Application of Boundary Element Methods in Modeling

Multidimensional Flame-Acoustic Interactions

Tim Lieuwen and Ben T. ZinnDepts. Of Mechanical and Aerospace Engineering

Georgia Institute of TechnologyAtlanta, GA 30318

20th World Conference on the Boundary Element MethodOrlando, Fl., Aug. 19-22, 1998

Flame - Acoustic Interactions

Combustion Noise Pulse Combustors Combustion Instabilities

F lam eA coustic D istu rbances

F u e l + A ir

Flame - Acoustic Interactions

Visualization taken with Mr. Hector Torres

7

3

1

5

75

3

1

1

Premixed Fuel+Air

P’

time

Goal of Study

Develop relatively simple tool capable of semi-quantitative analysis of flame acoustic interactions

Develop insight to suggest simplifications for analytical approaches to problem

Approach

Noting that in typical systems– Discrepancy between acoustic and flame length scales

• Acoustic Wavelength ~ 1 m

• Flame Thickness ~ 0.1- 1 mm

– Mach Numbers typically low• e.g. gas turbine combustors, M~0.04

– Nearly Isothermal flow except for rapid heating near flame

Approach

0'pk'p 2c

2 0'pk'p 2h

2 0)'p()'p(

'q)p/)1(()'u()'u(

F la m e

R e g io n o f M u ltid im e n s io n a lA c o u st ic M o tio n s

H o t C o m b u stio nP ro d u cts

C o ldR e a c ta n ts

In c id e n tW a v e

R e fle c te dW a v e

Tra n sm itte dW a v e

Solve Wave E qn . In “C old” R eg ion

U sing B E M

Solve Wave E qn . In “H ot” R eg ion

U sing B E M

M atch So lutions A cross flam e R eg ion

0'pk'p 2c

2 0'pk'p 2h

2 0)'p()'p(

'q)p/)1(()'u()'u(

M o m e n tu m B ala n ce

E n erg y B alan ce :

Results

No flame response to perturbations

Results

With Flame Response to Perturbations

Results

Ratio of transverse and axial velocity component over the flame surface

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x/Lflame

|Vy|

/|V

x|

Area Discontinuity and Flame(i.e., temperature jump)

Area Discontinuity (No Flame)

Results

Comparison of magnitude of the acoustic pressure along the combustor wall and flame surface

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

0 0.5 1 1.5 2 2.5

X/Lflame

No

rmal

ized

Pre

ssu

re A

mp

litu

de

With Oscillating Heat Release

Passive Flame

Pressure at flame surface

Pressure along combustor wall

Conclusions

Acoustic velocity field near flame two dimensional

Acoustic pressure reasonably one dimensional

BEM methods useful tool for modeling flame acoustic interactions

Future Work

Flame Dynamics Mean Flow Effects

– May be significant in determining energy flux

Time Domain Formulation– Linear Acoustics / Nonlinear Flame

Dynamics