140

## Full text

(1)

(2)

(3)

(4)

thesis

to

parents,

and

andto

(5)

on an aircraft.

these are

### fuel

efficiency, greater maneuverability, and an

### This

thesis explorestheconcept of a

supported

the

ofvirtual spars

a

### wing

of uniform cross-section.

### With

no cross-sectional support to the wing, the skin

thearea

### between

thevirtual spars experiences a certain amount of

### due

to

the various aerodynamic

on the wing.

thesis

a process

### (minimizing)

the number of virtual spars required to support the

### wing

while

(6)

ABSTRACT i

TABLE OFCONTENTS ii

LIST OFTABLES iv

LIST OFFIGURES v

CHAPTER1 - INTRODUCTION 1

1.1BACKGROUND 1

1.2BRIEFOVERVIEW 2

CHAPTER 2- CHOOSINGTHEAIRFOILS

5

2.1DETERMINING AIRFOIL SHAPES 5

2.2AERODYNAMIC PROPERTIESAND APPROXIMATIONS 7

2.2.1 Physical CharacteristicsandSpecifications 7

2.2.2 Aerodynamic PropertiesandValues 7

2.2.3

### Wing

Skin Properties 12

CHAPTER 3- DATA SETUPUSING

MICROSOFT

EXCEL 97 AND VBA 14

3.1THE NEED FOR MACROS 14

3.2PREPARING THE DATA FORANALYSIS 14

CHAPTER 4- XFOIL 16

4.1GENERAL DESCRIPTIONOFTHE PROGRAM 16

4.2USINGXFOILTO OBTAIN THE PRESSURE COEFFICIENT DISTRIBUTION 17

CHAPTER 5

-MICROSOFT

EXCEL97 AND VBA REVISITED 22

5.1 GROUPCPXMACRO 22

5.2EXPLANATIONOF GROUPCPX MACRO 23

CHAPTER6

-MATLAB

ANALYSIS 24

6.1BRIEF INTRODUCTIONTO

MATLAB

24

6.2OVERVIEWOFTHE ANALYSIS PROCESS

### (MASTER.M)

25

6.3DESCRIPTION OF INDIVIDUAL FUNCTIONS 27

6.3.1

### Setting

theRelevant Parameters (Parameters.m) 27

6.3.2

### Approximating

theAirfoilPerimeter

28

6.3.3

### Dividing

theAirfoil Perimeter

39

6.3.4

### Determining

Element Orientation

45

6.3.5

### Establishing

Pressure ValuesatNodes

47

6.3.6Finite Element Analysis

53

6.3.7

### Optimizing

Each Nodal Support

68

6.3.8

### Controlling

theOverall FEAandOptimizationProcess

### (FEAJDpt.m)

71

CHAPTER 7- RESULTS 74

CHAPTER8- DISCUSSIONOF RESULTS AND CONCLUSION 80

APPENDIX A- C5 AIRFOIL COORDINATES DATA

83

APPENDIXB

-MICROSOFT

(7)

B.l CONVMACRO 86

B.l.l Conv Variables 86

B.1.2ConvCode 86

B.2CONVALL MACRO 87

B.2.1 ConvAll Variables 87

B.2.2 ConvAll Code 87

B.3GROUPCPX MACRO 89

B.3.1 GroupCpx Variables 89

B.3.2GroupCpxCode 89

APPENDIXC

C.l THEORY REFERENCES 91

C.2PRIMARY PROBLEM FORMULATIONS 92

C.3CPXS SUBROUTINE(FORTRAN

### 77)

94

C.4PRESSURECOEFFICIENT VSX DATA 95

C.5PRESSURE COEFFICIENTSVS.XPLOTS 100

APPENDIX D

-MATLAB

M-FILES- VARIABLESAND CODE

103

D.lMASTER.M 103

D.l.l Master.m Variables 103

D.1.2Master.m Code 105

D.2 Parameters.m 108

D.2.1 Parameters.m Variables 108

D.2.2 Parameters.m Code 709

D.3 Arcapprox.m 110

D.3.1ArcApprox.m Variables 110

D.3.2 ArcApprox.m Code Ill

D.4MAPTOP.M 112

D.4.1 MapToP.m Variables 112

D.4.2 MapToP.mCode 113

D.5 GetAlpha.m 114

D.5.1 GetAlpha.mVariables 114

D.5.2 GetAlpha.mCode 115

D.7FEA_OPT.M 119

D.7.1 FEAjOpt.m Variables 119

D.7.2FEAJDpt.mCode 120

D.8 0PT.M 122

D.8.1 Opt.m Variables 122

D.8.2Opt.m Code 123

D.9FEA.M 124

D.9.1FEA.m Variables 724

D.9.2 FEA.m Code 725

APPENDIX E- MAPLEVFINITE ELEMENT ANALYSIS 127

(8)

