Some issues and methods in
particles tracking
Laurent DUMAS
Université Paris 6 (L.AN.) & Ecole Normale supérieure (D.M.I.)
•
Lecture 1 (August 19
th
):
an academical survey
Particle methods for rarefied gas and two phase flows
•
Lecture 2 (August 27
th
):
an industrial approach
Slag deposition and pressure oscillations in Ariane V boosters
1. The Ariane V launcher
2. The ASSM program
3. Description of the flow in the Ariane V boosters
2.1 Experimental measurements
2.2 Qualitative behavior
2.3 Characteristic values
4. Slag deposition
4.1 The Lagrange /Euler computations
4.2 The Euler /Euler computation
4.3 Comparison of the results
5. Pressure oscillations
5.1 The Navier Stokes computations
5.2 The LES computations
6. Conclusion
1. The Ariane V launcher
•
Ariane
V,
the
european
space
launcher
has
a
simplified
architecture
which
comprises
the
following
elements
:
The
main
cryogenic
stage
(
158
tons
of
O
2
/H
2
)
develops
a
thrust
of
1140
kN
in
vacuum
.
The
stage
operates
for
10
min
.
Two
boosters
(
2
*
238
tons
of
solid
propellant),
each
developing
a
thrust
of
5300
kN
.
They
lead
to
the
lift
off
of
the
launcher
and
are
jettisoned
at
an
altitude
of
65
km
after
a
burn
time
of
120
s
.
An
upper
composite
section
made
of
the
upper
stage
(
10
tons
of
storable
propellant),
the
equipment
bay,
the
payload
(one
or
two
satellites
of
mass
lesser
than
6
tons)
and
the
fairing
.
1. The Ariane V launcher
First flight: October 1997
Schematic view of the Ariane V booster
2. The A.S.S.M. Program
(Aerodynamics of Solid Segmented Motors)
•
Joint
and
long
term
program
aimed
at
understanding
and
numerically
reproducing
some
problems
occurring
in
solid
segmented
motors
with
a
submerged
nozzle
such
as
Ariane
V
boosters
.
•
Header
:
CNES
•
Members
:
industrials
(Aérospatiale,
SEP,
SNPE,
Bertin)
national
organisms
(ONERA,
universities,
etc
...
)
•
Program
divided
into
different
axes
:
ignition
dense
phase
(slag
deposition,
combustion)
stability
(pressure
oscillations),
etc
...
members and references of
the ASSM program
•
Modeling
of
slag
deposition
in
solid
rocket
motors
”
J
.
F
.
Chauvot,
LD,
K
.
Schmeisser
(Aérospatiale),
31
th
AIAA
Joint
Propulsion
conference,
San
Diego,
1995
.
•
“
Prévision
du
dépot
d’alumine
dans
les
moteurs
a
propergol
solide
”
P
.
Bellomi
(BPD),
LD,
Y
.
Fabignon
(ONERA),
L
.
Jacques
(SEP),
G
.
Lavergne
(ONERA),
International
symposium
on
propulsion,
Paris,
1996
.
•
“
Stochastic
models
to
the
investigation
of
slag
accumulation”
N
.
Cesco
(ONERA),
LD,
Y
.
Fabignon
(ONERA),
A
.
Hulin
(Bertin),
T
.
Pevergne
(SEP)
;
33
th
AIAA
Joint
Propulsion
conference,
Seattle,
1997
.
•
“
Vortex
shedding
phenomena
in
solid
rocket
motors”
:
F
.
Vuillot
(ONERA)
;
Journal
of
Propulsion
and
Power,
1995
.
•
“
Simulation
des
grandes
échelles
:
application
aux
moteurs
a
propergol
solides
segmentés”
J
.
H
.
Silverstrini,
P
.
Comte,
M
.
Lesieur
(LEGI),
conference
on
propulsive
flows
in
space
transportation,
Bordeaux,
1995
Some
experiments
at
real
flight
conditions
have
been
made
and
have
given
the
following
results
:
Slag deposition:
between 2 and 2.2 tons of Alumina
(Al
2
O
3
) in the chamber after flight
Pressure oscillations
:
amplitude
: 120 mb (0.3%) at t=95 s
main frequency
: first acoustic mode of the combustion chamber
These
two
values
causes
a
loss
on
the
payload
of
the
order
of
400
kg
.
Moreover,
the
low
frequency
of
pressure
oscillations
makes
the
possible
coupling
with
the
launcher
structural
mode
a
point
of
concern
.
3.1
Experimental measurements
Propellant blocks 2 and 3
Alumina deposition
Alumina trajectories
Second segment
Third segment
Thermal protections
23 m
1.5 m
: recirculation area
3.2 Qualitative behavior of the flow
in the Ariane V boosters at t=95s
Ejection of
combustion products
(gas+Al+Al
2
O
3
)
: turbulent shear layer region giving rise to vortex shedding
Modelisation of pressure oscillations
•
Coupling
of
vortex
shedding
with
acoustics
:
•
The
prediction
of
the
stability
of
a
motor
can
be
achieved
by
means
of
analytical
tools
but
quantitative
results
are
only
available
with
a
full
numerical
approach
.
Acoustic
feedback
Acoustic
excitation
Vortex
generation
Vortex
impingement
•
Liquid
alumina
at
ejection
(if
instantaneous
combustion
of
Al)
:
Bimodal diameter distribution (1micron

