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Department of Applied Mechanics A Distinctive Feature of A Distinctive Feature of A Distinctive Feature of A Distinctive Feature of Turbulent Combustion of Turbulent Combustion of Turbulent Combustion of Turbulent Combustion of Lean

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SLIDE 1

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Andrei N. Lipatnikov Andrei N. Lipatnikov Andrei N. Lipatnikov Andrei N. Lipatnikov

Department of Applied Mechanics Chalmers University of Technology

A Distinctive Feature of A Distinctive Feature of A Distinctive Feature of A Distinctive Feature of Turbulent Combustion of Turbulent Combustion of Turbulent Combustion of Turbulent Combustion of Lean Lean Lean Lean Hydrogen Hydrogen Hydrogen Hydrogen-

  • Air

Air Air Air Mixtures Mixtures Mixtures Mixtures

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SLIDE 2

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Contents of the Lecture

Background

Laminar premixed flame Turbulence The major physical mechanism of premixed turbulent combustion

Experimental data on turbulent burning velocity

Ordinary hydrocarbon-air mixtures Lean hydrogen-air mixtures

Why does molecular transport substantially affect turbulent combustion at high Reynolds number?

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SLIDE 3

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Contents of the Lecture

Background

Laminar premixed flame Turbulence The major physical mechanism of premixed turbulent combustion

Experimental data on turbulent burning velocity

Ordinary hydrocarbon-air mixtures Lean hydrogen-air mixtures

Why does molecular transport substantially affect turbulent combustion at high Reynolds number?

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SLIDE 4

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

The Physical Mechanism of Flame Propagation in Premixed Reactants

( )

( )

j j kj k j j k

w x J Y u x Y t ρ ρ ρ + ∂ ∂ − = ∂ ∂ + ∂ ∂

        Θ − ∝ T t w

j r j

exp 1

;

j k k kj

x Y D J ∂ ∂ − = ρ

( )

( )

T j Tj j j

w x J T u x T t ρ ρ ρ + ∂ ∂ − = ∂ ∂ + ∂ ∂

j Tj

x T J ∂ ∂ − = ρκ Molecular transport: Chemical Reactions: Heat release

Heat transport

From the paper by Williams, F.A., “Progress in knowledge of flamelet structure and extinction," Progress in Energy and Combustion Science 26: 657-682 (2000).

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SLIDE 5

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

the heat release in chemical reactions

and

the molecular transport of the heat into the unburned mixture. Flame propagation in premixed reactants is caused by

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SLIDE 6

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

The Physical Mechanism of Flame Propagation in Premixed Reactants

( )

( )

j j kj k j j k

w x J Y u x Y t ρ ρ ρ + ∂ ∂ − = ∂ ∂ + ∂ ∂

        Θ − ∝ T t w

j r j

exp 1

;

j k k kj

x Y D J ∂ ∂ − = ρ

( )

( )

T j Tj j j

w x J T u x T t ρ ρ ρ + ∂ ∂ − = ∂ ∂ + ∂ ∂

j Tj

x T J ∂ ∂ − = ρκ Molecular transport: Chemical Reactions:

Θ≈20 000o K

δr δT

From the paper by Williams, F.A., “Progress in knowledge of flamelet structure and extinction," Progress in Energy and Combustion Science 26: 657-682 (2000).

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SLIDE 7

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

The key peculiarity of premixed combustion is as follows:

major chemical reactions that control the heat release are confined to very thin reaction zone!

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SLIDE 8

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Typical Values of Laminar Flame Speed and Thickness

  • SL≈0.4 m/s
  • κu≈0.02 cm2/s
  • δr≈0.05 mm
  • δτ≈0.5 mm
  • SL≈2 m/s
  • κu≈0.05 cm2/s
  • δr≈0.02 mm
  • δτ≈0.2 mm

Tm u L

w S κ ∝

L u Tm u L

S w κ κ δ ∝ ∝ Hydrocarbon-air flames: Hydrogen-air flames:

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SLIDE 9

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Laminar Flame Speed

St F F

Y Y F

,

= CH4 H2

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SLIDE 10

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Turbulent Flows

Photograph by Corke & Nagib Photograph by Dimotakis et al.

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SLIDE 11

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Main Characteristics of Turbulence

∫

+

= =

τ

η η τ

t t

d u t u U ) , ( 1 ) , ( ) ( x x x

[ ]

2 1 2

) ( ) , ( 1       − = ′

∫

+τ

η η τ

t t

d u u u x x ) ( ' ) ( ' ) ( ' ) ( ' ) ( x x u x u x x u x u x f + + = ) ( ' ) ( ' ) ( ' ) ( ' ) ( x x v x v x x v x v x g + + =

∫

∞

=

||

) ( dx x f LE

∫

∞ ⊥ =

) ( dx x g LE

rms turbulent velocity

x x u u v v

Integral length scale

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SLIDE 12

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Turbulence Spectrum

1 ' Re >> = ν L u

t

L u 3 ' ∝ ε

1 ' Re ; ;

4 1 4 1 4 1 4 3

≈ = ∝ ′ ∝

−

ν η ε ν ε ν η

η η η

u u λ π 2 = k

From the book by S.B. Pope “Turbulent Flows”, Cambridge University Press, Cambridge, UK, 2000.

