In this Chapter
Aerodynamic design may as well be the largest and the oldest problem in the already vast field of aerodynamics.
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 computer approach is probably only limited by the hardware power, although
there are still enormous difficulties in treating a large class of problems.
Design techniques have not evolved farther farther than the rule-of-thumb until the
development of the wind tunnel. The experimental work has produced classes of
airfoils widely used by the aeronautic industry for some thirty years (Abbott-Von
Doenhoff, 1959).
The most notable change in the situation after the wind tunnel is probably the
massive introduction of CFD, although it there will be some time before this approach
will be fully exploited. This survey is focused on the rational methods
developed developed over the past two decades, because by any standard they
represent the most significant advances achieved in this field.
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:
The accuracy of all design methods is at most equal to the accuracy of the flow model
used. Since many fluid dynamic issues are still poorly understood (for example flow
separation on a three-dimensional high-lift system; flow properties after the stall
point), and the development of aerodynamic models is an ongoing process, there is
clearly a class of problems that cannot be treated with confidence at the present
time, in particular determination of accurate drag data.
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
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.
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.
Turbomachinery: Methods for turbomachinery and gas
turbines for power generation have slowly evolved from cut-and try methods. They
include a number of ad-hoc methods from preliminary sizing (with one-dimensional flow
approximation) to a final design (multi-disciplinary, non-convex methods), AGARD LS-195.
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.
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).
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.
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).
Design of multi-element airfoils include the non-linear effects of one element onto
the others. Particularly sensitive areas are the cove of the main airfoil trailing
edge and the leading edge of the flap.
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.
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.
The aerodynamic performances can be controlled directly by using optimization
methods, generally based on some gradients evaluation (direct
methods). The optimization aims at minimizing some objective function
characteristic of the airfoil/wing performances. They can be classified according to
the state equations and the gradient method used.
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.
Some methods, developed more recently, are hybrid, in that their approach to the
aerodynamic optimization is essentially based on non aerodynamic techniques. These
include control theory, evolution theory, simulated annealing, expert systems,
multi disciplinary methods and the like.
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
Computer Aided Design
Aerodynamic Design
Introduction of CFD
Summary of Methods
Accuracy Requirements
Design Objectives
Wing Design
Aerodynamic Systems
Airfoil Design
Low Reynolds Numbers
High Reynolds Numbers
Transonic Airfoils
Multi-Element Airfoils
Methods for Airfoils and Wings
Inverse Methods
Indirect Methods
Optimization Methods
Hybrid Methods
Nature of the Equations
Selected References
