The problem, in fact, consists in designing aerodynamic
systems and/ or any of their components, propulsion systems or any or their components
to perform specified operations in a range of design points.

The field spans all the
aerodynamic knowledge, and stretches into design as considered a separate engineering
science. Coverage of aerodynamic design would require books.

Recent progress in software and computer hardware has made available sophisticated
methods for real time simulations of full configurations. Integrated CAD- grid
generation- and finite element systems have placed the design to a very rational
level from a cut-and-try approach followed for many years.

CATIA, Unigraphics,
ICEM/CFD, are just a few of these systems. Many corporations, research institutions
and even universities have access or develop their own design technology.

The methods are: inverse and indirect, optimization techniques of base systems, all
of which are based on some solid fluid dynamic ground and are coupled with
appropriate methods to adjust a first guess performance to shapes that perform
according to specified targets. Both systems and targets come in a very large variety
of possibilities.

Airfoils and wings are the most important theoretical problems,
although industry is interested in more general methods for the design of systems in
complete configuration (fighters, supersonic transport, etc.). The field is in
continuous evolution and the technical literature is quite large. Some of the
topics discussed here include:

In the design of airfoils typical targets include prescribed pressure or velocity
distributions, lift range, maximum lift, minimal drag, shock-free suction side in
transonic flow and type of stall at subsonic speeds, under geometrical constraints
that may include one or more of the following: thickness ratio, maximum camber,
leading edge radius, trailing edge angle. The design point can be single or multiple
(the latter case is obviously more constrained).

**Figure 1: Multi-point airfoil design**

### Wing Design

The design of a wing may include some aspects of the design problems as listed above,
but the task becomes more complicated because of the third dimension, which adds
further difficulties: spanwise variation of lift, tip effects, three- dimensional
turbulent transition, etc. The definition of the planform is generally done outside
the loop, although a design system can be devised in a such a way as to include the
planform optimization as a part of the problem in a hierarchical approach.

### Aerodynamic Systems

More complex problems are the design of a propeller, helicopter rotor,
turbine/compressor cascade. Propellers and rotors add the rotary aerodynamics to the
picture, while the turbine cascade adds the interference between blades (Gostelow,
1984). Interference is also encountered in the wing-body and wing-nacelle design and
optimization. The methods required must be fully three-dimensional.

Airfoils are designed for all range of speeds, from very low Reynolds numbers (Re =
30,000) speeds up to supersonic range. Reynolds and Mach numbers often dictate what
kind of performances are to be expected.

### Low Reynolds Numbers

Design methods at low Reynolds number must be able to take into account the strong
viscous effects that lead to laminar separation bubbles, extensive boundary layer
effects, turbulence transition, hysteresis in the force coefficients, non-linear
behavior. The range of Reynolds numbers is roughly 50,000 to 500,000 (lower Reynolds
numbers are not yet fully investigated).

### High Reynolds Numbers

Design methods for intermediate speeds (Reynolds numbers between 500,000 and several
million) must have the same characteristics of the methods working at the lowest
speed range, although the laminar separation bubble can be missing, the flow may be
fully turbulent (depending also on the free stream turbulence, surface conditions,
etc.). Methods that feature a calculation of the boundary layer are today a standard.

### Transonic Airfoils

At higher speeds we find airfoils in the transonic range. One classical problem is
the design of supercritical (nearly shock-free) airfoils, optimization of basic
airfoils to remove the shock whenever occurs (drag minimization problem).

### Multi-Element Airfoils

The number of design techniques developed in the past few years has been exploding.
The field can be considered almost saturated. Here is a short list: direct methods,
indirect methods, inverse methods, one-shot methods, methods based on automatic
control, methods based on gradient minimizers, methods based on heuristic approach.
Then there are methods specifically developed to treat multi-point design.

### Inverse Methods

Methods that solve the problem of determining the shape of the airfoil or wing (if
there exists any) corresponding to specified surface pressure distribution under
fixed flow conditions are called inverse methods.

Other methods are characterized by the fact that in principle one has no direct
control over the global aerodynamic performances (such as lift, drag and pitching
moment). These methods, called indirect, use manipulation of generally non-physical
parameters. They include solutions in the hodograph plane, and fictitious gas
approach for the supersonic bubbles. These methods are now obsolete.

Several options are available, for which is not easy to say how their efficiency
compares. However, most of them take the flow solver as a reliable black
box. Alternatively, one can embed the adjoint equations with the constraints, like in
the *single-cycle* and the *one-shot* method, and solve a larger
problem that includes the design variables.

The residual-corrector method of Takanashi for transonic wings features aspects of
inverse methods and optimization techniques.

For steady incompressible potential flow the problem is linear in the flow equations
and non-linear in the boundary conditions. Compressible and transonic flows are both
non-linear in the flow equations and the boundary conditions.

Early transonic design has aimed mostly (if not uniquely) to wave drag reduction,
e.g. to the design of shock-free aerodynamic shapes. In most cases the inverse
problem is ill-posed; for others, more complex, satisfactory conditions have not yet
been formulated. These cases include low-Reynolds number airfoil flows and some
internal flows. Occasionally, ill-posed methods turned out to work and produce
(luckily) good numerical results.

**Related Material**