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SLIDE 13

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Effect of Turbulent Velocity

  • n Flame Speed
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SLIDE 14

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Physical Mechanism of the Increase in Flame Speed by Turbulent Velocity

SL

Picture from the paper by Fox, M.D. and Weinberg, F.J. “An experimental study of burner stabilized turbulent flames in premixed reactants”, Proceedings of the Royal Society of London, A268:222-239, 1962.

δt

δL«δt

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SLIDE 15

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Physical Mechanism of the Increase in Flame Speed by Turbulent Velocity

t f L t

S U Σ Σ =

L l << << η

4 3

Re

−

⋅ =

t

L η

u t

L u ν ' Re =

SL L

l«L

SL Σf Σt u'1 u'2>u'1

Σf2>Σf1

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SLIDE 16

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Contents of the Lecture

Background

Laminar premixed flame Turbulence The major physical mechanism of premixed turbulent combustion

Experimental data on turbulent burning velocity

Ordinary hydrocarbon-air mixtures Lean hydrogen-air mixtures

Why does molecular transport substantially affect turbulent combustion at high Reynolds number?

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SLIDE 17

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Effect of Laminar Flame Speed

  • n Turbulent Burning Velocity
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SLIDE 18

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Effect of Laminar Flame Speed

  • n Turbulent Burning Velocity

Turbulent burning velocity Ut is increased by the laminar flame speed SL, all other things being equal. The larger the laminar flame speed, the higher the rate of the increase in the burning velocity by rms turbulent velocity

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SLIDE 19

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Effect of Laminar Flame Speed

  • n Turbulent Burning Velocity

2 4 6

r.m.s. turbulent velovity, u’, m/s

0.5 1 1.5 2

burning velocity, m/s 2H2+O2+12N2

2 4 6

r.m.s. turbulent velovity, u’, m/s

1 2 3 4 5

burning velocity, m/s 2H2+O2+12N2 2H2+O2+9N2

2 4 6

r.m.s. turbulent velovity, u’, m/s

1 2 3 4 5

burning velocity, m/s 2H2+O2+12N2 2H2+O2+9N2 2H2+O2+7N2

2 4 6

r.m.s. turbulent velovity, u’, m/s

1 2 3 4 5

burning velocity, m/s 2H2+O2+12N2 2H2+O2+9N2 2H2+O2+7N2 2H2+O2+6N2

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SLIDE 20

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Empirical Parameterization for Turbulent Burning Velocity

' u S U

L t

+ =

const ' = du dUt

A linear increase in burning velocity Ut by turbulent velocity u'

+

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SLIDE 21

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Empirical Parameterization for Turbulent Burning Velocity

; ' Pr Re

L L t

L S u δ ⋅ =

( )

Pr ; Ka Da; Pr ; Re ; ' ; ' '

3 1

F S u F L S u F u U

t L L L t

=         =         = δ

2 1 2

Re ' Ka

−

        ∝

t L

S u

; ' Da

L L

L u S δ ⋅ =

d u c L b a t

S L u' U ν ⋅ ⋅ ⋅ ⋅ = const

a+c+d=1; a+b+c+2d=1

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SLIDE 22

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Empirical Parameterization for Turbulent Burning Velocity

d u c L b a t

S L u' U ν ⋅ ⋅ ⋅ ⋅ = const

' du dUt

a≈0.5-0.75 c=0.5-0.6

is increased by SL!

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SLIDE 23

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Why Does Turbulent Burning Velocity Depend Non-Linearly

  • n the Laminar Flame Speed?

SL t1 t2 t3

Self-propagation

  • f laminar flame

fronts reduces the instantaneous flame surface area, i.e., Σf decreases when SL increases!

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SLIDE 24

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Is Turbulent Burning Velocity Always Increased by the Laminar Flame Speed?

2 4 6

r.m.s. turbulent velocity, m/s

1 2 3

burning velocity, m/s

C2H6/air, F=1.0 H2/air, F=5.0 H2+2.8O2+10.5Ar

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SLIDE 25

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Strong Effect of the Lewis Number

  • n Increase in Burning Velocity

7 1 1 ≈ ′ ⋅ ′ ⋅ u d dU S u d dU S

t L t L

2 4 6

r.m.s. turbulent velovity, u’, m/s

1 2 3

burning velocity, m/s C2H6/air, F=1.0 H2/air, F=5.0 H2+2.8O2+10.5Ar

L t

S u d dU ∝ ′

Ordinary mixtures:

Lean to rich hydrogen flames:

Seven times!!!

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SLIDE 26

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

An Important Peculiarity of Hydrogen-Air Mixtures

  • Molecular diffusion coefficient of hydrogen DH2 in

the air on the order on 0.6 cm2/s

  • Molecular diffusion coefficient of oxygen DO2 in the

air on the order on 0.2 cm2/s

  • Molecular heat diffusivity of the air κ on the order
  • n 0.2 cm2/s

Hydrogen-based Lewis number LeH2=κ/DH2 is substantially lower than unity in lean mixtures!

