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Improvements in ECN Wake Model
Versteeg, M.C.; Ozdemir, H.; Brand, A.J.
Gepubliceerd door: Publicatie datum:
ECN Windenergie 9-8-2013
ECN publicatienummer: Publicatie type:
ECN-M--13-018 Conferentiebijdrage
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Wind turbines extract energy from the flow field so that the flow in the wake of a wind turbine contains less energy and more turbulence than the undisturbed flow, leading to less energy extraction for the downstream turbines. In large wind farms, most turbines are located in the wake of one or more turbines causing the flow characteristics felt by these turbines differ considerably from the free stream flow conditions. The most important wake effect is generally considered to be the lower wind speed behind the turbine(s) since this decreases the energy production and as such the economical performance of a wind farm. The overall loss of a wind farm is very much dependent on the conditions and the lay-out of the farm but it can be in the order of 5-10%.

Apart from the loss in energy production an additional wake effect is formed by the increase in turbulence intensity, which leads to higher fatigue loads. In this sense it becomes important to understand the details of wake behavior to improve and/or optimize a wind farm layout. Within this study improvements are presented for the existing ECN wake model which constructs the fundamental basis of ECN’s FarmFlow wind farm wake simulation tool [1].

The ECN wake model is called WakeFarm [2, 3, 4] and, based on the original UPMWAKE model proposed by Crespo et al. [5, 6], that simulates the wind turbine wakes by solving the steady parabolized Navier-Stokes equations in perturbation form in three-dimensions. The basic background flow is modeled by an atmospheric wind profile model based on Monin-Obukhov similarity theory [7]. The similarity relations suggested by Businger [8] et al. are used. Furthermore the perturbation variables are initialized by a near wake model where the parabolization is not justified since the axial-pressure gradient term is neglected.

Schepers [2] pointed out the problem in the near wake and used an empirical velocity-deficit profile as a boundary condition for the far wake. This approach depends on a data-fit with experimental data and the physics of the flow are not modeled explicitly. Schepers and Van der Pijl [4] proposed a model for the near wake based on the free-wake vortex method where the wind turbine is modeled by an actuator disc model and the wake is represented by discrete constant strength vortex rings. They obtained the solution with a panel method. A near wake model is presented here based on a free wake-vortex method as well, where the radius of the wake and vorticity strength of discrete vortex rings are varied as suggested by Øye [9]. The induced velocities are obtained by a semi-analytical solution of the Biot-Savart law.

The diabatic wind profiles for the surface layer of the atmospheric boundary layer have been investigated extensively [8, 10]. The atmospheric stability model based on Monin-Obukhov [7] theory is only valid within the surface layer of the atmospheric boundary layer. Previous studies [11, 12, 13] show that boundary layer height varies typically between 50-200m under stable conditions and 500-1000m under unstable conditions. A need for a model that extends to the entire boundary layer height is obvious considering the sizes of modern wind turbines. Blackadar [14] and Lettau [15] studied a wind shear model covering the entire boundary layer height under neutral condition. Gryning et al. [16] extended this model to cover all stability conditions of the atmosphere based on measurements extending in to the mixing layer region where the surface layer scaling is connected with the geostrophic drag law. More recently similar work is done by Pe˜na et al. [17]. Sathe et al. [18] showed that the loads are predicted smaller with the model proposed by Gryning when compared to models based only on surface layer wind profiles.

Within this study the ECN wake model is extended further based on the model proposed by Gryning et al. [16]. The numerical solution obtained by the ECN wake model using Gryning model is compared with the solution obtained by surface layer model and with the available data obtained by EWTW measurements.

The outline of this paper is as follows: First of all the governing equations of the ECN wake farm model are presented. Then the near wake modeling is discussed and the results compared with the original near wake modeling and EWTW data as well as the results obtained for various near wake implementation cases are shown. The details of the atmospheric stability model are given and the comparison with the solution obtained for the original surface layer model and with the available data obtained by EWTW measurements are presented. Finally the conclusions are summarized.

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