### 1.1 List

of softwarepackagesutilized in this thesis

### Table 2.1 Some

generalcharacteristicsof the

### Properties

of the standard atmosphere for an altitude of

ft

properties of

skin on

wing

6.1-

### Sample

results of optimal nodal support spacings for oneiterationon

all

airfoils

### -Uniform

assignment of kout value for all

airfoilsfrom

### Table 6.1

based on a minimum kout value (c5d,kout=

-

### List

of variables used in

macro

-

### List

of variables used m

macro

-

### List

of variables used in

macro

### List

of variables used in

### Table D.2

-Listof variables used in

### List

of variables used in

D.4-

### List

of variables used in

### List

of variables used in

D.6-

### List

of variables used in

### List

of variables used in

D.8-

### List

of variables usedin

(9)

### Example

of a nodal support spacing around an airfoil

1.2-

### Example

of deflected skin material between supports

edge of

airfoil in

of all

### C5A

airfoil cross-sections

-

re-scaled

airfoils

variance

-

### Example

of a pressure coefficient distribution

-

### Example

of a pressure distribution at high altitude

-

### Division

of a wing into sections and individualelements

### Figure 3.1

-Flowchart for the

macro

-Plotof

vs.

xc5a.ps

-

chart for the

macro

### Figure 5.2

-Sampleof an optimal nodal support distribution

-

### Flow

chart for

theoverall analysis process

-Flowchart for

-

### Plot

of c5a airfoil coordinates

-

defined by

points

and a center and

points

-

### Determining

the

center of an arc defined by

### 3

poestts on the arc

-

### Initial

arc approximation using the first

datapoints

### 6.7

-

of a second arc approximation

-

### Closer

view of thefirsttwo arc approximations

-

of concave arcs

### D)

on the c5a airfoil

-

### Plot

of all arcs used toapproximate the c5a airfoil

### Flow

chart for arcapproximation function

-

### Mapping

apoe^jt alongan arc into global coordfnates

### Figure 6. 13

-Howtodeterminewhichgoverning arc to follow

### 6. 14

-ResultsofMapToPfunctionforthec5a airfoil

-

### Close-up

view of c5a airfoilof

### 6. 14

indicated by the open square

-Flowchart for

function

### Variable

and sign convention for the

function

-Flowchartfor

function

### 6. 19

-Plotofpressurecoefficientdata from

-

### Four

pointsto be fit usestg a cubic polynomial

### Cubic

polynomialfit to original four points ...49

6.22-

### Pressure

coefficientresults of the

function

-

chartfor the

function

-

### Generalized

displacementsand forces for the

frame element

=

-

frame

element

-

pressures

(10)

beam

-

### Distinguishing

between local and global degrees offreedom

-Flowchart for

function

-

### Example

of the nodal support spacing optevuzationprocess

chart for

function

-Flowchart for

function

7.1-

=

M

### (1/32 IN),

ALLOWABLE DEFLECTION=

-Trial

=

M

### (1/32 IN),

ALLOWABLE DEFLECTION=

-Trial

=

m

### (1/8 in),

allowable deflection=

-Trial

=

m

### (1/8 in),

allowable deflection=

-

### Magnified

view of the trailing edge of the results from

(Figure

-

### Magnified

vmw of the leadentg edge of the results from

(Figure

of

vs.

xc5a.ps

-

of

vs.

xc5b.ps

C.3-

of

vs.

xc5d.ps

4-

of

vs.

xc5c.ps

(11)

-

the

### dawn

of civilization, man

upward to the

### sky

and observed nature's airborne creatures;

### from

the smooth, effortless

### soaring

of the majestic eagle, to the

energetic

ofthe

### Early

civilizations most

### looked

on these

creatures with awe, and

### in many

cases even reveredthem.

animals seemedto

the

constraints of

and were able to

such

### freedom

of movement, as to

man

envious.

### From

thetime that mankind

took

### hold

ofthe "airfoil" concept, to the

computer airfoil

### design

and analysis programs of

aircraft

on a single

### frame

of mind... aconstant,

airfoil

### in

speed, altitude, etc.,oftoday's aircraft, and

the

to

and

than

### any

otheranimal, therestill exists onemajorskillthatmost

animals

thatour aircraft

### simply

cannot compare with... maneuverability.

of

wings providethe

### (rudders, flaps,

stabilizers, etc.) provide some

maneuverability,

### but

none can provide the aircraft with the

### agility

of a creature that can change the actual shape of

at

time.

a

that almost all

### flying

animals possess, and use to their advantage.

no

### known

aircraft at this time can

this

### Flaps

provide a certain amount of change of shape, and some aircraft, such as the

this

use

sections of a

airfoils

theroot ofthe

to the

tip.

none can

### actively physically

change the shape ofthe airfoil cross-section of

the

thisremainsto

### be

onetraitof nature's

animalsthatman

not

abletomimic.

