The power calculation is based on the one-equation model presented by Aditya Choukulkar et al [71], where they proposed a new formulation for calculating the expected power from a wind turbine in the presence of wind shear, turbulence, directional shear and direction fluctuations. The model uses turbulence parameters at varying heights on the rotor swept area to estimate power production.
The formulation to quantify the wind power content is given as, Peq= 1
whereirepresents the vertical slices on the rotor swept area. Cp is the power coefficient, σui2 is the variance of velocity fluctuations atithlevel,U¯iis the wind speed atithlevel,σ2φ
i
is direction fluctuation atith level, andAi is rotor area atith level. This model was used to calculate turbine power.
In this study, results from the simulations without turbine were used for the power calcula-tion. The turbulence intensity and the power difference were also calculated and presented alongside the calculated power production in Table 4. The power difference is defined as;
It is observed that the magnitude of power produced in all the cases is comparatively Table 4.Comparison of power output for forest and non -forest cases
Forest Cases I (%) Power (KW) Power Difference (%)
NF 5.37 550.53 –
close to the expected power output for the model turbine as presented in Figure 31 [1].
Table 4 shows that there is no substantial difference in the power production in forest and non forest cases. In the forest cases, the highest power difference occurred in the sparse pine forest while the least is obtained in the Larch forest in August. Examining the effect
Figure 31.Power curve for the NREL 5MW turbine [1]
of turbulence on power production, various studies have shown that turbulence intensity increases the magnitude of power at lower wind speed and decreases the magnitude near rated wind speed [72], [73]. Considering the mean flow velocity in this study, the results are in agreement with the fact demonstrated in [72].
Nonetheless, comparing the results with the results from the studies of Agafonova [18], where she made use of the Actuator Line Model (ALM) using LES to study the turbulence and power production in cases with and without forest, there appeared to be a significant difference in the power production between forest and no forest cases and the power produced in non forest case was higher than in the forest case [18]. Thus, it was expected that the power produced in the non forest case should be higher than the forest cases, but the reverse is the case in these results as presented in Table 4 and this was attributed to one of the limitations in the power model in use [71].
5 Conclusions
The impact of forest types on wind power production was investigated in this study and the variation in wind power production in different forest cases was examined. A case of no forest and five forest cases with varying densities were considered, and two cases of heterogeneous forest data were also investigated. The OpenFOAM software was used, with the NREL 5MW turbine and forest model and the steady state RANS SIMPLE solver was employed. The results from the simulations of wind farms without turbine were validated with an LES results from [74] and the results showed the highest TKE for sparse forest. For the Larch forests considered at different seasons, there was no significant difference in the TKE produced in the three cases considered, whereas, the study showed that Oak tree produces more TKE than Birch, Beech and Larch forests. Meanwhile, the TKE difference in the case of no forest compared to the dense Pine forest chosen as a reference forest case was approximated to be84.13% .
The heterogeneous forest cases were also compared with homogeneous forest and it was concluded that an experimental verification has to be carried out to ensure the validity of the results.
A turbine simulation was performed to have a visual understanding of the velocity wake over different forest cases. It was found out that the case with no forest has the longest wake development such that the velocity recovers towards the outlet of the domain, while the velocity recovers faster in the forest cases.
Finally, the magnitude of power was calculated and it was seen that even though there are remarkable differences in the turbulence intensity of the cases considered, there were no significant differences in the values of power. This was later discovered to be due to the power equation model used which was found to be currently inaccurate for the cases we examined in this study.
In view of some of the limitations encountered and stated in this study, there is a lot to be done to improve the present work. Considering more forests with similar LAI values can make the forest cases more comparable. The study on heterogeneous forests can be taken up also in order to validate the projection method used to collect the forest data and to establish a definite relation between the LiDAR data and the LAD profile data. Furthermore, a full rotating ADM approach in RANS simulation would have given better results to predict power production, or the ALM approach with LES could also be implemented to have a more reliable power predictions. The power equation model can also be improved or a better and more accurate approach should be adopted to calculate the power production from different forest types.
