JetFlame -1 School of Aerospace Engineering Copyright © 2004-2005 by Jerry M. Seitzman. All rights...

AE/ME 6766 CombustionJetFlame -1

School of Aerospace Engineering

Copyright © 2004-2005 by Jerry M. Seitzman. All rights reserved.

Laminar Nonpremixed CombustionLaminar Nonpremixed Combustion




Laminar Jet FlamesLaminar Jet Flames

• Reacting jet will be “similar” to nonreacting/mixing flow except1. Fuel and oxidizer must react at some f2. Heat release = constant probably not a good

assumption– buoyancy effects (body force term)– Thermal expansion driven flow fields

3. Must include diffusion of products (and intermediates/radicals)

4. Now there will be source and sink terms in the species conservation (and energy) equations




Diffusion Flame – Fast KineticsDiffusion Flame – Fast Kinetics• Where will flame “sit” in terms of ?• For Da >> 1 (chem small; very fast chemistry)

– reaction zone should be very thin• as soon as fuel and oxidizer meet, they will react

• Consider 1-d diffusion of fuel into air

>>1 <<1

fuel oxid.

<1

<<1>>1fuel oxid.

>1• For fast (infinite rate), single-step reaction, flame

sits at stoichiometric surface: Flame Sheet Approx.

>>1 <<1

fuel oxid.

=1




Jet Flame DescriptionJet Flame Description

• Overventilated vs. underventilated flames– overall excess fuel, underventilated

– overall excess air, overventilated

(always the case for open air flame)Fm

Oxm

overventilated

under-ventilated

stoichOxFOxF mmmm

stoichOxFOxF mmmm




• Fuel, oxidizer diffuse toward flame sheet

• Products (T) diffuseaway

Jet Flame DescriptionJet Flame Description

r

2R

x

x=x1

x=x2

flame sheet

r

1

x

1

x2

f

• Flame tip– final fuel

burnout– buoyancy

r=0

YOx

YP

YF

x1

YOx

YP

LfFlameLength

YF

(f=fstoich)

• Mixture fraction– continuous




Mixture Fraction ContoursMixture Fraction Contours• With no heat release, flame would follow fstoich

contour from nonreacting solution

x

r

f




Historical DevelopmentHistorical Development• Burke & Schumann (1928)

– “classical” analytic solution(Lewis&von Elbe, Kuo)

– assumed ux=const, ur=0 • so mom. equation not needed

(can’t account for buoyancy)– assumed flame sheet, single D– reasonable results for Lf of circular flames

• Roper (1977)– removed ux=const. limitation

– results improved for buoyant and non-circular jets

• Numerical solutions (e.g., Kee & Miller, AIAA J. 16,1978)– can include finite rate kinetics, differential diffusion

FmOxm




Conservation EquationsConservation Equations

• Examine conservation equations for simplest case

• Assumptions– as for nonreacting case: laminar, steady,

axisymmetric, quiescent/infinite reservoir, Fickian diffusion, no axial diffusion (const)

– for flame: normal thermal diffusion, no radiative transfer, negl. viscous dissipation, constant pressure, flame sheet approx., Le=1

• Mass 01

rx urrr

ux

(1)




Conservation EquationsConservation Equations• Axial momentum

gr

ur

rruur

rruur

xrx

xrxx

111

axial conv. radial conv. radial diffusionbody force(buoyancy)

(2)

• Species/Energy– next we could write 2 species conservation eq’ns.

• e.g., YF, YOx with YP=1YFYOx

– energy equation in terms of T– BUT run into problems with boundary conditions

(at flame)




Flame Boundary ConditionsFlame Boundary Conditions• Example

– species conservation

ii

irix mr

YDr

rrYur

rrYur

xr

111

axial conv. radial conv. radial diffusionsource/sink

j

i

j

i

j

i

ijj

iii W

W

m

mnn

– chemical term is 0 everywhere except at flame sheet– so flame is boundary between 2 solutions

(inside/outside) but don’t know where the flame is!• all we know is the mass fluxes into the flame

governed by stoichiometric proportions

• Same problem for energy equation in terms of T




Conserved ScalarsConserved Scalars

• Solution to this problem - write equations in terms of scalars that have no sources or sinks in the flow– scalar that “exists” on both sides of flame and whose

“integral” is constant (like mass flow rate of jet fluid in nonreacting case)

• Examples

Z Yi ij

j

N

j

1

ij = mass proportion of element i in species j

16/44, CHH

– total enthalpy, hsens+hchem, if negligible radiation, viscous dissipation, body force work(+ no conduction to bodies)

