Optimum aerodynamic design of transonic wing based on viscous adjoint method

Aerodynamic shape optimization design of transonic wing is performed based on viscous adjoint method using compressible Reynolds-Averaged Navier-Stokes equations. The viscous adjoint equations, boundary conditions and gradient formulas for inverse design and drag minimization design of viscous flow are derived. A numerical method is developed for solving adjoint equations. The procedure of optimization has been established by an effective combination of grid generation, flow and adjoint equations solution, gradient solution and quasi-newton algorithm. The multigrid techniques are added to accelerate the convergence of flow and adjoint equations to improve the efficiency of design. Design examples including inverse problem and drag minimization are performed for transonic wing. The results indicate that the present method can be successfully applied to optimization design of transonic wing. Satisfactory designs are usually obtained with 20-30 design cycles.