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RMYRESE RCH

L BOR TORY

3-D

ParachuteDescent

Analysis

Using

CoupledComputationalFluidDynamic

and

Structural

Codes

Jubaraj

Sahu

Gene

R .

Cooper

RichardJ.

Benney

ARL-TR-1435

SEPTEMBER

1997

9 9 7 7

2 8

^GQTJAin

Y

*m

g

Approved

fo rpublic

release;

distr ibution

is

unlimited.

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8/10/2019 3-D P D A U C CFD

3/31

Army

Research

Laboratory

Aberdeen Proving

Ground,

M D1005-5066

ARL-TR-143

5 eptember

1997

3-D

Parachute

Descent

Analysis

Using

Coupled

Computational

FluidDynamicand

Structural

Codes

JubarajSahu

Gene

R .Cooper

Weapons

& MaterialsResearch

Directorate,

A R L

RichardJ.

Benney

Natick

Research,Development ,and E ngineering

Center

U.S.Ar my

Soldier

SystemsC o mma n d

Approved

for

public

release;

distribution

isunlimited.

8/10/2019 3-D P D A U C CFD

4/31

Abstract

A computat ional

tool

thatmodelsth eterminaldescentcharacteristics

of

a

singler

luster

of

parachutes

s

echnology

hat

s

eeded

y

parachute

designers

an d

engineers. s

part

ofa

technology

program

annex

(TPA), ointffortetween

heU.S.

Army

NatickResearch,

Development,

nd

Engineering

Center

N R D E C )

nd

he

U.S.

A r m y

Research

Laboratory

A R L )

o

evelop

his

omputational

ool

s

now

under

way.

sfirstffort,t tempts

re

beingmade

o

nalyzeboth

two-dimensional(2-D)and

three-dimensional

(3-D)flowfieldsarounda

parachutesing ouplingrocedurenwhichth eluiddynamicsre

coupled

to

2-D

and

3-Dtructural

dynamic

S D )

codes.

This

effortuses

computational

fluid

dynamic

C F D )

odes

to

alculate

pressure

ield,

whichis

then

used

asaninputloadfo rtheDode.

pecifically,

this

report

resents

he

methods

nd

esults

fhe

low

ield

lus

he

structural

characteristics

of

a

single

axisymmetric parachute

and

a

3-D

gore

configuration

forth eerminalescentvelocity.Computed

resultsave

been

obtained

sing

he

ayload

weight

nd

unstretched

onstructed

geometry

of

th e

canopies

as

input.

ignificant

progresshas

been

made

in

determining th eterminaldescentflowfieldalong

withth e

terminal

shape

of

th e

parachute. discussion

of

th e

fluid

andstructuraldynamics

codes,

couplingprocedure,andth eassociatedtechnicaldifficultiesispresented.

Examples

of th e

codes 'current

capabilitiesare

shown.

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TABLEOF

CONTENTS

Page

LIST

OF

FIGURES

1 .

NTRODUCTION

2.

OLUTION

TECH NIQ U E

2.1

omputat ionalFluid

Dynamics

Model

2.2urrent

Structural

Dynamics

Model

2.3ouplingProcedure

3.O D E LGEOMETRY

A ND

COMPU TA TIONA LGRID

4.

ESULTS

5.

ONCLUDINGREMARKS 4

6.

EFERENCES 7

DISTRIBUTION

LIST

9

REPORTDOCUMENTATION

PAGE

3

in

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LISTO F FIGU R ES

Figure ag e

1 .omputational

Grid

for Axisym metric

Parachute

2.

nExpandedView

of th e

Grid

Near

th e

arachute

3 .

elocity Vectorsfor

Axisymmetric

Parachute,a=0

4.omparison

of

Pressure

Distributions

(axisymmetric

case)

5.ingle

Gore

Surface

Grid

6.-D Computat ionalGrid

fo rGore 0

7 .

ressureContours

fo rGore,

a

=

0 0

8.

omputedSurfacePressure

fo r

Gore,

a

=0 ,

(inneran d

outer)1

9.

omparison

ofGoreShapesfo r

Different

Coupling

Iterations,a

=

0

2

10.

-D Gore

PressureDistributions

at

Different

Circumferential

Locations

3

11.

omparison

ofPressure

Distributions(3-D gore,inner

surface)4

12.

omparison

of

Pressure

Distributions

(3-D

gore,

outer

surface)

4

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INTENTIONALLYLEFTBLANK

VI

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3-D

PA R A CH U TE

DESCENT

ANALYSIS

USINGCOU PLED

C O M P U T A T I O N A L

FLUIDDYN AMI C

A ND

T R U C T U R A LC O D E S

1

NTRODUCTION

Parachutes

have

been

an

interest

tom an

fo r

more

than2,000

years.

1

brief

butgood

review

of th e

history

ofparachutes

is

presented

in

Cockrell

(1987),

2

Knacke(1987),

3

andth e

U.S.A irForce

1978

and1963ParachuteDesign

Guides.

4

'

5

he

consideration ofparachutes

as

high-performance

aerodynamic

decelerators

did

not

take

place

untilth emiddle

of thiscentury.

Oneof

th e

featuresofparachutesthatisbeingstudiedhereisth e

fluidflowfield

around

one

or

moreparachutes

being

used

asdecelerators

fo rheavy

payloads

droppedfrom in-flight

aircraft.

n

particular,

this

workinvestigates

th ecoupling

of

th e

flow

field

around

non-ribbon

parachutes

withth edynamic

structure

of

th e

parachutes

themselves.

