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Introduction to the Ainslie Wake Model (Eddy Viscosity Model) Single w ake w ind speeds [m/s] 300 9.841 9.681 250 9.522 9.362 200 9.203 9.043 8.884 150 8.724 8.565 100 8.405 8.246 Radial distance [m] 50 0 -50 8.086 7.927 7.767 7.608 7.448 7.289 7.129 -100 6.97 6.811 6.651 -150 6.492 6.332 -200 6.173 6.013 -250 5.854 5.694 -300 5.535 5.375 5.216 0 200 400 600 800 Dow nstream distance [m] 1 000 1 200 5.056 4.897 Figure 5: Eddy viscosity model – calculation from WindPRO. A plot from WindPRO is shown in Figure 5. Note, that wind speeds within the near wake zone are approximated through the solution at the near wake distance. References [1] Shames, Irving H.: Mechanics of Fluids, McGraw-Hil International Editions, 1992 [2] Tennekes, H. & J.L. Lumley, A First Course in Turbulence, The MIT Press, 1972 [3] Ainslie, J.F: Calculating the flowfield in the wake of wind turbines, Journal of Wind Engineering and Industrial Aerodynamics, 27 (1988), 213-224. [4] Lange, Bernard; H.P. Waldl; A.G. Guerrero; D. Heinemann & R.J. Barthelmie: Modelling of Offshore Wind Turbine Wakes with the Wind Farm Program FLaP, Wind Energy, 2003 6:87-104. [5] Vermeulen, P.E.J: An experimental analysis of wind turbine wakes, Proceedings of the International Symposium on Wind Energy Systems, Lyngby, 1980. [6] Wendt, John F. (Ed.): Computational Fluid Dynamics – An introduction, 2 nd Edition, Springer-Verlag, 1996. Page 3-7
Introduction to the G.C.Larsen Wake Model 4. Introduction to the G.C. Larsen Model (EWTS II) Introduction This model is a semi analytical model – derived from asymptotic expressions from Prandtl’s rotational symmetric turbulent boundary layer equations. Because of the asymptotic expressions, the model might be somewhat conservative for close spacings. The model is reported in [1] and is also the recommended wake model – for use with wake loading - in the project report from the European Wind Turbine Standards II Project, an EU-funded project finalized in 1999 [2]. This introduction is based on the EWTS-report [2]. A online introduction of the model can be found in the Risø report ‘A simple wake model’ [3] – this report is available online. Model Equations Assuming that similarity exist between deficits at different downstream positions and only moderate velocity deficits, then the wake radius can be described by: R w ⎡ 35 ⎤ = ⎢ 2 ⎥ ⎣ π ⎦ 1/ 5 2 5 [ 3c ] 1/ [ C Ax] 1/ 3 1 T (1) where c 1 is a non-dimensional mixing length, described by l is Prandtl’s mixing length c −1/ 3 1 = l( CT Ax) The c 1 parameter does – according to reference [2] – to some degree separate the rotor drag dependence and thus the c 1 is expected to be relative insensitive to the design and size of the rotor. An alternative and approximated specification of the c 1 parameter is found in section 5.1 of the EWTS II report [2], where the parameter is estimated as seen below in equation (2). This specification is adopted in WindPRO. −1/ 2 ⎡ D ⎤ −5 / 6 c1 = ⎢ ( 0 ) 2 ⎥ CT Ax (2) ⎣ ⎦ where C T is the thrust coefficient A is the rotor area D is the diameter of the upstream rotor x 0 is an approximation parameter, determined by the equation (3) below 3 ⎛ 2R9.5 ⎞ x 0 = 9.5D ⎜ ⎟ −1 (3) ⎝ D ⎠ In the equation above the R 9.5 parameter is determined as: R R 9.5 nb [ R + min( h, R )] = 0.5 nb nb = max( 1.08D,1.08D + 21.7D( I − 0. 05 a ) (4) where Ia is the ambient turbulence intensity at hub height Page 4-1
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Page 11 and 12: Introduction to the N.O. Jensen Wak
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Page 21 and 22: Wake Combination Models 5. Wake Com
Page 23 and 24: Introduction to Turbulence and Wake
Page 25 and 26: Introduction to Turbulence and Wake
Page 27 and 28: Introduction to the Turbulence Mode
Page 29 and 30: Turbulence Model - Frandsen & DIBt
Page 31 and 32: Turbulence Model - D.C. Quarton & T
Page 33 and 34: Turbulence Model - G.C. Larsen 11.
Page 35: Case Studies - Wake Loss Calculatio

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