In the present study, we investigate the phenomenon of transition of a thermoacoustic system involving two-phase flow, from aperiodic oscillations to limit cycle oscillations. Experiments were performed in a laboratory scale model of a spray combustor. A needle spray injector is used to generate a droplet spray having one-dimensional velocity field. This simplified design of the injector helps in keeping away the geometric complexities involved in the real spray atomizers. We investigate the stability of the spray combustor in response to the variation of the flame location inside the combustor. Equivalence ratio is maintained constant throughout the experiment. The dynamics of the system is captured by measuring the unsteady pressure fluctuations present in the system. As the flame location is gradually varied, self-excited high-amplitude acoustic oscillations are observed in the combustor. We observe the transition of the system behavior from low-amplitude aperiodic oscillations to large amplitude limit cycle oscillations occurring through intermittency. This intermittent state mainly consists of a sequence of high-amplitude bursts of periodic oscillations separated by low-amplitude aperiodic regions. Moreover, the experimental results highlight that during intermittency, the maximum amplitude of bursts, near to the onset of intermittency, is as much as three times higher than the maximum amplitude of the limit cycle oscillations. These high-amplitude intermittent loads can have stronger adverse effects on the structural properties of the engine than the low-amplitude cyclic loading caused by the sustained limit cycle oscillations. Evolution of the three different dynamical states of the spray combustion system (viz., stable, intermittency, and limit cycle) is studied in three-dimensional phase space by using a phase space reconstruction tool from the dynamical system theory. We report the first experimental observation of type-II intermittency in a spray combustion system. The statistical distributions of the length of aperiodic (turbulent) phase with respect to the control parameter, first return map and recurrence plot (RP) techniques are employed to confirm the type of intermittency.

Issue Section:
Gas Turbines: Combustion, Fuels, and Emissions
Keywords:
Combustion, Sprays, Thermoacoustics
Topics:
Combustion, Combustion chambers, Flames, Limit cycles, Oscillations, Pressure, Sprays, Turbulence, Combustion systems, Statistical distributions, Signals, Phase space, Fluctuations (Physics)

References

1.
Rayleigh
,
J. W. S.
,
1878
, “
The Explanation of Certain Acoustical Phenomena
,”
Nature (London)
,
18
(
455
), pp.
319
–
321
.
2.
British Petroleum
,
2013
,
Statistical Review of World Energy
,
Workbook
,
London
.
3.
Chishty
,
W. A.
,
2005
, “
Effects of Thermoacoustic Oscillations on Spray Combustion Dynamics With Implications for Lean Direct Injection Systems
,” Ph.D. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA.
4.
Kumagai
,
S.
, and
Isoda
,
H.
,
1955
, “
Combustion of Fuel Droplets in a Vibrating Field
,”
Int. Combust. Proc.
,
5
(
1
), pp.
129
–
132
.
5.
Tanabe
,
M.
,
Morita
,
T.
,
Aoki
,
K.
,
Satoh
,
K.
,
Fujimori
,
T.
, and
Sato
,
J.
,
2000
, “
Influence of Standing Sound Waves on Droplet Combustion
,”
Int. Combust. Proc.
,
28
(
1
), pp.
1007
–
1013
.
6.
Saito
,
M.
,
Hoshikawa
,
M.
, and
Sato
,
M.
,
1996
, “
Enhancement of Evaporation/Combustion Rate Coefficient of a Single Fuel Droplet by Acoustic Oscillation
,”
Fuel
,
75
(
6
), pp.
669
–
674
.
7.
Okai
,
K.
,
Moriue
,
O.
,
Araki
,
M.
,
Tsue
,
M.
,
Kono
,
M.
,
Sato
,
J.
,
Dietrich
,
D. L.
, and
Williams
,
F. A.
,
2000
, “
Combustion of Single Droplets and Droplet Pairs in a Vibrating Field Under Microgravity
,”
Prog. Combust. Ins.
,
28
(
1
), pp.