The

flow

around

parachuteshas

beenstudiedby many

investigators

2

'

6

'

7

using

analytical

methods

fo rpredicting

canopy

pressure

distributions.ockrell

(1987)

2

presents

a

summary

of

potentialflowsolutions

describingsteady

state

canopy

pressure

fields,and

Reference

describes

closed form analyticalsolutionsfo rth evelocity

potential

aroundsphericalcups.hesestudies

havebeenextended

by

Klimas

(1972),

7

who

considered placing

a

vortexsheet

tocoincide

with

th e

location

of

a

real

canopy. e

used

an

axisymmetric

Stake's

stream functionto

model

viscous

andpermeablematerial

effects.

he

theoreticalpredictions

gave

onlyfairnumericalresults,but

th e

internal

flow

behaviorwas

reasonably

good.

Researchershave

continued tostudy

th eflow

around

parachutes

usingnumericalmethods

tosolve

th e

governing

equations.A two-dimensional

computational

fluiddynamic

(CFD)code

has

been

used

by

th e

U.S.Ar my

Natick

Research,

Development ,

an dEngineering

Center

(NRDEC) .R D E C

has

applied

thiscode

to

flowproblemsthathave

axial

symmetry

andhave

calculatedth eflowand

pressure

fieldsaroundparachutes.

ne

l imitationofusing

a

two-

dimensional

(2-D)code

is

that

th e

parachutesof

interest

areusually

not

axisymmetric .

Therefore,thisreportis

going

to

investigateth ethree-dimensional

(3-D)properties

of

flows

around

parachutes.

he

pressure

distributions

calculated

on

th e

to p

side

and

underneath

th e

parachutes

are

then

used

to

couple

th efluid

dynamics

to

th e

structure

codes

used

to

model

th e

structural

propertiesof

th e

parachute

itself.

Thetotaldrag

ofparachutes

in

a

clusterhas been

shown

experimentally

to

be

lessthanth e

sum

of

th edrags

of

th e

individual

canopies.

he

ability

to

predict

th e

flow

fieldcharacteristics,

terminaldescentpositions/shapes,and

th e

drag

onclustersofparachutes

isneeded

to

assistin

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th e

development

of

improvedparachute

clusterdesignand

should

allowfo roptimization studies

to

be

performed

numerically. jointeffort

between

N R D E C

an d

th e

U.S.

A rmy

Research

Laboratory(ARL)

to

develop

this

computat ionaltool

has

begunwithmodeling

flowabout

parachutes

in 3-D.

his

effortis

using3-DC FD

codes

in conjunctionwith

3-D

structural

dynamics

(SD)

codes.

The

aerodynamic

characteristics

associated

with

a

single

orcluster

of

parachutes

in

th e

terminal

descent

phaseare

extremelycomplex

to

model .hecomplexityariseslargely

from

th e

factthatth eflowfield

depends

on

th ecanopyshape,which

itselfdepends

on

th eflowfield.

correct

model

mus t

include

th e

coupled

behavior

of

th eparachute

system's

structural

dynamics

withtheaerodynamics

of

th e

surrounding

flow

field.

he

coupled

model

is

being

developed

to

yield

th e

terminal

descentcharacteristicsofsingle

orclustered

parachutes

includingvelocity,

shape,drag,

pressure

distribution,

and

th eother

flow

fieldcharacteristics.

As

a

startingpoint,

th eterminal

descentcharacteristics

of

a

half-scale

C -9 solid

flat

circular

parachute

are

determined.

hegoalfor

this

stepis

to

predict

th e

parachute's

terminal

descent

shape,

velocity,

pressure

field,

velocity field,etc.,

whenthepayload

weightan dunstretched

constructedgeometryof th e

canopy

are

givenas

input.his3-D capabilityis

needed

to

allow

designengineers

to

optimize

a

single

parachute

design(for terminaldescentcharacteristics)

ona

computer.he

effecton

th e

parachute's

terminal

descentcharacteristics because

of

modifications

ofa

gore

shape,suspensionline

length,etc.,

ca n

beinvestigated withouthaving

to

manufacture

prototypesand

perform

multipledrop

tests.

he

3-D

CFD/SD

capability

being

developed

will

ultimately

be

applied

to

th eparachute

cluster

problem

to

investigateth e

flowfield

surroundingvariousU.S.Ar myclusteredparachute

configurations.

This

report

describes

th e

progress

made

in

th e

development

of

th e

C FD

and

SD

models .

The

approach

usedto

coupleth e

tw o

codes

is

also

described.xamples

of

th e

codes'current

capabilities

are

presented.

2 OLUTIONTECHNIQUE

2.1

omputat ional

Fluid

DynamicsModel

The

computat ional

methodused

in

th epresentanalysis

solves

th eincompressibleNavier-

Stokesequations

in

3D(INS3D)

8

generalizedcoordinates

fo rlow-speedflows.histechnique

is

basedon th emethod

of

artificial

compressibility

and

an

upwind

differencing

scheme.he

pseudo-compressibi l i ty

algorithm couplesth epressure

andvelocityfields

atth e

same

t ime

level

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and

produces

a

hyperbolicsystem

ofequations.

he

upwinddifferencing

leads

to

a

more

diagonal

system

and

doesnot

requirea

user-specified

artificial

dissipation.he

viscous

flux

derivatives

are

computedusingcentral

differencing.his

codeiscapable

of

computing

both

steady

state

and

time

accurateflow

fields.

The

governingequations

are

numericallyrepresentedan d

solvedusing

a

nonfactored Gauss-

Seidal

line-relaxation scheme.

his

maintains

th estability

and

allowsa

largepseudo- t ime

step

to

betaken

to

obtain

steadystateresults. etails

of th enumericalmethod

are

given

in

Rogers ,

Wiltberger,

and

Kwak

(1993)

9

and

Kwak

(1989).

