An Investigation of Induced Drag Minimization Using a Newton-Krylov Algorithm

Abstract

We present an optimization algorithm for the study of induced drag minimization, with applications to unconventional aircraft design. The algorithm is based on a discrete-adjoint formulation and uses an efficient parallel-Newton-Krylov solution strategy. We validate the optimizer by recovering an elliptical lift distribution using twist optimization; we believe this an important, and under-appreciated, benchmark for aerodynamic optimization. The algorithm is further illustrated using several design examples, including planform, spanwise vertical shape, and box-wing optimization.

Induced-Drag Minimization of Nonplanar Geometries Based on the Euler Equations

“…According to linear aerodynamic theory, an elliptical spanwise lift distribution produces the minimum induced drag when the wake is planar. This provides a challenging benchmark for optimization algorithms, because an order-perturbation of the elliptical lift distribution produces an order-2 perturbation in the induced drag [36]. Hence, obtaining the elliptical lift distribution requires sufficient accuracy in the drag prediction.…”

Integrated Geometry Parameterization and Grid Movement Using B-Spline Meshes

“…Using increments helps improve the robustness of the mesh movement while maintaining linearity; note, however, this approach does have implications for gradient-based optimization, 25,27 since K (i) is a function of b (i−1) . Element stiffness is controlled using a spatially varying Young's modulus.…”

A High-Order Parallel Newton-Krylov Flow Solver for the Euler Equations

“…1,2 In order to meet these design requirements, several research groups around the world are developing numerical methods to optimize aircraft that will aid aircraft manufacturers. [3][4][5][6][7][8][9][10][11][12][13][14][15][16] The process for aerodynamic shape optimization is shown in Figure 1, and the aim of this work is to develop an efficient and robust flow solver using high-order methods, which will then be used as a platform for aerodynamic shape optimization. Flow solvers have been developed with high-order finite-element, finite-volume and finite-difference schemes.…”