Aeroelastic Optimization of a High Aspect Ratio Wing
Authors
Abstract
Two fundamental aspects of aircraft wings are considered in this work: their aerodynamics and their structural properties. Although originating in different disciplines, these two aspects should be studied together because structural behaviour influences aerodynamics and vice-versa, leading to what is known as the aeroelastic behaviour of the wing.With respect to aerodynamics, lift and drag are the forces that allow the airplane to take off and sustain itself in the air. Although the absence of drag would make it impossible for the airfoil to fly, engineers generally seek to minimize it, as an increase in drag implies an overhead on aircraft maneuvers and greater fuel consumption. Drag is minimized by long elliptical wings, but such wings are difficult to manufacture in comparison to other shapes. Long wings are generally more aerodynamic, but a longer span naturally implies greater structural weight, thus reducing flight range. The range formulas of Breguet relate the lift and drag produced by the wing, the amount of fuel available and the weight of the aircraft to the maximum distance the aircraft can fly.
Aeroelasticity, on the other hand, is concerned with the fact that when in flight, the wing structure is under the influence of several forces that deform its original shape. Understanding these forces and how they change the aero-dynamic behaviour of the airfoil is very important. In particular, such forces and the corresponding deformation may create a positive feedback loop, and the wing may bend so much that it breaks.
Accurately modelling the aeroelastic behaviour of a given wing may be computationally very demanding. Therefore, less accurate but simpler models are used for optimization purposes at the initial design stages. Such models must, nevertheless, remain valid to a certain extent, in order for optimized preliminary designs be useful at a later stage.
In this work, the integration between wing aeroelastic models and optimizers is considered, with a view to allowing more accurate and more computationally demanding wing models to be used for optimization. This was accomplished through two different approaches. In the first approach, the precision at certain intermediate steps was reduced without affecting the output.
More specifically, Gauss-Seidel iterations were used to achieve faster but less precise solutions for systems of linear equations arising in given model. In the second approach, a partial set of data was reused from one iteration to the next, reducing running time but still preserving the precision of the original method.
Although the models studied are not the most suited for incrementalization, it is shown that it is possible to reduce computation time without affecting model validity or the optimization results.