REFERENCES
[1] Jason Jonkman, Sandy Butterfield, Walter Musial, and George Scott. Definition of a 5-mw reference wind turbine for offshore system development. Technical report, National Renewable Energy Lab.(NREL), Golden, CO (United States), 2009.
[2] Bert Blocken, Ted Stathopoulos, and Jan Carmeliet. Cfd simulation of the atmo-spheric boundary layer: wall function problems. Atmospheric environment, 41:238–
252, 2007.
[3] Bert Blocken, Jan Carmeliet, and Ted Stathopoulos. Cfd evaluation of wind speed conditions in passages between parallel buildings—effect of wall-function rough-ness modifications for the atmospheric boundary layer flow. Journal of Wind Engi-neering and Industrial Aerodynamics, 95:941–962, 2007.
[4] Nigel Wood. Wind flow over complex terrain: a historical perspective and the prospect for large-eddy modelling. Boundary-Layer Meteorology, 96:11–32, 2000.
[5] Bert Blocken, Arne van der Hout, Johan Dekker, and Otto Weiler. Cfd simulation of wind flow over natural complex terrain: case study with validation by field measure-ments for ria de ferrol, galicia, spain. Journal of Wind Engineering and Industrial Aerodynamics, 147:43–57, 2015.
[6] Ashvinkumar Chaudhari et al. Large-eddy simulation of wind flows over complex terrains for wind energy applications. Acta Universitatis Lappeenrantaensis, 2014.
[7] Ashvinkumar Chaudhari, Ville Vuorinen, Oxana Agafonova, Antti Hellsten, and Jari H¨am¨al¨ainen. Large-eddy simulation for atmospheric boundary layer flows over complex terrains with applications in wind energy. In11th World Congress on com-putational mechanics, WCCM, pages 5205–5216, 2014.
[8] Ashvinkumar Chaudhari, Antti Hellsten, Oxana Agafonova, and Jari H¨am¨al¨ainen.
Large eddy simulation of boundary-layer flows over two-dimensional hills. In Progress in Industrial Mathematics at ECMI 2012, pages 211–218. Springer, 2014.
[9] Peter Petrov, Angel Terziev, and Ivan Genovski. Wind flow simulation over flat terrain using cfd based software.
[10] John Roy Garratt. The atmospheric boundary layer. Earth-Science Reviews, 37:89–
134, 1994.
[11] Nilay Sezer-Uzol and Lyle Long. 3-d time-accurate cfd simulations of wind turbine rotor flow fields. In44th AIAA Aerospace Sciences Meeting and Exhibit, page 394, 2006.
[12] Mukesh Marutrao Yelmule and Eswararao Anjuri Vsj. Cfd predictions of nrel phase vi rotor experiments in nasa/ames wind tunnel. International Journal of Renewable Energy Research (IJRER), 3:261–269, 2013.
[13] David Hartwanger and Andrej Horvat. 3d modelling of a wind turbine using cfd. In NAFEMS Conference, United Kingdom, 2008.
[14] Scott Wylie and Simon Watson. Cfd study of the performance of an operational wind farm and its impact on the local climate: Cfd sensitivity to forestry modelling.
InEGU General Assembly Conference Abstracts, volume 15, page 14068, 2013.
[15] JC Lopes da Costa, FA Castro, JMLM Palma, and Peter Stuart. Computer simulation of atmospheric flows over real forests for wind energy resource evaluation. Journal of Wind Engineering and Industrial Aerodynamics, 94:603–620, 2006.
[16] Cian James Desmond, Simon J Watson, Sandrine Aubrun, Sergio Avila, Philip Han-cock, and Adam Sayer. A study on the inclusion of forest canopy morphology data in numerical simulations for the purpose of wind resource assessment. Journal of Wind Engineering and Industrial Aerodynamics, 126:24–37, 2014.
[17] B Dalp´e and Christian Masson. Numerical simulation of wind flow near a forest edge. Journal of wind engineering and industrial aerodynamics, 97:228–241, 2009.
