Fractal analysis is undertaken to characterize flame surface fluctuations on an unconfined turbulent premixed flame and the resulting far-field acoustics fluctuations. Results indicate that combustion noise is monofractal and is characterized by an anticorrelated structure with a Hurst exponent less than 0.5. The anticorrelated nature was identified in the pressure fluctuations as well as flame surface fluctuations for small time-scales. Additionally, results suggest that flame surface fluctuations are multifractal for large time scales. The calculated Hurst exponent increases noticeably with the equivalence ratio and decreases slightly with Reynolds number for the investigated operating conditions. Variation in the Hurst exponent for combustion noise data is compared with a case study of synthetic fluctuations comprised of linear combinations of white and 1/f2 noise. These results provide a more detailed characterization of the temporal structure of flame surface fluctuations and resulting noise emission from turbulent premixed flames than is presently known.

References

References
1.
Dowling
,
A. P.
, and
Mahmoudi
,
Y.
,
2015
, “
Combustion Noise
,”
Proc. Combust. Inst.
,
35
(
1
), pp.
65
100
.
2.
Giammar
,
R. D.
, and
Putnam
,
A. A.
,
1970
, “
Combustion Roar of Turbulent Diffusion Flames
,”
ASME J. Eng. Power
,
92
(
2
), p.
157
.
3.
Strahle
,
W. C.
,
1978
, “
Combustion Noise
,”
Prog. Energy Combust. Sci.
,
4
(
3
) pp.
157
176
.
4.
Ducruix
,
S.
,
Schuller
,
T.
,
Durox
,
D.
, and
Candel
,
S.
,
2003
, “
Combustion Dynamics and Instabilities: Elementary Coupling and Driving Mechanisms
,”
J. Propul. Power
,
19
(
5
), pp.
722
734
.
5.
Chakravarthy
,
S. R.
,
Sampath
,
R.
, and
Ramanan
,
V.
,
2016
, “
Dynamics and Diagnostics of Flame–Acoustic Interactions: A Review
,”
Combust. Sci. Technol.
, 189(3), pp. 395–437.
6.
Morgans
,
A. S.
, and
Duran
,
I.
,
2016
, “
Entropy Noise: A Review of Theory, Progress and Challenges
,”
Int. J. Spray Combust. Dyn.
,
8
(
4
), pp.
285
298
.
7.
Strahle
,
W. C.
,
1971
, “
On Combustion Generated Noise
,”
J. Fluid Mech.
,
49
(
2
), pp.
399
414
.
8.
Chiu
,
H.
, and
Summerfield
,
M.
,
1974
, “
Theory of Combustion Noise
,”
Acta Astronaut.
,
1
(
7–8
), pp.
967
984
.
9.
Peters
,
N.
, and
Franke
,
C.
,
1990
,
The Fractal Concept of Turbulent Flames
,
Springer
,
Berlin
, pp.
40
50
.
10.
Clavin
,
P.
, and
Siggia
,
E. D.
,
1991
, “
Turbulent Premixed Flames and Sound Generation
,”
Combust. Sci. Technol.
,
78
(
1–3
), pp.
147
155
.
11.
Strahle
,
W. C.
,
1985
, “A More Modern Theory of Combustion Noise,” Recent Advances in the Aerospace Sciences,
Springer
,
Boston, MA
, pp.
103
114
.
12.
Mahan
,
J. R.
,
1984
, “
A Critical Review of Noise Production Models for Turbulent, Gas-Fueled Burners
,” National Aeronautics and Space Administration, Washington, DC, Report No.
NASA-CR-3803
. https://ntrs.nasa.gov/search.jsp?R=19840018316
13.
Price
,
R.
,
Hurle
,
I.
, and
Sugden
,
T.
,
1969
, “
Optical Studies of the Generation of Noise in Turbulent Flames
,”
Symp. (Int.) Combust.
,
12
(
1
), pp.
1093
1102
.
14.
