neutral conditions
u* § z ln ¨ k ¨© z o
U ( z)
· ¸¸ , ¹
(6)
where U is the wind speed, כݑthe friction velocity, k the Von Karman constant (0.41) and ݖ the surface roughness. The friction velocity is calculated using the following expression [14]
u*2
U102 (0.8 0.065U102 ) u10 3 ,
(7)
with ܷଵ being the wind speed at 10 m height. We calculate ݖ using the Charnock model [15]
zo
Dc
u*2 g
(8),
where ߙ and g are respectively the Charnocks parameter and the gravity constant. In this study we use ߙ = 0.016, which is within the values recommended by [16]. Input wind data at 10 m height is obtained from the High Resolution Limited Area Model (HIRLAM), operated by the Norwegian Meteorological Institute [17]. 2.2. Regional Ocean Modeling System To calculate the ocean response to anomaly wind forcing caused by a large wind farm we apply the Regional Ocean Modeling System (ROMS) model. ROMS is a free-surface, terrain following model that solves the primitive equations on a staggered Arakawa C-grid [18]. Surface boundary forcing is calculated using the TOGA COARE bulk parameterization [19], whereas vertical mixing is calculated using the k-ϵ generic length scale algorithm [20]. The 3-D fields at the open boundaries are calculated using the adaptive boundary condition algorithm presented by [21], whereas sea surface and 2-D momentum fields are calculated using respectively the Chapman [22] and Flather [23] radiation boundary conditions. For active open boundary conditions we set the nudging time scale equal to 12 hours, whereas for passive boundary conditions it is set equal to 180 days. In the horizontal the applied grid resolution is 500 m, whereas the number of vertical sigma layers is set equal to 20. For surface forcing we use the 6 hourly 12 km meteorological data obtained from the HIRLAM model [17], whereas at the open boundaries data from the Norkyst-800 model is used [24], combined with tidal data from the TPXO tidal model [25], [26]. 3. Case study 3.1 Havsul area The area of focus in the present study is located in the Havsul region off the Møre coast, as shown in Figure 1. The bathymetry is characterized as extremely chaotic with the seabed dominated by bed-rock [27]. The topography is associated with small islands, high coastal mountains and fjords. The offshore wind conditions in the Havsul
216
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
Figure 1: Applied model domain of the Havsul area at the western coast of Norway. The region in red denotes the location of the modeled wind farms. area are considered viable for wind energy installations due to relative high wind speeds [11]. The complex topography causes mesoscale atmospheric phenomena with strong winds along the coastline such as low level coastal jets [28]. Using the NORA 10 dataset [29] the prevailing wind direction is found to be southwest, with a mean value of 217.5 °. The time period considered in this study is from March 11, 2014 to March 13, 2014. During this period the wind speed in the Havsul area was higher than 15 m/s and the wind direction southwest. 3.2 Wind farm design In order to run the wake model described in Section 2.1, information about the wind turbines and the wind farm is required. For the thrust coefficient, ܥ௧ , and the wake decay constant κ, we will in the present study use the values 0.4 and 0.05, respectively. The diameter of the turbine, ݎ , and the height of the turbine are set equal to respectively 120 m and 90 m. In addition to the above mentioned parameters, the geographical coordinates of the turbines are used as input to the model. In this study two different wind farm designs are considered: Wind Farm Design 1 and Wind Farm Design 2. Both are made up by 70 turbines, and arranged to be aligned with the mean wind direction (217.5 °). For Wind Farm Design 1 the turbines are organized in straight rows and columns, whereas for Wind Farm Design 2 the rows are curved. In addition Wind Farm Design 1 has a close to quadratic shape, compared to Wind Farm Design 1 which is made up by 5 rows and 14 columns. The two farms are located at approximately the same location, as illustrated in Figure 2. In Figure 3 we show the wakes at 10 m height generated by Wind Farm Designs 1 and 2, for wind direction equal to 217.5 ° (normal flow), and 10 m wind speed equal to 20 m/s. It is seen that the wind speed is decreasing downwind in both cases and that areas not shadowed by upwind turbines do not experience wind speed reduction. 3.3 Ocean model experiments Using the ocean circulation model and wind wake model described in Section 2, sensitivity experiments of the vertical oceanic motion to wind farm design may be performed. First we calculate the wake induced by the wind farm. The modified wind field obtained from this simulation will be used as input to the ROMS model, which
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
again is used to calculate the vertical oceanic velocity. By varying the wind farm design (Wind Farm Design 1 and 2), we will investigate the change in vertical oceanic velocity due to variations in the wind farm induced wakes. For the time period March 11, 2014 to March 13, 2014 we apply the ROMS model to perform three simulations of the oceanic conditions in the Havsul area: Model run 1, Model run 2 and a control run. The control run is forced by unperturbed wind velocities, i.e. winds not affected by the presence of a wind farm, whereas for Model runs 1 and 2 the model is forced by anomaly wind due to wind farm induced wakes. Input to the wake model that is used to force Model run 1 and Model run 2 are respectively Wind Farm Design 1 and Wind Farm Design 2. For all three model experiments a spin up period of 2 days is applied, where the model is forced by unperturbed wind velocity.
