In aerodynamic design, good performance is generally required under a range of operating conditions, including off-design conditions. This can be achieved through multipoint optimization. The desired performance objective and operating conditions must be specified, and the resulting optimization problem must be solved in such a manner that the desired performance is achieved. Issues involved in formulating multipoint optimization problems are discussed. A technique is proposed for automatically choosing sampling points within the operating range and their weights to obtain the desired performance over the range of operating conditions. Examples are given involving lift-constrained drag minimization over a range of Mach numbers. Tradeoffs and their implications for the formulation of multipoint problems are presented and discussed.

We present and examine a number of improvements to a gradient-based algorithm for aerodynamic optimization. A Newton-Krylov algorithm is used to solve the compressible Navier-Stokes equations, the gradient is computed using the discrete-adjoint method with a preconditioned Krylov solver, and the optimum is found through a quasi-Newton algorithm with a rank-two update formula. Constraints are imposed by penalizing the objective function. Improvements are made in three areas: 1) thickness constraints are generalized to permit the location of maximum thickness to be determined by the optimizer or alternatively to constrain the cross-sectional area; 2) new scalings of design variables and initial estimates of the inverse Hessian matrix in the quasi-Newton method are investigated; 3) the algebraic grid perturbation algorithm is replaced by an algorithm based on a spring analogy. In each case, the effect of the improvements on the performance of the algorithm is presented.

In aerodynamic design, good performance is generally required under a range of operating conditions, including off-design conditions. This can be achieved through multipoint optimization. The desired performance objective and operating conditions must be specified, and the resulting optimization problem must be solved in such a manner that the desired performance is achieved. Issues involved in formulating multipoint optimization problems are discussed. A technique is proposed for automatically choosing sampling points within the operating range and their weights to obtain the desired performance over the range of operating conditions. Examples are given involving lift-constrained drag minimization over a range of Mach numbers. Tradeoffs and their implications for the formulation of multipoint problems are presented and discussed.