School of Aerospace Engineering

Flame Thickness and Flame Speed Jerry Seitzman 0.2

2500

Mole Fraction

1500

CH4 H2O HCO x 1000 Temperature

0.1

1000

0.05

500

Temperature (K)

2000

0.15

Methane Flame 0

0 0

0.1

0.2

0.3

Distance (cm)

AE/ME 6766 Combustion

FlameThicknessSpeed -1 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

School of Aerospace Engineering

Flame Speed • Recall S Lo 

2 f

1Y f ,1

 RR    chem

• Just a scaling law - not exact – example for HC/air STP reactants 5 4 2 •  ~ 10  10 m s 4 3 •  chem ~ 10  10 s (after reactants “preheated”) • S Lo ~ O0.01  1 m s 

FlameThicknessSpeed -2 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

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Flame Thickness • “Define” thickness of flame as T   T2 Ti q preheat and reaction zones  f   ph   R T1 • Estimate from preheat zone x R ph energy balance at interface T T dT  2 1 1S Lo c p Ti  T1    f dx i T2 Turns gets 2   1 because he      f  f chem S Lo 1c p S Lo assumes PH=R 2 • Consider time scales    1  diff  f   f  chem  chem  chem AE/ME 6766 Combustion

FlameThicknessSpeed -3 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

School of Aerospace Engineering

Zeldovich Number • Compare preheat and reaction zone thicknesses T • Match heat flux at interface T i

– assume stepwise linear T profiles T1 T T T T  i 1  2 i

 ph R T2  R  ph  T2  Ti  Ti  T1  • What is (T2-Ti)? d RRT2   Ce  E T2  Ti 

a

RT2

dT

RRT2  1  Ea RT22 RRT2  Ea RT22





RRT2   

ph

FlameThicknessSpeed -4

R

x

RRT2   RRTi  T2  Ti

 R RT22 Ea  1 Zeldovich #    PH T2  T1 Ze

• Ze=O(10) for HC flames  PH10R Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

0

T2

High Ea (and q) thin reaction zones

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Physical/Chemical Effects on SLo, f o • Scaling laws for SLo, f S Lo  RR 1  f   S L • Predicts how premixed flame parameters will be influenced by changes in chemical and physical properties of the reactants

Chemical • Equiv. ratio () • Fuel type • Additives/diluents

• • • •

Physical Pressure Unburned temp. (T1) Burned temp. (T2) , D, cp AE/ME 6766 Combustion

FlameThicknessSpeed -5 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

School of Aerospace Engineering

Scaling Models • Reaction rate • Diffusivity

RR  A fuel, ox  neE

a

  1c p T1T m 1  pc p W m

FlameThicknessSpeed -6 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

Kinetic Theory

RT2

atoms triatomics

  T W 

m  0.5  0.8

p T1

cp  cp W

m

1  W1

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Pressure Dependence n2 1 n1 p p2 p p

S Lo  RR 1  10

CH4/air

CH4/air =1 77F SL (ft/s)

• p>2 atm SoL~ p0.5 n~1 • p~0.1-0.5 atm SoL ~p0.25 n~1.5

n=1-1.5

1

1.41 p 0.5

1.15 p 0.25

0.1 0.1

1

10

100

Pressure (atm)

AE/ME 6766 Combustion

FlameThicknessSpeed -7 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

School of Aerospace Engineering

Pressure Dependence S p o L

n2 2

• Most hydrocarbons, n2 SoL  as p • n based on global kinetics – can change with , p as important chemical steps change

• Propane 0.16  0.22  1 – S Lo S Lo,ref   p pref  • H2 – SoL  as p for lean, SoL  as p for rich FlameThicknessSpeed -8 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

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Initial Temperature Dependence • From our model S Lo  T1T m 2T2 n 2 e • However T2 also changes with T1 – though not too strongly – e.g., methane – T1 300600K T2 22302360K

 Ea 2 RT2

m  0.5  0.8

2360K, 3790F

2230K, 3550F

AE/ME 6766 Combustion

FlameThicknessSpeed -9 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

School of Aerospace Engineering

Initial Temperature Dependence S Lo  T11.5 2

• From HC experiments • Compare to model S Lo  T1T m 2T2 n 2 e  Ea 2 RT2 • Suggests T1 effect is mostly preheating

Dugger et al., Ind Engr. Chem. 47 (1955)

T11.5

– less preheating  T11.9 required before reaction zone – not T2 effect, only 1.2 (see next slide) T 300600K gives 3.5-4 increase in S 1

FlameThicknessSpeed -10 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

L

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Final Temperature Dependence • From models

