Multi-Objective Aerodynamic Exploration of Elements’ Setting for High-Lift Airfoil Using Kriging Model

Abstract

A multi-objective design exploration for a three-element airfoil consisted of a slat, a main wing, and a flap is carried out. The lift curve improvement is important to design high-lift system, thus design has to be performed under various angle of attacks. The objective functions considered here are to maximize the lift coefficient at landing and near stall conditions simultaneously. Genetic Algorithm (GA) is used as an optimizer. Although it has advantage of global exploration, its computational cost is expensive. To reduce the computational cost, the Kriging surrogate model which is constructed based on several sample designs is introduced. The solution space is explored based on the maximization of Expected Improvement (EI) value corresponding to objective functions on the Kriging models. The improvement of the model and the exploration of the optimum can be advanced at the same time by maximizing EI value. In this study, a total of 90 sample points are evaluated using the Reynolds averaged Navier-Stokes simulation (RANS) for the construction of the Kriging model. Through the present exploration process, several designs were obtained with better performance than the baseline setting in each objective function. To obtain the information of the design space, functional Analysis of Variance (ANOVA) which is one of the data mining techniques showing the effect of each design variable on the objectives is applied. Main-effects of the design variables are calculated to recognize the effect of design variables on the objective functions. This result suggests that the gap and the deflection of the flap have a remarkable effect on each objective function and the gap of the slat has an effect on near stall condition.