Premixed flame propagation
in Hele
-
Shaw cells:
What Darrieus & Landau didn’t tell you
http://ronney.usc.edu/research
Paul D. Ronney
Dept. of Aerospace & Mechanical Engineering
University of Southern California
Los Angeles, CA 90089
-
1453 USA
National Tsing
-
Hua University
October 7, 2005
University of Southern California
Established 125 years ago
this week!
…jointly by a Catholic, a Protestant and a Jew
-
USC has
always been a multi
-
ethnic, multi
-
cultural, coeducational
university
Today: 32,000 students, 3000 faculty
2 main campuses: University Park and Health Sciences
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Naming gift by Andrew & Erma Viterbi
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-
founder of Qualcomm, co
-
inventor of CDMA
1900 undergraduates, 3300 graduate students, 165 faculty, 30
degree options
$135 million external research funding
Distance Education Network (DEN): 900 students in 28 M.S.
degree programs; 171 MS degrees awarded in 2005
More info:
http://viterbi.usc.edu
Paul Ronney
B.S. Mechanical Engineering, UC Berkeley
M.S. Aeronautics, Caltech
Ph.D. in Aeronautics & Astronautics, MIT
Postdocs: NASA Glenn, Cleveland; US Naval Research Lab,
Washington DC
Assistant Professor, Princeton University
Associate/Full Professor, USC
Research interests
Microscale combustion and power generation
(10/4, INER; 10/5 NCKU)
Microgravity combustion and fluid mechanics
(10/4, NCU)
Turbulent combustion
(10/7, NTHU)
Internal combustion engines
Ignition, flammability, extinction limits of flames
(10/3, NCU)
Flame spread over solid fuel beds
Biophysics and biofilms
(10/6, NCKU)
Paul Ronney
Introduction
Models of premixed turbulent combustion don’t agree with
experiments nor each other!
Introduction
-
continued...
…whereas in “liquid flame” experiments, S
T
/S
L
in
4
different flows
is consistent with Yakhot’s model with
no
adjustable parameters
Motivation (continued…)
Why are gaseous flames harder to model & compare
(successfully) to experiments?
One reason: self
-
generated wrinkling due to flame
instabilities
Thermal expansion (Darrieus
-
Landau, DL)
Rayleigh
-
Taylor (buoyancy
-
driven, RT)
Viscous fingering (Saffman
-
Taylor, ST) in Hele
-
Shaw cells
when viscous fluid displaced by less viscous fluid
Diffusive
-
thermal (DT) (Lewis number)
Needed: simple apparatus for systematic study of DL, RT,
ST & DT instabilities & their effects on burning rates
Hele
-
Shaw flow
Flow between closely
-
spaced parallel plates
Momentum eqn. reduces to linear 2
-
D equation (Darcy’s
law)
1000's of references
Practical application to combustion: flame propagation in
cylinder crevice volumes
Joulin
-
Sivashinsky (CST, 1994) model
Linear stability analysis of flame propagation in HS cells
Uses Euler
-
Darcy momentum eqn.
Combined effects of DL, ST, RT & heat loss (but no DT effect
-
no
damping at small
l
)
Dispersion relation: effects of thermal expansion (
⤬ 癩獣o獩瑹t
change across front (F) & buoyancy (G) on relationship between
scaled wavelength (
⤠慮d 獣sl敤 gro睴w r慴攠(
)
Characteristic wavelength for ST = (
㘩
(
u
Uw
2
/
av
): smaller
scales
dominated by DL (no characteristic wavelength)
Objectives
Measure
Propagation rates
Wrinkling characteristics
of premixed flames in Hele
-
Shaw cells
as a function of
Mixture strength (thus SL) (but density ratio (
)
& 癩獣s獩瑹t
捨慮g攠⡦
b
-
f
u
) don’t vary much over experimentally accessible
range of mixtures)
Cell thickness (w)
Propagation direction (upward, downward, horizontal)
Lewis number (vary fuel & inert type)
and compare to JS model predictions
Apparatus
Aluminum
frame
sandwiched
between
Lexan
windows
40
cm
x
60
cm
x
1
.