### The

goal of an adaptable airfoil cross-section need not achieve a

change

### in

(12)

mind: payload, speed, weight, altitude, purpose, etc.

airfoil

optimized

these

andthe

oncethat

### is

constructed, inefficiencies

arise.

optimization at

### cruising

speed and altitude

### is lost

the entire time the

aircraft

or

at

### lower

speeds and altitudes

at

### higher

speeds and altitudes.

to stretch the

and

the

an

optimal

atmosphere,

not work as well

### in

the atmosphere of another

planet.

### Hence

valid reasons exist

the realm of

### actively

controlled airfoil

shapes.

### The issue

of active shape control of wings

moreefficient

several years

studies

### using

variable

camber, twist or surface shape control to adapt the

ofthe

to

conditions.

### This

thesis explores the

of several

### wing

cross-section shapes through the

manipulation of anumberof

supports"

### firmly

clamped to theskin at

"optimal" points

around the airfoil.

to the

### large

number of variables that enter

the

### design

of such a

complicatedsystem, several simplifications

employed

### in

orderto obtain an

### initial

approximation ofthenumber and

### location

ofthenodal control points aroundthe airfoil.

### The

goal of this thesis

to

the

of

a

support"

nodal support

### in Figure 1.1 is defined

as a virtual spar

the

### length

of the wing, which completely clamps the

skin

place.

this

these nodal

supports are the

### only

means of support and manipulation of the wing.

spanwise

### wing

skin support, the skin

expected to

the gaps

### between

nodal

(13)

?> 0'

OriginalMapped Airfoil Deflected Airfoil

o Supports

e e e~-Q o o -e

44Supports Required A\rageSpacing=0.39105m

2 3 4 5 6

ActualChord,m.a.c. =8.4818m

Figure 1.1- Example

ofa nodal supportspacingaround an airfoil

0.2

-0.1

-0.15

Original MappedAirfoil

Deflected Airfoil

O Supports

(.05 8.1 8.15 8.2 8.25 8.3 8.35 8.4 8.45

ActualChord,m.a.c.=8.4818m

(14)

results

a

the

airfoil shape.

### The

goal ofthis thesis

to

### define

and maintain various airfoil shapes within a specified

tolerance while

### minimizing

the number of nodal supports required.

### This

support minimization objective

accomplished

tothe

### following

analysis process:

airfoils.

theaerodynamic

on the

airfoils

### based

on specifiedparameters.

each airfoil

### into

a specified number of

elements.

the

to the

### finite

elementsestablished

optimal support

on skin

to

applied

wherethe

are

through

elementanalysis.

### The

scopeofthis thesis

a

### basic understanding

ofaerodynamics, a

more

of

### finite

element analysis, and a

of

optimization.

thesis also

### involves

the use of several

### different

software packages and

associated

### programming

syntaxes/languages

### Software

Language/Syntax Used

Acknowledgements

Microsoft

Excel 97

Visual Basicfor

Applications

data

### files

for import into

MATLAB

Microsoft Corporation.

Allrightsreserved.

XFOIL 6.8 FORTRAN

### Obtaining

pressure

coefficient

distributionforeach airfoil

Created

Mark

### Professor,

MIT Departmentof AeronauticalandAstronautical

### Engineering

MATLAB

5.2

Built-in (similarto

Bulkof

programming

optimization,

plotting)

1984-1998

The

### MathWorks,

Inc. Allrights reserved.

MAPLE V

Release4.00

Built-in Symbolic

Computations

Maple Inc.

Allrights reserved.

Table 1.1 Listof software packages utilizedinthis thesis.

to the

that a good

of this thesis

the

### form

of computer code, the

various

### functions

andsubroutineswill

represented

conceptual

### flow

charts so as to avoidthe

ofthesyntax

### The

actual algorithms employed are

their

andpresented

### in

several appendices.

