AME 514 Applications of Combustionronney.usc.edu/AME514/Lecture8/AME514-S17-lecture8.pdf · AME 514...
Transcript of AME 514 Applications of Combustionronney.usc.edu/AME514/Lecture8/AME514-S17-lecture8.pdf · AME 514...
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AME 514
Applications of Combustion
Lecture 8: Case studies (turbulence without thermal expansion and vice versa)
2 AME 514 - Spring 2017 - Lecture 8
Turbulent combustion (Lecture 1)! Motivation (Lecture 1)! Basics of turbulence (Lecture 1)! Premixed-gas flames
! Turbulent burning velocity (Lecture 1)! Regimes of turbulent combustion (Lecture 1)! Flamelet models (Lecture 1)! Non-flamelet models (Lecture 1)! Flame quenching via turbulence (Lecture 1)! Case study I: "Liquid flames" (Lecture 2)
(turbulence without thermal expansion)! Case study II: Flames in Hele-Shaw cells (Lecture 2)
(thermal expansion without turbulence)! Nonpremixed gas flames (Lecture 3)! Edge flames (Lecture 3)
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3 AME 514 - Spring 2017 - Lecture 8
Constant density "flames" - motivation! Models of premixed turbulent combustion don't agree with
experiments nor each other!
0
5
10
15
20
25
30
0 10 20 30 40 50
x
Turbulence Intensity (u'/SL)
Turb
ulen
t Bur
ning
Vel
ocity
(ST/S
L)Yakhot 1988
Gouldin 1987 (ReL=1,000)
Experiment(Bradley, 1992)
(ReL=1,000)
Bray 1990 (zero heat release) (large heat release, ρ
f/ρ∞ = 7)
Pope & Anand 1987 (zero heat release) (large heat release)
Sivashinsky 1990
Bychov 2000ρ
f/ρ∞ = 7
(Where ReL is not reported, predictions are independent of Re
L)
4 AME 514 - Spring 2017 - Lecture 8
"Liquid flame" idea! See Epstein and Pojman, 1998 ! Use propagating acidity fronts in aqueous solution ! Studied by chemists for 100 years ! Generic form
A + nB → (n+1)B - autocatalytic ! Δρ/ρ << 1 - no self-generated turbulence ! ΔT ≈ 3 K - no change in transport properties ! Zeldovich number β ≈ 0.05 vs. 10 in gas flames
Aqueous fronts not affected by heat loss!!! ! Large Schmidt number [= ν/D ≈ 500 (liquid flames) vs. ≈ 1
(gases)] - front stays "thin" even at high Re
Ka ~ u '/ LTSL2 /D
~ νu 'LI
LILT
u '2
SL2Dν~ ReL
−1/2 u 'SL
"
#$
%
&'
2
Sc−1
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5 AME 514 - Spring 2017 - Lecture 8
Gaseous vs. liquid flames! Most model employ assumptions not satisfied by real flames
! Adiabatic (gas flames: sometimes ok) (Liquid flames TRUE!) ! Homogeneous, isotropic turbulence over many LI (gas flames: never
ok) (Liquid flames: can use different apparatuses where this is more nearly true)
! Low Ka or high Da (thin fronts) (gas flames: sometimes ok) (Liquid flames: more often true due to higher Sc)
! Lewis number = 1 (gas flames: sometimes ok, e.g. CH4-air) (Liquid flames: irrelevant since heat transport not a factor in propagation)
! Constant transport properties (gas flames: never ok, ≈ 25x increase in ν and α across front!) (Liquid flames: TRUE)
! u' doesn't change across front (gas flames: never ok, thermal expansion across flame generates turbulence) (but viscosity increases across front, decreases turbulence, sometimes almost cancels out) (Liquid flames: TRUE)
! Constant density (gas flames: never ok!) (Liquid flames: true, although buoyancy effects still exist due to small density change)
! Conclusion: liquid flames better for testing models!
