Premixed Flames: Intro. to Flame Methane Flame CH4H2O...

1

FlameStretchSpeedMeasure -1

School of Aerospace Engineering

Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman

and Ben Wilde. All rights reserved.

AE/ME 6766 Combustion

Premixed Flames: Intro. to Flame Stretch

Effects, Flame Speed Measurements

Jerry Seitzman and

Ben Wilde

Methane Flame

0

0.05

0.1

0.15

0.2

0 0.1 0.2 0.3

Distance (cm)

Mo

le F

rac

tio

n

0

500

1000

1500

2000

2500

Te

mp

era

ture

(K

)

CH4

H2O

HCO x 1000

Temperature






Overview

• Goals of this section are:

1. examine influence of non-1D behavior on flames

2. define flame stretch and stretched flames

3. study dependence of flame properties, especially

flame speed on flame stretch, and the influence of

Lewis number(s)

4. describe various methods used to experimentally

measure flame speed

2






Idealized Premixed Flame• So far we have focused on the simplest possible

premixed flame configuration– 1-dimensional, planar, adiabatic (including no

radiation), steady, no buoyancy

• product temperature Tob = Tad

• mass burning flux uuu ρuS

oL = ρbub

• Controlling processes– diffusion: thermal and mass

– reaction rates and exothermicity

• So solution, e.g., SoL, is fundamental property of

fuel/oxidizer mixture for given initial state– reactant composition

– reactant temperature and pressure

u=unburned b=burned

uu=SL ub=Sb

Premixed

ReactantsProducts






• Real flames are typically– non-adiabatic

– non-uniform and 3-dimensional

– unsteady

– occur within gravity field

• In general,– uu SL ≠ So

L

– equivalently, mass burning flux ≠ ρuS

oL

– SL can depend on velocity field and flame geometry

• Following focus is non-1d(unsteady?) flames Day et al. Combustion and Flame (2009)

rendering of 1200K isotherm from DNS of

a turbulent =0.37 H2 flame colored by

local H2 consumption rate,

Reactants

Non-Ideal Premixed Flames

𝝎fuel ~ 3 1d, adiabatic result

3






Stretched Flames: Basics

• Flames subject to aerodynamic non-uniformity and/or unsteady effects are called Stretched Flames

• Flames can be distorted, wrinkled or displaced by non-uniform or unsteady flow fields- called Hydrodynamic Stretch

• Stretched flames respond to non-uniform or unsteady flow fields they encounter by modification of the temperature and/or species profiles in the diffusive zone, changing flame propagation rate- called Flame Stretch

• Hydrodynamic stretch and flame stretch are inherently coupled concepts!

R

P






• Flame stretch causes misalignment between convective

and diffusive fluxes in flame

• Can impact many

flame properties

– propagation speed,

shape, stability

and can explain

interesting

phenomena observed in non-ideal flames

Stretched Flames: Physical Perspective

flame curvature can cause stretch

Note: stretch effects would not be observed in flames that are

infinitely thin - kinematic restoration would dominate

Reactant velocity

Diffusive fluxes

ref:

Ech

ekki

an

d M

un

ga

l,

4






Example: Bunsen Flames Tips• Non-ideal behavior observed for luminosity at tips

of Bunsen flames for different fuel-air mixtures (fuel type and equivalence ratio)

Propane(C3H8) Methane(CH4)

= 1.38 1.520.53 0.58

d=10mm

ref: Mizomoto, Asaka, Ikai and Law, Proc. Combust. Inst. 20, 1933 (1984)

reducedenhanced

enhanced

reduced






Tip Opening

• Example: propane flames with increasing rich , tip weakens until flame locally extinguished (“opens”)


= 1.07 1.321.17

1.41 1.43 1.47

ref: Mizomoto, Asaka, Ikai and Law, Proc. Combust. Inst. 20, 1933 (1984)

tip open

5






Bunsen Tip Flame

Temperature Data

ref: C.K. Law, Combustion Physics

• Curvature/stretch can cause

enhancement or reduction

in flame temperature

– compares measured Ttip to

calculated Tad

– CH4 vs. C2H4 vs. C3H8

CH4-air

C3H8-air

C2H4-air

Tad

Ttip

reduced enhancedreduced“Leaner”

“Richer”enhanced reducedreduced

trend?

