Christian Masson

A Viscous Three-Dimensional Differential/Actuator-Disk Method for the Aerodynamic Analysis of Wind Farms

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.

Influence of Atmospheric Stability on Wind Turbine Power Performance Curves

The impact of atmospheric stability on vertical wind profiles is reviewed and the implications for power performance testing and site evaluation are investigated. Velocity, temperature, and turbulence intensity profiles are generated using the model presented by Sumner and Masson. This technique couples Monin-Obukhov similarity theory with an algebraic turbulence equation derived from the k-e turbulence model to resolve atmospheric parameters u*, L, T*, and Zo. The resulting system of nonlinear equations is solved with a Newton-Raphson algorithm. The disk-averaged wind speed u disk is then evaluated by numerically integrating the resulting velocity profile over the swept area of the rotor. Power performance and annual energy production (AEP) calculations for a Vestas Windane-34 turbine from a wind farm in Delabole, England, are carried out using both disk-averaged and hub height wind speeds. Although the power curves generated with each wind speed definition show only slight differences, there is an appreciable impact on the measured maximum turbine efficiency. Furthermore, when the Weibull parameters for the site are recalculated using u disk, the AEP prediction using the modified parameters falls by nearly 5% compared to current methods. The IEC assumption that the hub height wind speed can be considered representative tends to underestimate maximum turbine efficiency. When this assumption is further applied to energy predictions, it appears that the tendency is to overestimate the site potential.

An Aerodynamic Method for the Analysis of Isolated Horizontal-Axis Wind Turbines

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.

Appropriate Dynamic-Stall Models for Performance Predictions of VAWTs with NLF Blades

This paper illustrates the relative merits of using Natural Laminar Flow (NLF) airfoils in the design of Vertical Axis Wind Turbines (VAWT). This is achieved by the application of the double-multiple-streamtube model of Paraschivoiu to the performance predictions of VAWTs equipped with conventional and NLF blades. Furthermore, in order to clearly illustrate the potential benefit of reducing the drag, the individual contributions of lift and drag to power are presented. The dynamic-stall phenomena are modelled using the method of Gormont as modified by several researchers. Among the various implementations of this dynamic-stall model available in the literature, the most appropriate and general for NLF applications has been identified through detailed comparisons between predicted performances and experimental data. This selection process is presented in the paper. It has been demonstrated that the use ofNLF airfoils in VAWT applications can lead to significant improvements with respect to conventional design only in a very low wind speed range, the extent of which is negligible with respect to the VAWT operational wind speeds.

AERODYNAMIC SIMULATIONS OF WIND TURBINES OPERATING IN ATMOSPHERIC BOUNDARY LAYER WITH VARIOUS THERMAL STRATIFICATIONS

This paper presents a numerical method for performance predictions of wind turbines immersed into stable, neutral, or unstable atmospheric boundary layer. Tile flowfield around a turbine is described by the Reynolds’ averaged Navier-Stokes equations complemented by the k-e turbulence model. The density variations are introduced into the momentum equation using the Boussinesq approximation and appropriate buoyancy terms are included into the k and e equations. An original expression for the closure coefficient related to the buoyancy production term is proposed in order to improve the accuracy of the simulations. The turbine is idealized as actuator disk surface, on which external surficial forces exerted by the turbine blade on the flow are prescribed according to the blade element theory. The resulting mathematical model has been implemented in FLUENT. The results presented in the paper include the power output and wake development under various thermal stratifications of an isolated wind turbine. In stable stratification, the power output is 4% lower than in neutral condition, while in unstable situation, the power is 3% larger. The predicted wake velocity defects are qualitatively in agreement with experimental observations.Copyright

On the Rotor Effects upon Nacelle Anemometry for Wind Turbines

The objective of this paper is to study the typical atmospheric turbulent flow around the rotor and nacelle of a HAWT, in order to (i) investigate the impact of the turbines rotating blades on the flow field over the nacelle, i.e. the rotor-nacelle interaction; (ii) assess the appropriate anemometer location on the nacelle, and therefore (iii) establish the relationship between wind speed measured near the nacelle and free stream wind speed. The paper presents a numerical method for investigating the effects of rotating rotor blades on the nacelle anemometry of a horizontal axis wind turbine (HAWT). The flow field around the turbine and nacelle is described by the Reynolds averaged Navier-Stokes equations. The k – ε model has been chosen for the closure of time-averaged turbulent flow equations. The rotor is modelled using the actuator-disk concept. The simulation results were performed using a commercial wind turbine rated at 750kW. In general, good qualitative agreements have been found, supporting the validity of the proposed method. However, quantitatively, the accuracy of the simulation results should be confirmed before any use is made in power performance testing.