6 AME 514 - Spring 2017 - Lecture 8
Approach - chemistry! Simpler chemistry than gaseous flames! Color-changing or fluorescent pH indicators! Original: arsenous acid - iodate system
IO3- + 5I- + 6H+ → 3 I2 + 3 H2O
H3AsO3 + I2 + H2O → 2 I- + 2 H+ + H3AsO4__________________________________________________
IO3- + 3 H3AsO3 → I- + 3 H3AsO4
... autocatalytic in iodide (I-)! Later: iodate-hydrosulfite system
IO3- + 6 H+ + 6e- → I- + 3 H2O
S2O4-2 + 4 H2O → 6 e- + 8 H+ + 2 SO4
-2_________________________________________________
IO3- + S2O4
-2 + H2O → I- + 2 SO4-2+ 2 H+
! Simple solutions! Non-toxic! "Lightning fast" (up to 0.05 cm/sec)
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7 AME 514 - Spring 2017 - Lecture 8
Comparison of gaseous & liquid flames
PropertyStoichiometric
hydrocarbon-air flameAutocatalytic chemical front
Reaction mechanism Many-step, chain-branching
Two-step, straight-chain
SL 40 cm/sec 0.03 cm/secβ = E/RTad 10 0.05Δρ/ρf 6 0.0003Δν/νR 25 0.02Sc 1 500Impact of heat loss Critical IrrelevantEase of LIF imaging Tough ($$$) Trivial
8 AME 514 - Spring 2017 - Lecture 8
Taylor-Couette apparatus
Mirror
CylindricalLens
Ar -ion LaserSheet
Ar +Laser
BeamSplitter
3-D TraversingSystem
LDV Probe
Fiber
Reactant(Fluorescing)
sST
Product(Not fluorescing)
+ Innercylinder
OuterCylinder
Fiber-OpticTransmitter
Photo-multiplier Computer
Rotation
RotationMotor
Motor
FFTSignalAnalyzer
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9 AME 514 - Spring 2017 - Lecture 8
Capillary-wave apparatus
Mirror
Ar -ion LaserSheet
Ar +Laser
BeamSplitter 3-D Traversing
System
LDV Probe
Optical Fiber
Reactant(Fluorescing)
Product(Not fluorescing)
+
Fiber-OpticTransmitter
Photo-multiplier
FFTSignalAnalyzer
Computer
Loudspeaker
VibratingPlatform
CylindricalLens
Vibration
s
10 AME 514 - Spring 2017 - Lecture 8
Results - flow characteristics
! Ronney et al., 1995 ! Taylor-Couette, counter-rotating, "featureless turbulence" regime
! ≈ homogeneous except near walls ! Gaussian velocity histograms ! Time autocorrelation (τa) nearly exponential ! LI ≡ √(8/π)u'τa ≈ 1/2 cylinder gap
! Capillary wave ! Mean velocity ≈ 0, u' ≈ constant across dish except near walls ! u' ~ z ! u' ≡ average over z - interpret as if 2-d
! Vibrating grid (Shy et al., 1996) ! Fairly homogeneous & isotropic in central region ! Kolmogorov-like spectrum
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11 AME 514 - Spring 2017 - Lecture 8
0
200
400
600
800
1000
-0.2 -0.1 0 0.1 0.2
Coun
ts
Velocity (cm/sec)
Mean: +0.75 cm/secu' = 4.60 cm/secSkewness = 0.0581Flatness =3.305
TC flow, axial, Reo=4500
Results - flow characteristics
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200
Auto
corr
elat
ion
coef
ficie
nt
Time (milliseconds)
Autocorrelation time= 48.8 ms
Exponential fit
0
0.02
0.04
0.06
0.08
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 0.2 0.4 0.6 0.8 1
Axial rmsRadial rmsCirc. rmsCirc. mean
RMS
velo
city
flu
ctua
tion
(cm
/sec
)
Mean velocity (m
/sec)
Outerwal l
Innerwal l
(ro - r) / (r
o - r
i)
-1
0
1
2
3
4
-1
0
1
2
3
4
0 0.5 1 1.5 2
MeanRMS
SkewnessFlatness/3
Mea
n an
d RM
S ve
loci
ty (
cm/s
ec) Skew
ness and Flatness/3
Depth, mm
12 AME 514 - Spring 2017 - Lecture 8
Results - liquid flames
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13 AME 514 - Spring 2017 - Lecture 8
Results! Thin "sharp" fronts at low Ka (< 5)! Thick "fuzzy" fronts at high Ka (> 10)! No global quenching observed, even at Ka > 2500 !!!! High Da - ST/SL in 4 different flows consistent with Yakhot model
! High Ka - ST/SL lower than at low Ka - consistent with Damköhler model over 1000x range of Ka!