[18] Oxana Agafonova et al. A numerical study of forest influences on the atmospheric boundary layer and wind turbines. Acta Universitatis Lappeenrantaensis, 2017.
[19] Fernando Port´e-Agel, Hao Lu, and Yu-Ting Wu. A large-eddy simulation framework for wind energy applications. InThe fifth international symposium on computational wind engineering, volume 23, 2010.
[20] Luca Lavaroni, Simon J Watson, Malcolm J Cook, and Mark R Dubal. A comparison of actuator disc and bem models in cfd simulations for the prediction of offshore wake losses. InJournal of Physics: Conference Series, volume 524, page 012148.
IOP Publishing, 2014.
[21] Hugo Olivares-Espinosa, Simon-Philippe Breton, Christian Masson, and Louis Dufresne. Turbulence characteristics in a free wake of an actuator disk: comparisons between a rotating and a non-rotating actuator disk in uniform inflow. InJournal of Physics: Conference Series, volume 555, page 012081. IOP Publishing, 2014.
[22] A Chaudhari, O Agafonova, A Hellsten, and J Sorvari. Numerical study of the impact of atmospheric stratification on a wind-turbine performance. InJournal of Physics: Conference Series, volume 854, page 012007. IOP Publishing, 2017.
[23] Wen Zhong Shen, Jens Nørkær Sørensen, and Jian Hui Zhang. Actuator surface model for wind turbine flow computations. Proceedings of EWEC 2007, 2007.
[24] I Dobrev, F Massouh, and M Rapin. Actuator surface hybrid model. InJournal of Physics: Conference Series, volume 75, page 012019. IOP Publishing, 2007.
[25] Benjamin Sanderse, SP Pijl, and Barry Koren. Review of computational fluid dy-namics for wind turbine wake aerodydy-namics. Wind energy, 14:799–819, 2011.
[26] Gilbert Strang and George J Fix. An analysis of the finite element method, volume 212. Prentice-hall Englewood Cliffs, NJ, 1973.
[27] Rainald L¨ohner. An adaptive finite element scheme for transient problems in cfd.
Computer Methods in Applied Mechanics and Engineering, 61:323–338, 1987.
[28] George Karniadakis and Spencer Sherwin. Spectral/hp element methods for compu-tational fluid dynamics. Oxford University Press, 2013.
[29] P Chen and I Jadic. Interfacing of fluid and structural models via innovative struc-tural boundary element method. AIAA journal, 36:282–287, 1998.
[30] Bassem Barhoumi, Safa Ben Hamouda, and Jamel Bessrour. A simplified two-dimensional boundary element method with arbitrary uniform mean flow. Theoreti-cal and Applied Mechanics Letters, 7:207–221, 2017.
[31] Abhinav Golas, Rahul Narain, Jason Sewall, Pavel Krajcevski, Pradeep Dubey, and Ming Lin. Large-scale fluid simulation using velocity-vorticity domain decomposi-tion. ACM Transactions on Graphics (TOG), 31:148, 2012.
[32] Lorena A Barba. Vortex Method for computing high-Reynolds number flows: In-creased accuracy with a fully mesh-less formulation.PhD thesis, California Institute of Technology, 2004.
[33] Xiaowen Shan. Simulation of rayleigh-b´enard convection using a lattice boltzmann method. Physical Review E, 55:2780, 1997.
[34] D Arumuga Perumal and Anoop K Dass. A review on the development of lattice boltzmann computation of macro fluid flows and heat transfer. Alexandria Engi-neering Journal, 54:955–971, 2015.
[35] Shiyi Chen and Gary D Doolen. Lattice boltzmann method for fluid flows. Annual review of fluid mechanics, 30:329–364, 1998.
[36] Parviz Moin and Krishnan Mahesh. Direct numerical simulation: a tool in turbu-lence research. Annual review of fluid mechan[75], ics, 30:539–578, 1998.
[37] Mikael Mortensen and Hans Petter Langtangen. High performance python for di-rect numerical simulations of turbulent flows. Computer Physics Communications, 203:53–65, 2016.