1

ocompute

turbulentflows,aturbulence

modelmustbe

specified.hepresentcalculationsuse th e

one-equation turbulencemodel

developed

by

Baldwin

and

Barth

(1991).

1

1

n

this

model ,

a

transport

equationissolved

fo r

th e

turbulentReynoldsnumber .hisequationis

derivedfrom asimplified

form of

th e

standard

two-

equation

k-e

turbulence

model .he

one-equationmodelhas

th eadvantage

that

itdoesnot

require

th e

turbulent

length

scale

to

be

specified.

t

issolved

using

th e

same

Gauss-Seidal-type

line-

relaxationschemeused tosolve

th e

mean

flowequations.

2.2

urrent

Structural

Model

The

currentstructuralmode lbeing

used

for thismodeling

effortisth e

CAnopy

Loads

Analysis(CALA)code.

12

henextgenerationfor thestructuralhalf

of

th eterminal

descent

model

of

round

parachutes

will

be

a

three-dimensional

membrane/cable

finite

element-based

code.

13

A LA

is

a

static

code

that

predicts

th e

steady

state

shape

and

stressesfo r

round

parachutes.

A LA

requiresth eparachute'sdimensions

and

a

steadystatepressuredistribution

alonga

radial

(meridional

arc

length)

as

input. radialis

defined

as

th econtinuation

of

a

suspension

line

from

th e

skirt

along

ameridional

ar c

length to

th e

apex

of th e

canopy.he

radial

canalsobevisualizedasth e

connection

of

tw o

adjacentgores.

Thepressuredistribution

acrossth esurface

of

th e

canopy

issuppliedby

th eC FDcodeas

a

function

of

th e

3-D

deformed

canopy

shape.

heC AL A

codeassumptions

transform

th e

pressure

distribution

into

nodal

forces

that

are

tangential

and

normal

to

th eradialposition.

he

C AL A

code

assumes

that

th e

horizontal

members

(defined

as

th e

curved

strip

of

a

gore

connecting

tw o

adjacent

radials)

ofagore

form

sections

ofcircular

arcs

and that

th epressure

distribution isuniform alongth ehorizontalmembers .hehorizontalmembers

lie

in

planesthat

are

definedbythe

surfacenormalvectorsfrom two

adjacent

radialscomprisingonegore.

he

CALA

codedefines

th estaticforce

perunit radiallength

applied

to

a

radial

location.Theseforce

equationsincludeth evariable\|/,whichisdefined

as

the

gore

bulgeangle.|/ isdetermined

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iteratively

fo r

th e

currentiteration'ssurface

configuration

based

on

the

constructed

goreshape.

The

forces

include

approximations

of th e

hoop

force

contribution

based

on th e

gore

geometry.

The

C A L A codereiteratesth eshape

by

assuming

an

initial

guess

for the

vent

linetension.

The

code

outputs

th e

canopy

shape,

stresses,

gore

bulge

angles,

total

drag,

etc.

he

radial

shape

is

extracted

from th e

output

and

used

in

aFormulaTranslator(FORTRAN)code

withth e

C A L A

assumptions

to

generate

a

se t

of3-D

data

representingth e

shape

of

a

gore.

2.3

oupling

Procedure

A tthist ime,

th e

codes

are beingmanual ly

coupled.heresultssection thatfollows

describes

th e

currentmodeling

capability.hissection

outlinesth e

steps

that

ar e

taken

tomode l

either

single

orclustersofparachutes

as

th e

model

progresses

overth e

nextyear.

heprocess

beginswithth estructuralmodel ,

whichrequiresth e

geometry

of

th e

canopy

and

suspensionl ines

as

input. guessed

surfacepressure

distributionisused

by

th e

structuralcodeto

determine

a

firstguess

deformedshapefo rth e

canopy

orcanopies.

Ifth e

parachutesystem

isa

singlecanopy,

th eshapedeterminedissupplied

to

th eC FD

code

as

is .

C FD

meshis

generatedaround

th e

surface

shape

provided.

heC FD

code

solves

fo r

th e

flow

fieldcharacteristics

with

a

prescribedin-flow

velocity.

he3-D

surface

pressure

distributionis

extractedfrom

th e

CFDresults

an dfe dinto

th e

structural

code.

hestructural

codeis

executedwithth enewsurfacepressuredistribution andpredicts

a

newdeformed

shape.

The

total

vertical

dragiscalculated,basedonusingth e

shape

and

pressure

distribution.

he

new

shape

is

fe d

backto

a

grid

generator

program,

an d

a

mesh

isgenerated.his

newmesh

is

usedin

th e

C FD

code,

and

computat ions

are performed

toobtain

th esteadystate

resultwith

th e

same

in-flow

velocity.

he

process

is

continued

manually

until

shape

and

pressure

distribution

converge.

he

solution

m ay

diverge

for

relatively

poor

initial

guesses

ofpressure

distribution,

in

whichcase,th eprocess

m ayinvolve

a

more

elaboratecouplingprocedure.

To

mode l

acluster

of

canopies,

th e

predicted

single

parachute

shape

is

rotated

by

an

initial

guessed

angle

about

the

confluence

point.