Shivashankara
,
B. N.
,
Strahle
,
W. C.
, and
Handley
,
J. C.
,
1975
, “
Evaluation of Combustion Noise Scaling Laws by an Optical Technique
,”
AIAA J.
,
13
(
5
), pp.
623
627
.
15.
Kotake
,
S.
, and
Takamoto
,
K.
,
1987
, “
Combustion Noise: Effects of the Shape and Size of Burner Nozzle
,”
J. Sound Vib.
,
112
(
2
), pp.
345
354
.
16.
Rajaram
,
R.
, and
Lieuwen
,
T.
,
2009
, “
Acoustic Radiation From Turbulent Premixed Flames
,”
J. Fluid Mech.
,
637
, pp.
357
385
.
17.
Nawroth
,
H.
, and
Paschereit
,
C. O.
,
2015
, “
Effects of Shear Layer Manipulation on Noise Emissions of a Turbulent Jet Flame
,”
AIAA
Paper No. 2015-0303.
18.
Candel
,
S.
,
Durox
,
D.
,
Ducruix
,
S.
,
Birbaud
,
A.-L.
,
Noiray
,
N.
, and
Schuller
,
T.
,
2009
, “
Flame Dynamics and Combustion Noise: Progress and Challenges
,”
Int. J. Aeroacoustics
,
8
(
1
), pp.
1
56
.
19.
Wäsle
,
J.
,
Winkler
,
A.
, and
Sattelmayer
,
T.
,
2005
, “
Spatial Coherence of the Heat Release Fluctuations in Turbulent Jet and Swirl Flames
,”
Flow, Turbul. Combust.
,
75
(
1–4
), pp.
29
50
.
20.
Hirsch
,
C.
,
Wäsle
,
J.
,
Winkler
,
A.
, and
Sattelmayer
,
T.
,
2007
, “
A Spectral Model for the Sound Pressure From Turbulent Premixed Combustion
,”
Proc. Combust. Inst.
,
31
(
1
), pp.
1435
1441
.
21.
Swaminathan
,
N.
,
Xu
,
G.
,
Dowling
,
A. P.
, and
Balachandran
,
R.
,
2011
, “
Heat Release Rate Correlation and Combustion Noise in Premixed Flames
,”
J. Fluid Mech.
,
681
, pp.
80
115
.
22.
Gouldin
,
F.
,
Hilton
,
S.
, and
Lamb
,
T.
,
1989
, “
Experimental Evaluation of the Fractal Geometry of Flamelets
,”
Symp. (Int.) Combust.
,
22
(
1
), pp.
541
550
.
23.
Strahle
,
W. C.
, and
Jagoda
,
J. I.
,
1989
, “
Fractal Geometry Applications in Turbulent Combustion Data Analysis
,”
Symp. (Int.) Combust.
,
22
(
1
), pp.
561
568
.
24.
North
,
G.
, and
Santavicca
,
D.
,
1990
, “
The Fractal Nature of Premixed Turbulent Flames
,”
Combust. Sci. Technol.
,
72
(
4–6
), pp.
215
232
.
25.
Santavicca
,
D. A.
,
Liou
,
D.
, and
North
,
G. L.
,
1990
, “
A Fractal Model of Turbulent Flame Kernel Growth
,”
SAE
Paper No. 900024.
26.
Strahle
,
W. C.
,
1991
, “
Turbulent Combustion Data Analysis Using Fractals
,”
AIAA J.
,
29
(
3
), pp.
409
417
.
27.
Kabiraj
,
L.
,
Saurabh
,
A.
,
Nawroth
,
H.
, and
Paschereit
,
C. O.
,
2015
, “
Recurrence Analysis of Combustion Noise
,”
AIAA J.
,
53
(
5
), pp.
1199
1210
.
28.
Kabiraj
,
L.
,
Saurabh
,
A.
,
Nawroth
,
H.
,
Paschereit
,
C. O.
,
Sujith
,
R. I.
, and
Karimi
,
N.
