Aerodynamic Shape Optimization Benchmarks with Error Control and Automatic Parameterization

Abstract

Results are presented for four optimization benchmark problems posed by the AIAA Aerodynamic Design Optimization Discussion Group. The benchmarks are intended to exercise optimization frameworks on representative airfoil and wing design problems. All problems involve drag minimization subject to geometric and aerodynamic constraints. Our design approach involves two forms of adaptation. First, the shape parameterization is gradually and automatically enriched from an initially coarse search space. Second, adjoint solutions are used to drive adaptive mesh refinement to control discretization error. The error threshold is tailored so that the finest meshes, with the greatest accuracy, are used only when nearing the optimum. On the inviscid airfoil design problem, while reducing the drag by a factor of 10, we show how the combination of progressive parameterization and tiered discretization error control can dramatically accelerate the optimization. On the viscous airfoil design problem, we use inviscid analysis-driven optimization to reduce the total drag by a factor of two. Next, we improve the span efficiency factor of a wing by performing twist optimization. Finally, we optimize the Common Research Model wing, managing to hold drag roughly fixed, while targeting an initially-violated pitching moment constraint. Our approach aims to introduce greater complexity and accuracy only when necessary to improve the design, and also support a greater degree of automation.

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

“…This is the inviscid drag reduction of a NACA0012 at M = 0.85 and α = 0. A considerable number of papers have been published on this case [1,2,46,47,48,49,50,51,52,53,54] and it has been shown to be a particularly difficult problem to optimise due to a range of characteristics such as multiple local minima [52], non-symmetric solutions [53] and hysteresis [54].…”

Impact of Shape Parameterisation on Aerodynamic Optimisation of Benchmark Problem

“…Meheut [20] compared a number of optimised aerofoil shapes from six different institutes [4,5,7,13,14,16] with the same flow solver. This produced a range of final drag results (all similar to values declared in the original publications) ranging from 32 to 86 drag counts on a mesh with 1024 points around the aerofoil.…”

“…This case has previously been investigated with a variety of different parameterisation methods: Bèzier Curves [1,2]; B-Splines [3,4,5,6,7]; NURBS [8]; Class/Shape Transformations (CSTs) [9]; Hicks-Henne bump functions [10]; Bèzier Surface FFD [11]; PARSEC [12]; Radial basis function domain element (RBF-DE) deformation [13,14] and Singular Value Decompositions (SVD) [14,15]. Due to the large range of factors influencing the results it is difficult to isolate contribution of the parameterisation method from these previous studies.…”

Unstructured Grid Adaptation: Status, Potential Impacts, and Recommended Investments Towards CFD 2030

“…30 Unstructured mesh adaptation yields a systematic procedure to generate meshes where the discretization error is controlled. Coupling mesh adaptation with shape optimization leads to better functional and gradient evaluation by ensuring that the solutions have equivalent accuracy during the design cycles.…”

“…Design requires the computations of increments, which can become buried in the noise created by changes in discretization error between two di↵erent grids. This can be addressed formally by including error estimation in the design process 30 or using an error estimate that is robust to small changes. 102 The adaptive process may be used to build large databases 12 for simulation or to form snapshots for reduced order modeling or uncertainty quantification.…”