# Gradient-Based Aerodynamic Optimization of an Airfoil with Morphing Leading and Trailing Edges
## 4 Conclusions  
A gradient-based aerodynamic shape optimization framework was established in this work, through coupling with a feasible morphing airfoil geometry parameterization. The parameterization was developed to introduce local shape changes, preserve the attachment of shape at the wing-box region, and provide skin length control during optimization. The presented optimization framework was then applied to a single point optimization problem, aimed at reducing the drag coefficient of a transonic RAE 2822 in viscous flow at the cruise stage using mLE and mTE. The main contributions are summarized as follows:  
1. We provided the setup of a gradient-based aerodynamic optimization framework that is able to combine two main tools: the CST parameterization of the airfoil and the open-source code SU2 as a CFD engine. The framework projects the gradient already presented by SU2 to the CST domain, allowing the pure analytical calculation of the gradient of the relevant aerodynamic quantities with respect to few CST design variables. Thus, the optimization becomes efficient when the gradients are available.
2. The optimization results show that a maximum drag reduction of 18.1% was achieved using mLETE. In comparison, the optimization obtained a 7% drag reduction using only mTE and 16% for mLE.
3. Compared with the mTE case, mLE is more suitable for eliminating the pressure drag.
4. The mechanisms of drag reduction using mLE and the trailing edge are different. The optimized mTE creates a relatively flat top, slows down the flow acceleration, extends the supersonic region along the surface, and terminates a weaker shock. The optimized mLE shows a larger curvature at the top, resulting in a maximum  
Figure 15: Slope and curvature of baseline and optimized mLETE airfoils. (**a**) Slope; (**b**) curvature.  
Mach appearing at the leading edge. The successional multi-stage acceleration and deceleration lead to a weaker shock at the end.  
The feasible morphing shape introduced in the paper does not include details about the morphing mechanism and the internal structures. The introduction of these components could further restrain the design space and limit the morphing capabilities, consequently limiting the improvement of aerodynamic performance.  
This paper concerns only two-dimensional aerodynamic optimization of a morphing airfoil under steady flow. Different optimization results may be obtained if the unsteadiness and the consequent shock wave movement are considered. The authors encourage the development and implementation of the adjoint method for gradient evaluation when considering the flow unsteadiness.  
Conceptualization, Z.Z., A.D.G. and C.S.; methodology, Z.Z., A.D.G. and S.R.; project administration, S.R. and C.Y.; software, Z.Z. and A.D.G.; writing--original draft, Z.Z.; writing--review and editing, S.R. and C.S. All authors have read and agreed to the published version of the manuscript.  
This research was partially funded by National Key Research and Development Program of China (grant number 2017 YFB0503002) and the National Natural Science Foundation of China (grant number 11402013).  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
[PERSON] acknowledges the financial support from the China Scholarship Council (grant number 201806020280).  
The authors declare no conflict of interest.