Airfoil Optimization Using Practical Aerodynamic Design Requirements

Abstract

Practical aerodynamic design problems must balance the goal of performance optimization over a range of on-design operating conditions with the need to meet design constraints at various off-design operating conditions. Such design problems can be cast as multipoint optimization problems where the on-design and off-design operating conditions are represented as design points with corresponding objective/constraint functions. Two methods are presented for obtaining optimal airfoil designs that satisfy all design objectives and constraints. The first method uses an unconstrained optimization algorithm where the optimal design is achieved by minimizing a weighted sum of the objective functions at each of the operating conditions. To address the competing design objectives between on-design and off-design operating conditions, an automated procedure is used to efficiently weight the off-design objective functions so as to limit their influence on the overall optimization while satisfying the design constraints. The second method uses the constrained optimization algorithm SNOPT, which allows the aerodynamic constraints imposed at the off-design operating conditions to be treated explicitly. Both methods are applied to the design of an airfoil for a hypothetical aircraft where the problem is formulated as an 18-point multipoint optimization.

Aerodynamic Shape Optimization of Benchmark Problems Using Jetstream

“…12,[29][30][31][32][33] The phenomenon only seems to arise under very specific flow conditions that produce a sufficiently ill-posed problem. When the flow conditions are adjusted to a Mach number of 0.75 and lift coefficient constraint of 0.6, non-unique solutions are no longer observed.…”

Comparison of Local and Global Constrained Aerodynamic Shape Optimization

“…Within the context of aerodynamic shape optimization, the presence of a multimodal search space is highly dependent on the extent of the surface representation and the fidelity of the flow analysis tool, although the true aerodynamic optimization problem is independent of these two modules. As such, if given a surface representation method or a specific flow analysis tool, if a multimodal space can be proved using either one of these then it logically follows that a multimodal space must exist for the true aerodynamic optimization problem, and this has been shown for aerofoil optimizations 26,51,53 and primarily for three-dimensional wing 24 and aircraft topology 33 optimizations, however Chernukhin and Zingg 33 have also shown that for a B-spline based parameterization of the surface, drag minimization of the RAE2822 aerofoil has one global optimum. It is therefore imperative to have a surface parameterisation that can represent all possible shapes.…”

Constraint handling in agent-based optimization by independent sub-swarms

“…Furthermore, the design space that describes many ASO problems often contains local optima and has constraints on solutions such as lift and volume, so presents a difficult problem for optimization algorithms to solve. State-of-the-art automated optimization algorithms have recently produced notable results for high fidelity two-dimensional [1], [2] and three-dimensional [3], [4], [5] ASO problems.…”