### Each

respective algorithm

accompanied

a

(15)

makethe

would no

### designing

a single airfoil to meet all

constraints.

the

would

several

### different

airfoil shapes to allow

### for

optimal performance under a

of

circumstances.

speed,

### lift,

maneuverability, and overall

would no

### longer be limited

to one solid airfoil.

the goal would

### be

such that a pilot of an

aircraft could

### just dial in

an airfoil shape onacomputer, andthen gettheperformance

required

### from

thatparticular airfoil shape.

even more

situation would

### be

one where the shape ofthe

controlled

a computer that

monitors the

current

conditions.

### Concerning

the shape of the airfoil, shape coordinates can

obtained through

published

### books,

through the aircraftmanufacturers, or even

the

### Since

the goal ofthisthesis

### in

the analysis of several airfoils,

would

### Upon

exploration of the

Database1 on the

a

of

### five

airfoils seemedto stand out as

as

### catering

to thegoals ofthis thesis.

airfoil shapes

### belong

to the Lockheed-Georgia

### These

airfoil shapes were

### designed

as

"boxed"

sets that were connected

the root ofthe

to the tip.

was

### implemented

as a redesign to the

model's wings

and then

### it

was carried over

and used onthecurrent

model as

well.2

airfoil

chosen

### for

this

thesis were c5a.dat, c5b.dat, c5c.dat, c5d.dat, and c5e.dat, and these

### five

geometries are

web site maintained

Michael

### Selig,

DepartmentofAeronauticalandAstronautical

ofIllinoisat

### Urbana, Illinois,

61801. Informationisavailableforuse undertheGNU General PublicLicense: http://amber.aae.uiuc.edu/~m-selig/pd/gpl.html.

2

(16)

and

printoutofthe

given

### in Appendix A.

0.2

-0.2

-0.3

X c5a o c5b -f c5c ? c5d 0 c5e

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 x-cfim,(%chord)

Figure 2.1- Plot

of allLockheed-GeorgiaC5Aairfoil cross-sections

0.08

-0.06

### "'

X c5a 0 c5b

+ c5c n c5d 0 c5e

O 6 0

### 8&&88i*.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 x-dim,(%chord)

Figure2.2

(17)

### These

airfoils werechosen

### geometry wing

would utilize each shape while subject to similar performance requirements.

### The

cross sections would then

### be

varied enough to alter the aerodynamic capabilities of a

prototype

as needed

of

all

airfoils

### simultaneously

at

specified positions

### along

the wing, this thesis explores the

### ability

to change the entire

### from

one airfoil shapeto

oftheother

shapes.

and

### The

most current version of the

the

the

aerodynamic

used

was collected

on the

specifications.3

### Again,

the

same airfoil cross sections were utilizedonthe

as

the

### C5A,

sothe application of

to the

airfoils

appropriate.

### The design

parameters relevant to this thesis are

given

span

m

area

ft2

m2

### Long

range cruise speed

gross weight

### kg

Table2.1 Somegeneral characteristics oftheLockheed-GeorgiaC5B.

and

that thevalues

### for

speed andweight characteristics noted

are

### high,

nearmaximumvalues.

was

as a means of

the

### XFOIL

programtosee

3

Generalcharacteristicsfor theLockheed-GeorgiaC5

### Galaxy

obtainedfromtheLockheed-Martin web site at:

(18)

would converge

a

number.

### However,

a reasonable test ofthe

### finite

element analysis routine was also

one

### in

which at some point on the airfoil

there would exist a negative

pressure

### (pL)

that would cause the skin of the

to

outwards.

### In

order to establish the pressure

### distribution

on the airfoil/wing, the

pressure coefficient

must

example of a

shown

-0.2 2

1 ~ ^~

^^-^~~*i "

i 1 1 1 1

Lower Surface

CL ^-"*w *"*

o o-

"V^ ^~

^

^^

<D

'o

it CD -1 _

O ?" '

O

3

UpperSurface

05 S

0) o

-

i. CL

-3

-4

i i i i i

0.2 0.4 0.6

x-dim,

### (%chord)

0.8 1.2

Figure 2.3- Exampleof a pressurecoefficientdistribution

### This

pressure coefficient

convertedto

pressure values

=

(19)

### )

, the pressure coefficient

not

than -4

the

### best way

to achieve a negative

pressure

with a

as noted

to

a

pressure

can

achieved

values at a

altitude.

pressure

would

### be

similarto thepressure

x 10

2.5

7a 1.5 a.

3 05 01

0.5

-0.5

-0.2

UpperSurface

0.2 0.4 0.6

x-dim,

### (%chord)

0.8 1.2

Figure 2.4-Exampleof a pressuredistribution

athighaltitude

### 2.4,

note that even though thepressure values

### for

theupper surface are

### lower

than

thepressure values

the

surface

### lift),

theupper surface pressure values are

positive

on the airfoil).