977
–
983
.
8.
Dattarajan
,
S.
,
Lutomirski
,
A.
,
Lobbia
,
R.
,
Smith
,
O. I.
, and
Karagozian
,
A. R.
,
2006
, “
Acoustic Excitation of Droplet Combustion in Microgravity and Normal Gravity
,”
Combust. Flame
,
144
(
1–2
), pp.
299
–
317
.
9.
Duvvur
,
A.
,
Chiang
,
C. H.
, and
Sirignano
,
W. A.
,
1996
, “
Oscillatory Fuel Droplet Vaporization-Driving Mechanism for Combustion Instability
,”
J. Propul. Power
,
12
(
2
), pp.
358
–
365
.
10.
Dubey
,
R. K.
,
MaQuay
,
M. Q.
, and
Carvalho
,
J. A.
, Jr.,
1998
, “
An Experimental and Theoretical Investigation on the Effect of Acoustic on Spray Combustion
,”
Int. Combust. Proc.
,
27
(
2
), pp.
2017
–
2023
.
11.
Carvalho
,
J. A.
, Jr.,
Ferreira
,
M. A.
,
Bressan
,
C.
, and
Ferreira
,
J. L. G.
,
1989
, “
Definition of Heater Location to Drive Maximum Amplitude Acoustic Oscillations in a Rijke Tube
,”
Combust. Flame
,
76
(
1
), pp.
17
–
27
.
12.
Sujith
,
R. I.
,
2005
, “
An Experimental Investigation of Interaction of Sprays With Acoustic Fields
,”
Exp. Fluids
,
38
(
5
), pp.
576
–
587
.
13.
Lei
,
S.
, and
Turan
,
A.
,
2009
, “
Nonlinear/Chaotic Analysis, Modelling and Control of Combustion Instabilities Due to Vaporizing Sprays
,”
Chaos Soliton Fract.
,
42
(
3
), pp.
1766
–
1779
.
14.
Kabiraj
,
L.
,
Saurabh
,
A.
,
Wahi
,
P.
, and
Sujith
,
R. I.
,
2012
, “
Route to Chaos for Combustion Instability in Ducted Laminar Premixed Flames
,”
Chaos
,
22
, p.
023129
.
15.
Kabiraj
,
L.
,
Sujith
,
R. I.
, and
Wahi
,
P.
,
2012
, “
Bifurcations of Self-Excited Ducted Laminar Premixed Flames
,”
ASME J. Eng. Gas Turbine Power
,
134
(
3
), pp.
1
–
7
.
16.
Nair
,
V.
,
Thampi
,
G.
, and
Sujith
,
R. I.
,
2014
, “
Intermittency Route to Thermoacoustic Instability in Turbulent Combustors
,”
J. Fluid Mech.
,
756
, pp.
470
–
487
.
17.
Kabiraj
,
L.
, and
Sujith
,
R. I.
,
2012
, “
Nonlinear Self-Excited Thermoacoustic Oscillations, Intermittency and Flame Blowout
,”
J. Fluid Mech.
,
713
, pp.
376
–
397
.
18.
Kabiraj
,
L.
,
Sujith
,
R. I.
, and
Wahi
,
P.
,
2012
, “
Investigating the Dynamics of Combustion-Driven Oscillations Leading to Lean Blowout
,”
Fluid Dyn. Res.
,
44
(
3
), p.
031408
.
19.
Gotoda
,
H.
,
Shinoda
,
Y.
,
Kobayashi
,
M.
, and
Okuno
,
Y.
,
2014
, “
Detection and Control of Combustion Instability Based on the Concept of Dynamical System Theory
,”
Phys. Rev. E
,
89
(
2
), p.
022910
.
20.
Nair
,
V.
,
Thampi
,
G.
,
Sulochana
,
K.
,
Sarvana
,
G.
, and
Sujith
,
R. I.
,
2012
, “
System and Method for Predetermining the Onset of Impending Oscillatory Instabilities in Practical Devices
,” Provisional Patent No. WO2014054050A1.
