AME 514 Applications of Combustion Lecture 9: Nonpremixed flames, edge flames

AME 514

Applications of Combustion

Lecture 9: Nonpremixed flames, edge flames

2AME 514 - Spring 2015 - Lecture 9

Turbulent combustion (Lecture 3) 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)


Non-premixed flames

Nonpremixed: no inherent propagation rate (unlike premixed flames where propagation rate = SL)

No inherent thickness (unlike premixed flames where thickness ~ /SL) - in nonpremixed flames, determined by equating convection time = /U = -1 to diffusion time 2/ ~ (/)1/2

Have to mix first then burn Burning occurs near stoichiometric contour where reactant fluxes in

stoichiometric proportions (otherwise surplus of one reactant) Burning must occur near highest T since w ~ exp(-E/RT) is very

sensitive to temperature (like premixed flames) Simplest approach: “mixed is burned” - chemical reaction rates faster

than mixing rates Recall stoichiometric mixture fraction Zst = mass fraction of fuel stream

in a stoichiometric mixture of fuel and oxidant streams

n = stoichiometric coefficient, M = molecular weight, Y = mass fraction



Nonpremixed turbulent jet flames Laminar: Lf ~ Uodo

2/D Turbulent (Hottel and Hawthorne, 1949)

D ~ u'LI; u' ~ Uo; LI ~ do Lf ~ do (independent of Re) High Uo high u' Da small – flame “lifts off” near base (why base first?) Still higher Uo - more of flame lifted When lift-off height = flame height, flame "blows off" (completely extinguished)


Scaling of turbulent jets

Hinze (1975) Determine scaling of mean velocity ( ), jet width (r jet) and mass

flux through jet ( ) with distance from jet exit (x) Assume u'(x) ~ , LI(x) ~ rjet(x) Note that mass flux is not constant due to entrainment! Conservation of momentum flux (Q):

Kinetic energy flux (K) (not conserved - dissipated!)

KE dissipation



do

Uo

rjet(x)x

u(x)_

entrainment

m(x).

≈12˚



Combine


Liftoff of turbulent jets

Scaling suggests mean strain ~ Redo3/2/x2

For fixed fuel & ambient atmosphere (e.g. air), strain rate at flamelet extinction (ext) ≈ constant

Liftoff height (xLO) ~ (/ext)1/2 Redo3/4 ~ uo

3/4do3/4

Experiments - closer to xLO ~ uo1do

0 - but how to make dimensionless? Need time scale, i.e. xLO ~ uo

1do/w, where ≈ w SL2/ ≈ SL

2/, leading to xLOSL/ ~ uo/SL

G. Mungal (Stanford) Cha and Chung, 1996



Similar trend (xLO ~ uo1do/w) seen in other fuels, scaled by highest SL of

fuel/air mixture and fuel density ratio function g X

LOS

L/

gUO/SL

Kalghatgi (1984)



Summary of theories / experiments in Lyons (2007) Premixed flame theory: SL ≈ at x = xLO

Critical scalar dissipation (Peters & Williams, 1983): w ≈ mean turbulent strain at x = xLO

Turbulent intensity theory ST ≈ at x = xLO (Kalghatgi, 1984) - but which ST? Flamelet or distributed? Which model? Need to have stoichiometric (or close) mixture for maximum ST - 2 conditions need to be satisfied - stabilization point may not be at jet centerline

Large eddy concept (Pitts, 1988) – flame is somehow attached to large eddies

Lifted flame stabilized as ensemble of edge flames (next) What are predictions? Homework problem!


EDGE FLAMES - motivation

Reference: Buckmaster, J., “Edge flames,” Prog. Energy Combust. Sci. 28, 435-475 (2002)

Laminar flamelet model used to describe local interaction of premixed & nonpremixed flames with turbulent flow

Various regions of turbulent flow will be above/below critical extinction strain (ext)

Issues Can flame “holes” or “edges” persist? Will extinguishment in high- region spread to other regions? Will burning region re-ignite extinguished region? Will at edge locate (edge) be at higher or lower strain than

extinction strain for uniform flame (ext)? How is edge propagation rate affected by ? Lewis number effects?


