Theoretical Investigation of Unsteady Flow Interactions with

a Planar Flame

Tim Lieuwen and Ben T. Zinn

Schools of Mechanical and Aerospace Engineering

Georgia Institute of Technology

Atlanta, GA

* Research Supported by AGTSR and AFOSR; Dr. Dan Fant and Dr. Mitat Birkan, Contract Monitors

Acoustic - Flame Interactions Play an Important Role in the Unsteady Behavior of Many

Combustion Systems• Combustion Instabilities

• Pulse Combustion

• Combustion Noise

Premixed Fuel + Air

Past Investigations of Low Frequency Acoustic - Flame

Interactions• Interaction of flame sheet with normally impinging acoustic

disturbance– B.T. Chu, Fourth Symposium on Combustion, 1953.

• Interaction of plane wave with the flame in realistic combustor geometries– Marble and Candel, 17th Symposium on Combustion, 1978

– Yang and Culick, Comb. Sci. and Tech., Vol. 45, 1986

– Fleifel et al., Comb. and Flame, Vol. 106, 1996

– Dowling, J. Fluid Mech., Vol. 346, 1997

Chu’s Investigated Geometry

Typical Investigated Geometry in Other Studies

• Infinitely long flame

• Normal Disturbances

• Accounts for flame response

• Finite flame

• Oblique Disturbances

• Wrinkled flame

• Multidimensional Acoustic field

• Neglect vorticity production

• Neglect flame speed response

Investigated Geometry

Cold Reactants

Hot Products

Incident AcousticWave

Reflected WaveTransmitted

Wave

Convected Vorticaland EntropyDisturbances

Flame Front

Xf (y,t)

Assumptions

• Thin, infinitely long flame

• Uniform, isentropic, low Mach number mean flows

• Molecular transport effects neglected

• Time harmonic, plane wave disturbances– Results independent of frequency

Equations

Mass: 0ut

(1)

Momentum: puut

u

(2)

Energy: 0sut

s

(3)

Unsteady Solutions

P r e s s u r e : tiiknyxikxik ee)eDeD('p

x V e l o c i t y C o m p o n e n t :

tiiknyM/)nM1(ikxv

y

xxikxxikx ee)eV)nM1(

nM e

c

nDe

c

nD('u xy

y V e l o c i t y C o m p o n e n t :

tiiknyM/)nM1(ikxv

xikyxikyee)eVe

c

nDe

c

nD('v xy

D e n s i t y :

tiiknyM/)nM1(ikxs

xik2

xik2

ee)eec

De

c

D(' xy

Matching Conditions

M a s s : 2211 SS

N o r m a l M o m e n t u m : 2222

2111 SpSp

T a n g e n t i a l M o m e n t u m : 0y

X)uu(vv f

2121

E n e r g y : )2

uuh(S)

2

uuh(S 22

22211

111

Matching Conditions

M a s s : 2

2

2

2

1

1

1

1

S

'S'

S

'S'

)

N o r m a l M o m e n tu m : )c

'u

c

'u(M

p

'p

p

'p

1

1

2

21x

21

T a n g e n t i a l M o m e n tu m : 0c

'unM)1(

c

'v

c

'v

1

11x

2

2

1

1

E n e r g y : 0)S

'S)1(

p

'p)1(

p

'p(M

c

'u

c

'u

1

1121x

1

1

2

2

F la m e P o s i t i o n :1y

1

11x

1

1

f nM1

S

'SM

c

'u

i'kX

Flame Response

• Flame response enters through flame speed, S1

– S1=f(p1, T1)

• Upstream Conditions Isentropic:

• Typical values of for laminar hydrocarbon flames: 0.4 -0.5

1

12

11

1

1

T

'T

p

'p

S

'S

p

'p

p

'p)

1(

S

'S 1121

1

1

Solution

• Get 5 linear, algebraic equations for 5 unknown amplitudes:

1) Reflected acoustic wave

2) Transmitted acoustic wave

3) Vortical wave

4) Entropy wave

5) Flame position

Velocity Vectors Phase: 0 degrees

-25 -20 -15 -10 -5 0 5 10 15 20 250

5

10

15

20

25

Velocity Vectors Phase: 90 degrees

-25 -20 -15 -10 -5 0 5 10 15 20 250

5

10

15

20

25

Velocity Vectors Phase: 180 degrees

-25 -20 -15 -10 -5 0 5 10 15 20 250

5

10

15

20

25

Velocity Vectors Phase: 270 degrees

-25 -20 -15 -10 -5 0 5 10 15 20 250

5

10

15

20

25

-6%

-5%

-4%

-3%

-2%

-1%

0%

1%

2%

0 50 100 150

Angle of Incidence

No

rma

lized

Aco

us

tic

En

erg

y P

rod

uc

tio

n

Incident Disturbance Amplified

Incident Disturbance Damped

Effect of Incident Angle on Production of Acoustic Energy - No Flame Speed Response

Normalized Energy Production

Reflected + Transmitted - Incident Energy

Incident Energy=

-6%

-4%

-2%

0%

2%

4%

6%

8%

0 50 100 150

Angle of Incidence

No

rmal

ized

Aco

ust

ic E

ner

gy

Pro

du

ctio

n

=0

=0.5

=1Incident Disturbance Amplified

Incident Disturbance Damped

Effect of Flame Response on Production of Acoustic Energy

p

'p

S

'S 1

1

1

Effect of Vorticity ProductionNo Flame Speed Response

-6%

-4%

-2%

0%

2%

4%

6%

8%

10%

0 50 100 150

Angle of Incidence

No

rma

lized

Aco

us

tic

En

erg

y P

rod

uc

tio

n Vortical Coupling Ignored

Vortical Coupling Correctly Accounted for

Mechanisms of Acoustic Damping by Flame

• Excitation of vortical mode acts as important source of acoustic damping– For flame speed Mach number = 0.005, up to

14% of incident acoustic energy is dissipated– Same amount of acoustic damping provided by

exit nozzle of combustor with ambient mean flow Mach number = 0.03

Important features of Planar Acoustic - Flame Interactions

• In order to determine the acoustic energy production by a flame, must account for:– Excitation of Vorticity– Flame Speed Fluctuations

• All acoustic energy produced by unsteady enthalpy flux through flame– Flame area fluctuations have no effects

Future Work

• What are additional effects that occur when non planar flames or disturbances interact?

• Effects of flame response due to flame curvature, stretch, etc.

• Incorporate results into combustion stability models

Supporting Slides

Mechanism of Acoustic Energy Production

Mechanism of Acoustic Energy Production by Flame

• Unsteady heat release produced by unsteady enthalpy flux through flame

• Energy added to acoustic field when heat release and pressure are in phase

c1111c11 h)'SS'('qhSq

c1111111 h)'S'pS''p('q'p