21.
Unni
,
V. R.
,
Nair
,
V. V.
, and
Sujith
,
R. I.
,
2015
, “
System and Method for Detecting Precursors to Control Blowout in Combustion Systems
,” Provisional Patent No. WO2015068176A2, Priority date Nov. 8, 2013.
22.
Pomeau
,
Y.
, and
Manneville
,
P.
,
1980
, “
Intermittent Transition to Turbulence in Dissipative Dynamical Systems
,”
Commun. Math. Phys.
,
74
(
2
), pp.
189
–
197
.
23.
Nair
,
V.
, and
Sujith
,
R. I.
,
2013
, “
Identifying Homoclinic Orbits in the Dynamics of Intermittent Signals Through Recurrence Quantification
,”
Chaos
,
23
(
3
), p.
033136
.
24.
Xiao
,
Y.
,
Wang
,
Y.
, and
Lai
,
Y. C.
,
2009
, “
Dependence of Intermittency Scaling on Threshold in Chaotic Systems
,”
Phys. Rev. E
,
80
(
5
), p.
057202
.
25.
Hammer
,
P. W.
,
Platt
,
N.
,
Hammel
,
S. M.
,
Heagy
,
J. F.
, and
Lee
,
B. D.
,
1994
, “
Experimental Observation of On–Off Intermittency
,”
Phys. Rev. Lett.
,
73
(
8
), pp.
1095
–
1098
.
26.
Frank
,
M.
, and
Schmidt
,
M.
,
1997
, “
Time Series Investigation on an Experimental System Driven by Phase Transitions
,”
Phys. Rev. E
,
56
(
3
), p.
2423
.
27.
Sacher
,
J.
,
Elsasser
,
W.
, and
Gobel
,
E. O.
,
1989
, “
Intermittency in the Coherence Collapse of a Semiconductor Laser With External Feedback
,”
Phys. Rev. Lett.
,
63
(
20
), pp.
2224
–
2227
.
28.
Haucke
,
H.
,
Ecke
,
R. E.
,
Maeno
,
Y.
, and
Wheatley
,
J. C.
,
1984
, “
Noise-Induced Intermittency in a Convecting Dilute Solution of 3He in Superfluid 4He
,”
Phys. Rev. Lett.
,
53
(
22
), pp.
2090
–
2093
.
29.
Margull
,
U.
,
Spangler
,
J.
, and
Prettl
,
W.
,
1994
, “
Intermittent Breakdown of Current-Oscillation Tori in n-Type GaAs Epitaxial Layers
,”
Phys. Rev. B: Condens. Matter
,
50
(
19
), pp.
14166
–
14170
.
30.
Herzel
,
H.
,
1991
, “
Experimental Evidence of Homoclinic Chaos and Type-II Intermittency During the Oxidation of Methanol
,”
Physica D
,
48
(
2
), pp.
340
–
352
.
31.
Schuster
,
H. G.
, and
Just
,
W.
,
2005
,
Deterministic Chaos: An Introduction
, 4th ed.,
Wiley-VCH Verlag GmbH & Co. KGaA
, Weinheim, Germany.
32.
Freng
,
D. L.
,
Zheng
,
J.
,
Huang
,
W.
, and
Yu
,
C. X.
,
1996
, “
Type-I Like Intermittent Chaos in Multicomponent Plasmas With Negative Ions
,”
Phys. Rev. E
,
54
(
3
), pp.
2839
–
2843
.
33.
Richetti
,
P.
,
Argoul
,
F.
, and
Arneodo
,
A.
,
1986
, “
Type-II Intermittency in a Periodic Driven Nonlinear Oscillator
,”
Phys. Rev. A
,
34
(
1
), pp.
726
–
729
.
34.
Huang
,
J. Y.
, and
Kim
,
J. J.
,
1987
, “
Type-II Intermittency in a Coupled Nonlinear Oscillator: Experimental Observation
,”
Phys. Rev. A
,
36
(
3
), pp.
