Transcript AME 436 Energy and Propulsion

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
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Paul Ronney
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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!
Pope & Anand (ze r o he at re le as e )
(lar ge he at r e le as e )
30
Turbulent Burning Velocity (S
T
/S L )
Br ay (ze r o he at re le as e )
(large he at r e le as e )
Sivas hins k y
25
Yak hot
20
15
Exper im e nt
x (Re =1,000)
T
10
Gouldin (Re T=1,000)
5
0
0
10
20
30
Turbulence Intensity (u'/S
40
L
)
50
Introduction - continued...
Propagation rate (S T /S L )
 …whereas in “liquid flame” experiments, ST/SL in 4
different flows is consistent with Yakhot’s model with no
adjustable parameters
Hele-Shaw
Capillary wave
Taylor-Couette
Vibrating grid (Shy et al. )
Theory (Yakhot)
Power law fit to expts.
100
10
Power law fit (u'/S
L
> 2):
S T /S L = 1.61 (u'/S L ).742
1
0.1
1
10
100
"Turbulence" intensity (u'/S L )
1000
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
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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 (), viscosity
change across front (F) & buoyancy (G) on relationship between
scaled wavelength () and scaled growth rate ()
 Characteristic wavelength for ST = (/6)(uUw2/av): smaller scales
dominated by DL (no characteristic wavelength)
 1  2 1  

  (1   )   

 F  G   
 0;


