ame 514 applications of combustionronney.usc.edu/ame514/lecture8/ame514-s17-lecture8.pdf · ame 514...

• 1

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)

• 2


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)


"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

• 3


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!


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)

• 4


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


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

• 5


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


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

• 6


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


Results - liquid flames

• 7


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"

# $ $

%

& ' '


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

• 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


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

• 9


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)


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

• 10


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


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

• 11


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


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

• 12


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


Hele-Shaw videos - "baseline" case

6.8% CH4-air, horizontal, 12.7 mm cell

• 13


Hele-Shaw videos - upward propagation

6.8% CH4-air, upward, 12.7 mm cell


Hele-Shaw videos - downward propagation

6.8% CH4-air, downward, 12.7 mm cell

• 14


Hele-Shaw videos - high Lewis number

3.2% C3H8-air, horizontal, 12.7 mm cell (Le ≈ 1.7)


Hele-Shaw videos - low Lewis number

8.6% CH4 - 34.4% O2 - 57.0% CO2, horizontal, 12.7 mm cell (Le ≈ 0.7)

• 15


Hele-Shaw videos - thin cell

9.5 CH4- air, horizontal, 3 mm cell


Hele-Shaw videos – very low Le (H2-O2-N2)

10% H2 / 90% O2, 12.7 mm cell

• 16


Hele-Shaw videos – very low Le (H2-O2-N2)

7.4% H2 / 92.6% O2, 12.7 mm cell


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


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


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"


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"

• 19


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)


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"

• 20


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"


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


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


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


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


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


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


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


• 25


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


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)


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


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 ?


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.

ame 514 applications of combustionronney.usc.edu/ame514/lecture8/ame514-s17-lecture8.pdf · ame 514...

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