27
or
0
.
635
or
0
.
32
cm
test
section
CH
4
&
C
3
H
8
fuel,
N
2
&
CO
2
diluent
-
affects
Le,
Peclet
#
Upward,
horizontal,
downward
orientation
Spark
ignition
(
3
locations,
≈
plane
initiation)
Exhaust
open
to
ambient
pressure
at
ignition
end
-
flame
propagates
towards
closed
end
of
cell
Results
-
video
-
“baseline” case
6.8% CH
4
-
air, horizontal, 12.7 mm cell
Results
-
video
-
upward propagation
6.8% CH
4
-
air, upward, 12.7 mm cell
Results
-
video
-
downward propagation
6.8% CH
4
-
air, downward, 12.7 mm cell
3.0% C
3
H
8
-
air, horizontal, 12.7 mm cell (Le ≈ 1.7)
Results
-
video
-
high Lewis number
Results
-
video
-
low Lewis number
8.6% CH
4
-
32.0% O
2
-
60.0% CO
2
, horizontal, 12.7 mm cell (Le ≈ 0.7)
Results
-
stoichiometric, baseline thickness
9.5% CH
4
-
90.5% air, horizontal, 12.7 mm cell
9.5% CH
4
-
90.5% air, horizontal, 6.3 mm cell
Results
-
stoichiometric, thinner cell
9.5% CH
4
-
90.5% air, horizontal, 3.1 mm cell
Results
-
stoichiometric, very thin cell
Broken flames at very low Pe, Le < 1
6.0% CH
4
-
air, downward, 6.3 mm cell (Pe ≈ 30(!))
Results
-
qualitative
Orientation effects
Horizontal propagation
-
large wavelength wrinkle fills cell
Upward propagation
-
more pronounced large wrinkle
Downward propagation
-
globally flat front (buoyancy suppresses
large
-
scale wrinkles); oscillatory modes, transverse waves
Thinner cell: transition to single large “tulip” finger
Consistent with Joulin
-
Sivashinsky predictions
Large
-
scale wrinkling observed even at high Le
Broken flames observed near limits for low Le but only
rarely & not repeatable
For practical range of conditions, buoyancy & diffusive
-
thermal effects cannot prevent wrinkling due to viscous
fingering and/or thermal expansion
Evidence of preferred wavelengths, but selection
mechanism unclear
Lewis number effects
8.6% CH
4
-
34.4% O
2
-
57.0% CO
2
Horizontal propagation
12.7 mm cell, Pe = 85
6.8% CH
4
-
93.2% air
Horizontal propagation
12.7 mm cell, Pe = 100
3.0% C
3
H
8
-
97.0% air
Horizontal propagation
12.7 mm cell, Pe = 166
Results
-
propagation rates
3
-
stage propagation
Thermal expansion
-
most rapid, propagation rate ≈ (
u
/
b
)S
L
Quasi
-
steady (slower but still >
S
L
)
Near
-
end
-
wall
-
slowest
-
large
-
scale wrinkling suppressed
Results
-
quasi
-
steady propagation rates
Horizontal, CH
4
-
air (Le ≈ 1)
Quasi
-
steady propagation rate (S
T
) always larger than S
L
-
typically S
T
≈ 3S
L
even though u’/S
L
= 0!