[38] N Stergiannis, C Lacor, JV Beeck, and R Donnelly. Cfd modelling approaches against single wind turbine wake measurements using rans. InJournal of Physics:
Conference Series, volume 753, page 032062. IOP Publishing, 2016.
[39] Stefan Wallin and Arne V Johansson. An explicit algebraic reynolds stress model for incompressible and compressible turbulent flows. Journal of Fluid Mechanics, 403:89–132, 2000.
[40] Philippe R Spalart. Detached-eddy simulation. Annual review of fluid mechanics, 41:181–202, 2009.
[41] B Caruelle and F Ducros. Detached-eddy simulations of attached and detached boundary layers. International Journal of Computational Fluid Dynamics, 17:433–
451, 2003.
[42] David C Wilcox et al. Turbulence modeling for CFD, volume 2. DCW industries La Canada, CA, 1993.
[43] Ricardo Vinuesa, Azad Noorani, Adri´an Lozano-Dur´an, George K El Khoury, Philipp Schlatter, Paul F Fischer, and Hassan M Nagib. Aspect ratio effects in turbu-lent duct flows studied through direct numerical simulation. Journal of Turbulence, 15:677–706, 2014.
[44] Yoshihide Tominaga and Ted Stathopoulos. Cfd modeling of pollution dispersion in a street canyon: Comparison between les and rans. Journal of Wind Engineering and Industrial Aerodynamics, 99:340–348, 2011.
[45] Zhengtong Xie and Ian P Castro. Les and rans for turbulent flow over arrays of wall-mounted obstacles. Flow, Turbulence and Combustion, 76(3):291, 2006.
[46] W Rodi. Comparison of les and rans calculations of the flow around bluff bodies.
Journal of wind engineering and industrial aerodynamics, 69:55–75, 1997.
[47] Salim Mohamed Salim, Riccardo Buccolieri, Andrew Chan, and Silvana Di Sabatino. Numerical simulation of atmospheric pollutant dispersion in an ur-ban street canyon: comparison between rans and les. Journal of Wind Engineering and Industrial Aerodynamics, 99:103–113, 2011.
[48] Guillaume Boudier, LYM Gicquel, Thierry Poinsot, D Bissieres, and C B´erat. Com-parison of les, rans and experiments in an aeronautical gas turbine combustion cham-ber. Proceedings of the Combustion Institute, 31:3075–3082, 2007.
[49] K Hanjalic. Will rans survive les? a view of perspectives. Journal of fluids engi-neering, 127:831–839, 2005.
[50] Joseph Boussinesq. Essay on the theory of running waters. Print. national, 1877.
[51] Qingyan Chen and Weiran Xu. A zero-equation turbulence model for indoor airflow simulation. Energy and buildings, 28:137–144, 1998.
[52] PRaA Spalart and S1 Allmaras. A one-equation turbulence model for aerodynamic flows. In30th aerospace sciences meeting and exhibit, page 439, 1992.
[53] DC Wilcox. Turbulence modelling for cfd. dcw industries, la ca˜nada. CAL, USA, 1998.
[54] Jean Cousteix Tuncer Cebeci. Modeling and computation of boundary-layer flows:
laminar, turbulent and transitional boundary layers in incompressible and com-pressible flows. Springer, 2nd revised and extended ed. edition, 2005.
[55] EA Fadlun, R Verzicco, Paolo Orlandi, and J Mohd-Yusof. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations.
computational physics, 161:35–60, 2000.
[56] Ville Vuorinen and K Keskinen. Dnslab: A gateway to turbulent flow simulation in matlab. Computer Physics Communications, 203:278–289, 2016.
[57] Dudley Brian Spalding, BE Launder, AP Morse, and G Maples. Combustion of hydrogen-air jets in local chemical equilibrium: A guide to the charnal computer program. 1974.
[58] Roger H Shaw and Ulrich Schumann. Large-eddy simulation of turbulent flow above and within a forest. Boundary-Layer Meteorology, 61:47–64, 1992.
