Turbinas

NAFEMS Conference 2008 United Kingdom

3D MODELLING OF A WIND TURBINE USING CFD
David Hartwanger* and Dr Andrej Horvat†
Intelligent Fluid Solutions (South Africa) david.hartwanger@intelligentfluidsolutions.co.uk
† *

Intelligent Fluid Solutions (United Kingdom) andrej.horvat@intelligentfluidsolutions.co.uk

Key words: CFD, Wind Turbine, Efficiency Abstract
Turbine efficiency remains acritical component of the overall economic justification for a potential wind farm. There is therefore a requirement for prediction methodologies that are capable of addressing the in-situ performance of multiple turbine installations within a specific local environment and operating in a range of conditions. The work presented here is the first stage in a programme of work that aims to develop apractical engineering methodology for the CFD-based assessment of multiple turbine installations. In this first stage a CFD benchmarking exercise was performed using the wind turbine design in the Unsteady Aerodynamics Experiment (UAE) conducted by the US National Renewable Energy Laboratory. Initially blade sections were analysed in 2D and the results used to construct and validate a 3D CFD modelof the turbine. The 3D results were used to develop estimates for actuator disk induction factors. Finally these factors were used to modify the classical actuator disk treatment of wind turbines. The results from the modified actuator disk model were in good agreement both with CFD and experiment. 1.0 Maximum Ideal Efficiency

The ideal, frictionless efficiency of a wind turbine was predictedby A. Betz in 1920 using a simple one-dimensional model. The rotor is represented by an “actuator disk” that creates a pressure discontinuity of area A and local velocity V [1, 2]. The control volume of the model is defined by a stream tube whose fluid passes through the rotor disk. The wind at the inlet to the model has an approach velocity V0 over an area A0 , and a slower downstream velocity V3over a larger area A3 at the outlet. A simple schematic of the model is given in Figure 1.

Figure 1. Control volume for the idealised actuator-disk analysis

1

The actuator disc approach uses the following assumptions: (1) The flow is ideal and rectilinear across the turbine i.e. steady, homogenous, inviscid, irrotational, and incompressible. (2) Both the flow and thrust are uniformacross the disk. (3) The static pressure at the upwind and downwind boundaries is equal to the ambient static pressure. The wind exerts an axial thrust, T on the turbine in the flow direction. An equal and opposite force is exerted by the turbine on the wind through its mounting with the ground. By applying a horizontal momentum relation between sections 0 and 3 the thrust at the rotor disk can befound : & (1) ∑ Fx = −T = m(V0 − V3 ) = ρAV (V0 − V3 ) where ? is the density of the air. The thrust at the turbine is also the differential pressure between stations 1 and 2 multiplied by the disk area:

T = ( p1 − p 2 ) A

(2)

It can be shown that the pressures, p1 and p2 , can be obtained by applying Bernoulli’s equation to portions of the control volume upstream and downstream of theturbine where no work is done. Therefore: 1 p1 − p 2 = ρ ( 02 − V32 ) V (3) 2 Substituting this result into (2) and equating with (1) yields:
1 (V0 + V3 ) 2 where V is the stream velocity at the turbine. V=

(4)

Continuity and momentum therefore require that the velocity V through the disk equal the average of the wind speed and the downstream wake velocity. The fractional decrease in windvelocity between the free stream and rotor plane can be expressed in terms of an axial induction factor, a: V −V a= 0 (5) V0 The maximum value of a = ½, since this requires V3 to reduce to zero. Substituting a into the above relations, the thrust at the turbine disk can be written as:
T= 1 ρAV02 4a (1 − a ) 2

(6)

The power coefficient, Cp , defined as the extracted power over the total available...