A Method For Airfoil Parameterization By B-spline Based On The Normal Constraints

Airfoil design is very important for shape design of aircraft and study on aerodynamic. In order to shorten the development period, reduce the research cost, study the combination of optimization design method based on numerical computation of airfoil aerodynamic performance and numerical wind tunnel experiments becomes the focus of recent researches. Before the numerical computation of airfoil aerodynamic performance, the airfoil needs to be parameterized. The parameterization of airfoil will affect the optimization design of the airfoil.The number of parameters, smoothness, continuity, and the ability to control airfoil optimization process are the criteria for the evaluation of the resulting parameterization of airfoil. In this paper, a method for construction of airfoil parameterization by B-spline based on the normal constraints is presented. The method represents airfoil with a cubic B-spline curve defined over non-uniform knot vector, which is obtained by fitting of airfoil data using the least square method, the normal constraints, and iteration. The organization of the method is as follows. Firstly, the basic idea of algorithm of the improved cubic B-spline parameterization method is presented. Then, we generalize the algorithm to adaptively select the knot vector of the cubic B-spline curve according to the characteristic of the data points. Finally, using airfoil representation, we give a method to fit the wing surface in three dimensional space, and present the basic idea of the algorithm.The experiments show that the presented method performed very well for some typical airfoils. The resulting curve is smooth and with C2 continuity. What's more, there are fewer parameters of airfoil function compared with some classical methods, which is used for the airfoil optimization design.