ABSTRACT Recent improvements to the capabilities of a hybrid Navier-Stokes potential flow methodology for modeling horizontal axis wind turbine (HAWT) configurations are presented. The study focuses on three issues: the effects of turbulence models and transition models, the effects of prescribed wake states on predicted rotor performance, and the effects of non-axial flow (yaw) on power generation. Comparisons with measured data for a rotor tested at the National Renewable Energy Laboratory (NREL) is presented.68729

INTRODUCTION

A computational research effort is underway at Georgia Tech in the area of horizontal-axis wind-turbine aerodynamics. The research focuses on understanding the flow mechanisms that affect the performance of wind turbines in non-axial and non-uniform inflow. The effort also addresses the development of efficient computational techniques that complement existing combined blade element-momentum theory methods.

This work is an extension of a 3-D hybrid Navier-Stokes/potential flow solver that has been developed at Georgia Tech for horizontal axis wind turbines (HAWT). In this approach the three-dimensional unsteady compressible Navier-Stokes equations are solved only in a small region, on a body-fitted grid surrounding the rotor blade. Away from the blades, the potential flow equation is solved. The vorticity shed from the blades is modeled as vortex filaments once the vorticity leaves the Navier-Stokes region. These filaments are freely convected by the local flow. Since the costly Navier-Stokes calculations are done only in regions close to the wind turbine blades, and because much of the vorticity is tracked using Lagrangean techniques, this method is an order of magnitude more efficient than Navier-Stokes methods.

The basic hybrid Navier-Stokes potential flow methodology and its application to HAWT under axial-flow conditions are documented in AIAA-99-0042 (Xu and Sankar, 1999).  

SCOPE OF THE PRESENT STUDY

This paper describes recent enhancements to the flow solver, and applications to configurations of interest. The enhancements focused on the following three areas: transition and turbulence modeling, physically consistent wake modeling, and modeling of yaw effects. These three areas are briefly discussed below.

Transition and Turbulence Modeling Issues:

Studies were done to assess the effects of two turbulence models and two transition models on the predicted performance. A one-equation Spalart-Allmaras turbulence model (Shur et al. 1998) and the baseline zero-equation Baldwin-Lomax turbulence model were studied. 

As a consequence of the low relative velocities and small chord lengths encountered in HAWT systems, a significant portion of the boundary layer over the blade can be laminar. The location of the transition line affects the profile power consumed by the rotor, and can impact the power generation. To predict the transition position, two existing transition models, one by Eppler, and a second based on Michel's criterion, were used. The Eppler model is used in many NREL sponsored design codes, and is an obvious first candidate for transition prediction. Michel’s criterion (Michel 1984) is developed based on measurements in two-dimensional, incompressible flow. These models are used in many aircraft industry boundary layer codes, such as those developed by Tuncer Cebeci (1989).

Wake Geometry Modeling:

The prescribed wake model in the hybrid Navier-Stokes/Potential flow analysis has been modified to properly reflect the states that a rotor can assume, as the wind speed changes. It is based on the theory and phenomenology of rotor states, which was presented by Glauert (1937) and was extended by Wilson and Lissaman (1972) to wind rotors.

Yaw Effects:

Finally, a numerical procedure for modeling skewed wind (yaw) conditions has been developed. As in axial flow simulations, the yaw calculations only need to model the aerodynamics of a single blade. Other blades will experience the same load and flow pattern 1/N revolutions later, where N is the number of blades. For a three-bladed rotor the computational domain covers a 120 portion of the rotor disk. The present procedure thus retains the efficiency of hybrid method even for yaw conditions. In contrast to the hybrid method, a full Navier-Stokes solver would require the modeling of all blades, significantly increasing the computational effort.