A

CFD

mesh

can

be

created

around

th e

surface

shape

providedandcan

use

symmetry

boundaryconditionsthatdepend

onth enumber

ofparachutes

in

th e

cluster.heC FD

code

solvesfor the

flowfieldcharacteristics withaprescribedin-flow

velocity

alongth evertical

axis.he

3-D

surface pressure

distribution is

extracted

from th e

C FD

results,andth enetradialforceonth e

canopy

is

determined.hecanopyshape

isthenrotated

in

th edirectionthatisconsistentwithth epredictednetforce.henewcanopy

gridlocationis

supplied

to

th eCFD code,anewmeshiscreated,

andth eresulting

surfacepressuredistribution

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isused

to

determine

th e

direction

and

extent

of

rotation

required

to

reach

a

forceequilibrium

in

th e

"radial"

direction.erunning

th estructural

codewith

th e

new

surface

pressure

distribution,

onceth e

radial

forces

havebeen

reduced

to

near

zero,

is

then

performed

an d

th e

process

continued.

he

total

vertical

dragispredicted,based

on theshape

and pressure

distributionof

th e

single

canopy

multiplied

by

th e

total

number

of

canopies

being

modeled

in

th e

cluster.

3 MODEL

GEOMETRY AND

COMPUTATIONAL

GRID

Thecoupledmodelwas

used

todetermine

th e3-D terminaldescent

characteristics

of

ahalf-

scaleC-9canopy.

he

half-scaleC-9 isa

solid

cloth,flat

circular

canopy

composed

of28gores.

The

constructeddiameteris14

feet,

and

suspension

lines

are12

feet

long.hehalf-scale

C-9

canopyhas

beenused

in

a

variety

of

experiments

and

it s

opening

behavior

was

predicted

with

an

axisymmetric

coupledmodel

developed

atNatick.

1

4

his

canopy

was

studied

with

th e

manually

coupled

codes,

andth eterminaldescent

results

are

compared

to

th e

results

obtainedfrom

previousstudiesat Natick.

To

start,an

axisymmetric

parachute

shape

was modeled

to

gainconfidence

in

th e

3-D C FD

code's

predictive

capability

of th e

flow

field

characteristics

around

parachute-likeshapes.he

terminal

descentshapefrom the

axisymmetricmodel

(case

in

reference14)wasused

to

define

th egrid. computat ionalmeshw as

generatedaroundaquarter

of

th e

canopy

to

usesymmetry

boundary

conditions

fo r

th eaxisymmetric

test

case.

The

surface

grid

alongwith

a

longitudinal

cross

section

of

th e

full

grid

is

shown

in

Figure

1 .

he

full

grid

consists

of

48

points

in

th e

streamwise

direction,19

points

in

th e

circumferentialdirection,

an d

80

points

in

th e

normal

directionaway

from

th ebody

surface.

he

gridpoints

are clustered

nearth ebody

surface

for

viscous

turbulentflow

computations.

heouter,in-flow,

an ddownstream boundaries

are

placed

sufficiently away

from

th e

body

surfacethat

they

do

not

interfere

with

th e

convergenceand

accuracy

of th ecomputed

flow

field

results.

he

grid

wasobtained

by

th eEagleview

15

grid

generationprogram usingan

algebraic

methodand

ellipticsmoothing

procedure.A nexpanded

view

of

th e

computationalgrid

near

th e

parachute

bodysurface

is

shown

in

Figure

2.hisfigure

showsth e

computat ionalgrid

fo r

both

end

planes

in

the

circumferential

direction. lso

included

is

a

shadedparachute body

surface.

tshows

th e

gridclustering

near

th e

body

surface

more

clearlyfo r

th e

outer

part

of

th e

bodysurface

and

th e

skirt.hegrid

was

obtained

fo r

a

circumferential

plane

andthen rotatedaround to

obtain thefull

gridcontaining19planes

in th e

circumferential

direction.

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Figure

1 .

omputational

Grid

fo rAxisvmmetr ic

Parachute.

Figure

2.

A n

Expanded

Viewof

th e

Grid

Near

th eParachute.

8/10/2019 3-D P D A U C CFD

15/31

4.

RESULTS

The

inputvelocity

used

is

18feet

per

second,

which

was

th e

terminal

descent

velocity

determined

from

theaxisymmetricmodel. ll

numericalcomputations

were

performedat thisin -

o

flow

velocity

and

at

a

=

0

esults

are

now

presented

for

th e

axisymmetric model .

he

computed

results

were

obtainedusingth eNS3D

code.

igure3showsa

velocity

vectors

field

in

th evicinity

of

th e

axisymmetr ic

parachute

shape.

he

incoming

flowstagnates

atth ebody

surface,

an daseparatedflow

region

isformedin

front.

t

alsoshows

flow

separatingat theskirt

and thenforminga

large

region

of recirculatory

flow

behind

th e

body.

his

separated

flow

region

in

th e

wakegivesrise

to

lower

surfacepressure

onth e

outer

body

surface.

t

f

f

t

t

t

V

tA\u\ ii; /- 7 //tt

t

t

\.W t

Vtltll

nttt

U

M

C

Figure

3.

elocityVectorsfor Axisymmetric

Parachute,a=

0

The

pressure

distribution

on

the

inner

an d

outer

surfaces

of

th e

canopy

from

both

codes

is

compared

in

Figure4.n this

figure,

nondimensionalpressurecoefficientisplottedas

a

functionof

th emeridional

length.

ere,

th emeridional

length

isth edistancethatismeasured

from

the

apex

(vent)

of th eparachute

to

th eouter

section

(skirt)

alongth e

canopy

surface.

hetotalmeridional

8/10/2019 3-D P D A U C CFD

16/31

lengththus

corresponds

tohalf

of

th e

diameter

of

th eparachute

in

th e

unstretched position(1 4

feet

diameter).

he

computed

pressure

distributions

obtained

using

th e

INS3D

code

are compared

with

th e

previouscomputedpressuredistributions

using

a

2-D code.

hetw o

sets

of

computedresults

agree

very

well

fo r

both

outerandinner

surface

pressures.

hepressuredistributions

are

very

close,

especially

noting

th e

fact

that

th e

axisymmetriccoupled

model

had

not

completely

dampened

at

th etime

fo r

whichth e

shape

was

extracted.

mall

differences

can

b e

observed

betweenthese

resultsnearth e

skirt

of th e

axisymmetric

parachute.

s

expected,

th e

innersurface

pressureis

quite

uniform

and

is

alo t

higherthan

th e

predicted

pressureon

th e

outer

surface.

his

gives

rise

to

dragforce,whichis

consistentwithth epayloadfo rthisparachute

atthisterminal

velocity.

