lecture 5. laminar premixed flames structures and propagation · premixed fuel/air mixture: flame...

Lecture 5. Laminar Premixed Flames

Structures and Propagation

X.S. Bai Laminar Premixed Flames

Premixed flames


Premixed flames causing coal mine explosion


A mine explosion in the Ukraine resulted in 36 dead, 14 missing, and this guy looking very terrible indeed. The explosion was methane gas, and they were mining coal. August 2001. http://cellar.org/showthread.php?t=452


Most cars run with SI engine


SGT-750 37 MW, 40% Launched nov 2010

Gas turbine engines


Premixed fuel/air mixture: auto-ignition

Premixed fuel/air mixture

Auto-ignition sites


Hydrogen/air auto-ignition

Initial temperature

Ignition delay time H2 + M = H + H + M

Low T0

High T0

thermal runaway and radical runaway

Induction period


Hydrogen/air auto-ignition

Ignition delay time of H2/air mixture


Structures and propagation of laminar premixed flames

•  Structures of laminar premixed flames •  Burning velocity of lamniar premixed flames •  Propagation of laminar premixed flames in flow field •  Stabilization of premixed flames •  Laminar premixed flame instability


Laminar premixed flames: Bunsen burner


Laminar premixed flames

Reaction zone

Hot gas radiation


Experimental observations of flames


CH2O CH photo

Vo=0.45 m/s, phi=1.17; Vin=11m/s, phi=1.1


Structure of premixed flames


Premixed fuel/air mixture: flame propagation

Premixed fuel/air mixture

Preheat zone

Reaction zone

Post flame zone


Structure of premixed flames

•  Preheat zone: heating up the reactants

•  Inner-layer: radical formation

•  Oxidation-layer: finishing the remaining reactions

•  Post-flame zone: hot products, NOx formation


Analysis of flames: the post-flame zone

Flame front

Unburned fuel/air mixture

Burned hot products

YF,u / YA,u =! / "A, and YF,u +YA,u =1

YF,u =!

!+ "A

, YA,u ="A

!+ "A

, and YO,u =0.233"A

!+ "A

, YN,u =0.767"A

!+ "A

,

F + A = P 1 γA 1+γA



! >1

YF,b =YF,u "YA,u / #A = (!"1)YA,u / #A =YF,u!"1!

=!"1!+ #A

,

YO,b = 0, YN,b =YN,u =0.767#A

!+ #A

YP,b =1"YF,b , P includes N

Flame front


Burned hot products



Flame front


Burned hot products

,

, , , , ,

, ,

10

1 1(1 ) ,

1

F b

A b A u A F u A u A F u AA

P b A b

Y

Y Y Y Y Y

Y Y

γ γ γγ

Φ <

=

−Φ −Φ= − = −Φ = =

Φ Φ +

= −Both A and P include N



Flame front


Burned hot products

0 0, , , ,

0 0 0, , , , , ,

[ ( )] [ ( )]

[ ( )] [ ( )] [ ( )]u F u F p F u ref A u A p A u ref

b F b F p F b ref A b A p A b ref P b P p b b ref

h Y h c T T Y h c T T

h Y h c T T Y h c T T Y h c T T

= + − + + −

= + − + + − + + −



0

T

Tu

Ф=1 Ф

( )rb u

p A

HT T

c γ−Δ Φ

= +Φ +

( ) 1rb u

P A

HT TC γ−Δ

= +Φ +

( ) 11

rb u

P A

HT TC γ−Δ

= ++


Laminar burning velocity

•  How fast can a laminar flame propagate? •  What is the mechanism of flame propagation? •  What are the influencing factors?


Laminar burning velocity

Flame front


Burned hot products

Laminar burning velocity (also called laminar flame speed): the speed at which the flame front propagates towards the unburned mixture


Derivation of laminar burning velocity

Flame front


Burned hot products

Assumptions - 1 D -  steady state -  unity Lewis number -  low Mach number

!!!t

+"#!v!= 0

!!!v!t

+ !!v "# !v =#" pI +!( )

!DhDt

!DpDt

="# !""h ! !" 1! 1Lei

$

%&&

'

())hi"Yi

i =1

N

*$

%&&

'

())+!Qr +! :"

!v

!!Yi!t

+"#!Yi v!="#!Di"Yi +"i


Development of flame speed theory

•  Mallard: –  Ann Mines 7, 355 (1875)

•  Mallard & Le Chatelier: –  Ann Mines 4, 274 (1883)

•  Bernard Lewis and G Von Elbe (1937)

•  Zeldovich, Frank-Kamenetskii (1938) and Semenov (1940)

•  Peters, Seshadri, Williams (1990s)



