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Introduction to the N.O. Jensen Wake Model 2. Introduction to the N.O. Jensen Wake Model The N.O. Jensen wake model is a simple single wake model. The model is documented in the paper ‘A Simple Model for Cluster Efficiency’ by I. Katić et al [1] and is based on the assumption of a linearly expanding wake diameter. This note gives an introduction to the N.O. Jensen wake model and how it is implemented in WindPRO. Figure 1: The N.O. Jensen wake model - overview. Single Wake Calculation When calculating the velocity deficit, the reduced wind speed, V, downwind of the turbine is derived from: ( 1− 1− C ) ( 1 2kX ) 2 1− V / U = T + D (1) Comparing this equation with the previously derived equation for the wind speed just downwind of the turbine (2), it is obvious that the assumption is a linearly expanding wake width. V 0 U = 1− C T (2) where V 0 is the wind speed directly after the turbine of consideration However it is noticed, that it is not the actual wake wind velocity that is subject for this expansion assumption, but rather the velocity deficit δV i =(1-V i /U). Note, that the velocity deficit is defined through the free wind speed, U. A plot from a calculation in WindPRO is shown in Figure 2. Note, that the wake velocity deficit is uniform given a certain downstream position. Page 2-1
Introduction to the N.O. Jensen Wake Model Single w ake w ind speeds [m/s] Radial distance [m] 300 250 200 150 100 50 0 -50 -100 -150 -200 -250 -300 0 200 400 600 Dow nstream distance [m] 800 1 000 1 200 10 9.834 9.669 9.503 9.338 9.172 9.006 8.841 8.675 8.509 8.344 8.178 8.013 7.847 7.681 7.516 7.35 7.185 7.019 6.853 6.688 6.522 6.356 6.191 6.025 5.86 5.694 5.528 5.363 5.197 5.032 4.866 4.7 Figure 2: N.O. Jensen wake model - wake development after a single turbine. Multiple Wake Calculation Katic et al. [1] suggests, that multiple wakes are calculated through the ‘sum of squares of velocity deficits’ wake combination model. Thus, the N.O. Jensen model initially implemented in the WindPRO PARK module as well as the WAsP / Park module uses the sum of squares of velocity deficit to calculate a combined wake contribution. The combined effects of multiple wakes are found as: δV n n−1 = ∑ kn k = 1 ( ) 2 δV This model is treated in a succeeding chapter. References [1]I. Katić, J. Højstrup & N.O. Jensen, A Simple Model for Cluster Efficiency, European Wind Energy Association, Conference and Exhibition, 7-9 October 1986, Rome, Italy. Page 2-2
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: 1. Introduction to Wake Modelling R
Page 13 and 14: 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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