The Objective Space and the Formulation of Design Requirement in Natural Laminar Flow Optimization

Design requirement is as important in aerodynamic design as in other industries because it sets up the objective for the samples in design space to approach. Natural Laminar Flow (NLF) optimization belongs to the type of aerodynamic design problems featured by the combination of distinct aerodynamic performance, where the design requirement is often formulated in form of summation of laminar-related performance and pressure drag performance with different weight assignment according to different perspectives. However, the formulations are rather experience-oriented and are decided non-quantitatively. Inspired by data manipulation approaches in design space (spanned by design variables of geometrical representation parameters) in many aerodynamic designs, this paper proposes new formulations of design requirement in NLF optimization via consideration of objective space (projection of design space through aerodynamics) and shows the impact of the corresponding formulation of design requirement to the result of NLF optimization in cases of transonic airfoil and aero engine compressor blade design from two perspectives: Pareto front convergence and improving effect of accessory performance. The paper uses Principal Component Analysis (PCA) to obtain the eigenvectors of objective space to extract the intrinsic information about specific problem. The method is realized in two cases with satisfactory result.