,
2016
,
Recurrence Plots for t He Analysis of Combustion Dynamics
,
Springer International Publishing
,
Cham, Switzerland
, pp.
321
339
.
29.
Prasad
,
R. R.
, and
Sreenivasan
,
K. R.
,
1990
, “
The Measurement and Interpretation of Fractal Dimensions of the Scalar Interface in Turbulent Flows
,”
Phys. Fluids A: Fluid Dyn.
,
2
(
5
), p.
792
.
30.
Sreenivasan
,
K. R.
,
1991
, “
Fractals and Multifractals in Fluid Turbulence
,”
Annu. Rev. Fluid Mech.
,
23
(
1)
, pp.
539
604
.
31.
Kantelhardt
,
J. W.
,
Koscielny-Bunde
,
E.
,
Rego
,
H. H.
,
Havlin
,
S.
, and
Bunde
,
A.
,
2001
, “
Detecting Long-Range Correlations With Detrended Fluctuation Analysis
,”
Phys. A: Stat. Mech. Appl.
,
295
(
3–4
), pp.
441
454
.
32.
Arnold
,
J. S.
,
1972
, “
Generation of Combustion Noise
,”
J. Acoust. Soc. Am.
,
52
(
1A
), p.
5
.
33.
Ramachandra
,
M. K.
, and
Strahle
,
W. C.
,
1983
, “
Acoustic Signature From Flames as a Combustion Diagnostic Tool
,”
AIAA J.
,
21
(
8
), pp.
1107
1114
.
34.
Nair
,
V.
, and
Sujith
,
R. I.
,
2014
, “
Multifractality in Combustion Noise: Predicting an Impending Combustion Instability
,”
J. Fluid Mech.
,
747
, pp.
635
655
.
35.
Kabiraj
,
L.
,
Steinert
,
R.
,
Saurabh
,
A.
, and
Paschereit
,
C. O.
,
2015
, “
Coherence Resonance in a Thermoacoustic System
,”
Phys. Rev. E
,
92
(
4
), p. 042909.
36.
Eke
,
A.
,
Hermán
,
P.
,
Bassingthwaighte
,
J.
,
Raymond
,
G.
,
Percival
,
D.
,
Cannon
,
M.
,
Balla
,
I.
, and
Ikrényi
,
C.
,
2000
, “
Physiological Time Series: Distinguishing Fractal Noises From Motions
,”
Pflügers Archiv-Eur. J. Physiol.
,
439
(
4
), pp.
403
415
.
37.
Peng
,
C.-K.
,
Buldyrev
,
S. V.
,
Havlin
,
S.
,
Simons
,
M.
,
Stanley
,
H. E.
, and
Goldberger
,
A. L.
,
1994
, “
Mosaic Organization of DNA Nucleotides
,”
Phys. Rev. E
,
49
(
2
), pp.
1685
1689
.
38.
Kantelhardt
,
J. W.
,
Zschiegner
,
S. A.
,
Koscielny-Bunde
,
E.
,
Havlin
,
S.
,
Bunde
,
A.
, and
Stanley
,
H.
,
2002
, “
Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series
,”
Phys. A: Stat. Mech. Appl.
,
316
(
1–4
), pp.
87
114
.
39.
Ihlen
,
E. A. F.
,
2012
, “
Introduction to Multifractal Detrended Fluctuation Analysis in Matlab
,”
Front. Physiol.
,
3
, p. 141.
40.
Gao
,
J.
,
Hu
,
J.
, and
wen Tung
,
W.
,
2011
, “
Facilitating Joint Chaos and Fractal Analysis of Biosignals Through Nonlinear Adaptive Filtering
,”
PLoS ONE
,
6
(
9
), p.
e24331
.
41.
Unni
,
V. R.
, and
Sujith
,
R. I.
,
2015
, “
Multifractal Characteristics of Combustor Dynamics Close to Lean Blowout
,”
J. Fluid Mech.
,
784
, pp.
30
50
.
You do not currently have access to this content.