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Introduction to the Ainslie Wake Model (Eddy Viscosity Model) D M = C b = 8D M T − 0.05 − (16C 3.56C T (1 − 0.5) D M T − 0.5) A /1000 Other authors specify a boundary condition where the initiation position (downwind position) varies. In Lange et al [4] reference to a study made by Vermeulen [5] is made. Vermeulen suggests that the near wake length is modeled through contributions from ambient turbulence, rotor generated turbulence and shear generated turbulence. The near wake length is divided into two regions; the first x h is modeled as: x h = r 0 ⎡⎛ dr ⎞ ⎢⎜ ⎟ ⎢⎣ ⎝ dx ⎠ 2 a ⎛ dr ⎞ + ⎜ ⎟ ⎝ dx ⎠ 2 λ ⎛ dr ⎞ + ⎜ ⎟ ⎝ dx ⎠ 2 m ⎤ ⎥ ⎥⎦ −0.5 where r 0 is an ‘effective’ radius of an expanded rotor disc, = [ D / 2] ( m 1) / 2 D is the rotor diameter C t the thrust coefficient The different contributions in the equation above are calculated as: ⎛ dr ⎞ ⎜ ⎟ ⎝ dx ⎠ ⎛ dr ⎞ ⎜ ⎟ ⎝ dx ⎠ ⎛ dr ⎞ ⎜ ⎟ ⎝ dx ⎠ 2 a 2 λ 2 m ⎧2.5I + 0.05 = ⎨ ⎩5I = 0.012Bλ = for I ≥ 0.02 for I < 0.02 r 0 + and m = 1 / 1− Ct ambient turbulence rotor generated turbulence [(1 − m) 1.49 + m ]/ (9.76(1+ m)) shear - generated turbulence where I is the ambient turbulence intensity B is the number of rotor blades λ is the tip speed ratio Page 3-3
Introduction to the Ainslie Wake Model (Eddy Viscosity Model) 100 Near wake length [m] Near wake length for a RD=44 m turbine 90 80 70 60 50 40 Thrust coefficient - Ct 30 0 0.1 0.2 Iamb=0.05 0.3 0.4 0.5 0.6 0.7 Iamb=0.20 0.8 0.9 1.0 Iamb=0.10 Iamb=0.15 Figure 3: Near Wake Length for a 44 meter Rotor-Diameter Turbine using the Vermeulen Equations. Top: Sensitivity to ambient turbulence. Bottom: Sensitivity to type of turbine and tip speed ratio. When the first near wake region, x h , have been calculated, one can calculate the full near wake length, x n , by: x = 1− 0.212 + 0.145m 0.134 + 0.124m n x h 0.212 + 0.145m 1− 0.134 + 0.124m Lange [4] reports that the equations save a singularity at about C t =0.97, so it is suggested that for C t ’s larger than 0.9, then the value for C t equal to 0.9 is used. A sample calculation for a 44-meter rotor diameter turbine is shown in Page 3-4
Page 1 and 2: WindPRO / PARK Introduction to Wind
Page 3 and 4: Table of Contents 1. Introduction t
Page 5 and 6: 1. Introduction to Wake Modelling 1
Page 7 and 8: 1. Introduction to Wake Modelling T
Page 9 and 10: 1. Introduction to Wake Modelling R
Page 11 and 12: Introduction to the N.O. Jensen Wak
Page 13: Introduction to the Ainslie Wake Mo
Page 17 and 18: Introduction to the Ainslie Wake Mo
Page 19 and 20: Introduction to the G.C.Larsen Wake
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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