Transcript Presenting a Technical Report

Dynamics of Front
Propagation in Narrow
Channels
Mohammed Abid, Jamal A. Sharif,
Paul D. Ronney
Department of Aerospace &
Mechanical Engineering
University of Southern California
Los Angeles, CA 90089-1453
Motivation

Premixed gas flame instabilities & buoyancy
effects not well understood due to





Large Dr/r - baroclinic production of vorticity
n, a, D increase ≈ 25x across flame
3d hydrodynamics with large Re
Effects most pronounced near extinction, but couple
strongly to flame stretch & heat losses
Practical applications



Accidental explosions - laminar flame  wrinkled flame
 turbulent flame  detonation
Industrial furnaces - large Grashof #
Fire safety in spacecraft
2
Approach

Hele-Shaw flow





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
Premixed-gas flames, PLUS propagating chemical
fronts in aqueous solution


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
d  Dr/r << 1 - No baroclinicity, Bousinnesq approximation
valid
DT ≈ 3 K - no change in transport properties
Not affected by heat loss
Large Schmidt # - front stays "thin” even at high Re
Simpler chemistry than gaseous flames
3
Types of flame instabilities





Thermal expansion (Darrieus-Landau, DL)
Rayleigh-Taylor (buoyancy-driven, RT)
Viscous fingering (Saffman-Taylor, ST) (flow in narrow
channels when viscous fluid displaced by less viscous fluid)
Diffusive-thermal (Lewis number)
Joulin & Sivashinsky (1994) - combined effects of DL, ST, RT
& heat loss (but no diffusive-thermal effect - no damping at
small l)
1  

1
  (1   )   

 F  G   
 0;

4

  4

3
2

G
 (1  )
f
f  fu
;   av ; F  b
;
2kU
ruUk
fav
ru (1  )g
fav U
;
rb
f  fb
; fav  u
ru
2
Dimensionless growth rate
(= (1+ )/2kU)
2
Upwar d
Hori zontal
Downwar d
DL only
2
1
0
0
1
2
3
Dim e ns ionle s s w ave le ngth (f /r Uk )
av
u
4
Objectives

Study behavior of flame propagation in Hele-Shaw
cells




Wrinkling characteristics
Propagation rates
Buoyancy effects
Compare variable-density flames &
constant-density aqueous chemical fronts
nearly
5
Chemical considerations

Iodate-hydrosulfite system
IO3- + 6 H+ + 6 e-  I- + 3 H2O
S2O42- + 4 H2O  6 e- + 8 H+ + 2 SO42----------------------------------------------------IO3- + S2O42- + H2O  I- + 2 SO42- + 2 H+
Autocatalytic in H+



Simple solutions
Non-toxic
"Lightning fast" (up to 0.05 cm/sec)
6
Apparatus (gaseous flames)
Plexiglas sheets
Aluminum plate
Unburned gas
Flame front
Spark
electrode
(1 of 2)
Video camera
Burned gas
Partial pressure
gas mixing system
Mixing chamber
Oxidizer
Exhaust
Diluent
Fuel
Relief
Valves
Spark
generator
Computer





Aluminum frame sandwiched between Lexan windows
40 cm x 60 cm x 1.27 cm test section
CH4 & C3H8 fuel, N2 & CO2 diluent - affects Le, Peclet #
Upward, horizontal, downward orientation
Spark ignition (1 or 3 locations)
7
Apparatus (liquid flames)
Lexan
sheets
Spacer
Air
Reactant
Diffuser
Product
Ignition
point



Valv e
Argon-ion
Laser
Acid
Solution
25cm x 20cm; 0.04cm < W < 0.2cm; 0.2 < Grw < 25
Color-changing or fluorescent pH indicators
Initiate at a point using acid solution
8
Results - gaseous flames - qualitative

Orientation effects

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
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
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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 + ?)
9
Results - gas flames - propagation rates


Propagation rate (ST) always larger than SL
3-stage propagation



Thermal expansion - most rapid
Quasi-steady
Near-end-wall - slowest - large-scale wrinkling suppressed
10
Results - gas flames - orientation effect

5
CH down
CH
4
CH
L

4
4
horiz
up
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
0
0
50
100
150
Peclet number
200
250
11
Results - gas flames - Lewis # effect


