High-Fidelity Wing Design Exploration with Gradient-Based Optimization

Abstract

Numerical optimization has been applied to wing design problems for over 40 years. Over the decades, the scope and detail of optimization problems have advanced considerably. At the present time, the state-of-the-art in wing design optimization incorporates high-fidelity modeling of the steady-state aeroelastic response of the wing at both on-design and off-design operating conditions. Reynolds-averaged solutions of the Navier–Stokes equations coupled with linear finite element anal- ysis offer the highest fidelity modeling currently tenable in an optimization con- text. However, the complexity of implementing and cost of executing high-fidelity aerostructural optimization have limited the extent of research on the topic. The goal of this dissertation is to examine the general application of these tools to wing design problems and highlight several factors pertaining to their usefulness and versatility. Two types of wing design problems are considered in this dissertation: refin- ing and exploratory. Refining problems are more common in practice, especially for high-fidelity optimization, because they start from a good design and make small changes to improve it. Exploratory problems are intended to have liberal parametrizations predisposed to have significant differences between the original and final designs. The investigation of exploratory problems yields novel findings regarding multimodality in the design space and robustness of the framework. Multimodality in the design space can impact the usefulness and versatility of gradient-based optimization in wing design. Both aerodynamic and aerostructural wing design problems are shown to be amenable to gradient-based optimization despite the existence of multimodality in some cases. For example, a rectangular wing with constant cross-section is successfully converted, through gradient-based optimization, into a swept-back wing with transonic airfoils and a minimum-mass structure. These studies introduce new insights into the tradeoff between skin- friction and induced drag and its impact on multimodality and optimization. The results of these studies indicate that multimodality is dependent on model fidelity and geometric parametrization. It is shown that artificial multimodality can be eliminated by improving model fidelity and numerical accuracy of functions and derivatives, whereas physically significant multimodality can be controlled with the application of geometric constraints. The usefulness of numerical optimization in wing design hinges on the ability of the optimizer to competently balance fundamental tradeoffs. With comprehensive access to the relevant design parameters and physics models of the aerostructural system, an optimizer can converge to a better multidisciplinary design than is pos- sible with a traditional, sequential design process. This dissertation features the high-fidelity aerostructural optimization of an Embraer regional jet, in which si- multaneous optimization of airfoil shape, planform, and structural sizing variables yields a significantly improved wing over the baseline design. For a regional jet, it is shown that the inclusion of climb and descent segments in the fuel burn com- putation has a significant impact on the tradeoff between structural weight and aspect ratio. Another study addresses the tradeoff between cruise performance and low-speed, high-lift flight characteristics. A separation constraint at a low-speed, high-lift condition is introduced as an effective method of preserving low-speed performance while still achieving significant fuel burn reduction in cruise.