### Figure 2.4

shows a small area of negative pressure

### (pulling

outwards on the airfoil)near the

edge ofthe airfoil onthe

upper surface.

negative

pressure

area

as a means of

the

### finite

element analysis.

4

(20)

### for

the purpose of this

an altitude of

m) was used to

### determine

theatmospheric properties

N/m2

kg/ma

of

### 295.07

m/s

Table2.2 Propertiesofthestandard atmosphereforanaltitude of40,000 ft (12,192m).5

the

of

either an

### inviscid flow

analysis ora viscous

analysis.

the

analysis,

### XFOIL

requires specific values

angle of attack

number

and

number

### in

ordertoperform

the more realistic viscous

analysis,

### XFOIL

also requires a value

the

coefficient

### Each

ofthese parameters required

can

the values

and

numbercan

calculated as6

= general

=

v

i \

= airfoils

=

v

= taperedwings

### (c

=mean aerodynamic

### )

v

5

Dataobtainedfrom: Aerodynamicsfor Engineers.

3rd

### Ed.,

JohnJ. Bertin &MichaelL.

1998 Prentice

### Hall, Inc.,

pp.650-651 Table 1.2b.

6

(21)

### depending

on the application.

these

the one that

### best

applies to this thesis

### is based

upon two yet undetermined values, the

stream

### (V)

andthe mean aerodynamic chord

.

stream

can

as

=

=

=

m/s

### determination

of the mean aerodynamic chord

of the airfoils

### is slightly

more complicated.

m.a.c,

the chord of an

wing, with

constantchord,

### having

thesame aerodynamic characteristics as theactual

wing.7

m.a.c.

given

m.a.c.=

V -R'^T

j

+c.

root chc

=

chord

### CR

=exposed root chord at side of

other words,

a

of

the

of a

root to tip.

exact values

the

### length

of the chord at the root and

### tip

were unavailable, an

approximation of the m.a.c. was made

the

area

the

span

which

calculatedto

__S__

m2

c=

m

### From this,

theReynoldsnumber can

calculatedas

~~v~

4.698136-5m2/s

=

### 41. 0E6

'

Definition from: FundamentalsofFlight.

2nd

(22)

coefficient can

on the

under

the total

### (L)

oftheplane equals

theweight

=

-pV2S

=

m/s)2(576

2'

=

### remaining

parameters required

### succeeding

analyses arethose

### pertaining

to theactual skinthatmakes

### up

theairfoil shape.

tothe

### fact

that theactual material composition ofthe

### C5

skin wasunavailable,

### 7075-T6,

a common aluminum

used

### in

aircraftapplications, was used

modulus of

and

thickness

will

altered

are given

of

### 10.4 E6

lb/in2 71.7E9N/m2

### 7.9375 E-4

m

Table2.3 Initialproperties ofAL 7075-T6skinonC5wing.

### This

thesis assumes aconstant airfoil size

the

### wing

with a chord equal to the m.a.c.

the pressure

remains constant

the wing.

### The

pressure coefficient

calculated

on a

### wing

of unit width, and an analysis ofa one-unit width section will

### be

usedto representtheresults

therest ofthe

wing.

### This

unity-width section

smaller sections

### (elements),

which

8

Equationobtainedfrom: FundamentalsofFlight,

2nd

Richard S.

1989

pp.

Equation

### (3.9)

9

AL7075-T6properties obtainedfrom: MechanicsofMaterials.2nd

Ed.. Ferdinand Beer &E.Russel

(23)

are utilized

the

### finite

element analysis.

the

of the

ndividuol

Element

Analyzed Section

### into

sections as well asthe

ofthesesections

### into individual

elements.

Figure2.5

-Divisionof awing intosections andindividualelements

assumption

thisthesis

that the

section will

a

### large

number of elements.

### Hence,

each skin element

can

approximatedas

the

### flat

approximation and awidth

### (vv)

equal toone unit allows

### for

thecalculationofthearea moment of

= =

m)(7.9375-

V A

### (2.11)

Z=4.16745-llm4

andthecross-sectional area

=wt =

m)(7.9375-4

=

### for

each skinelement.

that theairfoils

### have been

chosen, the coordinate

### data

obtained, and all relevant

parameters,

### design

specifications, and approximations

the next

to

the

(24)

-

MICROSOFT

a small

encountered even

analysis.

arises

the

### fact

thatthe

airfoil coordinate

arenot

a

that

usable

edge to

edge

### along

the upper surface and

edge to

edge

the

surface).