0.6

0.4

:ex-

8 0.2

-

Q _

8

Q _

Q _

0.2

0.4

0.6

XX

X X

X X

X X XXX

xx

o

Outer

Surface

x

Inner

Surface

nner

_[Natick)_

Outer... Natick]

0 0

1 0

2 0

3 0 4.0 5 0 6.0 7 0

Meridional

Length

feet)

8.0

Figure

4.

omparison

of

Pressure

Distributions

faxisymmetric

easel

Thenextstep

in

thismodeling

effort

involved extracting

a

3-D

grid

of

a

singlegore

from the

axisymmetric

shape.

his

was

done

by

applying

th e

CA LA

assumptions

of

th e

gore

shapeto

th eradial

node

points.

he

axisymmetric

shape

is

assumed

tocoincide

with

a

radial.

he3-D

gore

surface

was

obtained

using

this

procedure

and

further

smoothed

especially

near

th e

vent

region

to

eliminate

discontinuities

in

the

surfacedefinition.

he

smoothedsurfacegridis

shown

in

Figure

5.

hissurface

grid

contains

24

grid

points

in the

meridional

direction and

22

points

in

th ecircumferentialdirection.

8/10/2019 3-D P D A U C CFD

17/31

Figure5.

ingleGoreSurface

Grid

.

Thissurface

grid

was used

to

generate

a

3-D computational

grid

(see

Figure6)fo r

th ecalculation

offluid

flow

over th egore

configuration.

he3-D gore

grid

consists

of

53

x

22x84

in theaxial,

normal ,

and

circumferential

directions,

respectively.hesection

containing

th egoresurface

was

generated

using

an

O-topology.

nother

section

of

th e

grid

was

obtained

using

rectangular

mesh

topology.

oth

grid

components

were

generatedalgebraically

15

and then

appended

toform

th e

full

grid.heparachute

gore

surface

is

a

part

of

an interior grid

line,

andthus,

th eno-slip

boundarycondition is

applied

along

this

interior

boundary.orviscousflowcomputat ion,

which

is

of

interest

here,

th egrid

pointsar eclustered

near

th e

parachute

gore

surfacein

th e

normal

direction

to

resolve

th eflow

gradients

in the

boundary

layers.

Computed results

havebeenobtainedfo r

th e

3-D

gore

configurationand

are

nowpresented.

Figure

7

shows

th e

pressurecontoursfo r

a

circumferential

end plane.orth e

incomingflow,

th e

pressure

is

uniform

(free-stream pressure).

s

th e

flow

approaches

th einner

surface,pressure

builds

an d

forms

a

large

region

ofhigh

pressure

in th e

vicinity

of th einner

surface.

he

pressure

in the

wakeregionis

alow pressureregion.

l though

thereis

some

variation

of

pressure

in

the

lo wpressure

region,

th e

outersurface

pressure

is

a

lo t

lowerthanth e

inner

surface

pressure.he

flow

expands

around

th e

skirt

region

of

th e

gore,

an d

sharp

changes

in

th e

pressurefieldcan

be

observed

in

going

from

th e

inner

to

th e

outer

surface.

8/10/2019 3-D P D A U C CFD

18/31

Figure

6.

-D

Computat ional

Gridfo rGore

.

c

0.2

D

0.3

E

0.4

F

0.5

G

0.6

H

0.7

0.8

J

1.0

K

1. 1

L

1.2

M

1.3

N

1.4

0

1.5

P

1.6

Figure

7.

ressureContoursfo r

Gore,a

=

0

.

10

8/10/2019 3-D P D A U C CFD

19/31

Thecomputed pressure

m ap

on the

gore

surface

itselfis

shown

in

Figure

8

fo r

both

inner

an d

outersurfaces. l though

computat ions

wereperformed

on

one

gore

shape

because

of

symmetry,

th e

canopy

consists

of28gores,

whichare

al l

shown

in

this

figure. gain,

itshows

highpressure

onth e

inside

surface,

which

is

ratheruniform

except

fo r

th eskirt

region.

he

computed pressure

on

th e

outer

surface

is

lower

and

is

not

as

uniform.

Figure8.omputed

Surface

Pressure

fo r

Gore,

a=

0.(innerandouter).