Flame front


Burned hot products


!"!t+#$"v

!= 0

!"Yi!t

+#$"Yiv!=#$"Di#Yi +%i



Flame front


Burned hot products

Assumptions - 1 D -  steady state -  unity Lewis number -  low Mach number 0

!"!t+#$"v

!= 0

!"Yi!t

+#$"Yiv!=#$"Di#Yi +%i



Flame front


Burned hot products


!"!t+d"udx

= 0

!"Yi!t

+d"Yiudx

=ddx

"DidYidx

#

$%

&

'(+)i

0



Flame front


Burned hot products


!"!t+d"udx

= 0

!"Yi!t

+d"Yiudx

=ddx

"DdYidx

#

$%

&

'(+)i

0



Flame front


Burned hot products


!"!t+d"udx

= 0

!"u ="uSL = constant0 !"Yi!t

+d"Yiudx

=ddx

"DdYidx

#

$%

&

'(+)i *"uSL

dYidx

=ddx

"DdYidx

#

$%

&

'(+)i

SL



!uSLdYidx

=ddx

!DdYidx

"

#$

%

&'+(i ) !uSL

dYidx

"

#$

%

&'dx =

*+

++

, ddx

!DdYidx

"

#$

%

&'+(i

"

#$$

%

&''dx

*+

++

,

)!uSL(YP,b *0) =(P-L ) SL ./-L

x!"#

YP = 0,dYPdx

= 0

x = 0

x!+"

YP =YP,b ,dYPdx

= 0

δL



!uSLdYidx

=ddx

!DdYidx

"

#$

%

&'+(i ) !uSL

dYidx

"

#$

%

&'dx =

*+

*,L /2

- ddx

!DdYidx

"

#$

%

&'+(i

"

#$$

%

&''dx

*+

*,L /2

-

)!uSL(YP,b / 2*0) =!DYP,b *0,L

) SL,L .D

x!"#

YP = 0,dYPdx

= 0

x = 0

x!+"

YP =YP,b ,dYPdx

= 0



Flame front


Burned hot products

SL ! D!, D : mass diffusion cofficient [m2 /s]

"L ! D /! ! : reaction rate [1/s]


Dependence on fuel/air ratio


Dependence on flame temperature


Dependence on reactivity


Dependence on preheat temperature


Dependent on transport properties


Dependence on pressure


Syngas/air (CO/H2/air) flames – effect of reactivity and diffusivity

Author's personal copy

the laminar burning velocity of the biomass gases. Forhydrogen rich mixtures (with hydrogen mole fraction largerthan 20%, such as GG-H, GG-V, GG-L1, GG-L2, GG-S, PG-D andSG-50 listed in Table 1), co-firing with methane would lead toa decrease in the laminar burning velocities. In such cases, co-firing improves the burning velocity of methane and naturalgas rather than the BDGs, and this may help improving theperformance of natural gas based gas engines.

Co-firing hydrogen with BDGs would certainly improve theburning characteristics of the BDGs. Recent studies onhydrogen addition to methane (equivalent to purified landfillgas) have shown that the laminar burning velocity increasesmonotonically with the hydrogen volume fraction in the fuelblends [32], and the ignition of methane can be significantlyimproved with hydrogen addition [33]. For stretched flameswith curved flame front, hydrogen addition to methane can

not only increase the burning velocity (similar to the freelypropagating un-stretched flames), but also improve theextinction limits. It can also affect the flame instabilities[34–36], due to the low Lewis number of hydrogen.

3.3. Correlation between laminar burning velocity andBDG gas composition

To gain further insight into the inter-correlations between thelaminar burning velocity and BDG compositions, numericalsimulations are carried out for various BDGs reported in theliterature. The simulated laminar burning velocity, laminarflame thickness, and adiabatic flame temperature aresummarized in Table 3, with the compositions of the BDGsand their LHV given in Table 1. All flames are under

Fig. 10 – Laminar burning velocity and adiabatic flame temperature of syngas flames at atmospheric pressure and unburnedmixture temperature of 300 K.

Fig. 9 – Laminar burning velocity and adiabatic flame temperature as a function of equivalence ratio for gasification gas/airflames. GG-S: a model producer gas generated during the gasification of biomasswastes [3], GG-Va: gasification gas from theVarnamo plant [9].

i n t e r n a t i o n a l j o u rn a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 5 4 2 – 5 5 5 551

Diffusivity increases


Propagation of laminar premixed flame

y , ey

z , ez

x , ex

r

v p

SL , n

Unburned G<0 Burned

G>0

G(x,y,z,t)=0

Flame front (reaction zone)

!G!t

+!v "#G = S L #G


Planar flame in a pipe

•  Stable flame •  Flash back •  Blow-off •  Wall effect

u SL Unburned x< 0 burned

x> 0 x= 0 (at t=0) x


Bunsen flame

•  Conical shape •  Flame length vs R, u, SL

R r

u

G(x,r,t)=0

x

( , , ) ( ) 0G x r t x f r= + =

( )2 1Lu S f ʹ′= +

2 2

2( ) constantL

L

u Sf r rS−

= +

2 2

2( ) L

L

u Sx R rS−

= −


Bunsen flame stability

•  Rim effect •  Lifted flame •  blowout

Stable flame position B Stable flame

position A rim


Stabilization of premixed flames

•  Rim stabilization •  Pilot flame stabilization •  Bluff body stabilization

lecture 5. laminar premixed flames structures and propagation · premixed fuel/air mixture: flame...

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