Sensitivity Analysis to Control the Far-Wake Unsteadiness Behind Turbines

Abstract

Abstract:We explore the stability of wakes arising from 2D flow actuators based on linear momentum actuator disc theory. We use stability and sensitivity analysis (using adjoints) to show that the wake stability is controlled by the Reynolds number and the thrust force (or flow resistance) applied through the turbine. First, we report that decreasing the thrust force has a comparable stabilising effect to a decrease in Reynolds numbers (based on the turbine diameter). Second, a discrete sensitivity analysis identifies two regions for suitable placement of flow control forcing, one close to the turbines and one far downstream. Third, we show that adding a localised control force, in the regions identified by the sensitivity analysis, stabilises the wake. Particularly, locating the control forcing close to the turbines results in an enhanced stabilisation such that the wake remains steady for significantly higher Reynolds numbers or turbine thrusts. The analysis of the controlled flow fields confirms that modifying the velocity gradient close to the turbine is more efficient to stabilise the wake than controlling the wake far downstream. The analysis is performed for the first flow bifurcation (at low Reynolds numbers) which serves as a foundation of the stabilization technique but the control strategy is tested at higher Reynolds numbers in the final section of the paper, showing enhanced stability for a turbulent flow case.

Multiple Wind Turbine Wakes Modeling Considering the Faster Wake Recovery in Overlapped Wakes

“…The roughness length-based model treats wind turbines as obstacle elements or roughness elements that impact the atmospheric wind profile, which is specifically used in predicting the wake loss over a large wind farm or the wake interaction between wind farms [5]. The field model, or the computational fluid dynamics (CFD) model solves the Navier-Stokes equation to obtain detailed flow field information [6,7], and has high precision but is time consuming and computationally expensive, which hinders applications in engineering fields that require multiple computations of the wind farm power, such as wind farm layout optimization. The kinematic model (or empirical model) analytically obtains the wake velocity distribution behind a single turbine based on some ideal hypotheses.…”

Stochastic Wake Modelling Based on POD Analysis

“…The reduced wind speed and enhanced turbulence in the wake flow leads to power losses [1,2] and increased fatigue loadings [3]. Therefore, modeling of wakes plays a key role in the design process of wind turbines and entire wind farms [4][5][6][7] as well as in the emerging field of wind farm control [8][9][10][11][12].…”

Enhanced stability of flows through contraction channels: Combining shape optimization and linear stability analysis

“…Other flow sensitivities, e.g. to base flow modification or steady forcing 33,36,44,48,49 , have been defined in the literature but are not considered here. Generally speaking, sensitivity analyses define the "sweet spots" for the location of passive control mechanisms and the regions where small modifications lead to the largest modification of the eigenmode behaviour (e.g.…”

“…The numerical study of flow sensitivity relies on the use of adjoint solutions 29 . The importance of adjoint and sensitivity maps, together with the mathematical tools required for the study of the sensitive flow regions, to different parameters, were first introduced by Hill 30 , and have been used extensively to examine the receptivity to internal and external modifications 24,29,31 , and also by the authors Ferrer, de Vicente, and Valero 32 , Browne et al 33 , Iorio, González, and Ferrer 34 , Gonzalez, Ferrer, and Diaz-Ojeda 35 , Ferrer, Browne, and Valero 36 . Having determined the most sensitive flow regions, it becomes relatively simple to apply a flow control technique.…”