The

pressure

distribution

over

th e

gore

surface

wasused

by

th eCA LA

codetopredict

a

new

shapefo r

a

gore.he

pressure

distribution required

byC AL A

isassumed

to

be

constant

overth e

horizontal

members

of

th e

gore.herefore,

th eCFD predicted

surfacepressure

distribution

wasaveraged

over

the

gore

surfacetoobtain

an

averagepressuredistributionversus

meridional

arc

length

se t

of

data.

his

was

accomplished

by

averaging

th e

surface

pressure

values

atth e

radial

locationand th e

corresponding

gore

mid-pointvalues.

hispressure

distribution

wasused

as

inputby

th eC AL Acodewhich

outputth enewpredictedshape.he

shape

ofth e

radial

predicted

to

th e

CALA code

was

usedasan

input

to

a

F O R T R A Ncode

that

uses

th e

C A L A gore

shape

assumptions

to

generate

anew

3-D

gore

grid.hisnewgridwasused,

computat ions

wereperformed,

andCFD resultsofth e

resulting

flow

field

and

pressure

8/10/2019 3-D P D A U C CFD

20/31

distributions

were

obtained.his

coupling

procedurebetweenth eCFD an d

SD

codes

was

repeatedthree

t imes.he

threedifferent

gore

shapesthatresulted

from

this

analysis

areshown

in

Figure9.hechange

in

th e

gore

shape

from th e

first

iteration

to

th esecondwas

observed

to

be

bigger

than

that

from

th e

second

toth e

third

iteration

ofthis

coupling

procedure.

he

change

between

th e

shapes

between

th e

second

an d

th e

third

iteration

was

rather

small ,

which

indicates

th e

nearconvergence

of th e

body

shape

to

it s

final

terminal

descent

configuration.

The

outer

surface

pressure

distribution

over

th e

gore

(firstiteration)is

shown

asa

function

ofmeridional

gore

location

in

Figure10.

he

totalmeridional

lengthagaincorresponds

to

half

diameter

of

th eparachute

in

th e

unstretchedposition.hecomputedpressuredistributions

are

obtained

at

different

locations

in the

circumferential

direction.

he

first plane

in this

figure

refers

to

th eedge

of

th egorewhereasth e

half-plane

corresponds

to

th emid-section (center)

of

th e

gore.

The

difference

in

th e

outer

surface

pressuresis

rather

small

over

a

largeportion

of th egore

except

near

th e

skirt

region.

l though

not

shown

here

th e

same

is

true

of

th e

inner

surface

pressure

distributions.

or

th e

subsequent

figures

on

surfacepressurecomparisons,

th e3-D

gore

surface

pressureis

used

at

th e

half-planeorth e

mid-section.

Figure

9.

omparison

of

Gore

Shapes

fo r

Different

Couplin

g

Iterations,

a

=

0.

Thecomputed

pressure

distributionsareal lobtained

using

th eINS3D codean d

are

now

comparedbetweenthe

different

iterations

of

th e

coupling

procedure

described

earlier.he

inner

surfacepressuredistribution over

th e

3-D

goreisshownas

afunction

of

meridional

gore

location

12

8/10/2019 3-D P D A U C CFD

21/31

in

Figure

11. lso

included

in

this

figure

is

th ecomputed

pressure

distribution

fo r

th e

axisymmetricparachuteshape.

he

ressure

distribution

over

th e3-D

goreisnearlyconstant

near

the

apex

and

deviates

across

th e

gore

as

th eskirt

is

approached.

his

is

expected

because

th e

shape

is

nearlyaxisymmetric

near

th e

apex

an d

becomes

lessaxisymmetric towardthe

skirt.

The

C FD

code

was

ru n

with

th e

same

in-flow

velocity,

an d

th e

3-D

parachute

gore

surface

pressure

distribution

was

extracted

from

th e

CFD

results.hechange

in

inner

surface

pressure

is

small

between

th e

differentiterations

orgoreshapesandisespecially

smal lbetween

th e

second

an dthird

iterations.

hedifference

between

th e

predictedpressure

fo r

th e

gore

shapes

andth e

axisymmetric

configuration islarger,

whichindicatesth enecessity

of

3-D

modeling

of

th efluid

o

an d

structural

dynamics.

igure

12

showsth e

outer

goresurface

pressure

comparisons

ata

=

0

Thethree

sets

ofgoreshapesyieldsimilar

pressure

distributions.

The

difference

betweenth e

second

andth ethird

iteration

againis

smallercompared

to

that

between

th e

firstandth esecond

iteration.he

pressure

distributionsfo r

th e

different

gore

shapesdo

not

show

aslarge

avariation

in

pressure

as

is

observedfo rth e

axisymmetric parachuteshape.

The

computedsurfacepressures

fo r

both

3-D

gore

an d

axisymmetric

parachuteagree

rather

well

with

eachother

only

near

th e

apex

(vent).

s

expected,

th e3-D effect

is

felt

more

near

th e

skirt

of

th e

canopy.

he

pressure

differentialbetweenthe

innerand theoutersurfaceiswhatdetermines

th e

dragforce

for these

parachuteshapes

fo r

a

given terminal

descentvelocity.

o _

0.3

0.2

0.

0.0

0.1

-0.2

First

Plane

Half

Plane

0.0 1 0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

MeridionalLengthfeet)

Figure

10.

-D Gore

Pressure

Distributions

at

DifferentCircumferential

Locations .

13

8/10/2019 3-D P D A U C CFD

22/31

0.6

0.5

-

8 0.4

H

L

Q _

0.2

0.

-

0.0

First

teration

.Second

.Iteration

thirdJteration_

AXISYMMETRIC

0.0

1.0

2.0

3.0

4.0

5.0

6.0 7.0

8.0

MeridionalLengthfeet)

Figure11.

omparison

of

Pressure

Distributions

T3-D

sor

e,

innersurface).

0.4

-0.6

First

Iteration

Second1t

e

r

a

t _ l o n

Third

_ I

teratL

o

n

RXI

SYMMETRI

1

2 3 4 5 6 7 8

Meridional

Length

feet)

Figure

12.

omparison

ofPressure

Distributions

(3-D gore,

outer

surface

5.CONCLUDING

REMARKS

The

complexityof

modelingparachute characteristics and phenomena

in

terminaldescent

andduringth e

openingprocess

s tems

from

th e

coupling

between th e

structural

dynamics

of

th e

canopy,

linespluspay

load,

andth eaerodynamics

of

th e

surrounding

fluidmedium.