70 microns)
Total mass of Alumina ejected: 72 tons
Estimated velocity: 1 m/s
Temperature: 3272 K
Estimated turbulence rate: 20%
Density ratio
r
p
/
r
g
~ 1000
•
Adimensionalised numbers
:
Stokes number ~ 1 (large particles) or « 1 (small particles)
Reynolds number ~ 100 000
Particle volumetric fraction (a priori estimate)
a
p
« 1
The hypotheses of
one way coupling and dilute phase is assumed
3.3
Characteristic values
of the flow
in the Ariane V boosters
4.1 Slag deposition: Euler/Lagrange simulations
(Aérospatiale, SEP, Bertin, ONERA)
Time,
space
and
particle
diameter
discretisation
.
For
each
discretised
time
(
50
,
66
,
82
,
95
and
115
s),
computation
of
an
equivalent
stationary
one
phase
flow
with
a
Navier
Stokes
solver
and
a
k

e
model
.
Computation
of
particles
trajectories
in
the
previous
stationary
flow
with
(or
without)
dispersion
effects
due
to
turbulence
.
Evaluation
of
the
rate
of
entrapped
particles
.
Estimation
of
total
slag
deposition
by
space
and
time
interpolation
.
Particle tracking in a Lagrangian approach
•
C
omputation
of
the
trajectories
of
particles
by
solving
the
ODE
:
with
and
where
:
)
(
t
x
t
g
F
m
dt
dv
v
dt
dx
drag
1
r
d
u
v
C
g
g
p
p
p
drag
Re
)
Re
.
(
Re
.
687
0
15
0
1
24
g
g
drag
drag
u
v
u
v
d
C
F
2
8
1
•
The
dispersion
effects
due
to
turbulence
are
taken
into
account
with
the
Gossman

Ioannides
model
:
<u
g
>
is
replaced
during
a
time
t
by
<u
g
>+u’
where
u’
is
selected
from
a
Gaussian
distribution
with
a
variance
related
to
the
turbulence
energy
(
2
k/
3
)
.
t
is
deduced
from
the
lifetime
of
the
energy
containing
eddy
and
allows
for
the
particle
to
pass
through
the
eddy
before
it
decayed
.
•
In
this
case,
a
sufficient
number
of
random
trajectories
is
computed
for
each
class
of
particles
and
a
statistical
treatment
has
to
be
done
.
Dispersion effects in the Lagrangian approach
Details of the Euler/Lagrange computations
(t=95s)
•
Geometry
(SNPE)
:
extrapolation
from
experimental
measurements
.
•
Aerodynamic
computation
(SEP,
Aerospatiale)
:
comparison
of
a
computation
on
a
multi