Independent of Pe = S
L
w/
independen琠o映hea琠loss
Slightly higher S
T
/S
L
for thinner cell despite lower Pe (greater heat
loss) (for reasons to be discussed later…)
Horizontal, C
3
H
8
-
air
Very different trend from CH
4
-
air
-
S
T
/S
L
depends significantly on Pe &
cell thickness (why? see next slide…)
STILL slightly higher S
T
/S
L
for thinner cell despite lower Pe (greater heat
loss)
Results
-
quasi
-
steady propagation rates
C
3
H
8
-
air (lean): Le ≈ 1.7, lower S
T
/S
L
C
3
H
8
-
air (rich): Le ≈ 0.9, higher S
T
/S
L
(≈ 3), ≈ independent of Pe,
similar to CH
4
-
air
Results
-
quasi
-
steady propagation rates
Horizontal, CH
4
-
O
2
-
CO
2
(Le ≈ 0.7)
Similar to CH
4
-
air, no effect of Pe
Slightly higher average S
T
/S
L
: 3.5 vs. 3.0, narrow cell again slightly
higher
Results
-
quasi
-
steady propagation rates
Results
-
quasi
-
steady propagation rates
Upward, CH
4
-
air (Le ≈ 1)
Higher S
T
/S
L
for thicker cell
-
more buoyancy effect, increases large
-
scale wrinkling
-
≈ no effect of orientation for 1/8” cell
More prevalent at low Pe (low S
L
)
-
back to S
T
/S
L
≈ 3 for high Pe
Results
-
quasi
-
steady propagation rates
Downward, CH
4
-
air (Le ≈ 1)
Higher S
T
/S
L
for thinner cell
-
less buoyancy effect
-
almost no effect
for 1/8” cell
More prevalent at low Pe (low S
L
)
-
back to S
T
/S
L
≈ 3 for high Pe
How to correlate S
T
/S
L
for varying orientation, S
L
, w ???
Results
-
pressure characteristics
Initial pressure rise after ignition
Pressure ≈ constant during quasi
-
steady phase
Pressure rise higher for faster flames
Slow flame
Fast flame
Scaling analysis
How to estimate “driving force” for flame wrinkling?
Hypothesis: use
linear
growth rate (
) of⁊ou汩n
-
楶ash楮sky ana汹s楳 d楶楤edy wavenumber
k) (椮e⸠
phase ve汯c楴y
⽫) sca汥d by⁓
L
as a dimensionless
growth rate
Analogous to a “turbulence intensity”)
Use
largest value of growth rate
, corresponding to
longest
half
-
wavelength mode that fits in cell
, i.e., k
*
= (2
L⤯㈠
(L = width of cell = 39.7 cm)
“Small” L, i.e. L < ST length =
(
㘩
(
u
Uw
2
/
av
)
»
DL dominates
-
欠= 捯n獴慮t
»
Propagation rate should be independent of L
“Large” L, i.e. L >
(
㘩
(
u
Uw
2
/
av
)
»
ST dominates
-
欠in捲敡獥猠睩瑨 L
»
Propagation rate should increase with L
Baseline condition: (6.8% CH
4
-
air, S
L
= 15.8 cm/s, w = 12.7
mm): ST length = 41 cm > L
-
little effect of ST
Effect of JS parameter
Results correlate reasonably well with relation
S
T
/S
L
≈
1 + 0.64 (
歓
L
)
-
suggests dimensionless JS parameter IS the driving force
Effect of JS parameter
Very similar for CH
4
-
O
2
-
CO
2
mixtures …
Effect of JS parameter
… but propane far less impressive
Image analysis
-
flame position
Determine flame position
Video frames digitized, scaled to 256 pixels in x (spanwise) direction
Odd/even video half
-
frames separated
For each pixel column, flame position in y (propagation) direction (y
f
) is 1st
moment of intensity (
I
) w.r.t. position, i.e.