14

8/10/2019 3-D P D A U C CFD

23/31

This

report

hasdescribedongoing

research

beingconductedat

bothN R D E C

and

A R Lto

predict

th e

3-D

terminal

descent

characteristicsof

singleandclustersofround

parachutes.

his

involvesth e

coupling

of

a

2- D

and/or

3-D

CFD

codewith

2-D and/or3-D

parachutestructural

codes.

hesolution

to

th e

coupled

problem

is

expected

to

assist

in

th e

development

of

future

U.S.

Ar my

airdrop

systems

and

other

round

parachute

systems.

he

capability

of

accurately

predictingth e

behavior

ofparachute

systems

will

significantly

reduceth e

amount

of

testing

currently

required.he

predictionof th e

terminal

descentcharacteristics

ofahalf-scale

C-9

parachute

has

been

demonstrated

by

manuallycoupling

a

3-D

CFD

codeto

th e

CA LA

code.

3-D membrane/cable

finite

element

codewillbe used

as

thenext

generation structural

model.

Timewillalsobe

spent

combining

th etw o

codes

into

a

moreuser-friendlyenvironment

an d

enhancing

th e

pre-and

post-processing

codes

to

shorten

the

turnaround

t ime.

Thisreport

haspresented

th e

currentstatusof th e

modeling

effortandoutlined

th e

directionbeingpursued

to

address

th ecomplexityof the

parachute

characteristics

andth e

associatedflow

fields.

uture

computational

models

are expected

to

provide

better

understanding

of th e

physicsthat

govern

th eparachute

and

flowfield

interaction.he

codes

will

allowth e

user

to

examineth e

effect

of

ventsize,

vent

location,

varying

suspension

line

lengths,

etc.

15

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6.

REFERENCES

1 .aydew,

R .

C,eterson,

C.W.,

an d

Orl ik-Ruckemann,K.

J. ,Design

andTesting

ofHigh-

Performance

Parachutes, AGARDographNo.319,November

1991.

2.

ockrell,

D.

J. ,

The

Aerodynamics

of

Parachutes, A GA R Dograph

No.

295,

July

1987.

3.

nacke,T.W., Parachute RecoverySystemsDesignManual , NWCTP6575,Naval

Weapons

Center,China Lake,California,

June

1987.

4.

wing,

E.G.,Bixby,H.

W.,

an dKnacke,T.

W.,

RecoverySystemsDesignGuide,

AFFDL-TR-78-151,

December

1978.

5.

erformance

ofandDesignCriteria

fo r

DeployableAerodynamicDecelerators,U S A FA S D -

TR-61-597,

December1963.

6.

IA A Aerodynamic

Deceleration

Systems

Conference,

Houston,

Texas,

September

1966.

7.l imas,P.

C,

Internal

Parachute

Flows,

Journal

of

Aircraft

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Vol.9,

No.

4,

Apri l

1972.

8.

ogers,

S.E.,

Kwak,

D .,

an dKiris,C, Steady

andUnsteady

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of th e

IncompressibleNavier-Stokes

Equations, AIAA Journal.

Vol.

29,

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4,

pp.

603-610,

Apri l

1991

9.ogers,S.

E. ,

Wiltberger,

N.

L. ,

an dKwak,

D.,

EfficientSimulation

of

Incompressible

ViscousFlowoverSinglean d

Multielement

Airfoils, ournalof

Aircraft.Vol.

30,

No.

5,

pp.736-743,September-October1993.

10.

wak,

D .,

Computat ion

of

Viscous

Incompressible

Flows, NASA Technical

Memorandum

101090,

March

1989.

11.

aldwin,

B.

S.

andBarth,T.

J. ,

A One-Equation Turbulence

TransportModel

fo r

High

ReynoldsNumber

Wall-Bounded

Flows,

AIAA

PaperN o.

91-0610,1991.

12.

undberg,

W.D ., New

Solution

Method

fo r

Steady-State

Canopy

Structural

Loads,

JournalofAircraft.

Vol.

25 ,

No.

1. ,November

1988.

13 .enney,

R .

J. ,

and

Leonard,J. ,

A

3-D Finite

Element

Structural

ParachuteModel, Paper

No.

95-1563

3

1

AIAA Aerodynamic

Decelerator

Conference

M ay1995.

14.

tein,

K.

R .,

and

Benney,R .J. ,

ParachuteInflation:

A

Problem

in

Aeroelasticity, U.S.

A rmy

Natick

Research,

Development ,and

EngineeringCenter.

Natick

TechnicalRepor t

No.

NATICK/TR-94/015,

August

1994.

15.hompson,

J. ,

A

Composi te

Grid

Generation

Codefo r

3-D

Region

The

EA GLE

Code,

A IA A

Journal

.

Vol.

26 ,

No.

3,

pp.

271-272,

March

1988.