€
STSL
= expu ' SL( )2
ST SL( )2"
# $ $
%
& ' '
14 AME 514 - Spring 2017 - Lecture 8
Liquid flames - comparison to Yakhot (1988)! Liquid flame" experiments, ST/SL in 4 different flows is consistent with
Yakhot's model with no adjustable parameters
1
10
100
0.1 1 10 100 1000
Hele-ShawCapillary waveTaylor-CouetteVibrating grid (Shy et al. )Theory (Yakhot)Power law fit to expts.
Prop
agat
ion
rate
(S T/S
L)
"Turbulence" intensity (u'/SL)
Power law fit (u'/SL > 2):
ST/SL = 1.61 (u'/SL). 7 4 2
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15 AME 514 - Spring 2017 - Lecture 8
Results - liquid flames - propagation rates! Data on ST/SL in flamelet regime (low Ka) consistent with
Yakhot model - no adjustable parameters ! Transition flamelet to distributed at Ka ≈ 5
Ronney et al., 1995
0.01
0.1
1
0.1 1 10 100 1000 104
Capillary wave experimentsTaylor-Couette experiments
S T/SL (
expe
rimen
t) /
S T/SL (
theo
ry, Y
akho
t)
Karlovitz number (Ka)
Flamelet Distributed
16 AME 514 - Spring 2017 - Lecture 8
Results - liquid flames - propagation rates! Data on ST/SL in distributed combustion regime (high Ka)
consistent with Damköhler's model - no adjustable parameters
Ronney et al., 1995
0.4
0.6
0.81
3
0.1 1 10 100 1000 104
Experiments (Taylor-Couette)Experiments (capillary wave)
S T/SL (
expe
rimen
t) /
S T/SL (
theo
ry, D
amkö
hler
)
Karlovitz number (Ka)
Flamelet Distributed
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17 AME 514 - Spring 2017 - Lecture 8
Front propagation in one-scale flow! Turbulent combustion models not valid when energy concentrated at one
spatial/temporal scale! Experiment - Taylor-Couette flow in "Taylor vortex" regime (one-scale)! Result - ST/SL lower in TV flow than in turbulent flow but consistent with
model for one-scale flow (Shy et al., 1992) probably due to "island" formation & reduction in flamesurface (Joulin & Sivashinsky,1991)
€
STSL
= exp u ' SLST SL
1− exp − u ' SLST SL
#
$ %
&
' (
#
$ %
&
' (
#
$ % %
&
' ( (
0
50
100
150
200
250
0 100 200 300 400 500 600
Theory (Yakhot, multi-scale)Theory (1-scale)CW multi-scale experimentTC multi-scale experiment1-scale experiment
Fron
t pr
opag
atio
n ra
te (
S T/SL)
Turbulence intensity (u'/SL)
18 AME 514 - Spring 2017 - Lecture 8
Fractal analysis in CW flow! Haslam and Ronney, 1995! Fractal-like behavior exhibited! D ≈ 1.35 (⇒ 2.35 in 3-d) independent of u'/SL! Same as gaseous flame front, passive scalar in CW flow! Theory (Kerstein, 1988 & others):
! D = 7/3 for 3-d Kolmogorov spectrum (not CW flow)! Same as passive scalar (Sreenivasan et al, 1986)
! Problem - why is d seemingly independent of! Propagating front vs. passively diffusing scalar! Velocity spectrum! Constant or varying density! Constant or varying transport properties! 2-d object or planar slice of 3-d object
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19 AME 514 - Spring 2017 - Lecture 8
Fractal analysis in CW flow
104
105
1 10
Area
(nu
mbe
r of
pix
els)
Slope = 0.732d = 1.268
u'/SL = 220
Measurement scale (number of pixels)
Slope = 0.776d = 1.224
u'/SL = 77
1
1.1
1.2
1.3
1.4
1.5
0 50 100 150 200 250
Frac
tal d
imen
sion
Disturbance intensity (u'/SL)
All data at u'/SL > 60:
Mean = 1.31, RMS deviation 0.06
20 AME 514 - Spring 2017 - Lecture 8
Self-generated wrinkling due to instabilities
! What about self-generated "turbulence" due to inherent instabilities of flames not subjected to forced turbulence?
