Abstract: Based on the optimal control theory and Navier-Stokes equations, aerodynamic design of airfoil with multi-constraint conditions, such as aerodynamic and geometric constraint conditions, is studied. According to a given problem, the corresponding adjoint equations, boundary conditions and final cost function formulation are derived in the computational space. In order to achieve the requirements of the numerical solution, final formulations in the physical space is also achieved. Numerical methods are developed effectively. By integrating the aspects, such as the flow analysis, the solution of adjoint equations, gradient solution, optimal arithmetic and grid generation etc., an aerodynamic design method involving drag reduction is successfully developed. Testing results show that the method has outstanding merits in the above aspects. It is effective and feasible for aerodynamic design with a large number of design variables. Computational time consumption is less than the conventional aerodynamic design method.

Key words: aerodynamic design, optimal control theory, multi-constraint condition, Navier-Stokes equations