- Conference Article
- 10.1115/imece1995-0955
Airfoil Design via Control Theory Using Full-Potential and Euler Equations
- Nov 12, 1995
- Jeffrey C Lewis + 1 more +1
Until recently, airfoil design has largely been a process of trial and error that has relied heavily upon the intuition and experience of the designer. Using an experimental database for airfoils, a designer would normally employ an educated guess to make modifications to the design. He would then build a new model and test it in the wind tunnel. After several of these design iterations, an airfoil with the desired characteristics would be obtained. Now, with the development of advanced Computational Fluid Dynamics (CFD) codes, much of the trial and error process in aerodynamic design can be eliminated. A CFD code models air flow around a given geometry by numerically solving the governing equations of fluid dynamics on the computer. Rather than testing a new model in the wind tunnel at each design iteration, it is much faster and cheaper to test new airfoil designs with CFD calculations. However each new design requires many (several hundred) computationally intensive CFD calculations before an acceptable design evolves using an optimization procedure. This process is called direct design optimization. In order to alleviate the problems associated with the computationally intensive nature of the direct design methods, attempts have been made to calculate the shape of an airfoil that would have a specified flow distribution over its surface. This is essentially the inverse of a direct CFD calculation in which the shape of the airfoil is given and the flow is calculated; hence it is referred to as inverse design. Summaries of previous work in inverse design are given by Jameson [1], Cabuk and Modi [2], Lewis, Peters and Agarwal, [3] and Agarwal and Lewis [4], and Lewis [5]. In this paper, the inverse design has been formulated as a variational problem in which a control system minimizes the differences between the actual and the desired velocity (or pressure distributions) over the airfoil surface by making successive changes to the shape of the airfoil. A flow chart of the design method is shown in Fig. 1. First, an initial airfoil and the desired velocity (or pressure distribution) are input. The Mach number and angle of attack are also specified. Then a flow solver (Full Potential or Euler) computes the actual velocity and pressure distribution around the airfoil. Next, a cost functional, which represents the deviation of the actual velocity (or pressure distribution) from the desired velocity (or pressure distribution) is computed. If the cost functional has reached a minimum, then the process terminates. Otherwise, a variation is made to the shape of the airfoil such that the cost functional is reduced. The process is repeated so that the cost functional is minimized thereby minimizing the deviation between the actual and the desired velocity (or pressure distributions). The inverse design enhances the efficiency of the aerodynamic design process by several orders of magnitude. Several test cases are shown to demonstrate the method and its robust characteristics (accuracy, stability and efficiency) for aerodynamic design.
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