! First step: linear stability analysis of flat, steady flame ! Basic goal of linear stability analysis: determine growth rate of
instability (σ, units 1/time) as a function of disturbance wavelength (λ) or wavenumber (k = 2π/λ)
! Many types of instabilities may occur ! Thermal expansion (Darrieus-Landau, DL) ! Rayleigh-Taylor (buoyancy-driven, RT) ! Diffusive-thermal (DT) (Lewis number) ! Viscous fingering (Saffman-Taylor, ST) in narrow channels when
viscous fluid displaced by less viscous fluid ! Joulin & Sivashinsky (1994) - combined effects of DL, ST, RT &
heat loss (but no DT effect - no damping at small wavelength λ) ! Characteristic wavelength for ST = (π/6)(Uw2/ν): smaller
wavelengths dominated by DL
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21 AME 514 - Spring 2017 - Lecture 8
Self-generated flame wrinkling! Si, Wongwiwat, Gross and Ronney (2017?) ! Use Hele-Shaw cell
! Flow between closely-spaced parallel plates ! Described by linear 2-D equation (Darcy's law) ! 1000's of references
! Measure ! Propagation rates ! Wrinkling wavelengths
Petitjeans et al. (1999) - displacement of viscous glycern-water mixture (white) by less viscous water-dye mixture (dark) injected in lower-right corner
22 AME 514 - Spring 2017 - Lecture 8
Self-generated flame wrinkling! Practical applications to combustion
! Spark-ignition engines at time of combustion (below) ! Flame propagation in cylinder crevice volumes
Video courtesy Prof. Yuji Ikeda, Kobe University
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23 AME 514 - Spring 2017 - Lecture 8
Hele-Shaw apparatus
! Aluminum frame sandwiched between Lexan windows ! 40 cm x 60 cm x 1.27 or 0.635 or 0.318 cm test section ! H2, CH4 & C3H8 fuel, N2 & CO2 diluent - affects Le, Peclet # ! Upward, horizontal, downward orientation ! Spark ignition (3 locations)
Lexan sheets
Burned gas
Ballvalve
Flame front
Exhaust
Video camera
Sparkgenerator
Sparkelectrodes(3 pairs)
Mixing chamber
Partial pressuregas mixing system
Oxi
dize
r
Dilu
ent
Fuel
Exhaust manifold
Aluminum plate
Unburned gas
Computer
24 AME 514 - Spring 2017 - Lecture 8
Hele-Shaw videos - "baseline" case
6.8% CH4-air, horizontal, 12.7 mm cell
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25 AME 514 - Spring 2017 - Lecture 8
Hele-Shaw videos - upward propagation
6.8% CH4-air, upward, 12.7 mm cell
26 AME 514 - Spring 2017 - Lecture 8
Hele-Shaw videos - downward propagation
6.8% CH4-air, downward, 12.7 mm cell
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27 AME 514 - Spring 2017 - Lecture 8
Hele-Shaw videos - high Lewis number
3.2% C3H8-air, horizontal, 12.7 mm cell (Le ≈ 1.7)
28 AME 514 - Spring 2017 - Lecture 8
Hele-Shaw videos - low Lewis number
8.6% CH4 - 34.4% O2 - 57.0% CO2, horizontal, 12.7 mm cell (Le ≈ 0.7)
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29 AME 514 - Spring 2017 - Lecture 8
Hele-Shaw videos - thin cell
9.5 CH4- air, horizontal, 3 mm cell
30 AME 514 - Spring 2017 - Lecture 8
Hele-Shaw videos – very low Le (H2-O2-N2)
10% H2 / 90% O2, 12.7 mm cell
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31 AME 514 - Spring 2017 - Lecture 8
Hele-Shaw videos – very low Le (H2-O2-N2)
7.4% H2 / 92.6% O2, 12.7 mm cell
32 AME 514 - Spring 2017 - Lecture 8
Hele-Shaw 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
! Thinner cell - 1 large wrinkle fills entire cell ! 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 + ?)