Figure 2: Potential wind farm design at the Havsul area. Number of turbines are 70 in both examples
Figure 3: Wind farm induced for the two wind farm designs described in Section 3.2 (Wind Farm Design 1 and 2) at 10 m height. Wind direction is from southwest (217.5 °). Free slip wind speed at 10 m height is 20 m/s.
217
218
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
4. Results 4.1 Control run In Figure 4 the mean sea surface height and surface currents as well as the mean vertical velocity at low and intermediate depths (sigma layer 3), in the Havsul area are shown for the study time period (March 11, 2014 to March 13, 2014). The surface circulation is seen to be in geostrophic balance, and directed toward northeast. This is partly caused by the surface wind stress piling up water along the Norwegian coastline, resulting in offshore sea surface gradients that are balanced by the Coriolis force. For the vertical velocity both positive and negative values are seen, with values ranging from –250 m/day to 250 m/day.
Figure 4: Mean sea surface height and surface currents (upper) and vertical velocity at sigma layer 3 (lower) in the Havsul area for the time period March 11, 2014 to March 13, 2014. The black regions denote the area intended for wind farm installations. 4.2 Anomaly upwelling/downwelling It is seen from Figure 4 that for the unperturbed flow relatively high vertical velocities occur in the Havsul area during the study period. Therefore, in order to estimate the effect of offshore wind farms on the ocean circulation, we calculate the anomaly vertical velocity. It is defined as the difference between the vertical velocity of the control run and that of the two model experiments (Model run 1 and Model run 2). Results after 6 h, 12 h and 24 h of simulation, for sigma layer 3, corresponding to approximately 20 m depth in the vicinity of the wind farm, are shown in Figure 5. For both model runs the absolute value of the anomaly vertical velocity increases with time, and greatest values are seen west/northwest of the wind farms. However, both the anomaly upwelling and downwelling is more significant for Model run 2, where values exceed 90 m/day after 24 hours of simulation. In comparison, for Model run 1, anomaly vertical velocities are everywhere less than 50 m/day.
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
Figure 5: Anomaly vertical velocity at sigma layer 3, corresponding to approximately 20 m depth in the vicinity of the wind farms for the two model experiments: Model run 1 (left) and Model run 2 (right), after 6 h, 12 h and 24 h of simulation. Units are m/day. Also plotted are the locations of turbines included in the wind farm designs (black dots). Wind direction is from southwest for all cases. 4.3 Anomaly wind stress In Figure 6 the difference in sea surface stress between the control run and Model runs 1and 2 are shown (anomaly wind stress), for the area surrounding the wind farms, after 6 h, 12 h and 24 h of simulation. Due to the wakes generated by the wind farms, the anomaly wind stresses are directed southwestward, in opposite direction of the unperturbed wind. It is further seen that the anomaly wind stresses are relatively constant for the three time instances shown, as the wind direction is stable for this time period. At the boundaries of the wind farm the anomaly wind stress approaches zero, resulting in strong wind stress curl. 4.4 Anomaly currents In Figure 7 the difference in horizontal velocity at sigma layer 3, between the control run and Model runs 1and 2 (anomaly currents) after 6 h, 12 h and 24 h of simulations, are shown. It is seen that the anomaly currents are directed southwestward, opposite to the mean unperturbed currents (Figure 4). Amplitudes are of the order 3 cm/s and approximately constant for all three time instances. However, the anomaly currents west of the wind farms is seen to increase after 12 h and 24 h of simulations, in particular this is the case in Model run 2. 5. Discussion and summary From Figure 5 it was shown that the effect of including wind farms in the model simulations was altered vertical velocity near the wind farm. In studies of the ocean response to idealized wakes in a deep and layered ocean, such vertical motion has been attributed to Ekman pumping caused by the wind stress curl [8, 9]. From Figure 6 it is seen that the wind farms generate strong anomaly shear at its boundaries, and that the curl depends on the design of the wind farm, which may result in different upwelling and downwelling regimes in the case of pronounced Ekman pumping. However, the area surrounding the potential wind farms is relatively shallow, and during strong wind conditions, with intense vertical mixing, the surface Ekman layer reaches down to the sea floor (not shown). The strong vertical mixing results in a highly barotropic ocean and the effect of the earth’s rotation is therefore expected to be insignificant for the horizontal scales under consideration. This indicates that the vertical velocity anomalies seen in Figure 5 are not predominately due to Ekman pumping.
