Application of Boundary Element Methods in Modeling Multidimensional Flame- Acoustic Interactions...
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![Page 1: Application of Boundary Element Methods in Modeling Multidimensional Flame- Acoustic Interactions Tim Lieuwen and Ben T. Zinn Depts. Of Mechanical and.](https://reader036.fdocuments.us/reader036/viewer/2022072005/56649cea5503460f949b5960/html5/thumbnails/1.jpg)
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
![Page 2: Application of Boundary Element Methods in Modeling Multidimensional Flame- Acoustic Interactions Tim Lieuwen and Ben T. Zinn Depts. Of Mechanical and.](https://reader036.fdocuments.us/reader036/viewer/2022072005/56649cea5503460f949b5960/html5/thumbnails/2.jpg)
Flame - Acoustic Interactions
Combustion Noise Pulse Combustors Combustion Instabilities
F lam eA coustic D istu rbances
F u e l + A ir
![Page 3: Application of Boundary Element Methods in Modeling Multidimensional Flame- Acoustic Interactions Tim Lieuwen and Ben T. Zinn Depts. Of Mechanical and.](https://reader036.fdocuments.us/reader036/viewer/2022072005/56649cea5503460f949b5960/html5/thumbnails/3.jpg)
Flame - Acoustic Interactions
Visualization taken with Mr. Hector Torres
7
3
1
5
75
3
1
1
Premixed Fuel+Air
P’
time
![Page 4: Application of Boundary Element Methods in Modeling Multidimensional Flame- Acoustic Interactions Tim Lieuwen and Ben T. Zinn Depts. Of Mechanical and.](https://reader036.fdocuments.us/reader036/viewer/2022072005/56649cea5503460f949b5960/html5/thumbnails/4.jpg)
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
![Page 5: Application of Boundary Element Methods in Modeling Multidimensional Flame- Acoustic Interactions Tim Lieuwen and Ben T. Zinn Depts. Of Mechanical and.](https://reader036.fdocuments.us/reader036/viewer/2022072005/56649cea5503460f949b5960/html5/thumbnails/5.jpg)
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
![Page 6: Application of Boundary Element Methods in Modeling Multidimensional Flame- Acoustic Interactions Tim Lieuwen and Ben T. Zinn Depts. Of Mechanical and.](https://reader036.fdocuments.us/reader036/viewer/2022072005/56649cea5503460f949b5960/html5/thumbnails/6.jpg)
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 :
![Page 7: Application of Boundary Element Methods in Modeling Multidimensional Flame- Acoustic Interactions Tim Lieuwen and Ben T. Zinn Depts. Of Mechanical and.](https://reader036.fdocuments.us/reader036/viewer/2022072005/56649cea5503460f949b5960/html5/thumbnails/7.jpg)
Results
No flame response to perturbations
![Page 8: Application of Boundary Element Methods in Modeling Multidimensional Flame- Acoustic Interactions Tim Lieuwen and Ben T. Zinn Depts. Of Mechanical and.](https://reader036.fdocuments.us/reader036/viewer/2022072005/56649cea5503460f949b5960/html5/thumbnails/8.jpg)
Results
With Flame Response to Perturbations
![Page 9: Application of Boundary Element Methods in Modeling Multidimensional Flame- Acoustic Interactions Tim Lieuwen and Ben T. Zinn Depts. Of Mechanical and.](https://reader036.fdocuments.us/reader036/viewer/2022072005/56649cea5503460f949b5960/html5/thumbnails/9.jpg)
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)
![Page 10: Application of Boundary Element Methods in Modeling Multidimensional Flame- Acoustic Interactions Tim Lieuwen and Ben T. Zinn Depts. Of Mechanical and.](https://reader036.fdocuments.us/reader036/viewer/2022072005/56649cea5503460f949b5960/html5/thumbnails/10.jpg)
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
![Page 11: Application of Boundary Element Methods in Modeling Multidimensional Flame- Acoustic Interactions Tim Lieuwen and Ben T. Zinn Depts. Of Mechanical and.](https://reader036.fdocuments.us/reader036/viewer/2022072005/56649cea5503460f949b5960/html5/thumbnails/11.jpg)
Conclusions
Acoustic velocity field near flame two dimensional
Acoustic pressure reasonably one dimensional
BEM methods useful tool for modeling flame acoustic interactions
![Page 12: Application of Boundary Element Methods in Modeling Multidimensional Flame- Acoustic Interactions Tim Lieuwen and Ben T. Zinn Depts. Of Mechanical and.](https://reader036.fdocuments.us/reader036/viewer/2022072005/56649cea5503460f949b5960/html5/thumbnails/12.jpg)
Future Work
Flame Dynamics Mean Flow Effects
– May be significant in determining energy flux
Time Domain Formulation– Linear Acoustics / Nonlinear Flame
Dynamics