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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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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.
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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.
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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
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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.
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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.
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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
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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
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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
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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
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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
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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.
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BLANK
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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
.
Vol.9,
No.
4,
Apri l
1972.
8.
ogers,
S.E.,
Kwak,
D .,
an dKiris,C, Steady
andUnsteady
Solutions
of th e
IncompressibleNavier-Stokes
Equations, AIAA Journal.
Vol.
29,
No.
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.
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NO .OF
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MILL
R D
ADELPHIMD
0783-1197
DIRECTOR
USA R M YRE S E ARC HL A B O R A T O R Y
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DIRECTOR
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REPORTDOCUMENTATIONPAGE
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to
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Managementan dBudget,PaperworkReduct ionProject(0704-0188),Washington,
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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
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