Copyright © A. Filippone (1996-2001). All Rights Reserved.

Aerodynamic Design

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.

Computer Aided Design

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.

Aerodynamic Design

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).

Introduction of CFD

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.

Summary of Methods

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:

Accuracy Requirements

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.

Design Objectives

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).

Multi-Point Design

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.

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.

Airfoil Design

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

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.

Methods for Airfoils and Wings

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.


Indirect 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.

Optimization Methods

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.

Hybrid Methods

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.

Nature of the Equations

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

Selected References

  • Miele A (editor). Theory of Optimum Aerodynamic Shapes, Academic Press, 1965.

  • Abbott I von Doehnoff AR. Theory of Wing Sections. Dover ed, New York, 1959. AA.VV.

  • Labrujere TE, Sloof JW. Computational Methods for the Aerodynamic Design of Aircraft Components. In Ann. Rev. Fluid Mech., Vol. 25, pages 183-214. Cambridge Univ. Press, Cambridge, 1993.

  • AGARD, Turbomachinery Design Using CFD, AGARD LS-195, May 1994.

  • Journal of Aircraft, Vol. 35, No 1, Jan. 1999 (monographic issue).

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Copyright © A. Filippone (1996-2001). All Rights Reserved.