[59] Albert Betz. Wind-energie und ihre ausnutzung durch windm¨uhlen. Vandenhoeck, 1926.
[60] Martin OL Hansen. Aerodynamics of wind turbines. Routledge, 2015.
[61] F Hosoi and K Omasa. Estimating vertical leaf area density profiles of tree canopies using three-dimensional portable lidar imaging. InProceedings of the ISPRS work-shop Laser-scanning, volume 9, pages 152–157, 2009.
[62] Tomomi Takeda, Hiroyuki Oguma, Tomohito Sano, Yasumichi Yone, and Yasumi Fujinuma. Estimating the plant area density of a japanese larch (larix kaempferi sarg.) plantation using a ground-based laser scanner. Agricultural and Forest Mete-orology, 148:428–438, 2008.
[63] Bastian Nebenf¨uhr and Lars Davidson. Large-eddy simulation study of thermally stratified canopy flow. Boundary-layer meteorology, 156:253–276, 2015.
[64] Branislava Lalic and Dragutin T Mihailovic. An empirical relation describing leaf-area density inside the forest for environmental modeling. Journal of Applied Mete-orology, 43:641–645, 2004.
[65] Christian Hertel, Michael Leuchner, and Annette Menzel. Vertical variability of spectral ratios in a mature mixed forest stand. Agricultural and forest meteorology, 151:1096–1105, 2011.
[66] Dimitry Van der Zande, Jan Stuckens, Willem W Verstraeten, Bart Muys, and Pol Coppin. Assessment of light environment variability in broadleaved forest canopies using terrestrial laser scanning. Remote Sensing, 2:1564–1574, 2010.
[67] Jason Jonkman, Sandy Butterfield, Walter Musial, and George Scott. Definition of a 5-mw reference wind turbine for offshore system development. Technical report, National Renewable Energy Lab.(NREL), Golden, CO (United States), 2009.
[68] MH Baba-Ahmadi and Gavin Tabor. Inlet conditions for les using mapping and feedback control. Computers & Fluids, 38:1299–1311, 2009.
[69] Suhas Patankar. Numerical heat transfer and fluid flow. CRC press, 1980.
[70] A Chaudhari, Boris Conan, S Aubrun, and A Hellsten. Numerical study of how stable stratification affects turbulence instabilities above a forest cover: application to wind energy. InJournal of Physics: Conference Series, volume 753, page 032037.
IOP Publishing, 2016.
[71] Aditya Choukulkar, Yelena Pichugina, Christopher Clack, Ronald Calhoun, Robert Banta, Alan Brewer, and Michael Hardesty. A new formulation for rotor equivalent wind speed for wind resource assessment and wind power forecasting.Wind Energy, 19:1439–1452, 2016.
[72] Vladislav Akhmatov. Influence of wind direction on intense power fluctuations in large offshore windfarms in the north sea. Wind Engineering, 31:59–64, 2007.
[73] Andrew Tindal, Clint Johnson, Marc LeBlanc, K Harman, E Rareshide, and A Graves. Site-specific adjustments to wind turbine power curves. InAWEA Wind Power Conference, Houston, 2008.
[74] Ashvinkumar Chaudhari, Boris Conan, and Antti Hellsten. Effects of stable atmo-spheric conditoin and various forest densities on wind resource. on Wind Energy Harvesting, 2017.
[75] D Keith Walters and Davor Cokljat. A three-equation eddy-viscosity model for reynolds-averaged navier–stokes simulations of transitional flow. Journal of fluids engineering, 130:121401, 2008.
[76] Hermann Schlichting, Klaus Gersten, Egon Krause, Herbert Oertel, and Katherine Mayes. Boundary-layer theory, volume 7. Springer, 1960.
[77] Hubert Chanson Auth. Hydraulics of Open Channel Flow. An Introduction Basic Principles, Sediment Motion, Hydraulic Modelling, Design of Hydraulic Structures.
Elsevier, 2. ed edition, 2004.