Edge flames Flame propagates from a burning region to a non-burning

region, or retreats into the burning region Could be premixed or non-premixed

Kim et al., 2006

FLOW

Non-premixed edge-flame in a counterflow


Edge flames - nonpremixed - theory Daou and Linan, 1998 Configuration as in previous slide No thermal expansion Non-dimensional stretch rate = (/SL

2)1/2 or Damköhler number ~ SL

2/ ~ -2

SL = steady unstretched SL of stoichiometric mixture of fuel & air streams Effects of stretch

Low : flame advances, "triple flame" structure - lean premixed, rich premixed & trailing non-premixed flame branches

Intermediate : flame advances, but premixed branches weaker High : flame retreats, only nonpremixed branch survives Note that stretch rate corresponding to zero edge speed is always

less than the extinction stretch rate for the uniform (edgeless, infinite) flame sheet - edge flames always weaker than uniform flames - retreat in the presence of less strain than required to extinguish uniform flame

Le effects: as expected - lower Le yields higher edge speeds, broader extinction limits


Edge flames - nonpremixed - theory Daou et al., 2002


Daou and Linan, 1998 (lF = (LeFuel - 1))

Edge flames - nonpremixed - theory


Thermal expansion effect (Ruetsch et al., 1995): U/SL ~ (∞/f)1/2 with proportionality constant shown

Edge flames - nonpremixed - theory

(∞/f)1/2


Edge flames - nonpremixed - with heat loss Daou et al., 2002 = dimensionless heat loss ≈ 7.5/Pe2; Pe SLd/ (see Cha & Ronney, 2006) With heat loss: trailing non-premixed branch disappears at low - nonpremixed

flame extinguishes because mixing layer thickness ~ (/)1/2 (thus volume, thus heat loss) increases while burning rate decreases


Daou and Linan, 1999 - similar response of Uedge to stretch as nonpremixed flames - also note "spots"

Edge flames - premixed - theory


Experiments - nonpremixed edge-flames

Cha & Ronney (2006) Use parallel slots, not misaligned slots Use jet of N2 to "erase" flame, then remove jet to watch advancing edge,

or establish flame, then zap with N2 jet to obtain retreating flame


Edge flames - nonpremixed - experiment

Retreating

"Tailless"

Propagating


Edge flames - nonpremixed - experiment Behavior very similar to model predictions with heat loss - negative at

low or high , positive at intermediate with Uedge/SL ≈ 0.7(∞/f)1/2 (prediction: ≈ 1.8)

Propagation rates ≈ same for different gaps when scaled by strain rate except at low (thus low Vjet) where smaller gap more heat loss (higher )


Edge flames - nonpremixed - experiment

Dimensional Uedge vs. stretch () can be mapped into scaled Uedge vs. scaled stretch rate () for varying mixtures

Little effect of mixture strength when results scaled by , except at low , where weaker mixture lower SL higher

Dimensional Dimensionless

Numbers refer to molar N2 dilution when fuel and oxidant streams are mixed in stoichiometric proportions (CH4:O2:N2 = 1:2:N)


Edge flames - nonpremixed - experiment High stretch () or heat loss () causes extinction - experiments

surprising consistent with experiments, even quantitatively Very difficult to see "tailless" flames in experiments

Model assumes volumetric heat loss (e.g. radiation) - mixing layer thickness can increase indefinitely, get weak non-premixed branch that can extinguish when premixed branches do not

Experiment - heat loss mainly due to conduction to jet exits, mixing layer thickness limited by jet spacing

Experiment (Cha & Ronney, 2006) Prediction (Daou et al., 2002)


Edge flames - nonpremixed - experiment Lewis number effects VERY pronounced - at low Le, MUCH higher

Uedge than mixture with same SL (thus ) with Le ≈ 1 Opposite trend for Le > 1

Low Le (CH4-O2-CO2) High Le (C3H8-O2-N2)

(Lefuel = 0.74; LeO2 = 0.86) (Lefuel = 1.86; LeO2 = 1.05)


Edge flames - nonpremixed - experiment Zst = "stoichiometric mixture fraction" = fraction of fuel + inert in a stoichiometric

mixture of (fuel+inert) & (O2+inert) (1 > Zst > 0) High Zst: flame sits near fuel side; low Zst: flame sits near O2 side …but results not at all symmetric with respect to Zst = 0.5! Due to shift in O2 concentration profile as Zst increases to coincide more closely

with location of peak T, increases radical production (Chen & Axelbaum, 2005) (not symmetrical because most radicals on fuel side, not O2 side)