– mixture fraction, f– elemental (atom)

mass fraction




Conserved Scalar EquationsConserved Scalar Equations

• Species Mixture fraction

– only need 1 “species” equation to determine composition (flame sheet approximation)

• e.g., if f > fstoich (inside flame) only fuel and products, YF + YP = 1

0

r

fDr

rfur

rfur

x rx

0

r

hr

rhur

rhur

x rx

Le=1, =D

(3)

(4)

• EnergyTotal enthalpy

0

r

hDr

rhur

rhur

x rx




SummarySummary

• So we have four conservation equations with no source/sink terms– except in momentum eq’n. if body force important

• buoyancy effects

– equations similar except different diffusion coeffients (=D, )

• Schmidt number effects (Sc/D)

• Next normalize (2) – (4) and B.C




NormalizationNormalization

• Self-similar type solution(like nonreacting case)

Rxx *

r

2R

xRrr *

exx uuu *

err uuu *

eu

e *

,,

,*

oxeF

ox

hh

hhh

=0 in pure ambient

=1 in pure jet fluid

,,

,

oxeF

ox

yy

yyfox

oxox

FFF Y

W

WYy

P

PP

FFF Y

W

WYf

stoichffraction of product mass that comes from “fuel”

– same normalization as f (01)




Boundary ConditionsBoundary Conditions

• General axisymmetric jet

– @ r* = 0, any x*

– @ r* = – @ x* = 0, r* > 1

• For top hat/uniform exit profile

– @ x* = 0, r* 1

0* ru0 r

** ,, hfux

0

1

0 r*

1

x*




General Normalized Eq’n.General Normalized Eq’n.

• In terms of generalized variable,

*

*

*

***

*

***

*

1

rRer

rur

rur

x rx

**

2

*

eu

gRr

01

Sc

axial momentum

species/energy

=1/Fr, Froud #

Ru

Re eelocal

if Fr << / buoyancy controlled

• Since we used Le=1, h*=h*( f )– same for axial velocity if Sc=1 and negl. buoyancy

• Still need to relate *, h* to p, T




State RelationshipsState Relationships

• Virial state eq.

TR

Wp

h iY

f

FstoichF

PstoichF

YfYYfYf

1

stoichstoichF fffY 1

Need

WT ,to get 1 ii WY

0oxY

stoichP ffY 11

stoichP ffY 0FY stoichox ffY 1

cp• Yi=?

– for f > fstoich

– for f < fstoich




State RelationshipsState Relationships– for f = fstoich

fh *

1PY

,,, oxeFox hhfhh

YF

YoxYP

Simple, linear relations for•flame sheet approx. •Le=1•T if cp=constant

Flame broadening

• h=?

Yi

f

1

1fst

f

h

1fst

for pure fuel jet, pure ox ambient

hF,e

hox,




Summary of EquationsSummary of Equations

• Conservation equations for simple jet

• Mass

• Momentum (axial)

• Species, Energy (Le=1)

01 ***

**

**

*

rx urrr

ux

*

*

*

***

*

***

*

1

rRer

rur

rur

x j

rx

**

2

*

eu

gRr

=1/Fr, Froud #

01

*

*

*

***

*

***

*

rScRer

rur

rur

x j

rx




Solution to determine Solution to determine (r,x)(r,x)

• Start with simplest case

• Sc=1 (Le=1), Constant Density, Const. “Properties” , =D = = const– then all conservation equations become

– which gives identical solution as for nonreacting jet

01

*

*

*

**

*

**

*

rRer

rur

rur

x j

rx

2222

22*

6431

83

41

8

3111

xrReReR

xh

ReR

xf

ReR

x

u

u

jjjje

x




Solutions (Constant Density)Solutions (Constant Density)• Flame Location

– at f = fstoich

– for diluted oxygen,pure fuel

x

r

fstoich

stoich.oxygen/ fuel mass ratio

,

1

1

ox

stoichstoich

YFO

f

Discussion: why?

f=0

f=1– fstoich if you dilute oxidizer (flame gets bigger)

– similarly fstoich as dilute fuel (flame gets smaller)




Solutions (Constant Density)Solutions (Constant Density)• Flame Length

– use flame width

– when rflame=0

Discussion: why?

x

r

f

f=0

f=1

2121

18

31

3

8

x

R

f

Re

Rex

ffr

stoich

j

j

stoichflame

e

stoichstoich

jfflame

Q

ff

RReLx

1

8

3

8

3

stoich

ef f

DQL Lf for Qe/D or fstoich (dilute ox.)

