Study of aerodynamic shape optimization for natural laminar wing

Natural laminar wing is a potential technology to minimize the drag coefficient of an aircraft. The code of TRANAIR is used to optimize a natural laminar wing with subject to the constraints on lift coefficient, pitching moment coefficient and geometries height(20%, 80% and max height), and the optimization are carried out with multi-points conditions, C_L=0.45(M:0.735,0.755,0.765,0.775) and C_L=0.50(M:0.755). The nonlinear full potential equation is used to solve flow field, sequential quadratic programming and adaptive refinement Cartesian grids are applied to optimize the aerodynamic shape. Two parameter methods, non-uniform relational B-spline (NURBS) and class function/shape function transformation (CST), are used to represent wing shape and update the new geometry, although the CST method is usually used to describe aerofoil and the NURBS is more applied on three-dimensional curved surface. The optimization results shown that the NURBS method is better than the CST one, and the transition position of laminar flow to turbulent flow are moved backward obviously, the laminar region are more wide than before, and the C_D of the optimized wing decreased 4.5% at C_L=0.45(M:0.755).The optimization method is usable and effective for aerodynamic shape design such as natural laminar wing.