airfoil design methods

7/24/2019 Airfoil Design Methods

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http://www.desktop.aero/appliedaero/airfoils2/airfoildesign.html

Applied

Aerodynamics:

A Digital Textbook

0. Preface0.1 Detailed Table of

Contents

0.2 Instructions

1. Introduction1.1 Historical Notes

1.1.1 Early Attempts

1.1.2 Lilienthal

1.2 References and Related

Sites

2. FluidFundamentals2.1 Origin of Forces

2.1.1 Press ure Forces

2.1.2 Shear Forces

2.2 Dimensionless Groups

2.2.1 Dimensionless Force

Coefficients

2.2.2 Reynolds Number

2.2.3 Mach Number

2.3 Conservation Laws

2.4 Approximation

Concepts

2.5 Field Equations for Fluid

Flow

2.5.1Navier-Stokes

2.5.1.1Navier-Stokes

Derivation

2.5.2 Reynolds Averaged

Navier-Stokes

2.5.3 Euler

2.5.4 Full Potential

2.5.4.1 Full Potential

Derivation

2.5.5 Transonic Small

Disturbance

2.5.5.1 Small DisturbanceDerivation

2.5.6 Prandtl-Glauert

2.5.7 Acoustic

2.5.8 Laplace

2.6 Relating Pressure and

Velocity

2.6.1 Bernoulli Derivation

2.7 References

3. Solution Methods3.1 Theory and Experiment

Airfoil Design Methods

The process of airfoil design proceeds from a knowledge of

the boundary layer properties and the relation betweengeometry and pressure distribution. The goal of an airfoil

design varies. Some airfoils are designed to produce low

drag (and may not be required to generate lift at all.) Some

sections may need to produce low drag while producing a

given amount of lift. In some cases, the drag doesn't really

matter -- it is maximum lift that is important. The section may

be required to achieve this performance with a constraint on

thickness, or pitching moment, or off-design performance, or

other unusual constraints. Some of these are discussed further

in the section on historical examples.

One approach to airfoil design is to use an airfoil that was

already designed by someone who knew what he or she was

doing. This "design by authority" works well when the goals

of a particular design problem happen to coincide with the

goals of the original airfoil design. This is rarely the case,

although sometimes existing airfoils are good enough. In these

cases, airfoils may be chosen from catalogs such as Abbott

and von Doenhoff's Theory of Wing Sections, Althaus' andWortmann's Stuttgarter Profilkatalog, Althaus' Low Reynolds

Number Airfoil catalog, or Selig's "Airfoils at Low Speeds".

The advantage to this approach is that there is test data

available. No surprises, such as a unexpected early stall, are

likely. On the other hand, available tools are now sufficiently

refined that one can be reasonably sure that the predicted

performance can be achieved. The use of "designer airfoils"

specifically tailored to the needs of a given project is now

very common. This section of the notes deals with the

process of custom airfoil design.

Methods for airfoil design can be classified into two

categories: direct and inverse design.

Direct Methods for Airfoil Design

The direct airfoil design methods involve the specification of a

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3.2 Analytic Methods

3.3 CFD Overview

3.4 Panel Methods

3.4.1 Introduction

3.4.2 Geometry

3.4.3 AIC Matrix

3.4.4 Boundary Conditions

3.4.5 End Notes

3.5Nonlinear CFD

3.5.1 Finite DIfferences3.5.2 Finite Volume

Methods

3.6 References

4. 2-D Potential Flow4.1 Basic Theory

4.1.1 Uniform Flow

4.1.2 Vortex Flow

4.1.3 Doublet Flow

4.2 Sources and Vortices

4.2.1 Vortex Velocities

4.2.2 Method of Images

4.2.3 Cylinder Flows

4.2.4 Circulation and Stokes

Theorem

4.2.5 Free Vortices

4.3 Interactive Flow

Computation

4.4 References

5. Airfoils, Part I5.1 Airfoil History

5.2 Airfoil Geometry5.3 Airfoil Pressures

5.4 Cp and Performance

5.5 Geometry and Cp

5.6 Interactive Airfoil

Analysis

5.7 Airfoil Analysis

5.7.1 Conformal Mapping

5.7.2 Thin Airfoil Theory

5.7.2.1 Class ical Theory

5.7.2.2 Basic Results

5.7.2.3 Inverse Design

5.7.2.4 Thickness Effects5.7.2.5 General Airfoil

Analysis

5.7.3 Surface Panel

Methods

5.7.3.1 Sample Source Code

5.8 References

6. 2-D Compressibility6.1 Basic Results from

Theory

section geometry and the calculation of pressures and

performance. One evaluates the given shape and then

modifies the shape to improve the performance.

The two main subproblems in this type of method are

1. the identification of the measure of performance

2. the approach to changing the shape so that the

performance is improved

The simplest form of direct airfoil design involves starting with

an assumed airfoil shape (such as a NACA airfoil),

determining the characteristic of this section that is most

problemsome, and fixing this problem. This process of fixing

the most obvious problems with a given airfoil is repeated

until there is no major problem with the section. The design of

such airfoils, does not require a specific definition of a scalar

objective function, but it does require some expertise toidentify the potential problems and often considerable

expertise to fix them. Let's look at a simple (but real life!)

example.

A company is in the business of building rigid wing hang

gliders and because of the low speed requirements, they

decide to use a version of one of Bob Liebeck's very high lift

airfoils. Here is the pressure distribution at a lift coefficient of

1.4. Note that only a small amount of trailing edge separation

is predicted. Actually, the airfoil works quite well, achieving aClmaxof almost 1.9 at a Reynolds number of one million.