volumetric flowrate

function (p) jf mL – for given mass flowrate• reduce combustor length by having distributed nozzles




Solutions (Variable Density)Solutions (Variable Density)• Fay extended Burke-Schumann approach

– still Sc=Le=1 but with momentum equation, const– limited to Fr large (no buoyancy)

furef

Fconstff I

LLref

12,, = density in cold oxidizer

f= density at flame

F= density in cold fuel

Iu= mometum integral (>1)

constff LL ,

• Roper– includes buoyancy (see Turns)

/f /ref Iu(/f)1 1 13 2 2.45 3 3.77 4 5.29 5 7.2

after Turns Table 9.2




Problems with the Mixture Fraction Problems with the Mixture Fraction ApproachApproach

• Multistep Chemistry– even with fast chemistry (equilibrium chemistry)

will still have fuel and oxidizer coexisting– changes fY, h state relations - > use elemental

(atom) conserved scalars

• Finite Rate Chemistry– solution will depend on chemical time scales and

flow time scales (diffusion, residence time)

• Differential diffusion




Scalar DissipationScalar Dissipation

• Definition

– units of 1/s

• Essentially inverse of characteristic diffusion time in the flame

• Non zero scalar dissipation causes departures from equilibrium– Large enough values lead to flame extinction

2

2

ix

fD




also harder for H2 to diffuse against high velocities to get to flame

3.3-3.3 ft/s

16.4-16.4 ft/s

0

500

1000

1500

2000

2500

3000

0 0.02 0.04 0.06 0.08 0.1

Mixture Fraction (f )

T (

K)

0

1000

2000

3000

4000

5000

T (

R)

Finite Rate Kinetic EffectsFinite Rate Kinetic Effects• Can see effect of Da=flow/chem in opposed jet flow

– higher velocity gives less flow time (time to react)

ufuel

uoxEquilibrium

H2/airSTP

fstoichf=1

f=0




Partially Premixed CombustionPartially Premixed Combustion

• Practical systems involve combination of nonpremixed and premixed combustion– partially premixed combustion– stratified combustion

• Example, premixed flamesusually anchor diffusion flames– finite time for reactions

required– triple point flame

airair fuel

f=fstoich

lean premixed

richpremixed

SL

diffusion flame




Nonpremixed Lifted FlamesNonpremixed Lifted Flames

• Higher flowrate, longer distance to ignition point– less diffusion flame, more premixed

• As get to too high a jet velocity– can reach point where either

nonflammable– or even stoichiometric flame

too slow to propagateblowoff of nonpremixed flame

airair fuel

f=fstoich

lean premixed

rich premixed




0 5 10 15 20 25 30 35

Primary Particle Diameter, d (nm)

0

10

20

30

40

50

60

70

80

90

Hei

gh

t A

bo

ve

Bu

rner

, H

AB

(m

m)

-6 -3 0 3 6Distance from Center (mm)

0

2

4

6

8

10S

oo

t fv (

pp

m)

60 mm

20 mm

40 mm-6 -3 0 3 6

Distance from Center (mm)

0

2

4

6

8

10-6 -3 0 3 6

Distance from Center (mm)

0

2

4

6

8

10

Radius, R (mm)0-3-6 3 6

So

ot

Vo

lum

e F

ract

ion

(p

pm

)

Primary Particle Diameter (nm)

0

68

24

0

68

24

0

68

24

flamesheet

airair fuel

Soot in Diffusion FlamesSoot in Diffusion Flames• Typical results, ethylene-air




Soot – What is it?Soot – What is it?• Mostly graphitic carbon• Nucleation growth

dehydrogenation graphitization

• Branchy aggregates of primary particles

• Primary particle diameter dp

dp

500 nm

5 nm




Soot FormationSoot Formation• Soot primarily forms

due to “heating” (pyrolysis) of HC fuel species in oxygen deficient regions

• Large ring HC condense

• Particles grow and agglomerate

• Soot oxidizes in high T, oxygen regions




Soot EmissionsSoot Emissions• So soot primarily produced in regions of

– “high” fuel concentration (less oxidizer: O2, OH, ...)– high temperature (promotes pyrolysis and growth)

• Soot oxidized in regions of– high temperature– high oxidizer concentration

• So most soot made in combustor is subsequently destroyed (oxidized) unless– rich region remains unmixed– gases cooled (mixing, walls, soot radiation)

JetFlame -1 School of Aerospace Engineering Copyright © 2004-2005 by Jerry M. Seitzman. All rights...

Documents

Transcript of JetFlame -1 School of Aerospace Engineering Copyright © 2004-2005 by Jerry M. Seitzman. All rights...