17

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8/10/2019 3-D P D A U C CFD

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NO .OF

COPIES

ORGANIZATION

AD M I N I S T RAT O R

DEFENSETECHNICAL

INFO

CENTER

AT T N

DTICDDA

8725

JOHN

J

KINGMAN

R D

STE0944

FTBELVOIRA2060-6218

DIRECTOR

US

A R M Y

RE S E ARC HL A B O R A T O R Y

AT T NM S R LCSA LTA

R E C O R D S

M AN AG E M E N T

2800P O W D E R

MILL

R D

ADELPHIMD

0783-1197

DIRECTOR

USA R M YRE S E ARC HL A B O R A T O R Y

AT T NM S R LCILL

TECHNICAL

L I B RARY

2800P O W D E R

MILL

R D

ADELPHIMD

07830-1197

DIRECTOR

USARMY

R E S E A R C HL AB O RAT O RY

AT T NM S R L

CS

A LTP

TECH

PUBLISHINGB RAN C H

2800P O W D E R

MILL

R D

ADELPHIMD

0783-1197

U S AFWRIGHTAE RO N AU T I C AL

L AB O RAT O RI E S

ATTNAFWALFIMGDRJ

SHANG

M R

N

E

SC A G G S

W P A F B

H

5433-6553

C O M M AN D E R

N A V A L

S U R F A C E

W A R F A R E

CNTR

AT T N

OD E

B40

D R

W

Y A N TA

DAHLGREN

VA 22448-5100

C O M M AN D E R

N A V A L

S U R F A C E

W A R F A R ECNTR

AT T NO D E42 0R AW A R D L A W

INDIANHEADM D

0640-5035

D I RE C T O R

N AS A

LANGLEYRE S E ARC HCENTER

AT T N

TECH

L I B RARY

M R DM BUSHNELL

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REPORTDOCUMENTATIONPAGE

Form

Approved

OMB

N o.

0704-0188

Publicreporting

burdenfor

this

collection

of

information

is

est imated

to

average1ou r

pe r

response,including

the

time

for

reviewing

instructions,

searching

existing

datasources,

gatheringandmaintaining thedataneeded,andcompleting an d

reviewing

the

collection

of

information.

endcomment sregarding thisburden

estimate

or anyotheraspect

of

this

collection

of

information,including

suggestions

for

reducing thisburden,to Washington

Headquarters

Services,

Directorate

for

Information

Operat ions

an dReports,1215

Jefferson

Davis

Highway,Suite1204,Arlington,VA2202-4302, and

to

the

Office

of

Managementan dBudget,PaperworkReduct ionProject(0704-0188),Washington,

DC

0503.

1.

AGENCYUSEONLY

(Leave

blank) 2.

REPORTDATE

September

99 7

3.EPORT

TYPE

A ND

DATES

COVERED

Final

4.ITLEA NDSUBTITLE

3- D

Parachute

Descent

Analysis

Using

Coupled

Computational

Fluid

Dynamic

an d

StructuralCodes

5.

UNDING

NUMBERS

PR :

1L161102AH43

6.AUTHOR(S)

Sahu,J. ;Cooper,G.R .(ARL);

Benney,

R.J.(U.S.

Army

SoldierSystems

Command)

7.ERFORMINGORGANIZATIONNAME (S)A NDADDRESS(ES)

U.S.

Army

Research

Laboratory

Weapons

&

Materials

Research

Directorate

AberdeenProvingGround,M D1010-5066

8.

ERFORMING

ORGANIZATION

REPORTNUMBER

9.

PONSORING/MONITORINGAGENCYNAME (S)

AN DADDRESS(ES)

U.S.

Army

Research

Laboratory

Weapons

&

Materials

Research

Directorate

Aberdeen

Proving

Ground,MD1010-5066

10.

PONSORING/MONITORING

AGENCY

REPORT

NUMBER

ARL-TR-1435

11.SUPPLEMENTARYNOTES

12a.DISTRIBUTION/AVAILABILITYSTATEMENT

Approvedfo r

public

release;distributionisunlimited.

12b.

DISTRIBUTION

CODE

13 .

ABSTRACT

Maximum

200

words)

Acomputationaltoolthatmodelsth eterminaldescentcharacteristicsofasingleor acluster

of

parachutes

is

a

technology thatis

neededby parachutedesigners

an d

engineers.Aspartof

a

technologyprogram annex(TPA),a jointeffortbetween the U.S.

Army

Natick

Research,

Development,

an d

Engineering

Center

(NRDEC)

an d

th e

US-

Army

Research

Laboratory

(ARL)

to

develop

this

computational

tool

is

now

underway.Asafirsteffort,

attempts

ar e

being

made

to

analyze

both

two-dimensional

(2-

D )

an d

three-dimensional(3-D)

flow

fieldsarounda

parachute

usinga

coupling

procedure

in

which the

fluid

dynamics

ar e

coupled

to

2- D

an d3- D

structural

dynamic

(SD)codes.Thiseffort

uses

computational

fluid

dynamic

(CFD)

codes

to

calculate

a

pressure

field,

which

isthen

used

asan inputload

fo r

th e

SD code.

pecifically,

this

report

presents

th e

methodsan d

results

of

th e

flow

field

plusth e

structuralcharacteristics

ofa

single

axisymmetric

parachutean d

a

3-D

goreconfiguration fo rth eterminal

descentvelocity.Computedresultshavebeenobtainedusingthepayloadweightan d

unstretched

constructed

geometry

of th e

canopies

as

input.

ignificant

progressha sbeenmade

in

determiningthe terminaldescentflowfieldalongwith theterminal

shape

of

th e

parachute.

discussion

ofthefluidan dstructural

dynamics

codes,coupling

procedure,

an d

th e

associated

technical

difficulties

is

presented.

xamples

of

the

codes'

current

capabilitiesar e

shown.

14.SUBJECTTERMS

fluids-structures

compiling

Navier-Stokessolution

three-dimensional

flow

incompressible

flow parachutes

lo w

speed

flow

terminal

descent

15.

NUMBEROFPAGES

33

16.

RICE

CODE

17.ECURITYCLASSIFICATION

OFREPORT

18.

ECURITY

CLASSIFICATION

OFTHISPAGE

19.

ECURITY

CLASSIFICATION

OFABSTRACT

20.IMITATIONOFABSTRACT