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Optimum Design Methods for Aerodynamics

The operation of aircrafts, propulsion and energy conversion
systems and process industry equipment relies heavily on the
performance of their aerodynamic components. such as air
intakes, nozzles, wings, cascades, etc. The development of
reliable automated methods which will reduce the human
expertise interference in the design loop and will increase
the quality and duration of the products is one of the CFD
challenges for the next decade. Although the optimum
design concept is so old as the theory of aerodynamics itself,
the maturation of analysis methods and the continuously
increasing computer power have placed it back in stage. A
comprehensive review of the evolution of optimal shape
design methods has been presented by Dulikravich (Ref.1)
and more recently by Labrujere and Sloof (Ref.2).
In designing aerodynamic components engineers aim to
minimize or prevent losses associated with wall boundary
layer separation and/or the occurence of a shock. It is
known that boundary layer behavior, as well as the
occurence of a shock, is controlled by the characteristics of
the pressure distribution along the walls of the flow field.
The need, therefore, of having accurate and efficient inverse
design methods that provide the designer with a shape that
corresponds to a prescribed wall pressure or velocity (for
inviscid flow models) distribution is evident.
First attempts to develop such target pressure methods are
traced back in mid-forties when inverse potential methods
based on conformal mapping and potential theory have been
applied to the design of airfoils. In the fifties, Stanitz (Ref.3)
developed his inverse potential method for compressible
flows. Applying a body-fitted coordinate transformation,
Stanitz derived the inverse potential flow equations on a
"natural" computational plane employing the potential
function and the stream function as independent variables.
The two—dimensional (2-D) inverse problem can then be
solved if "target" velocity (or pressure) distributions are
imposed over the complete boundaries of the domain.
Stanitz's method being more flexible than the conformal
mapping ones has been extended to axisymmetric flows
(Ref.4) as Well as to turbomachinery flows including the
planar and the axisymmetric rotating or non-rotating
cascades (Refs 5—7). The 2-D potential target pressure
problem has been recently reconsidered by Barron (Ref.8),
who provided an alternative formulation using the Von—
Mises transformation by Volpe (Ref.9) who developed
iterative profile closure conditions for compressible flows
and by the present authors (Ref.10) who reformulated the
airfoil design problem using differential geometry principles.