Contrast & brightness adjusted to obtain “good” flame trace
Flame front lengths
Front length / cell width
-
measure of wrinkling of flame by instabilities
Relatively constant during test
Higher/lower for upward/downward propagation
Front length / cell width = A
T
/A
L
< S
T
/S
L
-
front length alone cannot
account for observed flame acceleration by wrinkling
Curvature in 3rd dimension must account for wrinkling
Assume S
T
/S
L
≈ (A
T
/A
L
)(U/S
L
), where U = speed of curved flame in
channel, flat in x
-
y plane
Flame front lengths
Even for horizontally
-
propagating flames, A
T
/A
L
not constant
-
decreases with increasing Pe
-
but (inferred) U/S
L
increases to
make (measured) S
T
/S
L
constant!
Flame front lengths
A
T
/A
L
similar with propane
-
but (inferred) U/S
L
lower at low Pe to
make (measured) S
T
/S
L
lower!
Flame front lengths
A
T
/A
L
correlates reasonably well with JS growth parameter for
CH
4
-
air and CH
4
-
O
2
-
CO
2
Less satisfying for C
3
H
8
-
air (high Le)
Expected trend
-
A
T
/A
L
increases as JS parameter increases
… but A
T
/A
L
> 1 even when JS parameter < 0
Results
-
wrinkling characteristics
Individual images show clearly defined wavelength
selection
Results
-
wrinkling characteristics
…but averaging make them hard to see
-
1/2 wave mode
dominates spectra…
Results
-
wrinkling characteristics
Shows up better in terms of amplitude x wavenumber…
Wrinkling
-
different mixture strengths
Modes 3
-
5 are very popular for a range of S
L
…
Wrinkling
-
different cell thicknesses
Characteristic wavelength for ST = 103 cm, 26 cm, 6.4 cm in 12.7, 6.35, 3.2
mm thick cells
-
for thinner cells, ST dominates DL, more nearly
monochromatic behavior (ST has characteristic wavelength, DL doesn’t)
Run 108
9.5% CH4
-
air
Horizontal propagation
6.35 mm cell
Wrinkling
-
different orientations
Upward = more wrinkling at large scales (RT encouraged); downward = less wrinkling at
large scales; smaller scales unaffected (RT dominant at large wavelengths)
Wrinkling
-
different fuel
-
O
2
-
inerts, same S
L
Slightly broader spectrum of disturbances at low Le, less at high Le
Conclusions
Flame
propagation
in
quasi
-
2
D
Hele
-
Shaw
cells
reveals
effects
of
Thermal
expansion
-
always
present
Viscous
fingering
-
narrow
channels,
high
U
Buoyancy
-
destabilizing/stabilizing
at
long
wavelengths
for
upward/downward
propagation
Lewis
number
–
affects
behavior
at
small
wavelengths
but
propagation
rate
&
large
-
scale
structure
unaffected
Heat
loss
(Peclet
number)
–
little
effect,
except
U
affects
transition
from
DL
to
ST
controlled
behavior
Remark
Most
experiments
conducted
in
open
flames
(Bunsen,
counterflow,
...
)
-
gas
expansion
relaxed
in
3
rd
dimension
…
but
most
practical
applications
in
confined
geometries,
where
unavoidable
thermal
expansion
(DL)
&
viscous
fingering
(ST)
instabilities
cause
propagation
rates
≈
3
S
L
even
when
heat
loss,
Lewis
number
&
buoyancy
effects
are
negligible
DL
&
ST
effects
may
affect
propagation
rates
substantially
even
when
strong
turbulence
is
present
-
generates
wrinkling
up
to
scale
of
apparatus
(S
T
/S
L
)
Total
=
(S
T
/S
L
)
Turbulence
x
(S
T
/S
L
)
ThermalExpansion
?
Remark
Computational studies suggest similar conclusions
Early times, turbulence dominates
Late times, thermal expansion dominates
H. Boughanem and A. Trouve, 27th Symposium, p. 971.
Initial u'/S
L
= 4.0 (decaying turbulence); integral
-
scale Re = 18
Thanks to…
National Tsing
-
Hua University
Prof. C. A. Lin, Prof. T. M. Liou
Combustion Institute (Bernard Lewis Lectureship)
NASA (research support)
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