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SLIDE 27

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Effect of the Lewis Number

  • n Turbulent Burning Velocity
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SLIDE 28

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Contents of the Lecture

Background

Laminar premixed flame Turbulence The major physical mechanism of premixed turbulent combustion

Experimental data on turbulent burning velocity

Ordinary hydrocarbon-air mixtures Lean hydrogen-air mixtures

Why does molecular transport substantially affect turbulent combustion at high Reynolds number?

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SLIDE 29

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Temperature Variations in Curved Flamelets

t J z H t J

B B A A A

δ δ δ δ ⋅ Σ ⋅ + ⋅ Σ ⋅ = ⋅ Σ ⋅

fresh gas products heat conductivity

t J z H t J

B A

δ δ δ δ ⋅ + ⋅ = ⋅

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SLIDE 30

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Temperature Variations in Curved Flamelets

t J z H t J

B A

δ δ δ δ σ ⋅ + ⋅ = ⋅ ⋅

fresh gas products heat conductivity

t J z H t J

B A

δ δ δ δ ⋅ + ⋅ = ⋅

σ=ΣA/ΣB<1

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SLIDE 31

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Temperature Variations in Curved Flamelets

t J z H t J

B A

δ δ δ δ σ ⋅ + ⋅ = ⋅ ⋅ t J z H t J

B A

δ δ δ δ ⋅ + ⋅ = ⋅

σ=ΣA/ΣB<1

planar c u r v e d

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SLIDE 32

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Mass Fraction Variations in Curved Flamelets

t J z Y t J

A B

δ δ δ δ σ ⋅ + ⋅ = ⋅ ⋅

fresh gas products heat conductivity fresh gas products diffusivity

t J z Y t J

B A

δ δ δ δ ⋅ + ⋅ = ⋅

σ=ΣB/ΣA>1

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SLIDE 33

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Mass Fraction Variations in Curved Flamelets

fresh gas products heat conductivity fresh gas products diffusivity

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SLIDE 34

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Effect of the Lewis Number on Burning Rate in Curved Flamelets

fresh gas products heat conductivity fresh gas products diffusivity Le=κ/D<1 Le=κ/D>1

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SLIDE 35

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Effect of Molecular Diffusivity on Burning Rate in Curved Flamelets

fresh gas products diffusion of oxygen fresh gas products diffusion of hydrogen lean mixture Very rich mixture

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SLIDE 36

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Temperature Variations in Strained Flamelets

w dx T d a dx dT u + =

2 2

∫

− =

r

wdx dx dT a

r δ

2 2

dx T d a dx dT u =

ρ=const: u=−σx; v=σy

r r r

dx dT a T u =

Reaction zone: Preheat zone: ur=SL

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SLIDE 37

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Temperature Variation in Strained Flamelets

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SLIDE 38

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Mass Fraction Variation in Strained Flamelets

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SLIDE 39

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Effect of the Lewis Number on Burning Rate in Strained Flamelets

a<D (Le<1) a>D (Le>1)

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SLIDE 40

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Effect of the Lewis Number on Burning Rate in Strained Flamelets

From the paper by Law, C.K. and Sung, C.J., “Structure, aerodynamics, and geometry of premixed flames”, Progress in Energy and Combustion Science 26: 459-505 (2000).

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SLIDE 41

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Effect of the Lewis Number on Quenching of Strained Flamelets

From the paper by Law, C.K. and Sung, C.J., “Structure, aerodynamics, and geometry of premixed flames”, Progress in Energy and Combustion Science 26: 459-505 (2000).

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SLIDE 42

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Effect of the Lewis Number on Quenching of Strained Flamelets

  • Radiation heat losses
  • Finite thickness of the

reaction zone

  • Complex chemistry

Quenching strain rate depends substantially

  • n the Lewis number:

quenching is impeded when Le decreases!

From the paper by Law, C.K. and Sung, C.J., “Structure, aerodynamics, and geometry of premixed flames”, Progress in Energy and Combustion Science 26: 459-505 (2000).

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SLIDE 43

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Why does Molecular Transport Substantially Affect Premixed Turbulent Combustion at High Reynolds Number?

⊥

Σ Σ =

f L t

S U

⊥

Σ Σ =

f c t

u U

( )

q f u u c

s s P d dl w Y u & & ≤ ⋅ Σ ⋅ ⋅ Σ =

∫∫∫

flamelet

~ 1 ρ ρ

Local variations in consumption velocity Local quenching

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SLIDE 44

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Flame Instabilities

Le<1

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SLIDE 45

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Why does Molecular Transport Substantially Affect Premixed Turbulent Combustion at High Reynolds Number?

⊥

Σ Σ =

f L t

S U

⊥

Σ Σ =

f c t

u U

( )

q f u u c

s s P d dl w Y u & & ≤ ⋅ Σ ⋅ ⋅ Σ =

∫∫∫

flamelet

~ 1 ρ ρ

Local variations in consumption velocity Local quenching

Flamelet instabilities

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SLIDE 46

Department of Applied Mechanics

Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Modeling of turbulent combustion

  • f lean hydrogen-air

mixtures?