A. Van dcr Velden
Synaps Inc.. Atlanta, GA, USA

16.1 Abstract

This paper will discuss examples of supersonic aerodynamic shape optimization as developed for Daimler-Benz Aerospace Airbus by Synaps. Inc,

First, we will introduce a general approach to aerodynamic shape design based on min­imization of energy consumption during aircraft life while considenng realistic constraints on lift, pitching and rolling moments and geometric dimensions. The analysis is performed using a potential code with real flow corrections and a decoupled boundary layer calculation. Finally, this method is applied to the design of the European Supersonic Civil Transport and the Oblique Flying Wing.

16.2 Introduction

Engineers have long sought to improve wing design methods Initially, simple geometric shape functions were used to characterize airfoil shapes, the NACA airfoil classification system using this method is described in reference [3301. Unfortunately these NACA airfoils had high drag at transonic speeds, and therefore more refined shapes with reduced (or not transonic shocks were required. More recently, successful transonic wings have been designed by defining a (nearly) shock-free transonic pressure distribution and using an inverse solver to find the corresponding airfoil geometry Though such methods can be applied in high-transonic flow, in supersonic flow

these methods loose their meaning because the optimal pressure distribution cannot be shock­less.

During the days of Concorde and the SST, methods not based on pressure distributions were introduced to solve supersonic aircraft design problems. These methods arc still in use to­day. A good overview paper on these methods was written by Baals, Robins and Harris 1331]. The method first area-rules the fuselage wing combination. The wing lift distribution is opti­mized with Langrangc’s method of undetermined multipliers 1349J(334| for minimum drag. This optimum lift distribution can then be inverted into the geometry using linear theory. But often, the wing shapes derived from such inverse methods exhibit camber kinks due to ill conditioned aerodynamic matrices that require post processing. Variations in the wing planform can also not be considered since it would require a recompuution of the aerodynamic matrices.

A solution that can be used for both transonic and supersonic flow was proposed by VandcrPlaats and Hicks (341). They applied numerical optimization techniques combined with a nonlinear flow analysis methods such as Euler to modify a wing shape such that an arbitrary objective function representing the design goals could be minimized. Although their work was done twenty years ago, computer speeds have MM increased sufficiently to make it practical with the shape functions they proposed. Recently Hicks. Reuther and Jameson have applied this tech­nique on supersonic wing body combinations using the Euler equations.

Since the underlying potential flow theory has appeared to work very well for prelimi­nary supersonic aircraft design, most manufacturers therefore sec no need to change to compu­tationally more expensive and less tested methods at this time. Another advantage of potential flow cited by some engineers involved in the ESCT project, was the inherent separation of wave drag, induced drag and friction drag. This separation of drag components helped to analyze prob­lem spots and the low computational effort reduced the critical design turn around time Though the author agrees with this view, the design method as practiced today is cumbersome and in­flexible as to the use of constraints and modeling of new types of configurations.

The current industrial supersonic wing design methods typically do not include leading edge suction criteria or vortex development Both phenomena influence the forces and moments significantly, especially at subsonic speeds.

This paper combines the direct numerical optimization of a completely flexible wing- body-nacelle configuration w ith an industrial potential flow code with corrections.

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