(Tmax) shifts rich shifts leanno shift






• Stretch effects exist because of coupling between flame surfaces and flow fields

• Assuming the flame is thin, smooth and continuous we can treat the flame as a 3-D surface

– flame surface moves, deforms, and accelerates/ decelerates

Unburned

Burned

n

n

n

,n n x t

Stretched Flames: Geometry

6






• Consider simple case of

propagating flame

• Flame stretch rate can be defined as

normalized rate of change of flame

surface area element

– a Lagrangian quantity

– units of flame stretch are s-1,

i.e., an inverse time scale or rate

1 dA

A dt

Williams (1975)

UnburnedBurned

dA

Flame Stretch Rate Definition

(VII.14)






Influence of Flame Stretch

• Two basic cases

– positive stretch (flame in tension)

– negative stretch(flame in compression)

• Diffusion for neg. stretch

– thermal diffusion () focuses heat into reactants, enhances reaction rate and thus SL

(same for mass diffusion of radicals)

– mass diffusion of reactants away from (and products to) center streamline, can reduce[reactants], and thus reaction rate and SL

PR

P

dt

dA

A

1

like

Bunsen tip

R P

R P

R P

related to strain, curvature,dilatation

7






• Given previous sign convention for

– can relate sign of to direction from which heat flux vectors cross the sidewalls of a differential flame tube (control volume) immediately adjacent to flame sheet

– heat flux into sides of control volume negative stretch rate

– heat flux out of sides of control volume positive stretch rate

1 dA

A dt

Stretch Rate () Sign ConventionCurved flame

in uniform velocity flow

Flat flame in diverging

flow






• So we have the following diffusivities of interest– thermal diffusivity (α) of mixture

– mass diffusivity (D) in general, but recall each species has different Dij (multi-component)

• so for reactants

– Df,j (or Df,M ) of fuel

– Dox,j (or Dox,M ) of oxygen

• Two effects arise because of non-equidiffusivities

– non-unity Le

• imbalance between thermal and mass diffusivity

– differential diffusion

• imbalance between species diffusivities, e.g., fuel and oxygen

• If all Lei=1, diffusive effects tend to counterbalance

Le Effects on Stretched Flames

and Le = /D

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Non-Equidiffusive Effects

• Flame response to stretch effects is strongest in flames with Lewis numbers much different from one

• Flame response in stretched flames depends on sign of stretch rate and Lewis number

– for fixed (premixed) mixture, flame response (e.g., dSL/d) will change entirely when stretch rate changes sign (e.g., positive to negative)

– for fixed stretch rate , flame response will change entirely when Le transitions from greater than to less than some critical value

• Theory predicts and experiments confirm that equi-diffusive (Le=1) stretched flames are insensitive to the magnitude of stretch






Stretch Effects: Bunsen Flames

• Stationary, axisymmetric flame

• Stretch (negative) induced by flame curvature– assuming uniform velocity

profile exiting the tube

• Diffusive fluxes do not align with convective fluxes

• Since negative stretch here

– if thermal conduction outweighs mass diffusion then flame speed enhanced ( vs. D) SL for Le > 1

• similarly SL for Le < 1

– but also must consider differential diffusion

9






0.581.52

Reexamine Bunsen Flame Tip Results• Fuel lighter than air (e.g., CH4)

– in “preheat” zoneW

f < W

mix < W

ox

– assuming molec. wt. dominates Dij

Df,M > mix > Dox,M

Lef < 1, Leox > 1

– so thermal vs “overall” mass diffusion will have some influence, but differential diffusion will tend to make mixture leaner near tip

– < crit Ttip and local SLflame weakened

– > crit Ttip and local SLflame enhanced

Methane(CH4)

negative stretch

W

mix,”lean” ~W

N2

W

mix,”rich” <W

N2

R

P






0.531.38

Reexamine Bunsen Flame Tip Results• Fuel heavier than air (e.g., C3H8)

