High-Incidence Airfoil Lift and Drag Estimates

Abstract

VARIOUS numerical tools are available to predict the lift and drag behavior of airfoils for preliminary design purposes. To be representative, these codes are typically limited to maximum incidence values close to stall [1,2]. For most applications, these predictions are satisfactory. However, with the large scale interest in and implementation of wind turbines, predictions far beyond stall are required. The need for such estimates are driven by the major numerical tools used for turbine performance estimates, e.g., Aerodyne, WTPerf, etc. [3,4]. These methods implement blade element momentum (BEM) theory, which requires two-dimensional (sectional) airfoil data. BEM analysis may, however, require airfoil data for incidences from 180 to 180 deg. Inaccurate airfoil force coefficient data are generally considered to contribute the largest error in BEM turbine power estimation. To meet the need for highincidence force coefficient estimation, various methodologies have been devised, e.g., those of Viterna and Janetzke [5], Spera [6], and Lindenburg [7]. These methods are all fully empirical with essentially little/no flow physics or theory underpinning their formulation. They are based on large scale experimental observations of the limited data available for high-incidence airfoil and plate testing. The methods are generally composed of an equation set that is implemented using statements conditional upon specified airfoil incidence, etc. Note that this is not implied as a criticism, but an indication of the complexity of the problem. It would be valuable to the aeronautics (rotorcraft) and renewable energy community to have an estimation method that consists of a single (as opposed to piecemeal) expression to estimate airfoil lift and drag from low to extreme incidence. Additionally, using a single unified equation would negate the requirement for tabular lookup data as well as interpolation within this data, as required for many BEM codes. This would greatly simplify the BEM input files and potentially improve accuracy, but would require some recoding of these applications. Consequently, such an approach is presented in this Note. The developed method combines established theory with empirical observation to yield performance estimates. It is not implied that the present method is not empirical; the inherent complication and variability of the flows to be modeled virtually necessitate empiricism. The approach is not suggested to provide exact solutions, but suitable engineering approximations for wind turbine power modeling or high-incidence airfoil aerodynamics. As such it is seen as complementary to the existent methods [5–7]. Following development, the method is compared with experimental data for validation.