Ingeniero

Computational Aerodynamics for Aircraft Design
Antony Jameson

∗

†

Abstract
This article outlines some of the principal issues in the development of numerical methods for the prediction of flows over aircraft and their use in the design process. These include the choice of an appropriate
mathematical model, the design of shock-capturing algorithms, the treatment of complex geometricconfigurations, and shape modifications to optimize the aerodynamic performance.

While computational methods for simulating fluid flow have by now penetrated a broad variety of fields, including
ship design, car design, studies of oil recovery, oceanography, meteorology, and astrophysics, they have assumed
a dominant role in aeronautical science. In the aircraft industry there is often a very narrowmargin between
success and failure. In the past two decades the development of new commercial aircraft successful enough to
make a profit for the manufacturer has proved an elusive goal. The economics of aircraft operation are such that
even a small improvement in efficiency can translate into substantial savings in operational costs. Therefore, the
operating efficiency of an airplane is a majorconsideration for potential buyers. This provides manufacturers
with a compelling incentive to design more efficient aircraft.
One route toward this goal is more precise aerodynamic design with the aid of computational simulation.
In particular it is possible to attempt predictions in the transonic flow regime that is dominated by nonlinear
effects, exemplified by the formation of shock waves. Theimportance of the transonic regime stems from the
fact that to a first approximation, cruising efficiency is proportional to ML/D, where M is the Mach number
(speed divided by the speed of sound), L is the lift, and D is the drag. As long as the speed is well below the
speed of sound, the lift-to-drag ratio does not vary much with speed, so it pays to increase the speed until the
effects ofcompressibility start to cause a radical change in the flow. This occurs when embedded pockets of
supersonic flow appear, generally terminating in shock waves. A typical transonic flow pattern over a wing is
illustrated in Fig. 1. As the Mach number is increased the shock waves become strong enough to cause a sharp
increase in drag, and finally the pressure rise through the shock waves becomes so large thatthe boundary layer
separates. The most efficient cruising speed is usually in the transonic regime just at the onset of drag rise, and
the prediction of aerodynamic properties in steady transonic flow has therefore been a key challenge.
Prior to 1965 computational methods were hardly used in aerodynamic analysis, although they were widely
used for structural analysis. There was already in place arather comprehensive mathematical formulation of
fluid mechanics. This had been developed by elegant mathematical analysis, frequently guided by brilliant
insights. Well-known examples include the airfoil theory of Kutta and Joukowski, Prandtl’s wing and boundary
layer theories, von Karman’s analysis of the vortex street, and more recently Jones’s slender wing theory (1), and
Hayes’s theory oflinearized supersonic flow (2). These methods, however, required simplifying assumptions of
various kinds, and could not be used to make quantitative predictions of complex flows dominated by nonlinear
effects. The primary tool for the development of aerodynamic configurations was the wind tunnel. Shapes were
tested and modifications selected in the light of pressure and force measurements togetherwith flow visualization
techniques. In much the same way that Brunelleschi could design the dome of the Florence cathedral through
∗ Reprinted
† The

from Science, Volume 245, pp. 361-371, 1989
author is McDonnell, Professor of Aerospace Engineering, Princeton, NJ 08544

1

a good physical understanding of load paths, so could experienced aerodynamicists arrive at efficient shapes...