4
  4

2

G
 (1  )
2kU
u (1  )g
fav U
; 
;
fav
f  fu
; F b
;
uUk
f av
b
f  fb
; fav  u
u
2
Dimensionless growth rate
((1+)/2kU)
3
Upw ard
Horizontal
Dow nw ard
DL only
2
1
Hy drocarbon-air f lame with
U = 20 cm/s, w = 12.7 mm
0
0
1
2
Dimensionless wavelength (f
3
av
/uUk)
Objectives
 Measure
 Propagation rates
 Wrinkling characteristics
of premixed flames in Hele-Shaw cells
as a function of
 Mixture strength (thus SL) (but density ratio () & viscosity
change (fb - fu) 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
Lexan sheets
Aluminum plate
Unburned gas
Flame front
Spark
electrodes
(3 pairs)
Burned gas
Video camera
Partial pressure
gas mixing system
Ball
valve
Oxidizer
Exhaust
Fuel
Exhaust
manifold
Spark
generator
Diluent
Mixing chamber
Computer
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Aluminum frame sandwiched between Lexan windows
40 cm x 60 cm x 1.27 or 0.635 or 0.32 cm test section
CH4 & C3H8 fuel, N2 & CO2 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
QuickTime™ and a
DV/DVCPRO - NTSC decompressor
are needed to see this picture.
6.8% CH4-air, horizontal, 12.7 mm cell
Results - video - upward propagation
QuickTime™ and a
DV/DVCPRO - NTSC decompressor
are needed to see this picture.
6.8% CH4-air, upward, 12.7 mm cell
Results - video - downward propagation
QuickTime™ and a
DV/DVCPRO - NTSC decompressor
are needed to see this picture.
6.8% CH4-air, downward, 12.7 mm cell
Results - video - high Lewis number
QuickTime™ and a
DV/DVCPRO - NTSC decompressor
are needed to see this picture.
3.0% C3H8-air, horizontal, 12.7 mm cell (Le ≈ 1.7)
Results - video - low Lewis number
QuickTime™ and a
DV/DVCPRO - NTSC decompressor
are needed to see this picture.
8.6% CH4 - 32.0% O2 - 60.0% CO2, horizontal, 12.7 mm cell (Le ≈ 0.7)
Results - stoichiometric, baseline thickness
QuickTime™ and a
DV/DVCPRO - NTSC decompressor
are needed to see this picture.
9.5% CH4 - 90.5% air, horizontal, 12.7 mm cell
Results - stoichiometric, thinner cell
QuickTime™ and a
DV/DVCPRO - NTSC decompressor
are needed to see this picture.
9.5% CH4 - 90.5% air, horizontal, 6.3 mm cell
Results - stoichiometric, very thin cell
QuickTime™ and a
DV/DVCPRO - NTSC decompressor
are needed to see this picture.
9.5% CH4 - 90.5% air, horizontal, 3.1 mm cell
Broken flames at very low Pe, Le < 1
QuickTime™ and a
DV/DVCPRO - NTSC decompressor
are needed to see this picture.
6.0% CH4- 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 & diffusivethermal 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% CH4 - 34.4% O2 - 57.0% CO2
Horizontal propagation
12.7 mm cell, Pe = 85
6.8% CH4 - 93.2% air
Horizontal propagation
12.7 mm cell, Pe = 100
3.0% C3H8 - 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)SL
 Quasi-steady (slower but still > SL)
 Near-end-wall - slowest - large-scale wrinkling suppressed
70
60
Ne ar-w all
r e gion
Distance (cm)
50
40
Quas i-s te ady
r e gion
30
20
The rm al
e xpans ion
r e gion
10
7.8% m e thane /air
12.5% m e thane /air
0
0
0.5
1
Time (seconds)
1.5
2
Results - quasi-steady propagation rates
 Horizontal, CH4-air (Le ≈ 1)
 Quasi-steady propagation rate (ST) always larger than SL - typically ST
≈ 3SL even though u’/SL = 0!
 Independent of Pe = SLw/  independent of heat loss
 Slightly higher ST/SL for thinner cell despite lower Pe (greater heat
loss) (for reasons to be discussed later…)
Results - quasi-steady propagation rates
 Horizontal, C3H8-air
 Very different trend from CH4-air - ST/SL depends significantly on Pe &
cell thickness (why? see next slide…)
 STILL slightly higher ST/SL for thinner cell despite lower Pe (greater heat
loss)
5
Horizontal, C3H8-air
ST/S
4
3
2
0.5"
0.25"
0.125"
1
0
0
50
100
150
200
Peclet number
250
300
Results - quasi-steady propagation rates
 C3H8-air (lean): Le ≈ 1.7, lower ST/SL
 C3H8-air (rich): Le ≈ 0.9, higher ST/SL (≈ 3), ≈ independent of Pe,
similar to CH4-air
5
Propane, horizontal
ST/SL
4
3
1/8"
2
1/4"
1
1/2"
Stoichiometric
Lean (high Le)
Rich (lower Le)
0
2.0
3.0
4.0
Fuel % (propane)
5.0
6.0
Results - quasi-steady propagation rates
 Horizontal, CH4-O2-CO2 (Le ≈ 0.7)
 Similar to CH4-air, no effect of Pe
 Slightly higher average ST/SL: 3.5 vs. 3.0, narrow cell again slightly
higher
5
Horizontal, CH 4-O2-CO 2
ST/SL
4
3
2
0.5"
0.25"
1
0.125"
0
0
50
100
150
Peclet number
200
250
Results - quasi-steady propagation rates
 Upward, CH4-air (Le ≈ 1)
 Higher ST/SL for thicker cell - more buoyancy effect, increases largescale wrinkling - ≈ no effect of orientation for 1/8” cell
 More prevalent at low Pe (low SL) - back to ST/SL ≈ 3 for high Pe
8
Upward, CH4-air
7
0.5"
0.25"
0.125"
5
.
ST/SL
6
4
3
2
1
0
0
50
100
150
Peclet number
200
250
Results - quasi-steady propagation rates
 Downward, CH4-air (Le ≈ 1)
 Higher ST/SL for thinner cell - less buoyancy effect - almost no effect
for 1/8” cell
 More prevalent at low Pe (low SL) - back to ST/SL ≈ 3 for high Pe
 How to correlate ST/SL for varying orientation, SL, w ???
4.0
Downward, CH4-
3.5
ST/S
3.0
2.5
2.0
1.5
0.5"
0.25"
0.125"
1.0
0.5
0.0
0
50
100
150
Peclet number
200
250
Results - pressure characteristics
 Initial pressure rise after ignition
 Pressure ≈ constant during quasi-steady phase
 Pressure rise higher for faster flames
60
1.15
50
20
1.05
Pressure
10
0
0
0.2
0.4
0.6
0.8
Time (sec)
Slow flame
1
Pressure (atm)
30
7.2% CH 4 in air
Horizontal propagation
50
1.3
Pressure
40
1.25
30
Position
1.2
20
1.15
1.1
9.5% CH 4 in air
Horizontal propagation
0
0.05
0.1
0.15
0.2
Time (sec)
Fast flame
10
0.25
0.3
Flame position (cm)
40
1.1
Flame position (cm)
Pressure (atm)
Position
1
60
1.35
Scaling analysis
 How to estimate “driving force” for flame wrinkling?
 Hypothesis: use linear growth rate () of JoulinSivashinsky analysis divided by wavenumber (k) (i.e.
phase velocity /k) scaled by SL 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)/2
(L = width of cell = 39.7 cm)
 “Small” L, i.e. L < ST length = (/6)(uUw2/av)
» DL dominates - /k = constant
» Propagation rate should be independent of L
 “Large” L, i.e. L > (/6)(uUw2/av)
» ST dominates - /k increases with L
» Propagation rate should increase with L
 Baseline condition: (6.8% CH4-air, SL = 15.8 cm/s, w = 12.7
mm): ST length = 41 cm > L - little effect of ST
Dimensionless growth rate
((1+)/2kU)
3
Upw ard
Horizontal
Dow nw ard
DL only
2
1
Hy drocarbon-air f lame with
U = 20 cm/s, w = 12.7 mm
0
0
1
2
Dimensionless wavelength (f
3
av
/uUk)
Effect of JS parameter
 Results correlate reasonably well with relation
ST/SL ≈ 1 + 0.64 (/kSL)
- suggests dimensionless JS parameter IS the driving force
8
7
CH4-air (all)
6
ST/S
5
4
3
2
1
0
-4
-2
0
2
4
JS growth parameter =/kSL
6
8
Effect of JS parameter
 Very similar for CH4-O2-CO2 mixtures …
14
12
ST/SL
10
8
6
4
CH4-O2-CO2 (all)
2
0
-2
0
2
4
6
8
JS growth parameter
10
12
14
Effect of JS parameter
 … but propane far less impressive
6
C3H8-O2-N2 (lean)
5
C3H8-O2-N2 (stoich-rich)
ST/SL
4
3
2
1
0
-1
0
1
2
JS growth parameter
3
4
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 (yf) is 1st
moment of intensity (I) w.r.t. position, i.e.
n
y f ( x)   yi I i
i1
n
I
i
i1
150
Y1
Y2
Y3
Y4
Y5
100
6.8% CH -air
4
12.7 mm thick cell
Horizontal propagation
0.166 sec between traces
50
p

