Investigation of the adjoint method in aerodynamic optimization using various shape parameterization techniques

This paper studies the effect of design variables vector on automatic aerodynamic shape optimization in the adjoint method. Three shape techniques are studied: surface points, relations of the NACA 4-digit airfoil series and Hicks-Henne "Bump" Functions. First, this paper presents the complete formulation of the optimal design problem for the Euler equations. Second, the implementation of these surface representation methods are explored. Finally, results are presented for inverse and drag minimization problems. The results show that the mechanism, value and the trend of drag reduction during the optimization strongly affected by the type of design vector.