Computational Fluid Dynamics (CFD) is a promising tool for the analysis and optimization of wind turbine positioning inside wind parks (also known as wind farms) in order to maximize power production. In this paper, 3-D, time-averaged, steady-state, incompressible Navier-Stokes equations, in which wind turbines are represented by surficial forces, are solved using a Control-Volume Finite Element Method (CVFEM). The fundamentals of developing a practical 3-D method are discussed in this paper, with an emphasis on some of the challenges that arose during their implementation. For isolated turbines, results have indicated that the proposed 3-D method attains the same level of accuracy, in terms of performance predictions, as the previously developed 2-D axisymmetric method and the well-known momentum-strip theory. Furthermore, the capability of the proposed method to predict wind turbine wake characteristics is also illustrated. Satisfactory agreement with experimental measurements has been achieved. The analysis of a two-row periodic wind farm in neutral atmospheric boundary layers demonstrate the existence of positive interference effects (venturi effects) as well as the dominant influence of mutual interference on the performance of dense wind turbine clusters.

The aerodynamic analysis of a wind turbine represents a very complex task since it involves an unsteady three-dimensional viscous flow. In most existing performance-analysis methods, wind turbines are considered isolated so that interference effects caused by other rotors or by the site topology are neglected. Studying these effects in order to optimize the arrangement and the positioning of Horizontal-Axis Wind Turbines (HAWTs) on a wind farm is one of the research activities of the Bombardier Aeronautical Chair. As a preliminary step in the progress of this project, a method that includes some of the essential ingredients for the analysis of wind farms has been developed and is presented in the paper. In this proposed method, the flow field around isolated HAWTs is predicted by solving the steady-state, incompressible, two-dimensional axisymmetric Navier-Stokes equations. The turbine is represented by a distribution of momentum sources. The resulting governing equations are solved using a Control-Volume Finite Element Method (CVFEM). This axisymmetric implementation efficiently illustrates the applicability and viability of the proposed methodology, by using a formulation that necessitates a minimum of computer resources. The axisymmetric method produces performance predictions for isolated machines with the same level of accuracy than the well-known momentum-strip theory. It can therefore be considered to be a useful tool for the design of HAWTs. Its main advantage, however, is its capacity to predict the flow in the wake which constitutes one of the essential features needed for the performance predictions of wind farms of dense cluster arrangements.

SUMMARYThis paper proposes and investigates fully coupled control-volume ÿnite element method (CVFEM) for solving the two-dimensional incompressible Navier-Stokes equations. The proposed method borrows many of its features from the segregated CVFEM described by Baliga et al. Thus ÿnite-volume discretization is employed on a colocated grid using either the MAW or the FLO schemes and an element-by-element assembling procedure is applied for the construction of the discretizations equations. In this paper, and unlike the case for most fully coupled formulations available in the literature, the Poisson pressure equation has been retained from the segregated approach. The use of a pressure equation leads to an unfavourable size increase of the fully coupled linear system, but signiÿcantly improves the system's conditioning. The fully coupled system obtained is solved using an ILUT preconditioned GMRES algorithm. The other important element in this paper is the proposal of a Newton linearization of the convection terms in lieu of the common Picard iteration procedure. A systematic comparison between two segregated and four fully coupled fomulations has been presented which has allowed for an evaluation of the individual beneÿts and strengths of the coupling and linearization procedure by studying lid-driven cavity problems and ows past a circular cylinder. All coupled formulations have proven to be signiÿcantly superior both in robustness and e ciency, as compared with the segregated formulation. In some circumstances, the coupled methods yield a converged solution of the system of discretized equations constructed using the FLO scheme, while the segregated formulations diverge. Compared to Picard's linearization, Newton's linearization is more e cient at reducing the number of iterations needed to converge, but requires more computational e ort per iteration from the linear equation solver. Furthermore, the Jacobian matrix should include contributions from the nonlinearity appearing at both the governing-equation level and the interpolation-scheme level to ensure Newton's method convergence. The key element in guaranteeing successful, fully coupled solutions lies in the use of an e cient linear equation solver and preconditioner.

This paper presents a numerical method for aerodynamic investigations on tower-shadow impacts for downwind horizontal-axis wind turbines. In this method, the flowfield is described by the incompressible three-dimensional Navier-Stokes equations. The rotor and tower are idealized respectively as actuator disk and flat plate permeable surfaces, on which external normal surficial forces are balanced by fluid pressure discontinuities. The external forces exerted by the rotor and tower on the flow are prescribed according to the blade-element theory. Dynamic behavior of the rotor aerodynamic characteristics is simulated using either Gormont or Beddoes-Leishman model. The resulting mathematical formulation is solved using a control-volume finite element method. The results presented in this paper include comparisons between predicted and measured data of azimuthal distribution of the angles of attack and the normal force coefficients related to the NREL's combined experiment phase III downwind rotor. In general, the proposed method has demonstrated its capability to represent adequately the measured data. It has been shown that the accuracy of the predicted results depend strongly on the dynamic-stall model as well as on the turbulence model employed.