• 17
33
Lewis number effects
8.6% CH4-34.4% O2-57.0% CO2 Horizontal propagation12.7 mm cell, Pe = 85
6.8% CH4 - 93.2% airHorizontal propagation12.7 mm cell, Pe = 100
3.0% C3H8 - 97.0% airHorizontal propagation12.7 mm cell, Pe = 166
9.9% H2 – 90.1% O2Horizontal
12.7 mm cell, Pe = ???
AME 514 - Spring 2017 - Lecture 8
34 AME 514 - Spring 2017 - Lecture 8
Hele-Shaw 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!
10
VIDEO PROCESSING
The existence of a flame speed depends on the acceleration being relatively small
• 18
35 AME 514 - Spring 2017 - Lecture 8
Propagation rates - CH4/air, horizontal! Horizontal, CH4-air (Le ≈ 1): ST/SL ≈ 3! Independent of Pe = SLw/α ⇒ independent of heat loss! Slightly higher ST/SL for thinner cell despite lower Pe (greater heat
loss) (for reasons to be discussed later…)
Horizontal; CH4-air: 0.5", 0.25", 0.125"
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
0 50 100 150 200 250Peclet number
ST/S
L
0.5"*0.5"0.25"*0.25"0.125"
36 AME 514 - Spring 2017 - Lecture 8
Propagation rates - C3H8-air, horizontal! Horizontal, C3H8-air: very different trend from CH4-air - ST/SL
depends significantly on Pe & cell thickness (why? next slide…)! STILL slightly higher ST/SL for thinner cell despite lower Pe (greater
heat loss)
Horizontal; C3H8-air: 0.5", 0.25", 0.125"
0
1
2
3
4
5
0 50 100 150 200 250 300
Peclet number
ST/S
L
0.5"*0.5"0.25"*0.25"0.125"
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37 AME 514 - Spring 2017 - Lecture 8
Propagation rates - C3H8-air, re-plotted ! C3H8-air: Le ≈ 1.7 (lean), lower ST/SL ! C3H8-air: Le ≈ 0.9 (rich) ST/SL ≈ independent of Pe, similar to
CH4-air
Propane, horizontal
0
1
2
3
4
5
2.0 3.0 4.0 5.0 6.0
Fuel % (propane)
ST/
SL
1/8"
1/4"
1/2"Stoichiometric
Lean (high Le) Rich (lower Le)
38 AME 514 - Spring 2017 - Lecture 8
Propagation rates - CH4-O2-CO2 (low Le) ! Horizontal, CH4-O2-CO2 (Le ≈ 0.7): similar to CH4-air, no
effect of Pe but slightly higher average ST/SL: 3.5 vs. 3.0, narrow cell again slightly higher
Horizontal; CH4-O2/CO2: 0.5", 0.25", 0.125"
0
1
2
3
4
5
0 50 100 150 200 250Peclet number
ST/S
L
0.5"* 0.5"
0.25"* 0.25"
0.125"
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39 AME 514 - Spring 2017 - Lecture 8
Propagation rates - orientation effect! Upward - ST/SL ⇓ as Pe ⇑ (SL increases, decreasing benefit of
