A set of linear equations describing the motion of an operating 3-bladed HAWT are obtained from the dynamic characteristics of the stationary turbine by adding rotating frame effects. The approach makes use of the Coleman multi-blade transformation to present all results relative to the fixed frame. The formulation is in terms of a selected number of stationary, real, mode shapes. The formulation is applied to the expression of both the aerodynamic loading and the displacement response in terms of the operating mode shapes. This technique is applied to the conditions of vertical wind shear and off-yaw operation of a hypothetical 46-m wind turbine. The principal objective of the paper is to enable the characteristic of the inflow to be related to the nature of the response. A second objective is to illustrate a method of extracting linearized models from general aeroelastic codes such as ADAMS™.

This paper presents a framework for the dynamic and aeroelastic analysis of a horizontal axis wind turbine modeled as a multi-flexible-body system. The multi-rigid-body portions of the system, composed of the nacelle and hub, are modeled as a system of interconnected rigid bodies using Kane’s equations. The flexible portions, composed of the the blades and tower, are represented using nonlinear beam finite elements, taken from a mixed formulation for the dynamics of moving beams. Each analysis leads to a set of symbolic equations that can be coupled symbolically to represent the dynamic behavior of the wind turbine. A solution procedure is implemented to assess the dynamic stability of the system. Here the solution is divided into two parts: a set of nonlinear ordinary differential equations governing the periodic steady-state operating condition, and a set of equations that are linearized about the steady-state operating condition governing the transient dynamics. The harmonic balance method is used for the nonlinear periodic steady-state solution, and the finite element in time method is proposed as an alternative method. Linearization of the equations about the steady-state operating condition yields system equations with periodic coefficients which are solved by Floquet approach to extract the modal parameters. For the aeroelastic analysis, aerodynamic loads from an aerodynamic model to be selected in the future will be inserted into the present framework. Then, the framework can produce a symbolic system matrix, potentially useful for control design. Numerical results are presented for the dynamic characteristic of HAWT’s with flexible tower and blades.

The effect of laminar separation bubbles on the surface pressure distribution and aerodynamic force characteristics of two quite different airfoils is studied numerically. The low-Reynolds-number Eppler E387 airfoil is analyzed at a chord Reynolds number of 1.0×10 5 whereas the NREL S809 airfoil for horizontal-axis wind turbines is analyzed at 1.0×10 6 . For all cases in the present study, bubble induced vortex shedding is observed. This flow phenomenon causes significant oscillations in the airfoil surface pressures and, hence, airfoil generated aerodynamic forces. The computed time-averaged pressures compare favorably with wind-tunnel measurements for both airfoils.

Surface pressure data were acquired using the NREL Unsteady Aerodynamics Experiment, a full-scale horizontal axis wind turbine, which was erected in the NASA Ames 80 ft × 120 ft wind tunnel. Data were collected first for a stationary blade, and then for a rotating blade with the turbine disk at zero yaw. Analyses compared aerodynamic forces and surface pressure distributions under rotating conditions against analogous baseline data acquired from the stationary blade. This comparison allowed rotational modifications to blade aerodynamics to be characterized in detail. Rotating conditions were seen to dramatically amplify aerodynamic forces, and radically alter surface pressure distributions. These and subsequent findings will more fully reveal the structures and interactions responsible for these flow field enhancements, and help establish the basis for formalizing comprehension in physics based models.

A numerical technique has been developed for efficiently simulating fully three-dimensional viscous fluid flow around horizontal axis wind turbines (HAWT). In this approach, the viscous region surrounding the blades is modeled using 3-D unsteady Navier-Stokes equations. The inviscid region away from the boundary layer and the wake is modeled using potential flow. The concentrated vortices that emanate from the blade tip are treated as piecewise straight line segments that are allowed to deform and convect at the local flow velocity. Biot-Savart law is used to estimate the velocity field associated with these vortices. Calculations are presented under axial wind conditions for a NREL two-bladed rotor, known as the Phase VI rotor, tested at the NASA Ames Research Center. Good agreement with the measurements is found. The computed results are used to develop improved engineering models for the loss of lift at the blade tip, and for the delay in the stall angle at inboard locations. The improved models are incorporated in a blade element-momentum (BEM) analysis to study the post-stall behavior of a three-bladed rotor tested at NREL.