### future

applications, not

airfoils

needed

and the

tediousness of

the

spurred the

of a

short

macros

thatwould

the

sortthrough

and prepare

use

and

### The

macros are stored

a

### file appropriately

named

workhorse.xls, andthe

macro

withthe

ofthis

ImportandConvert

AllC5 Airfoils

macro that

run

called

and

### it

makes a call to another subroutine

called

### This

smaller subroutine sorts through the two columns of

### data for

each airfoil andreorganizes

the

edge

edge

edge

process

the

macro

presented

code

### for Conv

(25)

Airfoils

Save Compilation File

as"allfoils.txt"

Ask for Airfoil -"-j Coordinates File Name

Open File

Rearrange Coordinate Data

(ConvMacro)

Separate Compilation File

Save Individual Data File for

XFOIL

Next Airfoil

Figure 3.1- Flow

chartfortheConvAllmacro

exit

### from ConvAll

the airfoil coordinate

reorganized

separate

### (xc5a.dat,

xc5b.dat,xc5c.dat, xc5d.dat, xc5e.dat) that are

and

coordinate

that

this

should

### be

notedthatthiscompilation

useful

### describes

all of the airfoils.

to

to

matrices with

columns.

with

columns could

the

### functions in

this thesis with some alterations

the code

### However,

the

variable number of airfoil coordinates

wouldnot

the

ofthis

each airfoil

re-divided

### into

an equal number of equal

### length

skin elements, at

which pointtheoriginal airfoil coordinates areno

needed.

next

to

### XFOIL

to obtain the pressure coefficient

### distribution based

on the parameters

(26)

a

overview of the

program as was

the

written

### by

the program's creator

of

and

references and

problem

are given

and

### C.2.

General Description

XFOIL is an interactive program for the design and analysis of subsonic

isolated airfoils. It consists of a collection of menu-driven routines

which perform various useful functions such as:

-Viscous (or

### inviscid)

analysis of an existing airfoil, allowing

* forced

or free transition

*

transitional separation bubble(s)

* limited

trailing edge separation

* lift

and

### drag

predictions just beyond CLmax

*

Karman-Tsien compressibility correction

- Airfoil design and redesign

### by

interactive specification of

a surface speed distribution via screen cursor or mouse. Two

such facilities are implemented.

*

Full-Inverse, based on a complex-mapping formulation

* Mixed-Inverse, an extension of XFOIL 's basic panel method Full-inverse allows multi-point design, while Mixed-inverse allows

relatively strict geometry control over parts of the airfoil.

-Airfoil redesign

### by

interactive specification of

new geometric parameters such as *

new max thickness and/or camber

new TE thickness

*

new camber line via geometry specification *

new camber line via

change specification

*

### flap

deflection

*

explicit contour geometry (via screen cursor)

-Drag polar calculation with fixed or varying Reynolds and/or Mach numbers.

-Writing and reading of airfoil geometry and polar save files

(27)

(Versaplot-derivative plot package used)

XFOIL is best suited for use on a good workstation. A high-end PC is also

effective, but must run Unix to support the X-Windows graphics.The source

code of XFOIL is

77. The plot

### library

also uses a few C routines for the X-Windows interface.

mentioned

the

### last

paragraph oftheprogram

a

workstation.

were

### easily

copied andcompiledon such asystem, and

upon

### running

the program,theuser seesthe

### startup

XFOIL Version 6.8

QUIT Exit program

.OPER Direct operating point(s)

.MDES Complex mapping design routine

.QDES Surface speed design routine

.GDES Geometry design routine

SAVE f Write airfoil to labeled coordinate file

PSAV f Write airfoil to plain coordinate file

ISAV f Write airfoil to ISES coordinate file MSAV f Write airfoil to MSES coordinate file

REVE Reverse written-airfoil node ordering

NORM Buffer airfoil normalization toggle

NACA i Set NACA 4,5-digit airfoil and buffer airfoil

PANE Regenerate paneled airfoil from buffer airfoil .PPAR Show/change paneling

.PLOP Plotting options

WDEF Write xfoil.def file with current settings

NAME s Change airfoil name

(28)

### For

each airfoil, the

that needs to

to

that

the

command

given and the

specified,

### data

and performs several

calculations

### based

onthosecoordinates as seen

### below.

Labeled airfoil file. Name: c5a

Number of input coordinate points: 61 Counterclockwise ordering

LE x,y = -0.00012 -0.00166

### |

Chord = 1.00012 TE x,y = 1.00000 0.00000

### j

Blunt trailing edge. Gap = 0.00258

Paneling parameters used. . . Number of panel nodes 140 Panel

### bunching

parameter 1.000 TE/LE panel

### density

ratio 0.150

Refined-area/LE panel

### density

ratio 0.200 Top side refined area x/c limits 1.000 1.000 Bottom side refined area x/c limits 1.000 1.000

XFOIL c>

that the airfoil

the next

to switch to the

### for

analysis.