buoyancy); highest propagation rates! ST/SL converges to ≈ 3 at large Pe – same as horizontal
Upward; CH4-air: 0.5", 0.25", 0.125"
0
1
2
3
4
5
6
7
8
0 50 100 150 200 250
Pe
ST/S
L
0.5"*
0.5"
0.25"
0.125"
40 AME 514 - Spring 2017 - Lecture 8
Results - orientation effect! Downward - ST/SL ⇑ as Pe ⇓ (decreasing penalty of buoyancy);
lowest propagation rates - but Pe isn't whole story…! ST/SL converges to ≈ 3 at large Pe
Downward; CH4-air
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 50 100 150 200 250
Pe
ST/S
L
0.5"*
0.5"
0.25"
0.125"
• 21
41
Scaling analysis! How to estimate “driving force” for flame wrinkling?! Hypothesis: use linear growth rate (σ) of Joulin-Sivashinsky
analysis divided by wavenumber (k) (i.e. phase velocity σ/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* = (2π/L)/2 (L = width of cell = 39.7 cm)
! “Small” L, i.e. L < ST length = (π/6)(ρuUw2/µav)» DL dominates - σ/k = constant» Propagation rate should be independent of L
! “Large” L, i.e. L > (π/6)(ρuUw2/µav)» ST dominates - σ/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
42 AME 514 - Spring 2017 - Lecture 8
Joulin-Sivashinsky model (1994)
€
Ω2 + (1+ Λ)Ω−1−ε2
4ε+
1+ ε4
F +G( )Λ& ' (
) * +
= 0; Ω≡σ (1+ ε)
2kU; Λ ≡
favρuUk
;
F ≡fb −εfuεfav
; G ≡ρu(1−ε)gfavU
; ε ≡ ρbρu
; fav ≡fu + fb
2; f = friction coefficient =12µ/w2
w = cell height; U = flame speed; k = wave number = 2π /λSubscripts u = unburned, b = burned, av = average
0
1
2
3
0 1 2 3
UpwardHorizontalDownwardDL only
Dim
ensi
onle
ss g
row
th r
ate
(σ(1
+ ε)/2
kU)
Dimensionless wavelength (fa v/ρuUk)
• 22
43
Scaling analysis! ST length smaller (thus more important) for slower flames and
smaller w - but these conditions will cause flame quenching - how to get smaller ST length without quenching?
! ST length = w (π/6)(µu/µav)(1/Pr)Pe for fixed cell width, minimum Pe ≈ 40 set by quenching - easier to get smaller ST length without quenching in thinner cells
44 AME 514 - Spring 2017 - Lecture 8
Results - orientation effect revisited! Results scale reasonably well with JS growth parameter
which is basically u'/SL, with ST/SL ≈ 1 + u'/SL
Includes upward, downward, horizontal, 1/2", 1/4", 1/8" cells
0
1
2
3
4
5
6
7
8
-4 -2 0 2 4 6 8
ST/
SL
JS growth parameter = σ/kSL .
