Airfoil Parameterization By Cubic NURBS Curve

Aerodynamic design is an important part of the content and the geometrical representation and the parameterization are key issues.The current airfoil design study usually combines the airfoil optimization method which is carried out by the numerical calculation that is based on aerodynamic performance with the wind tunnel test.The advantages of this research method are low cost and short cycle.Airfoil parameterization is the basis of numerical calculations,so the process of the airfoil parameterization is an important step in the design of the airfoil.The airfoil parameterization results will directly affect the final airfoil design results.The evaluation criteria of parameterization are usually composed of the smoothness,continuity and precision of the optimization results.Non-uniform rational B-spline(NURBS)method have many excellent properties,so it becomes the most important parametric representation of curve and surface in geometric design,and the cubic NURBS curve is used commonly.In order to ensure the smoothness and continuity and to meet the high precision fitting of the digital wind tunnel test,and to improve the fitting accuracy in the front part of the airfoil,this paper gives a airfoil parametric method by using NURBS curve.The method uses a cubic NURBS curve to express the airfoil,and uses the quasi-Newton algorithm fit airfoil data points so that results meet the high precision fitting requirements of the aerodynamic experiment.Through a large number of experimental results,for the typical airfoils the cubic NURBS curve airfoil parameterization method can be fitted with high precision,that is,the fitting error is less than47 10-× and the results are satisfied C2 condition.The method is easy to implement and has universal applicability,which is beneficial to the promotion of airfoil surface.The structure of this paper is as follows: The first chapter introduces research background and main work of the airfoil parameterization.The second chapter introduces the definition and properties of the NURBS curve and the B-spline airfoil parameterization method.In chapter 3,three NURBS curve airfoil parameterization method and related algorithm flows are proposed.In the fourth chapter,the parametric experiments of typical airfoils are carried out by the three NURBS curve method and compared with the existing method.