block
grid
(
20
000
elements)
and
on
a
unstructured
grid
(
8
000
elements)
.
•
Particle
tracking
(SEP*,
Aerospatiale,
Onera,
Bertin)
:
comparison
of
the
results
obtained
with
the
same
aerodynamic
field
and
the
same
discretisation
(
30
injection
points
located
on
the
third
block
and
10
particle
diameters
from
1
to
140
microns)
.
(*
without
dispersion
effects)
4.2 Slag deposition: Euler/Euler simulation
(SNPE)
Choice
of
a
particular
combustion
time
(
95
s)
and
of
a
particular
particle
diameter
value
(
35
microns)
.
Computation
of
an
unstationary
inviscid
two
phase
flow
on
a
fine
grid
(
50
000
elements,
duration
of
simulation
:
200
ms)
.
Evaluation of the rate of entrapped particles.
4.2 Particle tracking in a Eulerian approach
•
The
particles
are
considered
as
a
continuum
phase
with
a
volumetric
fraction
a
p
and
a
velocity
v
p
at
each
point
x
and
time
t
:
•
mass
conservation
:
•
momentum conservation
:
0
)
.(
u
x
t
p
p
p
p
r
a
r
a
p
g
p
p
p
p
p
p
p
p
u
u
g
u
u
x
t
u
r
a
r
a
r
a
r
a
)
.(
)
(
Euler/Euler simulation: main observations
A
particle
high
concentration
zone
is
created
at
the
nozzle
nose,
is
then
“pushed”
at
the
rear
end
by
the
arrival
of
another
curl,
a
part
of
these
particles
is
going
out,
Another
part
is
accumulating
.
The
particles
outgoing
from
the
end
of
the
block
are
periodically
deviated
.
4.3 Comparison of the results
•
The
estimation
of
the
amount
of
slag
deposition
is
very
sensitive
to
:
The
particle
diameter
distribution
The
chosen
method
(Euler
or
Lagrange,
dispersion
effects
or
not)
The
entrapment
criterion
.
•
Lagrangian
approach
:
The
amount
of
slag
deposition
obtained
by
the
four
different
teams
is
:
First criterion
(geometrical point): 872 kg < M < 2055 kg
Second criterion
(nose point): 1452 kg < M < 3600 kg
•
Eulerian approach
:
12
%
deposition
rate
for
the
chosen
case
against
2
to
6
%
in
the
corresponding
Lagrangian
approach
.
5.1 Pressure oscillations: Navier Stokes simulation
(
SNPE, ONERA, CERFACS
)
•
Different
computations
have
been
compared
on
a
test
case
of
a
2
D
planar
chamber
with
a
choked
nozzle
and
a
side
injection
along
two
directions
(
sub

scale
model
1
/
15
of
Ariane
V
boosters)
and
for
the
same
curvilinear
grid
(
10
000
elements)
.
Main conclusions of an organized workshop (1992):
Second
order
accurate
schemes
needed
to
capture
the
shear
layer
and
acoustic
motion
.
Van
Leer
’s
flux
splitting
too
dissipative
.
Implicit
schemes
unapropriate
.
Importance
of
boundary
conditions
.
Good
correlations
between
different
families
of
codes,
once
properly
validated
.
Cell
Reynolds
number
limitation
))
1
(
(Re
O
L
v
cell
cell
cell
r
5.2 Pressure oscillations: LES simulation
(LEGI)
•
Same
conditions
and
same
2
D
grid
.
•
Extrusion
of
the
2
D
grid
in
the
3
rd
direction
(
318
31
90
elements)
•
Large
Eddy
Simulation
with
the
filtered
structured
function
model
.
•
Duration
of
simulation
:
13
ms
(
75
hours
on
Cray
C
98
)
Main conclusions:
Main
frequency
mode
at
2300
Hz
(Navier
Stokes
:
2670
Hz)
Widening
of
the
kinetic
energy
spectrum
at
low
and
high
frequencies
.
Two
different
mechanisms
of
instability
generating
streamwise
vortices
.
6. Conclusions
•
Numerical
tools
have
been
developed
which
qualitatively
predict
the
flow
in
the
Ariane
V
boosters
.
•
Due
to
the
complexity
of
the
problem,
some
crude
hypotheses
have
been
made
to
estimate
slag
deposition
.
However,
in
the
absence
of
more
accurate
experimental
data
(particle
diameter,
exact
mechanism
of
slag
deposition),
the
chosen
level
of
modelisation
(stationary
Euler/
Lagrange)
seems
to
be
well
suited
.
•
The
numerical
simulations
of
pressure
oscillations
in
the
Ariane
V
boosters
are
still
under
progress
.
Indeed,
in
this
case,
the
level
of
accuracy
can
be
improved
with
a
better
numerical
modelisation
.
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