219
220
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
Figure 6: Difference in surface stress between Model run 1 and the control run (left) and Model run 2 and the control run (right) in the vicinity of the wind farms after 6 h, 12 h and 24 h of simulation. Units are N/ଶ . Also plotted are the locations of turbines included in the wind farm designs (red dots). Wind direction is from southwest for all cases.
Figure 7: Difference in horizontal velocity at sigma layer 3 between Model run 1 and the control run (left) and Model run 2 and the control run (right) in the vicinity of the wind farms area after 6 h, 12 h and 24 h of simulation. Units are cm/s. Also plotted are the locations of the turbines included in the wind farm designs (red dots). Wind direction is from southwest for all cases.
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222
Figure 8: Model depth [m] in the area near the wind farm (black dots) From Figure 7 it is seen that the oceanic response to reduced wind stress is decreased ocean currents in the flow direction. Due to varying topography in the area of the wind farms modification of the current speed must result in anomaly vertical oceanic motion. After 24 h of simulation strong anomaly vertical velocities west of the wind farm coincides with anomaly currents in the same area (Figures 6 and 7). In this area bathymetry gradients are strong (Figure 8), which indicates that vertical motion is mainly determined by variations in the horizontal flow field, and that this effect is more significant in Model run 2 than it is in Model run 1. In this study it has been shown that vertical oceanic motion may be induced by the presence of large wind farms. Using a wake model that allows for the calculation of the surface wind stress as a function of the wind farm design, it has further been shown that the ocean upwelling/downwelling is influenced by the wind farm design. We have outlined a method of how the ocean response to a specific wind farm design can be calculated, which allows for inclusion of ocean effects in future planning of new offshore wind projects. For the Havsul region it appears that topographic effects play a dominant role in generating vertical velocities, and that Ekman pumping is of less significance. Acknowledgements The authors would like to thank Magnar Reistad at the Norwegian Meteorological Institute, who kindly provided the NORA10 data. References [1] Archer, C.L., Jacobson, M.Z. Spatial and temporal distributions of U.S. winds and wind power at 80 m derived from measurements. J. Geophys.Res. 2003. 108 (D9), 4289. [2] Archer, C.L., Jacobson, M.Z. Evaluation of global wind power. J. Geophys. Res. 2005. 110, D12110. [3] Henderson, A.R., et al. Offshore wind energy in Europe — a review of the state-of-the-art. Wind Energy 6. 2003. p. 35–52. [4] Branover, G.G., Vasilýev, A.S., Gleyzer, S.I., Tsinober, A.B. A study of the behavior of the eel in natural and artificial magnetic fields and an analysis of its reception mechanism. J. Ichthyol. 1971. p. 608–614. [5] Tucker, V.A. A mathematical model of bird collisions with wind turbine rotors. J. Sol. Energy Eng. 1996. p. 253–262. [6] Baidya Roy, S., Pacala, S.W. Can large wind farms affect local meteorology? J. Geophys. Res. 2004. 109, D19101. [7] Rooijmans, P. Impact of a large-scale offshore wind farm on meteorology. Ms Thesis, Utrecht University, Utrecht. 2004. [8] Brostom, G. On the influence of large wind farms on the upper ocean circulation. J. Mar. Sys. 2008. p. 585-591. [9] Paskyabi, M.B., Fer, I. Upper Ocean Response to Large Wind Farm Effect in the Presence of Surface Gravity Waves. Energy Procedia 24. 2013. p. 245-254 [10] Valiela, I. Marine Ecological Processes. Springer-verlag, New York. 1995, 686 pp [11] Christakos K. Characterization of the coastal marine atmospheric boundary layer (MABL) for wind energy applications, Master Thesis, University of Bergen, 2013, URI: http://hdl.handle.net/1956/7186.