CH4-air (all)
• 23
45
Effect of JS parameter! Very similar for CH4-O2-CO2 mixtures …
0
2
4
6
8
10
12
14
-2 0 2 4 6 8 10 12 14
JS growth parameter
ST/
SL
CH4-O2-CO2 (all)
46
Effect of JS parameter! … but propane far less impressive
0
1
2
3
4
5
6
-1 0 1 2 3 4
JS growth parameter
ST/
SL
C3H8-O2-N2 (lean)
C3H8-O2-N2 (stoich-rich)
• 24
47 AME 514 - Spring 2017 - Lecture 8
Results - wrinkling wavelengths! Images digitized & flame front "position" determined, use
Fast Fourier Transport to determine wrinkling spectra, non-dimensionalize
! Dominant modes seen in FFT spectrum (right)
-30
-20
-10
0
10
20
30
40
0 100 200 300
pixel number
Fla
me p
osit
ion (
mm
)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5
Wave Number (cm^-1)
Mo
de a
mp
litu
de *
waven
um
ber
48 AME 514 - Spring 2017 - Lecture 8
Wrinkling - different mixture strengths! Modes 3 - 5 are very popular for a range of SL…
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5
Wave Number (cm^-1)
Am
plitu
de x
waven
um
ber
Run 5808.18% CH4-airHorizontal propagation12.7 mm cell
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 1 2 3 4 5
Wave Number (cm^-1)
Am
plitu
de x
waven
len
gth
Run 3349.5% CH4-airHorizontal propagation12.7 mm cell
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5
Wave Number (cm^-1)
Am
plitu
de x
waven
um
ber
Run 33611.7% CH4-airHorizontal propagation12.7 mm cell
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5
Wave Number (cm^-1)
Am
plitu
de x
waven
um
ber
Run 5846.8% CH4-airHorizontal propagation12.7 mm cell
• 25
49 AME 514 - Spring 2017 - Lecture 8
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)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 1 2 3 4 5
Wave Number (cm^-1)
Am
plitu
de x
waven
len
gth
Run 3349.5% CH4-airHorizontal propagation12.7 mm cell
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 1 2 3 4 5
Wave Number (cm^-1)
Am
pli
tud
e x
waven
um
ber
Run 108 9.5% CH4-air Horizontal propagation 6.35 mm cell
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1 2 3 4 5
Wave Number (cm^-1)
Am
plitu
de x
waven
um
ber
0
1
2
3
0 1 2 3
UpwardHorizontalDownwardDL only
Dim
ensi
onle
ss g
row
th r
ate
( σ(1
+ ε)/2
kU)
Dimensionless wavelength (fa v/ρuUk)
50 AME 514 - Spring 2017 - Lecture 8
Conclusions! Flame propagation in quasi-2D Hele-Shaw cells shows 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 since need only order 1/β
reduction in temperature (thus density ratio) due to heat loss to cause extinction, but need order 1 change in expansion ratio to cause significant change in flow
• 26
51 AME 514 - Spring 2017 - Lecture 8
Remark! Most experiments are 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 ?
52 AME 514 - Spring 2017 - Lecture 8
References! Epstein, I. R., Pojman, J. A. (1998). An Introduction to Nonlinear Chemical Dynamics,
Oxford University Press, ISBN 0-19-509670-3 ! Haslam, B. D., Ronney, P. D. (1995). “Fractal Properties of Propagating Fronts in a
Strongly Stirred Fluid,” Physics of Fluids, Vol. 7, pp. 1931-1937. ! Kerstein, A. R. (1988). Combust. Sci. Tech. 60, 163 ! Joulin, G., Sivashinsky, G.: Combust. Sci. Tech. 97, 329 (1991). ! Philippe Petitjeans, Ching-Yao Chen, Eckart Meiburg, and Tony Maxworthy (1999),
"Miscible quarter five-spot displacements in a Hele-Shaw cell and the role of flow-induced dispersion", Physics of Fluids, Vol. 11, pp. 1705-1716.
! Ronney, P. D., Haslam, B. D., Rhys, N. O. (1995). "Front Propagation Rates in Randomly Stirred Media," Physical Review Letters, Vol. 74, pp. 3804-3807.
! Shy, S. S., Ronney, P. D., Buckley S. G., Yakhot, V. (1992). "Experimental Simulation of Premixed Turbulent Combustion Using Aqueous Autocatalytic Reactions," Proceedings of the Combustion Institute, Vol. 24, pp. 543-551.
! S. S. Shy, R. H. Jang, and P. D. Ronney (1996). “Laboratory Simulation of Flamelet and Distributed Models for Premixed Turbulent Combustion Using Aqueous Autocatalytic Reactions,” Combustion Science And Technology, Vol. 113 , pp. 329 – 350.
! K. R. Sreenivasan, C. Meneveau (1986). "The fractal facets of turbulence," J. Fluid Mech. 173, 357.
! Yakhot, V. (1988). Combust. Sci. Tech. 60, 191.