S T o L

m2

n 2 2

T



e

Ea R 2T2

– typically dominated by expon. term

S e o L



SL  T20.3e16,850K T

2

2230K 2360K

Ea R 2T2

Ea/R ~ 15-30103 K for HC fuels AE/ME 6766 Combustion

FlameThicknessSpeed -11 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

School of Aerospace Engineering

Gas Properties • Nonchemical properties W , c p  • From models o 1 SL 

c pW m

m  0.5  0.8

• Light gases increase SoL (faster mean molecular speed, more diffusion) • Molar specific heat range limited Cold Atoms

1500K H2O

5 2  c p R  11 2

– also hard to change specific heat without changing adiabatic flame temperature FlameThicknessSpeed -12 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

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Equivalence Ratio • H2-air – peaks quite rich (~ = 1.7-1.9)

• Adiabatic flame temperature (T2) • Also diffusion – molec. weight of H2

• Minor cp influence FlameThicknessSpeed -13 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

AE/ME 6766 Combustion

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Equivalence Ratio • CH4-air –peaks slightly rich (~ = 1.1-1.2)

• For H-C fuels, primarily influence on adiabatic flame temperature (T2) • Reasonable match to model FlameThicknessSpeed -14 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

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Fuel Type • By organic type

S

SoL(STP) cm/s

L , max

– Alkanes CC ~1.1 40-50 – Alkenes C=C ~1.2 50-70 – Alkynes CC ~1.4 60-160 – H2 ~1.7 280

AE/ME 6766 Combustion

FlameThicknessSpeed -15 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

School of Aerospace Engineering

Fuel Type • Primary influence of fuel type is adiabatic flame temperature change – SL dependence with fuel scales with Tad

ref: Turns, Fig. 8.17 FlameThicknessSpeed -16 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

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Additives • Many fuel additives intended to change other fuel properties – small effect on SoL – – – –

reduce knock/preignition by raising ignition T increase lubricant properties of fuel reduce fuel line coking improve emissions

• If they influence reactions that control heat release or chain-branching steps, can change SoL – e.g., small amounts of H2O added to CO flames AE/ME 6766 Combustion

FlameThicknessSpeed -17 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

School of Aerospace Engineering

Diluents • Class exercise – explain

“Air” = 21% O2 and 79% diluent FlameThicknessSpeed -18 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

after Clingman et al., Proc. Comb. Inst. 4 (1953)

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Flame Thickness • Can show  f  p n 2

– Pressure – T2

f T e m2 2

 f  1 c pW m 

– cp,W –

Ea R 2T2

f minimum roughly at  where SL maximum

AE/ME 6766 Combustion

FlameThicknessSpeed -19 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

School of Aerospace Engineering

1D Laminar Flame Structure • Recall assumed flame structure

unburned burned

T Ti q

T2

T1 preheat zone

reaction zone

x Discussion point: SL for Le1

FlameThicknessSpeed -20 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

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H2 Flame Structure

ref: Glassman

• Calculations using Premix (Chemkin) – stoich. H2/air – 298K, 1 atm – “full” mechanism • O2 peaks as H2 drops  H2 diffuses faster • Heat release widely distributed FlameThicknessSpeed -21 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

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H2 Flame Structure

ref: Glassman

• Calculations using Premix (Chemkin) – stoich. H2/air – 298K, 1 atm – “full” mechanism • Peaks H production well into heat release zone • Diffusion of H upstream into reactants FlameThicknessSpeed -22 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

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H2 Flame Structure • Calculations

H+O2 HO2

– H2/air =0.6 – 298K, 1 atm

HO2+H 2OH H2+OH H2O+H

Preheat/Diffusion Layer H Consumption H Production Layer Layer

AE/ME 6766 Combustion

FlameThicknessSpeed -23 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

School of Aerospace Engineering

CH4 Flame Structure

ref: Glassman

• Calculations using Premix (Chemkin) – stoich. CH4/air – 298K, 1 atm – “full” mechanism

Preheat FlameThicknessSpeed -24 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

Primary Heat Release

Slow Secondary Heat Release

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CH4 Flame Structure

ref: Glassman

• Calculations using Premix (Chemkin) – stoich. CH4/air – 298K, 1 atm – “full” mechanism

H+O2 Fuel Final Burnout (CO) Conversion CH4+RCH3CH2O

FlameThicknessSpeed -25 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

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Flame Structure • Most hydrogen/hydrocarbon flames have at least three discernible zones 1. a preheat/diffusion dominated zone • can include (low q ) reactions due to radical diffusion 2. a primary reaction zone • major radical/intermediate production, intense q 3. a final oxidation (burnout) zone • thicker than primary reaction zone • slow approach to final equilibrium • final heat release FlameThicknessSpeed -26 Copyright © 2004-2005, 2012 by Jerry M. Seitzman. All rights reserved.

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