Lecture 6. Laminar Non-premixed Flames part 2. Bai Laminar Non-premixed Flames Where is the reaction zone? Zst Burnable mixture A F O 2 O 2 F F Fuel-rich mixing zone Reaction zone

Lecture 6. Laminar Non-premixed Flames

part 2

X.S. Bai Laminar Non-premixed Flames

Content

•  Structures of laminar non-premixed flames •  Mixture fraction •  Burke-Schumann flame-sheet model •  Jet diffusion flames •  Laminar diffusion flame at high mixing rate


Where is the reaction zone?

Zst

Burnable mixture

A F

Diffusion velocity: Fick’s Law

YiVi = Di!Yi, Vi = Di / Yi!Yi "Di / !

!Mixing length



Zst

Burnable mixture

A F

O2

O2

F

F

Preheat zone Post flame zone



Zst

Burnable mixture

A F

O2

O2

F

F




Zst

Burnable mixture

A F

O2

O2

F

F




Zst

Burnable mixture

A F

O2

O2

F

F




Zst

Burnable mixture

A F

O2

O2

F

F




Zst

Burnable mixture

A F

O2

O2

F

F




Zst

Burnable mixture

A F

O2

O2

F

F

Fuel-rich mixing zone Reaction zone Oxidizer-rich mixing zone



Zst

Burnable mixture

Fuel-rich Fuel-lean

T

Z Zst

Tst

T1 T2

0 1

Tcr

A F


Burke-Schumann flame-sheet structure

A P P F

Zst

1

Yi

Z

Reaction zone

Fuel-rich Fuel-lean

Reactions occur in a zero thickness sheet at Z=Zst

Soot problem


Burke-Schumann flame-sheet structure

Reaction zone

Reactions occur in a zero thickness sheet at Z=Zst

Fuel-rich Fuel-lean

T

Z Zst

Tst

T1

T2

0 1

NOx problem


Content



Laminar jet diffusion flames

Zst

Mixing layer

A non-reactive fuel jet

Fuel

Air

Zst

Burnable mixture


Laminar jet diffusion flames

Air

A+P

Air F+P

A jet diffusion flame Fuel

Fuel rich

Air rich

Reaction zone

a-b

c-d c-d

O2 F P

a-b

O2 F

1, 0, 1 1

stF A P

st st

Z Z ZY Y YZ Z− −

= = =− −

0, 1 , F A Pst st

Z ZY Y YZ Z

= = − =

soot NOx

Fuel rich zone

Fuel lean zone


Jet diffusion flame: mathematical description

Zst

Mixing layer

A non-reactive fuel jet

Fuel

Air

11F P F P st

A

Z Y Y Y Y Zγ

= + = ++

FZ Y=

Combustion

No combustion (pure mixing)

!!Z!t

+"# (!!vZ) ="# (!D"Z)

!!Yi!t

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

!!YF!t

+"#!YFv!="#!DF"YF +"F

!!YP!t

+"#!YPv!="#!DP"YP +"P

DF = DP = D, !F +!PZst = 0


Height of laminar jet flame

R

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F + P

A + P air

Lf

R

vf

x

Lf !vFR

2

D

!!Z!t

+"# (!!vZ) ="# (!D"Z)

!vF / Lf

!D / R20 Mixing layer analysis


Height of laminar jet flame

R

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F + P

A + P

air Lf

R

vf

x

Lf !vFR"D!vFR

2

D

X = vFt,

Y = R !VO2t = R !1!DO2t

Mixing layer analysis

YiVi = Di!Yi, Vi = Di / Yi!Yi "Di / !

X = Lf = vFtf ,

Y = 0 = R ! 1!DO2tf


Jet diffusion flame: experimental obervation

O

F

O

U x

Pe 50 Pe 50 Pe 200 Pe 1

Lf !vFR

2

D=vFRD

!

"#

$

%&R = Pe 'R


Propagation of laminar diffusion flame

N+5 PDE equations

!!!t+"#!v

!= 0

!!!v

!t+"!

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

!DhDt

!DpDt

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

$

%&&

'

())hi"Yi

i=1

N

*$

%&&

'

())+!Qr +# :"

"v

!!Yi!t

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


Burke-Schumann flame-sheet model

!!!t+"#!v

!= 0

!!Z!t

+"# (!!vZ) ="# (!""Z)

Yi = a + bZT = c+dZ

6 PDE equations

!!!v

!t+"!

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

!DhDt

!DpDt

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

$

%&&

'

())hi"Yi

i=1

N

*$

%&&

'

())+!Qr +# :"

"v

Burke-Schumann flame sheet relation


Content



Finite-rate chemistry effect

•  Burke-Schumann flame-sheet model is not always true; it is true only when the chemical reactions are much faster than the mixing of fuel and the oxidizer

•  If the mixing is very fast, what is going to happen?

Zst

Burnable mixture


Flamelet equation

!!Yi!t

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

Yi(x,y,z, t) =Yi(Z(x,y,z, t)),

!(x,y,z, t) =!(Z(x,y,z, t)),T(x,y,z, t) = T(Z(x,y,z, t))

Flamelet assumption:

!!Z!t

+"# (!!vZ) ="# (!D"Z)

Species transport

Mixture fraction


Flamelet equation

!12!"d2YidZ2

=#i

d2YidZ2

= !2!i

"#

! = 2D(!Z "!Z) Scalar dissipation rate: mixing rate

Damköhler number Da = (mixing time)/(chemical reaction time) Da ! 2!i"#


Finite rate chemistry effect

F O2

F O2

2

2id Y

dZ→∞

2

2 finiteid YdZ

=

Damköhler number infinity Damköhler not very high

iY iY

Z ZstZ

stZ

stZ


Effect of mixing rate

F O2

iYiY

Z Z

χ ↑

χ ↑

χ ↑

stZ stZ

Increase of scalar dissipation rate leads to •  the leakage of fuel to the oxygen rich side increases •  the leakage of oxygen to the fuel rich side increases •  the flame temperature decreases, as a result of insufficient oxidation of

the fuel


Flame quenching at high scalar dissipation rate

Adiabatic flame

With preheating

With radiation heat loss

Flame sheet Flamelet Quenched

PT

[ ]1P sχ −

qT

1qχ−


Laminar jet diffusion flame

Air

A+P F+P

Lift-off hight

Diffusion flame

Lean premixed flame Rich premixed

flame

Fuel inlet

c

Zst

Burnable mixture


Effect of mixng rate

•  For very small scalar dissipation rate the flame temperature is high; changing the scalar dissipation a little would not affect the flame temperature. This regime can be described by the simple Burke-Schumann flame sheet model.

•  For intermediate scalar dissipation rate, the flame temperature is lower than the Burke-Schumann flame temperature. Increasing the scalar dissipation rate leads to a decrease of the flame temperature until to a critical condition, at which the flame temperature changes rapidly. This regime may be called flamelet

•  For scalar dissipation rate higher than the quenching scalar dissipation rate, no flame exists. The flame is quenched.

Lecture 6. Laminar Non-premixed Flames part 2. Bai Laminar Non-premixed Flames Where is the reaction zone? Zst Burnable mixture A F O 2 O 2 F F Fuel-rich mixing zone Reaction zone

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