– in “preheat” zoneW

f >> W

ox > W

mix

– assuming molec. wt. dominates Dij

Df,M << Dox,M ~ mix

Lef >> 1, Leox ~ 1

– now differential diffusion will tend to make reactant mixture richer near tip

– > crit Ttip and local SLflame weakened

– < crit Ttip and local SLflame enhanced

Propane(C3H8)

negative stretch

R

PW

mix,”lean” ~W

N2

W

mix,”rich” >W

N2

10






Tip Opening Propane Flames• As we increase burner, diffusion effects at tip lead to

conditions that no longer can sustain a flame, e.g., too rich

• Richer propane mixture has more stretch sensitivity


= 1.07 1.321.17

1.41 1.43 1.47

max

stretch

location

at tip






Stretch Effects: Stagnation Flames• Stretch induced by flow strain

– example: stagnation flame (positively stretched)

– no flame curvature, BUT flow (velocity) field diverging

• reacting flow is decelerating, strained=a (strain rate) near centerline

– diffusion again not aligned with flow

• Examples– premixed reactants impinging on a

(stagnation) body

– premixed reactants impinging on flow moving in opposite direction (opposed jets)

Credit S. Adusumilli

du/dx =a

dv/dr = a

x

r

11






Stagnation Flame Example Results

S. Adusumilli, Effects of preheat temperature and vitiation on reaction kinetics of higher hydrocarbon fuels, 2019.

SL/S

o L

CH4-L

C3H8-L

C3H8-R

C2H4-L

Chemkin OPPDIF and USCII

• Tu=300 K– light and heavy fuels

have opposite sign slope (sensitivity) at =0.6

– ethene (MW=28) reduced sensitivity

– opposite sensitivity for propane at =0.6 and 1.4

• Tu=650 K– sensitivity to stretch

significantly reduced

– sign change of sensitivity for propane =1.4

1 atm 1 atm






1 2

( )( ) ( )( )

ba

F F

u uv n n u v n n

t1 t2t tt t

Stretch Effects: Unsteady Spherical Flames

• In general for “thin” flame, stretch is given by

• For spherical flame– flame curved, but flow velocities align with flame

surface normal; no tangential velocities

– stationary spherical flame would be stretch-less

– for unsteady spherical flame, stretch rate changes as function of radius, r=r(t); decreases with time for outwardly expanding flame

vF=local propagation velocity of flame surfaceti =tangent to flame surfacea=stretch due to tangential velocity gradients at the flame surfaceb=stretch due to unsteady flame curvature

R

P

r

(VII.15)

12






Flame Speed Corrections• For stretched flames, need to modify 1-d flame speed

to account for curvature, flow divergence effects

• For small perturbations (low stretch rates), asymptotic analysis (Markstein) leads to the following flame speed scaling

• Can be expressed in terms of a non-dimensional stretch rate called a Karlovitz number* (or stretch factor)

– and VII.16 becomes

f

o

L MaS

Markstein Length Markstein number

o

LLSS f

Ma

stretch

d-1

Ka

L

o

LL SKaMaSS KaMaSS L

o

L 1

*other Karlovitz number definitions used in turbulent combustion

(VII.16) (VII.17)

(VII.16a)

residence time within 1d unstretched laminar flame

characteristic time for flame stretchingo

L

f

o

Lf

S

S

1(VII.18)






0 0.1 0.2 0.3 0.40

1

2

Ka

L

o

LSS

Karlovitz Number Scaling

• Flame speeds of propane-air mixtures for different Ka

nearly linearscaling

Ma=Ma()

after Tseng et al., Combust. and Flame 95, 410 (1993)

KaMaSS L

o

L 1?

=

13






Markstein Number Dependence

Air/

Fuel

S crit Kamax

C3H8-8.8 1.44 0.8-1.8 0.25

C2H6-4 1.68 0.8-1.6 0.25

C2H4-2.9 1.95 0.8-1.8 0.24

H23.9 1.5 1-4.8 0.21

CH410.2 0.74 0.6-1.4 0.30

after Tseng et al., Combust. and Flame 95, 410 (1993)

Propane-Air

1 atm

Ma

crit

0 0.5 1 1.5 2

0

-2

-4

2

4

6

Correlation

Ma = 8.8(-1.44)

MaKaS

S

L

o

L 1

• What is Ma=Ma() relation?