Edge flames - nonpremixed - experiment Heat loss limit (low , thus low strain) - relationship between and

independent of mixture strength, gap, Le, Zst, etc. Recall high (high strain) limit depends strongly on Le but almost

independent of (page 24) Suggests relatively simple picture of non-premixed edge flames


Edge flames - premixed - theory Again larger Uedge for low Le Again 2nd extinction limit at low strain rates

Daou & Linan, CNF 1999; Daou et al., CTM 2003


Edge flames – twin premixed - images

Clayton, Cha, Ronney (2015?)

Lewis number effects very evident – curvature effects on leading edge


Edge flames – twin premixed - Uedge

Propagation rates scale with (ru/rb)1 not (ru/rb)1/2 Again 2 extinction limits, high & low strain rates


-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.1 0.2 0.3 0.4 0.5

Ued

ge /(

SL(

u/b))

CH4/Air

d = 7.5 mm

%CH4 = 5.2

5.65.3

5.8

6.06.5

short length flames

Twin premixed flames

-100

-50

0

50

100

10 100

5.2 Uedge [cm/s]5.35.65.85.8-SLF6.06.0-SLF6.56.5-SLF

Ued

ge [

cm/s

]

[1/s]

CH4/Air

d = 7.5 mm

%CH4 = 5.2

5.65.35.8

6.0

6.5

short length flames

Raw data Scaled data


Edge flames – twin premixed - Uedge

Lewis number effects similar to nonpremixed edge flames


Low fuel Le High fuel Le

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Ued

ge /(

SL(

u/b))

Le < 1, Twin premixed flamesCH

4/O

2/CO

2

retreating tails of SLF

4.455.46

SL =

6.40 cm/s

6.90(reference CH

4/Air Mixture)

-1.5

-1

-0.5

0

0.5

1

0 0.1 0.2 0.3 0.4 0.5

14.86

16.87

18.99

6.9 (as reference CH4/Air)

Ued

ge /(

SL(

u/b))

Le > 1, C

3H

8/Air mixture

SL [cm/s]

Twin premixed flames


Edge flames – twin premixed - regimes Regimes of behavior similar to nonpremixed edge flames

Experiments Model predictions

Clayton, Cha & Ronney, 2015? Daou et al., CTM 2003

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.05 0.1 0.15 0.2 0.25 0.3

low extshort lenth flameslow retreatinghigh retreatinghigh extepsilon (extinction)epsilon (retreating)epsilon (tailess flames)

Non

-dim

ensi

onal

flam

e th

ickn

ess

Heat loss factor

Twin premixed flamesCH

4/Air

short length flames

advancing

extinctionretreating

extinction [5]

retreating [5]

tailess flames [5]


Edge flames – single premixed - images



Edge flames – single premixed - Uedge

Propagation rates scale with (ru/rb)1/2 Structure similar to nonpremixed flame

– large temperature gradients on both sides of reaction zone, unlike twin premixed flame

Less Lewis number effect than nonpremixed or twin premixed, especially for Le > 1 -1.5

-1

-0.5

0

0.5

1

1.5

0 0.05 0.1 0.15

6.8%6.8% SLFscaled Uedge single %CH4 6.96.9% SLF7.20%7.20% SLF7.75%7.75% SLF8.30%8.30% SLF9.0 %9.0% SLF

Ued

ge /(

SL(

u/b)1/

2 )

CH4/Air

d = 7.5 mm

%CH4 = 9.0

7.2

8.37.75

retreating edges for tails of SLF

Single premixed flames

6.9 6.8

-2

-1

0

1

2

0 0.05 0.1 0.15 0.2 0.25 0.3

8.8511.013.120.8 (reference CH

4/Air)

Ued

ge /(

SL(

u/b)1/

2 )

Le < 1,CH

4/O

2/CO

2



SL [cm/s]

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

27.530.434.033.8 (reference CH

4/air)

Ued

ge /(

SL(

u/b)1/

2 )

Le > 1,C

3H

8/Air



SL [cm/s]