Flame position y (mm) relative to mean
 Contrast & brightness adjusted to obtain “good” flame trace
0
-50
-100
0
50
100
150
200
250
300
Transverse position (x) (mm)
350
Flame front lengths
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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 = AT/AL < ST/SL - front length alone cannot
account for observed flame acceleration by wrinkling
 Curvature in 3rd dimension must account for wrinkling
 Assume ST/SL ≈ (AT/AL)(U/SL), where U = speed of curved flame in
channel, flat in x-y plane
2.6
2
6.8% CH -air
4
Forgot to separate
odd/even lines here
1.8
Front length / cell width
Front length / cell width
2.4
Didn't forget here
1.6
1.4
6.8% CH -air
4
1.2
12.7 mm thick cell
Horizontal propagation
0.033 sec between frames
1
15
20
25
30
35
40
Frame number
45
50
55
12.7 mm thick cell
0.033 sec between frames
2.2
2
Upward
1.8
1.6
Horizontal
1.4
1.2
Downward
1
10
20
30
40
Frame number
50
60
70
Flame front lengths
 Even for horizontally-propagating flames, AT/AL not constant decreases with increasing Pe - but (inferred) U/SL increases to
make (measured) ST/SL constant!
3.5
S /S
T
3
L
(measured)
CH -air
2.5
4
12.7 mm thick cell
Horizontal propagation
U/S
2
L
(calculated)
1.5
A /A
T
L
(measured)
1
50
100
150
Peclet number
200
250
Flame front lengths
 AT/AL similar with propane - but (inferred) U/SL lower at low Pe to
make (measured) ST/SL lower!
3.5
3
S /S
T
(measured)
C H -air
3
2.5
L
8
12.7 mm thick cell
Horizontal propagation
2
U/S
A /A (measured)
T
L
(calculated)
L
1.5
1
50
100
150
200
Peclet number
250
300
Flame front lengths
 AT/AL correlates reasonably well with JS growth parameter for
CH4-air and CH4-O2-CO2
 Less satisfying for C3H8-air (high Le)
 Expected trend - AT/AL increases as JS parameter increases
 … but AT/AL > 1 even when JS parameter < 0
2.6
Horizontal, upward, downward propagation
3.1, 6.3 & 12.7 mm thick cells
All fuels/diluents
CH
-air mixtures
2.4
4
L
1.8
A /A
2
T
2.2
1.6
1.4
Stoichiometric
12.7 mm cell
1.2
1
-4
-2
0
2
4
6
JS growth rate parameter = /kS
8
L
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 SL…
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-O2-inerts, same SL
 Slightly broader spectrum of disturbances at low Le, less at high Le
Conclusions
 Flame propagation in quasi-2D 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 3rd dimension
 … but most practical applications in confined geometries, where
unavoidable thermal expansion (DL) & viscous fingering (ST)
instabilities cause propagation rates ≈ 3 SL 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
 (ST/SL)Total = (ST/SL)Turbulence x (ST/SL)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'/SL = 4.0 (decaying turbulence); integral-scale Re = 18
Thanks to…
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National Tsing-Hua University
Prof. C. A. Lin, Prof. T. M. Liou
Combustion Institute (Bernard Lewis Lectureship)
NASA (research support)