Blade rotation routinely and significantly augments aerodynamic forces during zero yaw HAWT operation. To better understand the flow physics underlying this phenomenon, time dependent blade surface pressure data were acquired from the NREL Unsteady Aerodynamics Experiment, a full-scale HAWT tested in the NASA Ames 80 ft × 120 Ft wind tunnel. Time records of surface pressures and normal force were processed to obtain means and standard deviations. Surface pressure means and standard deviations were analyzed to identify boundary layer separation and reattachment locations. Separation and reattachment kinematics were then correlated with normal force behavior. Results showed that rotational augmentation was linked to specific separation and reattachment behaviors, and to associated three-dimensionality in surface pressure distributions.

The performance of the NREL Phase VI horizontal axis wind turbine has been studied with a 3-D unsteady Navier-Stokes solver. This solver is third order accurate in space and second order accurate in time, and uses an implicit time marching scheme. Calculations were done for a range of wind conditions from 7 m/s to 25 m/s where the flow conditions ranged from attached flow to massively separated flow. A variety of turbulence models were studied: Baldwin-Lomax Model, Spalart-Allmaras one-equation model, and k-ε two equations model with and without wall corrections. It was found all the models predicted the normal forces and associated bending moments well, but most of them had difficulties in modeling the chord wise forces, power generation, and pitching moments. It was found that the k-ε model with near wall corrections did the best job of predicting most the quantities with acceptable levels of accuracy. Additional studies aimed at transition model development, and grid sensitivity studies in the tip region are deemed necessary to improve the correlation with experiments.

The effects of wind shear and turbulence on rotor fatigue and loads control are explored for a large horizontal axis wind turbine in variable speed operation from 4 to 20 m/s. Two and three blade rigid rotors are considered over a range of wind shear exponents up to 1.25 and a range of turbulence intensities up to 17%. RMS blade root flatwise moments are predicted to be very substantially increased at higher wind shear, and resultant fatigue damage is increased by many orders of magnitude. Smaller but similar trends occur with increasing turbulence levels. In-plane fatigue damage is driven by 1P gravity loads and exacerbated by turbulence level at higher wind speeds. This damage is higher by one to two orders of magnitude at the roots of the three blade rotor. Individual blade pitch control of fluctuating flatwise moments markedly reduces flatwise fatigue damage due to this source, and to a lesser degree the in-plane damage due to turbulence. The same is true of fluctuating rotor torque moments driven by turbulence and transmitted to the drive train. Blade root moments out of the plane of rotation aggregate to create rotor pitching and yawing moments transmitted to the turbine structure through the drive train to the yaw drive system and the tower. These moments are predicted to be relatively insensitive to turbulence level and essentially proportional to the wind shear exponent for the two blade rotor. Fluctuating moments are substantially reduced with individual blade pitch control, and addition of a teeter degree of freedom should further contribute to this end. Fluctuating pitching and yawing moments of the three blade rotor are substantially less sensitive to wind shear, more sensitive to turbulence level, and substantially lower than those for the two blade rotor. Mean rotor torque and hence power are essentially the same for both rotors, independent of wind shear, and somewhat reduced with individual blade pitch control of fluctuating flatwise moments. The same is true of mean rotor thrust, however fluctuations in rotor thrust are substantially reduced with individual blade pitch control. It appears, on balance, that higher wind shear coupled with turbulence effects should be accounted for in the fatigue design of large, long life turbines. Much more work is required on this problem.

A vortex lattice code, CAMRAD II, and a Reynolds-Averaged Navier-Stoke code, OVERFLOW-D2, were used to predict the aerodynamic performance of a two-bladed horizontal axis wind turbine. All computations were compared with experimental data that was collected at the NASA Ames Research Center 80-by 120-Foot Wind Tunnel. Computations were performed for both axial as well as yawed operating conditions. Various stall delay models and dynamics stall models were used by the CAMRAD II code. Comparisons between the experimental data and computed aerodynamic loads show that the OVERFLOW-D2 code can accurately predict the power and spanwise loading of a wind turbine rotor.

This paper presents a numerical method for investigating nacelle anemometry of an horizontal axis wind turbine. The flowfield 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 turbine is modeled using the actuator disk concept. Most of the nacelle region is represented by it real geometrical shape as wall boundary, except for the cooling system (radiator) of the electric generator which is modeled as a permeable surface with some prescribed pressure jump. The main purpose of this paper is to establish the relationship between the nacelle wind speed and free stream wind speed for an isolated turbine, in order to assess the impacts of the variation of some operational parameters (e.g. blade pitch angle changes), as well as atmospheric turbulence, on this relationship. The simulation results have been compared with the experimental data (from a typical stall-controlled wind turbine rated more than 600 kW and comercially available). In general, good qualitative agreements have been found proving the validity of the proposed method. However, the level of accuracy is still insufficient for use in power performance testing. On the other hand, the numerical method might be a useful tool for locating nacelle anemometers.