221
222
Ole Henrik Segtnan and Konstantinos Christakos / Energy Procedia 80 (2015) 213 – 222 [12] González-Longatt, F., Wall P., Terzija V. Wake effect in Wind Farm Performance: Steady-State and Dynamic Behaviour. Renewable Energy, 2011, p. 329-338 [13] Jensen, N.O. A note on wind turbine interaction. Risø-M-2411. Risoe National Laboratory, Roskilde, Denmark, 1983. 16 pp [14] Wu, J. Wind-Stress coe cients over Sea surface near Neutral Conditions-A Revisit. Journal of Physical Oceanography. 1980. p. 727-740. [15] Charnock, H. Wind stress over a water surface. Quart J Roy Meteorol Soc. 1955 p. 639–640 [16] Kraus, E.B. Atmosphere-Ocean interaction. Oxford University Press, London. 1972. 275 pp [17] Unden et al. HIRLAM-5 Scientific Documentation, HIRLAM-5 Project, SMHI, Norkoping, Sweden. 2002. 146 pp [18] Shchepetkin, A.F., McWilliams J.C. The Regional Ocean Modeling System: A split-explicit, free-surface, topography following coordinates ocean model, Ocean Modelling, 2005, 9, p. 347-404. [19] Fairrall, C.W., Bradley, E.F., Rogers, D.P, Edson, J.B., Young, G.S. Bulk parameterization of air-sea fluxes for tropical Ocean global atmosphere Coupled-Ocean Atmosphere Response Experiment. Journal of Geophysical Research. 1996. P. 3747-3764 [20] Rodi, W. Examples of calculation methods for flow and mixing in stratified fluids. Journal of Geophysical Research. 1987, (C5) p. 53055328 [21] Marchesiello, P., McWilliams J.C., Shchepetkin A.F., Open boundary conditions for longterm integration of regional oceanic models. Ocean Modeling. 2001, p. 1-20 [22] Flather, R.A. A tidal model of the northwest european continental shelf. Memoires de la Société Royale de Sciences de Liège. 1976. p. 141–164 [23] Chapman, D.C. Numerical treatment of cross-shelf open boundaries in a barotropic coastal ocean model. Journal of Physical Oceanography. 1985, p. 1060–1075 [24] Albretsen, J., Sperrevik, A.K., Staalstrøm, A., Sandvik, A.D., Vikebø, F., Asplin, L.. Norkyst-800 report no. 1. User manual and technical descriptions. Report 2; Institute of Marine Research; Nordnesgaten 50, P.O.Box 1870 Nordnes 5817 BERGEN; 2011. [25] Egbert, G.D, Bennet A.F., Foreman M.G.G. TOPEX/POSEIDON tides estimated using a global inverse model, Journal of Geophysical Research.1994, .p.821-24,852 [26] Egbert G.D., Erofeeva S.Y. Efficient Inverse Modeling of Barotropic Ocean Tides. J. Atmos. Ocean. Tech. 2002 p.183-204. [27] Frøysa, K.G (editor), NORCOWE Annual Report. 2010 43 pp [28] Konstantinos Christakos, George Varlas, Joachim Reuder, Petros Katsafados, Anastasios Papadopoulos, Analysis of a Low-level Coastal Jet off the Western Coast of Norway, Energy Procedia, Volume 53, 2014, Pages 162-172, ISSN 1876-6102, http://dx.doi.org/10.1016/j.egypro.2014.07.225. [29] Reistad, M., Breivik, Ø., Haakenstad, H., Aarnes, O.J., Furevik, B.R., Bidlot, J.R.. A high resolution hindcast of wind and waves for the North Sea, the Norwegian Sea, and the Barents Sea. Journal of Geophysical Research. 2011. 116:C05019, doi:10.1029/2010JC006402