Transcript PowerPoint Presentation - Presenting a Technical Report

Wrinkled flame propagation
in narrow channels:
What Darrieus & Landau
didn’t tell you
http://cpl.usc.edu/HeleShaw
M. Abid, J. A. Sharif, P. D. Ronney
Dept. of Aerospace & Mechanical Engineering
University of Southern California
Los Angeles, CA 90089-1453 USA
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
T
/S L )
Br ay (ze r o he at re le as e )
(large he at r e le as e )
Turbulent Burning Velocity (S

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...
…whereas in “liquid flame” experiments, ST/SL in 4
different flows is consistent with Yakhot’s model with
no adjustable parameters
Propagation rate (S T /S L )

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
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)
Joulin & Sivashinsky (1994) - combined effects of DL, ST, RT & heat
loss (but no DT effect - no damping at small l)
 1  

1
  (1   )   

 F  G   
 0;


4

4


2
2

G
 (1  )
2kU
u (1  )g
fav U
; 
;
fav
f  fu
; F b
;
uUk
f av
b
f  fb
; fav  u
u
2
Dimensio nless growth rate
((1+ )/2kU)
3
Upw ar d
Hor izontal
Dow nw ar d
DL only
2
1
0
0
1
2
Dimensionless wavelength (f
3
av
/u Uk)
Objectives

Use Hele-Shaw flow to study flame instabilities in
premixed gases





Flow between closely-spaced parallel plates
Described by linear 2-D equation (Darcy’s law)
1000's of references
Practical application: flame propagation in cylinder
crevice volumes
Measure


Wrinkling characteristics
Propagation rates
Apparatus
Lexan sheets
Aluminum plate
Unburned gas
Flame front
Spark
electrode
(1 of 2)
Burned gas
Video camera
Partial pressure
gas mixing system
Ball
valve
Oxidizer
Exhaust
Fuel
Exhaust
manifold
Spark
generator
Diluent
Mixing chamber
Computer





Aluminum frame sandwiched between Lexan windows
40 cm x 60 cm x 1.27 or 0.635 cm test section
CH4 & C3H8 fuel, N2 & CO2 diluent - affects Le, Peclet #
Upward, horizontal, downward orientation
Spark ignition (1 or 3 locations)
Results - videos - “baseline” case
QuickTime™ and a Video decompressor are needed to see t his picture.
6.8% CH4-air, horizontal, 12.7 mm cell
Results - videos - upward propagation
QuickTime™ and a Video decompressor are needed to see t his picture.
6.8% CH4-air, upward, 12.7 mm cell
Results - videos - downward propagation
QuickTime™ and a Video decompressor are needed to see t his picture.
6.8% CH4-air, downward, 12.7 mm cell
Results - videos - high Lewis number
QuickTime™ and a Video decompressor are needed to see t his picture.
3.2% C3H8-air, horizontal, 12.7 mm cell (Le ≈ 1.7)
Results - videos - low Lewis number
QuickTime™ and a Video decompressor are needed to see t his picture.
8.0% CH4 - 32.0% O2 - 60.0% CO2, horizontal, 12.7 mm cell (Le ≈ 0.7)
Results - videos - low Peclet number
QuickTime™ and a Video decompressor are needed to see t his picture.
5.8% CH4- air, horizontal, 6.3 mm cell (Pe ≈ 26(!))
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
Consistent with Joulin-Sivashinsky predictions
Large-scale wrinkling observed even at high Le;
small scale wrinkling suppressed at high Le
For practical range of conditions, buoyancy &
diffusive-thermal effects cannot prevent wrinkling
due to viscous fingering & thermal expansion
Evidence of preferred wavelengths, but selection
mechanism unclear (DT + ?)
Results - propagation rates
3-stage propagation




Thermal expansion - most rapid
Quasi-steady
Near-end-wall - slowest - large-scale wrinkling suppressed
Quasi-steady propagation rate (ST) always larger
than SL - typically 3SL even though u’/SL = 0!
70
60
Ne ar-w all
r e gion
50
Distance (cm)

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 - orientation effect

Horizontal
Upw ard
Dow nw ard
Horizontal (6.35 mm cell)
5
4
L

3
T

Horizontal - ST/SL ≈ independent of Pe = SLw/a
Upward - ST/SL  as Pe  (decreasing benefit of buoyancy);
highest propagation rates
Downward - ST/SL  as Pe  (decreasing penalty of buoyancy);
lowest propagation rates
ST/SL converges to ≈ constant value at large Pe
S /S

2
1
CH -air mixtures (Le - 0.9)
4
0
0
50
100
150
200
Peclet number S w/a
L
250
Results - Lewis # effect





ST/SL generally slightly higher at lower Le
CH4-air (Le ≈ 0.9) - ST/SL ≈ independent of Pe
C3H8-air (Le ≈ 1.7) - ST/SL  as Pe 
CH4-O2-CO2 (Le ≈ 0.7) - ST/SL  as Pe 
ST/SL ≈ independent of Le at higher Pe
Fragmented flames at low Le & Pe
7
CH -air
CH -air (6.35 mm cell)
C H8-air
C H -air (6.35 mm cell)
4
6
4
3
3
CH -O -CO
4
2
8
2
5
S T /S L

4
3
2
1
Horizontal orientation only
0
0
50
100
150
200
250
Peclet number S L w/a
300
Conclusions

Flame propagation in quasi-2D Hele-Shaw cells reveals
effects of





Thermal expansion - always present
Viscous fingering - narrow channels, long wavelengths
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
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