# Gradient-Based Aerodynamic Optimization of an Airfoil with Morphing Leading and Trailing Edges
## 1 Introduction  
With ever-increasing international awareness of economic efficiency and environmental protection, a more efficient aircraft design that reduces fuel consumption is urgent. The morphing technology developed in recent decades aims at addressing this issue through increasing efficiency during cruising, or better yet, during off-design points by adapting the wing shape or dedicated control surfaces. To date, most studies have focused on implementing the morphing technology by retrofitting the existing aircraft configurations by implementing new dedicated devices, such as leading and trailing edge morphing [1, 2, 3, 4, 5]. Aerodynamic optimization is an essential part in the definition of morphing shape. [PERSON] and [PERSON] [6] established an airfoil camer morphing optimization framework with Genetic Algorithms (GAs), in which the XFOIL solver based on potential flow theory with boundary layer correction was adopted. They used a third-order polynomial to accurately represent the camer-line deformation of the airfoil embedded with the Fish Bone Active Camber (FishBAC) system. In [7], the aerodynamic benefits of transport airfoil with morphing trailing edge wings were quantified by a gradient-based optimization optimizer coupled with a high-fidelity computational fluid dynamic (CFD) solver. The wing is parameterized by the free form deformation (FFD) method. The FFD control points near the trailing edge can move independently in the vertical direction to simulate the small perturbations of the morphing trailing edge. However, vertical deformation of the trailing edge increases or decreases skin length, resulting in additional axial stressthat is necessary to avoid. Generally, a morphing device consists of actuators, internal mechanisms, and skin, and it is designed to deform in a prescribed manner. Incorporating of the structural requirements in the aerodynamic optimization of morphing airfoil appears as beneficial to guarantee a good compromise between the aerodynamic performance and the energy requested to deform the structure, mainly the skin. Indeed, even during an aerodynamic optimization to define an optimal morphing shape when the internal structure does not exist, the skin's structural behaviors should be considered to obtain a feasible morphing shape that is not excessively deformed and at the same time easily controlled by the actuation and internal structure [3,8]. One possible approach to defining a feasible morphing shape is by evaluating the existing internal mechanisms. For the active trailing edge device reported in [9], the airfoil surface comprises rigid and flexible regions and is driven by three rotation inputs. Bezier curves controlled by four points at each flexible region are employed to represent the discrete kinematic model. Inspired by the conventional drop nose device, [PERSON] et al. [10] established leading edge deformation by imposing a rigid rotation first and smoothing the curve by variation of the camber line and thickness distribution. A fourth-order polynomial term of the camber line and thickness is used, and a total of 10 coefficients is needed. [PERSON] and [PERSON] et al. [11] used a parabolic function to deform the front quarter chord of the airfoil, and examined the unsteady aerodynamic characteristics. Other researchers discovered the potential of the existing class/shape transformation (CST) parameterization method in pursuing the development of a general morphing airfoil shape. As a result, the existence of specific morphing devices is unnecessary. CST parameterization was initially developed by [PERSON] [12] and proved to be one of the best candidates for parameterization under the criteria of completeness, flawlessness, intuitiveness, orthogonality, and parsimony [13], thereby improve smoothness when involving machining [14,15]. [PERSON] et al. [16] provided a procedure to maintain the skin length to minimize the axial stress.