• Simplest is linear correlation

Ma = S (crit)






Flame Speed Measurements

• How does one experimentally measure flame speeds?

• Measurements of SoL are difficult

– hard to achieve adabatic and 1-d conditions

– usually compromise and try to correct

• Various methods

– Bunsen-type burners (“simplest”)

– traveling tube

– spherically expanding flames

– soap bubbles

– flat flame burners

– stagnation flames

14






Bunsen (Tube) Burner Method

• Premixed fuel/air in cylindrical tube

– laminar

– various velocity profiles

– stationary flame when normal component of local approach velocity=SL

ref: Sébastien Ducruix

color schlieren

inner

cone

=1.05CH4/air

outer flame

(nonpremixed)

uun

SL






Bunsen (Tube) Burner Method

• Approaches

– measure , u (or un)

• u not necessarily same as uexit

• u, may not be constant (depends on exit profile)

– measure flame area, reactant volumetric flowrate

• how to identify flame surface?

– schlieren, shadow, luminosity,…?

uun

SL

uAm flameuexitL AmS

ref: Echekki and Mungal, Phys. Fluids A 2, 1523 ( 1990)

<1

particle

tracks

luminousity

flame

uexit

A

m

reactant volumetric flowrate

15






Bunsen Method: Flame Surface• Flame surface

measurement– luminous,

schlieren,shadow givedifferent Aflame

• Shadow closest to unburned region

– but not 1-d flame– stretch effects

• Luminosity corresponds to high T rxn zone

ref: Ibarreta and Sung, 3rd Joint US Section Meeting Comb. Instit.

SL SoL

Shadowgraph

Visible

Schlieren

Q

Shadowgraph

Visible

Schlieren

Q






Bunsen Method: Burned Surface Area

• Measure reaction zone area (Ab)

– from flame luminosity

• Unstretched laminar flame speed (SLo)

– flame curvature effect is small for Sb

– flame strain primarily restricted to tip

• use tall flames9 mm

Chemiluminescence image

CH4/C3H8 ~ 80:20 (vol.)

H2O/Air ~ 19% (mass)

5 atm, 650 K

F ~ 1.0

b

u

u

b

u

bb

u

o

bbo

LA

mAmSSS

ref: Kochar, Seitzman

16






Propagating Methods

• Transparent Tube

– fill tube with premix gases, ignite, watch flame propagate (make sure it is sustained propagation)

– gas moves ahead of flame front (compressed)

• uf > SL, and gases may be slightly preheated

• non-1d (boundary layer), buoyancy

• Spherical Flames

– fill closed(?) (spherical?) chamber,ignite and watch flame propagate

– unburned velocity (and p,Tu?) continuously increasing

– expanding (unsteady) flame experiences stretch ((t) ), extrapolate back to zero stretch

uf ur

dt

dRu

f

f

Rf






• Construct uniform velocity profile using porous plate, sintered metals, or small flow passages

• Burner is either water cooled or naturally cooled

• Flame can be essentiallyflat except at edges of burner

• Measurement of flamevelocity easy (uexit)

• Nonadiabatic

– measure cooling, extrapolate to Q=0

– or measure T profile through flame and compare with computation (works for low pressures, thick flames)

Flat Flame Burner

ref: Glassman

SL

Q

flatflame.com

17






Stagnation Flames

• Opposed

jets or jet and

stagnation

plate

• Nearly flat flames (no curvature),

but with aerodynamic “strain” due

to deceleration caused by

stagnation plane

– extrapolate to zero-strain to

obtain SLo

Flame

Stagnation plane

Flame

Stagnation planeStagnation plug

Nozzle

Stagnation plug

Nozzle

Stagnation plug

Nozzle

Stagnation plug

Nozzle

0

0.4

0.8

1.2

1.6

2

1 3 5 7 9 11

Distance from stagnation plane X (mm)

Axia

l ve

locity (

m/s

)

Su K=-du/dx

Plug

Nozzle

U

X

D

L Flame

ref: J. Natarajan PhD thesis

9 mm

Flo

w d

irec

tio

n

Stagnation plug

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