A control-volume finite element method for dilute gas-solid particle flows

Abstract The formulation of a co-located equal-order Control-Volume-based Finite Element Method (CVFEM) for the solution of two-fluid models of 2-D, planar or axisymmetric, incompressible, dilute gas-solid particle flows is presented. The proposed CVFEM is formulated by borrowing and extending ideas put forward in earlier CVFEMs for single-phase flows. In axisymmetric problems, the calculation domain is discretized into torus-shaped elements and control volumes: in a longitudinal cross-sectional plane, or in planar problems, these elements are three-node triangles, and the control volumes are polygons obtained by joining the centroids of the three-node triangles to the midpoints of the sides. In each element, mass-weighted skew upwind functions are used to interpolate the convected scalar dependent variables and the volume concentrations. An iterative variable adjustment algorithm is used to solve the discretized equations. The capabilities of the proposed CVFEM are illustrated by its application to two test problems and one demonstration problem, using a simple two-fluid model for dilute gas-solid particle flows. The results are quite encouraging.

TOWARD BLADE-TIP VORTEX SIMULATION WITH AN ACTUATOR-LIFTING SURFACE MODEL

This paper presents a new method based on the imposition of velocity discontinuities to model °ow perturbation due to existence of vortical structures. The proposed method uses actuator disk and lift- ing line concepts in order to provide a framework of analysis that respects conservation laws for mo- mentum, energy and vorticity, which is not the case of classical actuator disk methods used in the wind industry. The °oweld is described by the Euler equations. In the proposed mathematical model, the attitude toward °ow determination is entirely linked to the vorticity structure of the °ow, which is modeled by velocity discontinuities. Results are produced for three basic problems of interest : 2D uniform vorticity distribution, actuator disk with uniform loading andnite wing with prescribed dis- tribution of circulation. These cornerstone prob- lems have shown that numerical method gives fairly precise values regarding °ow streamlines, lift and induced velocities predictions for all problems in- vestigated. Induced drag prediction for thenite wing problem could not be measured since proper grid-independent solution to this problem could not be attained.

Automated method for transition prediction on wings in transonic flows

The use of stability analyzers based on the linear stability theory and coupled with the e n method in e owe eld calculationprocedures (viscous/inviscidinteractivemethods,Navier -Stokessolvers )hasbeenimpeded by thatthey require tremendous amounts of information, knowledge, and interaction from the user. A systematic procedure is proposed to obtain a linear stability analyzer suitable for integration in wing performance calculation methods. The proposed transition prediction method relies on the use of a database of stability characteristics of a model three-dimensional compressible boundary layer. A coupling method based on the physical parameters of the mean e ow, such as local Mach number, Reynolds number, and boundary-layer shape factor, allows the extraction from the database of quantities such as the amplie cation rate for a given frequency or the maximum amplie cation frequency of the boundary layer studied. The stability characteristics of the model boundary are precomputed, by the use of the compressible linear stability equations with the classical parallel e ow assumption and without curvature effects. The results obtained with the proposed automated stability analysis method have shown that it provides a qualitatively adequate representation of a transonic three-dimensional e ow stability characteristics: dominant instability type, frequency of maximum amplie cation, and amplie cation rate. Computations of the n factorwereperformed fortheAS409 conicalwingand two Bombardierbusinessaircraftwings. Forthesecases,the automated method n factors are higher than those obtained by a complete eigenvalue calculation. This difference is largely because the model boundary layer used does not provide a completely appropriate representation of the crosse ow velocity proe les. However, it is within the range of variation of the n factor from one case to the other, when the full eigenvalue solution is used. Comparison of the calculated n factors and the experimentally observed location of transition on the Bombardier wings has revealed a spanwise variation of the critical n factor, with both the complete and automated calculation methods. To improve the prediction of transition, a relation between the n factor at transition and a local Reynolds number (varying along the span )is proposed. The proposed automated method provides considerable reductions in both the computational time and the input required from the user, which allows it to be incorporated in the design cycle.

Convergence Criterion for a Far-Field Drag Prediction and Decomposition Method

a = speed of sound, m=s Cd = drag coefficient D = drag, N dm = minimal distance, m f = pressure and momentum forces, kPa M = Mach number n = unit normal vector nx; ny; nz P = pressure, kPa R = gas constant, J=kg K S = relative to a surface or a plane, m s = entropy, J=K T = temperature, K or, C v = velocity vector u; v; w , m=s = specific heat ratio H = variation of total enthalpy relative to freestream, J=kg s = variation of entropy relative to freestream, J=K = viscosity, N s=m = density, kg=m = deviatoric stress tensor x; y; z , N=m = domain volume, m