This paper investigates the boundary-layer characteristics of a wind turbine blade of small chord length. The three-dimensional form of momentum integral equations is derived and used to predict the boundary-layer growth and limiting streamline angles on the blade surface for both attached and separating flow. The chordwise skin friction coefficient is used to identify boundary layer separation and shear layer reattachment locations. The nature of flow near the axis of rotation is discussed and the physical mechanism associated with 3-D and rotational effects is identified. A semi-empirical correction law for the lift coefficient based on 2-D airfoil data is established. Comparing calculated and measured lift curves of a stall controlled wind turbine, it is shown that the proposed correction law may improve significantly the accuracy of the predictions.
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Blade rotation routinely and significantly augments aerodynam c forces during zero yaw horizontal axis wind turbine operation. To understand better the flow physics underlying this phenomenon, three-dimensional and rotational viscous effects on wind turbine blades are investigated by means of a 3-D boundary-Iayer model. The governing equations of the model are derived from 3-D primitive variable boundary-Iayer equations written in cylindrical coordinates in the rotating fratne of reference. The latter are integrated along the peripheral direction with the radial distance as parameter for a particular external flow. The skin friction coefficient is used to identify boundary layer separation and shear layer reattachment locations. Separation and reattachment kinematics shows at inboard locations that while the separation point location is not realIy atTected and remains near the leading edge, the reattachment point advances forward rapidly on the blade chord from the trailing edge as radial distance decreases. It is concluded that the rotational augmentation is linked to specific separation and reattachment state strictly determined by the Coriolis forces.
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The complex flow in the rotor root area is analyzed by means of the boundary layer approach. The approach involves a radial angular velocity (Ekman) boundary-layer on the rotor disk rotating with an angular velocity smaller than that of the fluid, and the circumferential velocity boundary-layer developing on blades. The first explains the smaller adverse pressure gradient at the leading-edge of blades by a vortex-induced sucking effect, and the other shows the contribution of Coriolis force to the closed separation behavior on the suction side of the inboard blade sections, that explains the stall-delay phenomenon. Three-dimensional incompressible steady momentum integral boundary layer equations are used to analyze the leading-edge separation bubble on a rotating blade, including the effect of enhanced rotation at strong winds. The stall-delay phenomenon is described as a three contribution process: vortex-induced sucking effect by an Ekman layer type boundary-layer followed by Coriolis force, which acts in the chordwise direction as a favorable pressure gradient, and centrifugal forces producing a spanwise pumping effect. It appears that the first two contributions play the primary role for the rise of the inboard stall-delay and the centrifugal pumping effect is much less important than generally was supposed before.
Two commonly used methods for predicting unsteady airloads are: 1) the panel method based on the surface distribution of singularity elements and 2) the indicial method for unsteady problems governed by the linearized partial differential equation and linearized boundary conditions. The panel method considered here involves a piecewise linear continuous distribution of singularities (sources and doublets) over the airfoil surface. Since the linearity assumptions of the indicial method do not allow for variations in the form of the chordwise pressure, this approach seems to be more economical from the computational point of view. The present study is aimed at the systematic assessment of the two approaches by considering a number of unsteady two-dimensional flows. Good agreement was found with measured airloads data for the two methods.
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In this paper, an advanced aeroelastic numerical tool for horizontal axis wind turbines (HAWT) is presented. The tool is created by coupling an unsteady aerodynamic model based on the lifting-line approximation with an elastodynamic model based on the beam approximation. The coupling is non-linear in the sense that at every time step the two models interact through data transfer from the one to the other. Two interfaces assure a constant communication between the two parts of the complete model. The aero-to-elastic interface defines the loads exercised on the structure, whereas the elastic-to-aero interface transmits the rates of deformations. The aeroelastic model is evaluated through comparisons of its predictions with experimental data as well as with predictions obtained by simpler models.
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