This glider was actually built and flown. It, in fact, won the

1989 U.S. National Championships. But it had terrible high

speed performance. At lower lift coefficients the wing

seemed to fall out of the sky. The plot below shows the

pressure distribution at a Clof 0.6. The pressure peak on the

lower surface causes separation and severely limits the

maximum speed. This is not too hard to fix.
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6.2 Effects on Airfoils

6.3 Linear Theory

6.3.1 Effect of Mach on Cp

6.4 Transonics

6.5 Supersonic Airfoils

6.6 References

7. Boundary Layers7.1 Viscous Drag

7.2 Effect on Pressures

7.3 Separation

7.3.1 Laminar Separation

7.3.1.1 Canonical Cp

7.3.1.2 Effective Length

7.3.2 Turbulent Separation

7.4 Boundary Layer Theory

7.4.1 Basic Theory and

Definitions

7.4.2 Laminar Boundary

Layers

7.4.3 Transition

7.4.4 Turbulent Boundary

Layers

7.4.5 Summary of Results

7.5 References

8. Airfoils, Part II:

Design8.1 Design Methods

8.2 Typical Design

Problems

8.2.1 Thick Sections

8.2.2 High Lift Sections8.2.3 Laminar Sections

8.2.4 Transonic Sections

8.2.5 Low Reynolds Number

Sections

8.2.6 Low Cm Sections

8.2.7 Multiple Design Points

8.3 High Lift Systems

8.4 References

9. 3D Potential Flow

9.1 General Theory9.1.1 Biot-Savart Law

9.1.2 Vortex Filament

Subroutine

9.2 Finite Wings

9.2.1 Wing Models

9.2.2 Lifting Line Theory

9.2.3 Induced Drag

9.2.3.1 Trefftz Plane Drag

9.2.3.2 Trefftz Plane Lift

9.2.4 Computational Models

9.2.4.1 Interactive

By reducing the lower surface "bump" near the leading edge

and increasing the lower surface thickness aft of the bump,

the pressure peak at low Clis easily removed. The lower

surface flow is now attached, and remains attached down to

a Clof about 0.2. We must check to see that we have not

hurt the Clmaxtoo much.

Here is the new section at the original design condition (still

less than Clmax). The modification of the lower surface has

not done much to the upper surface pressure peak here and

the Clmaxturns out to be changed very little. This section is a

much better match for the application and demonstrates how

effective small modifications to existing sections can be. The

new version of the glider did not use this section, but one that

was designed from scratch with lower drag.

Sometimes the objective of airfoil design can be stated more
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Computation

9.2.5 Simple Sweep Theory

9.2.5.1 Forward-Swept

Wings

9.3 Slender Bodies

9.3.1 Flow over Bodies

9.3.2 Slender Body Theory

9.4 References

10. Compressibility in3D10.1 Subsonic Effects

10.2 Supersonics

10.2.1 Sears-Haack Bodies

10.2.2 Supersonic Wing

Game

10.2.3 Simplified Wave Drag

Est

10.2.4 Oblique Wings

10.3 References

11. Viscosity in 3D11.1 3D Boundary Layers

11.2 High Angles of Attack

11.3 References

12. Wing Design12.1 Wing Design

Parameters

12.2 Lift Distributions

12.2.1 About Lift

Distributions12.2.2 Geometry and Lift

Distribution

12.2.3 Lift Distributions and

Performance

12.3 Wing Design in More

Detail

12.4Nonplanar Wings

12.5 References

13. Configuration

Aerodynamics13.1 Multiple Lifting

Surfaces

13.2 Longitudinal Stability

and Trim

13.3 Horizontal Tails

13.4 Canard Aircraft

13.4.1 Stability and Trim

13.4.2 Drag

13.4.3 Pros and Cons

13.4.4 Interactive

Calculations

positively than, "fix the worst things". We might try to reduce

the drag at high speeds while trying to keep the maximum CL

greater than a certain value. This could involve slowly

increasing the amount of laminar flow at low Cl's and

checking to see the effect on the maximum lift. The objective

may be defined numerically. We could actually minimize Cd

with a constraint on Clmax. We could maximize L/D or

Cl1.5/Cdor Clmax/ Cd@Cldesign. The selection of the figure

of merit for airfoil sections is quite important and generally

cannot be done without considering the rest of the airplane.

For example, if we wish to build an airplane with maximum

L/D we do not build a section with maximum L/D because

the section Clfor best Cl/Cdis different from the airplane CL

for best CL/CD.

Inverse Design

Another type of objective function is the target pressure

distribution. It is sometimes possible to specify a desired Cp

distribution and use the least squares difference between the

actual and target Cp's as the objective. This is the basic idea

behind a variety of methods for inverse design. As an

example, thin airfoil theorycan be used to solve for the shape

of the camberline that produces a specified pressure

difference on an airfoil in potential flow.

The second part of the design problem starts when one has

somehow defined an objective for the airfoil design. This

stage of the design involves changing the airfoil shape to

improve the performance. This may be done in several ways:

1. By hand, using knowledge of the effects of geometry

changes on Cpand Cpchanges on performance.

2. By numerical optimization, using shape functions to

represent the airfoil geometry and letting the computer decide

on the sequence of modifications needed to improve thedesign.
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13.5 Tailless Aircraft

13.6 References

14. Appendices14.1 Standard Atmosphere

Calculator

14.2 Universal Unit

Conversions

14.3 Vector Identities

14.4 Video Clip Index

14.5 Interactive Calculation

Pages

15. Problems

16. Index
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