5
4
L

3
T

ST/SL generally higher at lower Le
CH4-air (Le ≈ 1) - 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 convergence at large Pe uncertain
S /S

2
CH -air
4
C H -air
1
3
8
CH -O -CO
4
2
2
0
0
50
100
150
Peclet number
200
250
12
Results - liquid flames - fingering


FINGERING (???) for upward propagation
No wrinkling for downward or horizontal
propagation - unlike gaseous flames
Wavelength (l) nearly independent of SL & width
15
Downward propagation
Just after cell inversion
40s after inversion
60s after inversion
120s af ter inversion
180s af ter inversion
Wavelength ( l) (mm)

10
5
0
10
100
Peclet number = S Lw/D
240s af ter inversion
360s af ter inversion
13
Results - fingering - continued
Saffman & Taylor (1958)
1   2

kU    
1
2


No wavelength selection without surface tension!
Dµ = 0,  ≠ 0:
3
l  max  2
rg d cos()
l independent of U (~SL) &
K (~w2) but depends on
cell angle  - consistent
with experiments
4
min

2
r1  r2 gK
k
K



cos  
1   2  U
U1   2 
l/ l

Theory ( l/ l
min
= [cos( )]
-1/2
)
Experi ments
(squar es)
3
2
Best fi t:
l/ l min = 0. 963 [cos( )]
-0.496
1
0.1
Cosine (angle)
1
14
Results - fingering - continued


Zhu (1998) - wavelength selection due to curvature
(Markstein) effect on SL: l=max = 48πnD/gw2cos()d much too small (≈0.1 mm) & not correct effect of w, 
Surface tension issues



Can miscible interfaces have a surface tension?
l = 1 cm   ≈ 5 x 10-3 dyne/cm ≈ 7 x 10-5 water-air
Is this  reasonable?




Davis (1988): miscible systems  ~ C/t; t = interface thickness,
C = 2 x 10-6 dyne   ≈ 7 x 10-3 dyne/cm
If  ~ 1/t, t = D/SL for chemical front, water-air = 70 dyne/cm,
twater-air ≈ 10-7cm, liquid flame ≈ 7 x 10-3 dyne/cm
 Probably reasonable value - need rotating drop or capillary
wave experiment to check
Unlike a diffusing passive interface between miscible fluids,
chemical fronts have constant thickness  constant 
15
Results - liquid flames - propagation rates

Wrinkled fronts propagate quasi-steadily with rate
ST >> SL
100
Front position (mm)
80
Be s t fit: x = 6.82 + 0.267 t
60
40
20
0
0
50
100
150
200
250
300
Time (seconds)

Can ST be related to a “turbulence intensity”?
Estimated buoyant velocity ub ≈ max/kmax
U 
ub
SL 
g dK
3SL n
16
Results - liquid flames - propagation rates
ST of rising fronts in Hele-Shaw cells (K = w2/12)
consistent with Yakhot (1988) renormalization-group
model for Huygens’ propagation with U = u’/SL (!)
Experi ment (Hel e-Shaw)
Theory (Yakhot)
T
/S )
L
100
Propagation rate (S

10
1
0.1
1
10
"Turbulence" intensity (u'/S
100
L
)
17
Results - liquid flames - propagation rates
Data on ST/SL in 5 different flows consistent with
Yakhot’s model with no adjustable parameters
Tube
Hele-Shaw
Capi ll ar y wave
Taylor -Couette
Vibr ating gri d
Theory (Yakhot)
Power l aw fit
T
/S )
L
100
Propagation rate (S

10
Power l aw fit (u'/S
1
S /S
T
0.1
1
L
= 1. 61 (u'/S
10
"Turbulence" intensity (u'/S
L
L
> 2):
)
.742
100
L
)
18
Conclusions

Flame propagation in quasi-2D Hele-Shaw cells
reveals effects of








Thermal expansion
Viscous fingering
Buoyancy
Lewis number
Surface tension (!?)
Fronts in Hele-Shaw cells enable rational
comparisons of models & experiments
Flame propagation in cylinder crevice volumes
may be quite different from expectations based on
unconfined flame experiments
Rich dynamics observed even for aqueous 2d
system much simpler than freely propagating
gaseous flames
19