References Buckmaster, J. D., Combust. Sci. Tech. 115, 41 (1996). Buckmaster, J., "Edge flames," Prog. Energy Combust. Sci. 28, 435-475 (2002). Buckmaster, J. D. and Short, M. (1999). Cellular instabilities, sub-limit structures and edge-flames

in premixed counterflows. Combust. Theory Modelling 3, 199-214. M. S. Cha and S. H. Chung (1996). Characteristics of lifted flames in nonpremixed turbulent

confined jets. Proc. Combust. Inst. 26, 121–128 M. S. Cha and P. D. Ronney, "Propagation rates of non-premixed edge-flames, Combustion and

Flame, Vol. 146, pp. 312 - 328 (2006). R. Chen, R. L. Axelbaum, Combust. Flame 142 (2005) 62–71. R. Daou, J. Daou, J. Dold (2002). "Effect of volumetric heat-loss on triple flame propagation" Proc.

Combust. Inst., Vol. 29, pp. 1559 - 1564. R. Daou, J. Daou, J. Dold (2003). "Effect of heat-loss on flame edges in a premixed counterflow,”

Combust. Theory Modelling, Vol. 7, pp. 221–242 J. Daou, A Liñán (1998). "The role of unequal diffusivities in ignition and extinction fronts in

strained mixing layers," Combust. Theory Modelling 2, 449–477 J. Daou and A. Liñán (1999). "Ignition and extinction fronts in counterflowing premixed reactive

gases," Combust. Flame. 118, 479-488. Hinze, J. O. (1975) "Turbulence," McGraw-Hill. Hottel, H. C., Hawthorne, W. R., Third Symposium (International) on Combustion, Combustion

Institute, Pittsburgh, Williams and Wilkins, Baltimore, 1949, pp. 254-266. Joulin, G. and Clavin, P. (1979). Linear stability analysis of nonadiabatic flames: diffusional-thermal

model. Combust. Flame 35, 139. Kalghatgi, G. T. (1984). Lift-Off Heights and Visible Lengths of Vertical Turbulent Jet Diffusion

Flames in Still Air. Combust. Sci. Tech. 41, 17-29.


References Kaiser, C., Liu, J.-B. and Ronney, P. D., "Diffusive-thermal Instability of Counterflow Flames at Low

Lewis Number," Paper No. 2000-0576, 38th AIAA Aerospace Sciences Meeting, Reno, NV, January 11-14, 2000.

N. I. Kim, J. I. Seo, Y. T. Guahk and H. D. Shin (2006). "The propagation of tribrachial flames in a confined channel," Combustion and Flame, Vol. 146, pp. 168 - 179.

Liu, J.-B. and Ronney, P. D., "Premixed Edge-Flames in Spatially Varying Straining Flows," Combustion Science and Technology, Vol. 144, pp. 21-46 (1999).

Lyons, K. M. (2007). “Toward an understanding of the stabilization mechanisms of lifted turbulent jet flames: Experiments,” Progress in Energy and Combustion Science, Vol 33, pp. 211–231

Pitts, W. M. (1988). “Assessment of theories for the behavior and blowout of lifted turbulent jet diffusion flames,” 22nd Symposium (International) on Combustion, pp. 809–16.

Ruetsch, G. R., Vervisch, L. and Linan, A. (1995). Effects of heat release on triple flames. Physics of Fluids 7, 1447.

Shay, M. L. and Ronney, P. D., "Nonpremixed Flames in Spatially-Varying Straining Flows," Combustion and Flame, Vol. 112, pp. 171-180 (1998).

Sivashinsky, G. I., Law, C. K. and Joulin, G. (1982). On stability of premixed flames in stagnation-point flow. Combustion Science and Technology 28, 155-159.

R. W. Thatcher and J. W. Dold (2000). "Edges of flames that do not exist: flame-edge dynamics in a non-premixed counterflow." Combust. Theory Modelling 4, 435-457.

Vedarajan, T. G., Buckmaster, J. D. and Ronney, P. D., "Two-dimensional Failure Waves and Ignition Fronts in Premixed Combustion," Twenty-Seventh International Symposium on Combustion, Combustion Institute, Pittsburgh, 1998, pp. 537-544.

Documents

AME 514 Applications of Combustion Lecture 9: Nonpremixed flames, edge flames