Parametric approximation of airfoil aerodynamic coefficients at high angles of attack

Three methods for estimating the lift and drag curves in the 360° angle of attack (α) range with harmonic approximation functions were analyzed in the present work. The first method assumes aerodynamic response of a flat plate, the second utilizes even sine and even cosine approximation functions, and the third method, also utilizing trigonometric functions, was developed with the scope on stall-regulated turbines. The method of the even sine and cosine functions was further developed in the present work by using two independent harmonic approximations in the positive and negative α regions for the estimation of the lift and drag coefficients, and by using four independent harmonic approximations for the estimation of the moment coefficient. Further, it was determined that between α equal to 160° and -160°, the aerodynamic coefficients may be obtained with computationally inexpensive steady two-dimensional Computational Fluid Dynamics (CFD) computations. This was done by a comparison of the results obtained with 2D steady CFD with 3D unsteady CFD. In the present work, reference aerodynamic coefficients were used directly in this α region. Reference aerodynamic coefficients were also used directly in the α region between -30° and 30° as in this region the data is either available of may be computed with 2D CFD. In between the aforementioned α regions, the present approximation method produced lift, drag, and moment coefficient curves satisfactorily close to the reference by using several data points to tune the model, that would otherwise be calculated with 3D CFD.