Global Optimization Of Supercritical Airfoil With Naturally Bounded Hybrid Parameterization Method

Developing a robust and flexible geometry modelling parameterization method has become one of the core issues in the area of aircraft design.Classical aerodynamic shapes were typically defined using analytical and polynomial equations or splines interpolated through discrete points.These methods,such as Hicks-Henne and CST,B-Spline,have been applied in the CAD area.However,the existing parameterization methods have some disadvantages,such as excessive parameter quantity,parameters not containing aerodynamic features,generation of non-airfoil-like geometries and complicated definition of parameter variation ranges.Therefore,in order to overcome these disadvantages,a naturally bounded hybrid parameterization method is proposed in this paper.The method is able to generate airfoils with high quality using a small number of parameters while the control point positions are naturally bounded.Moreover,the control points are defined using non-dimensional polar coordinates,which simplifies the definition of parameter ranges.In order to prove the method effectiveness,the aerodynamic design of a typical narrow-body aircraft is taken as the background application of the proposed parameterization method.The optimization formulation is defined as minimizing the drag coefficient with fixed lift coefficient and several constraints of airfoil maximum thickness and pitching moment coefficient.Two optimization strategies are applied: two-step method and one-step method.The results reveal that the global optimal airfoil can be searched with high efficiency when using the proposed parameterization method,which can provide the designers with valuable information for further optimization.On the other hand,the designers are difficult to obtain the information about the relations among parameters and response values.Hence,it is in great need to perform the research on the visualization method for high-dimensional aerodynamic optimization.Based on the sample data,the relations among parameters and response values are first analyzed,and then the design space and response surface are displayed through multiple visualization methods to assist the designers to amend the parameter ranges and further reduce the time spent on CAE simulations.In this paper,a couple of new visualization techniques are proposed and implemented in a modular,dynamic and hybrid visualization tool,based on a combination of design of experiments method,response surface models and some data analysis methods.The tool is implemented in MATLAB and is capable of systematically presenting the high-dimensional design space,multi-dimensional response functions and their relationships.The applications on test functions and airfoil aerodynamic optimization indicate that the proposed visualization method is useful for designers to analyze high-dimensional data set and to increase the efficiency and quality of high-dimensional optimization problem.