Some issues and methods in particles tracking

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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
.