XFOIL C> OPER

! Redo last ALFA,CLI,CL, ASEQ, CSEQ,VELS

PACC Auto polar accumulation enable/disable toggle PADD Add point to polar save file and/or

### dump

file PFIL f Specify new polar save and/or

### dump

filenames

VISC r Viscous/Inviscid toggle

.VPAR Change BL parameter(s) RE r Change Reynolds number MACH r Change Mach number

TYPE i Change type of Mach,Re variation with CL INIT BL initialization

### flag

toggle

ITER Change viscous-solution iteration limit

ALFA r Prescribe alpha

CLI r Prescribe inviscid CL

CL r Prescribe CL

(29)

CSEQ rrr Prescribe a sequence of CLs

GRID

### Cp

vs x grid overlay toggle

PREF Reference

### Cp

overlay enable/disable toggle

FREF Reference CL,CD..

### display

enable/disable toggle

CPX Plot

### Cp

vs x

CPXS Save Cp vs x to a file

CPV Plot airfoil with pressure vectors (gee wiz)

-VPLO BL variable plots

.ANNO Annotate plot

HARD Hardcopy current plot

SIZE r Change plot-object size

CPMI r Change minimum

axis annotation

FMOM Calculate

### flap

hinge moment and forces

FNEW rr Set new

### flap

hinge point

VELS rr Calculate velocity components at a point

DUMP f Output Ue,Dstar,Theta,Cf vs s,x,y to file

CPMN

CAVI

.OPERi c>

Report minimum Cp

Auto cavitation accumulation enable/disable

as

. OPERi

) .OPERi

. OPERi

. OPERi

) .OPERi

I .OPERi

1 . OPERi

) .OPERi

c> alfa

an

### initial

angle ofattack; a= 2 was

chosen)

c> re

c> mach

o vise

toviscous

c> cl

coefficient

o cpx

vs.x)

0 hard

a

ofthe

vs.xplot)

c> cpxs

theactual

vs. x

toa

### file)

(30)

-2.D

-1.5

P

-1.0

-0.5

0.0

0. 5

1. D

XFOIL

V6.B c5b

Ma 0.7700

Re - 41.

00-10

a 3.8291 c, = 0.8274

CM

--D.098

Cn O.DD790 L/O= 1 10.33 Nrr- 9. DO

Figure 4.1- PlotofPressureCoefficientvs.X- xc5a.ps

command was not

### in

the original software.

was

ordertoobtain a

setthatcould

### collecting bits

and pieces ofother subroutines

several

### locations in

thesource code, this

### CPXS

subroutine was created

### by

the author ofthis thesis to write the appropriate

vs. x

to a

actual code

this subroutine

given

enteredas

### follows

.OPERi c> CPXS xc5a.cpx

where xc5a.cpx

the

where the

stored.

### Once

all ofthe airfoils

### been

analyzed, the end result should

### (xc5a.cpx,

xcSb.cpx, xc5c.cpx, xc5d.cpx,

xc5e.cpx),

and

### (xc5a.ps,

xc5b.ps, xc5c.ps,

(31)

### Note

that throughout the entire

analysis, no

to the

original airfoil

calculations

### done using

an airfoil ofthecorrectshape,

### but

with a unit chord.

### In

terms of the pressure coefficient

the results are

### based entirely

on the shape ofthe airfoil, not the size. Therefore these

values

to

ofthechord

the

analysis

### is

complete, another quick macro

### in

Excel will prepare the

(32)

-MICROSOFT

### At

this point of the variable

### wing geometry

analysis, there exists one

### file,

allfoils.txt, which contains the airfoil coordinate

### for

all the airfoils, and

separate

### files

that contain pressure coefficient

these

one

### (allcpx.txt)

proves much more efficient

### file

management purposes.

this

all

arethesame

which

are

this case

used

a

### default 140

panels around each airfoil.

of the

code

the current

created

the

### ConvAll

macro mentioned earlier

### After

suitable

perturbation, the new

macro

created

### in

the workhorse.xls

### invoked

with a clickofthe

Importand

All

Pressure

Distributions

code

### for

this macro and the variables used

that code can

### B. The basic

processthismacro worksthrough

given

### in Figure 5.1.

Define

Variables

Airfoils

*-| DistributionFile 1

Name

OpenFile

Next Airfoil -"

Save

CompilationFile as"allcpx.txt"

(33)

structure and

ofthismacro

to that ofthe

macro

major

are:

of

### importing

airfoilcoordinates, thismacro

### There is

no callto thesmaller

macro

single

generated

this

calledallcpx.txt

exit

the

macro, all

the pressure

coefficient

condensed

### in

to the allcpx.txt

allcpx.txt

### file,

andthe allfoils.txt airfoil coordinates

are next

where

are used

a sequence of

### MATLAB

R routines which work towards the end goal of

### determining

an optimal nodal support

### distribution

around the airfoils.

