Models of Lift and Drag Coefficients of Stalled and Unstalled Airfoils in Wind Turbines and Wind Tunnels

Equations are developed with which to calculate lift and drag coefficients along the spans of torsionally-stiff rotating airfoils of the type used in wind turbine rotors and wind tunnel fans, at angles of attack in both the unstalled and stalled aerodynamic regimes. Explicit adjustments are made for the effects of aspect ratio (length to chord width) and airfoil thickness ratio. Calculated lift and drag parameters are compared to measured parameters for 55 airfoil data sets including 585 test points. Mean deviation was found to be -0.4 percent and standard deviation was 4.8 percent. When the proposed equations were applied to the calculation of power from a stall-controlled wind turbine tested in a NASA wind tunnel, mean deviation from 54 data points was -1.3 percent and standard deviation was 4.0 percent. Pressure-rise calculations for a large wind tunnel fan deviated by 2.7 percent (mean) and 4.4 percent (standard). The assumption that a single set of lift and drag coefficient equations can represent the stalled aerodynamic behavior of a wide variety of airfoils was found to be satisfactory.