Gradient-Based Optimum Aerodynamic Design Using Adjoint Methods
In the second part, the adjoint methods are applied to the problem of minimizing drag coefficient, at fixed lift coefficient, for 2-D transonic airfoil flows. Reduced gradients of several functionals are derived through application of a Lagrange Multiplier Theorem. The adjoint system is carefully studied including the adjoint characteristic boundary conditions at the far-field boundary. A super-reduced design formulation is also explored by treating the angle of attack as an additional state; super-reduced gradients can be constructed either by solving adjoint equations with non-local boundary conditions or by a direct Lagrange multiplier method. In this way, the constrained optimization reduces to an unconstrained design problem. Numerical methods based on Jameson's finite volume scheme are employed to solve the adjoint equations. The same grid system generated from an efficient hyperbolic grid generator are adopted in both the Euler flow solver and the adjoint solver. Several computational tests on transonic airfoil design are presented to show the reliability and efficiency of adjoint methods in calculating the reduced (super-reduced) gradients.
- Doctoral Dissertations