### A

sample of such a support

### distribution is depicted in Figure 2.1.

w

-1

-3-Original Mapped Airfoil

Displacements

O Supports

e o- o e o o

44 Supports Required

Avsrage

=0.39105m

ooo e

6-2 3 4 5 6

Actual

m.a.c. =8.4818m

(34)

-MATLAB

MATLAB

mentioned

the

of the

this thesis

accomplished

### here.

MATLABallowsthree

means of

m-file

m-file

command

the most

of

a

### long

series of commands or

### many iterations

are required, then

at the

command

### line

will not suffice.

### This

thesis makes use ofthe command

### briefly

to

starttheanalysis process andtomonitor

progress.

script m-file

a moreefficient

of

m-file

atext

written

a

that

### is

understood andrun

script

m-file

theequivalent of

### typing

allthecommandsthatwould

entered

orderat

thecommand

### This

caters to therapid

### determination

ofresults, and a great

ofease

alterations.

### Also,

the script m-file provides

### for

the use of certain common

tools:

while

### if

statements, etc.,which when usedproperly,can

quite powerful.

### The

current analysis utilizes one main script m-file

### (Master.m)

to control

theoverall process.

m-file

### is very

similarto thescript m-file except

the

that

m-files are

generic

and

### usually

require specifictypes of

### input

toproduce

specific outputs.

major

### difference between

the script m-file andthe

m-file

the

of variables.

### A

variable assigned

ascriptm-file

assigned a

of

and

placed

### in

the active workspace, whereas the variables used

### function

m-files are clearedas soon asthe

complete.

### This

thesis employs several

m-files

(35)

### The

entire analysis process

governed

thescript m-file

### Master.m. This is

themain

controller of all the

### input

and output to and

the

requires no

### input

and produces no official "output".

since

a script

### file,

the

variables that are assigned

are stored

### in

the active workspace, which aids

### Master.m

also serves as a good

to place

commands to

represent

the results

each operation.

### For

the sake ofsimplicity, the

commands that

are

### included in

thecode arethose atthe

endthat

the

nodal support

### spacing

aroundtheairfoil.

actual code

### Master.m,

andthevariablesutilized

are given

mostsimple

### form,

theanalysis processtakes the

### form displayed in Figure 6.1.

Clear Previous

Results

Set Global Variables

SetParameters (Parameters.m)

Calculate Perimeter (ArcApprox.m)

Determine Perimeter Scale

Factor

(allcpx.txt)

Scale Coordinates andCpDistribution Accordingly

Re-determine Perimeter (ArcApprox.m)

Calculate ElementLength

MapAirfoil into Elements (MapToP.m)

Determine Global ElementOrientation

(GetAlpha.m)

LowerSurface

Store Nodal Coordinateand

(36)

chart given

### Figure 6.1 is

synonymous with the

process, which

explained

"Master"

at the command

calls

and

to run the

script

### function,

and allthepertinent variables are assigned values.

allfoils.txt

### is

andthetotalnumber of airfoils

quick

### determination

of the perimeter of the airfoil

the ArcApprox

this

a scale

calculated

### for

each airfoil so that all

### have

thesame perimeter.

allcpx.file

### is

and each pressure coefficient

### distribution

and each airfoil are

scaled.

### Another

pass around the airfoils with the

### function

creates several variables

used

theairfoil.

airfoil

mapped

### into

a set number of equal

### length

elements around theperimeter

the

### The

orientation ofeach ofthese elements with respect to a global coordinate system

the

### The

pressure coefficient

### fit

with a series of cubic polynomials

the

as ameansof

### determining

apressure valueateachelement node.

### The

airfoils are scaledtoactual size

elementanalysis.

element analysis

performed

the

and

### starting from

the

edge ofthe airfoil and

toward the

edge,

the

### lower

surface, then theupper.

### The FEAJDpt function

controls the optimization of support

across all

### five

airfoils,suchthatall airfoilsaretaken

account

theanalysis.

### The Opt function

employs a zero-order optimization method to maximize each

support

while

### staying

withinaspecified allowableskin

theactual

element analysis

each

### The

results of the optimization are saved to

and

### displayed

on a plot ofthe original

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