1495
–
1497
.
35.
Chatterjee
,
S.
, and
Mallik
,
A. K.
,
1996
, “
Three Kinds of Intermittency in a Nonlinear Mechanical System
,”
Phys. Rev. E
,
53
(
5
), pp.
4362
–
4367
.
36.
Ringuet
,
E.
,
Roze
,
C.
, and
Gouesbet
,
G.
,
1993
, “
Experimental Observation of Type-II Intermittency in a Hydrodynamic System
,”
Phys. Rev. E
,
47
(
2
), pp.
1405
–
1407
.
37.
Griffith
,
T. M.
,
Parthenos
,
D.
,
Crombie
,
J.
, and
Edwards
,
D. H.
,
1997
, “
Critical Scaling and Type-III Intermittent Chaos in Isolated Rabbit Resistance Arteries
,”
Phys. Rev. E
,
56
(
6
), pp.
6287
–
6290
.
38.
Klimaszewska
,
K.
, and
Zebrowski
,
J.
,
2009
, “
Detection of the Type of Intermittency Using Characteristic Patterns in Recurrence Plots
,”
Phys. Rev. E
,
80
(
2
), p.
026214
.
39.
Kurian
,
T.
, and
Fransson
,
J. H. M.
,
2009
, “
Grid-Generated Turbulence Revisited
,”
Fluid Dyn. Res.
,
41
(
2
), p.
021403
.
40.
McManus
,
K. R.
,
Poinsot
,
T.
, and
Candel
,
S. M.
,
1993
, “
A Review of Active Control of Combustion Instability
,”
Prog. Energy Combust. Sci.
,
19
(
1
), pp.
1
–
29
.
41.
Jahnke
,
C. C.
, and
Culick
,
F. E. C.
,
1993
, “
An Application of Dynamical Systems Theory to Nonlinear Combustion Instabilities
,”
J. Propul. Power
,
10
(
4
), pp.
508
–
517
.
42.
Takens
,
F.
,
1981
, “
Detecting Strange Attractors in Turbulence
,”
Lect. Notes Math.
,
898
, pp.
366
–
381
.
43.
Cao
,
L.
,
1997
, “
Practical Method for Determining the Minimum Embedding Dimension of a Scalar Time Series
,”
Physica D
,
110
(
1
), pp.
43
–
50
.
44.
Fraser
,
A. M.
, and
Swinney
,
H. L.
,
1986
, “
Independent Coordinates for Strange Attractors From Mutual Information
,”
Phys. Rev. A
,
33
(
2
), pp.
1134
–
1140
.
45.
Marwan
,
N.
,
Carmenromano
,
M.
,
Thiel
,
M.
, and
Kurths
,
J.
,
2007
, “
Recurrence Plots for the Analysis of Complex Systems
,”
Phys. Rep.
,
438
(
5
), pp.
237
–
329
.
46.
Eckmann
,
J. P.
,
Kamphorst
,
S. O.
, and
Ruelle
,
D.
,
1987
, “
Recurrence Plots of Dynamical Systems
,”
Europhys. Lett.
,
4
(
9
), pp.
973
–
977
.
47.
Hasson
,
C. J.
,
Van Emmerik
,
R. E. A.
,
Caldwell
,
G. E.
,
Haddad
,
J. M.
,
Gagnon
,
J. L.
, and
Hamill
,
J.
,
2008
, “
Influence of Embedding Parameters and Noise in Center of Pressure Recurrence Quantification Analysis
,”
Gait Posture
,
27
(
3
), pp.
416
–
422
.
48.
Schmid
,
S. R.
,
Hamrock
,
B. J.
, and
Jacobson
,
B. O.
,
2013
,
Fundamentals of Machine Elements
, 3rd ed.,
McGraw-Hill
, New York, Chap. 7.
49.
Ditlevsen
,
O.
, and
Madsen
,
H. O.
,
1996
,
Structural Reliability Methods
,
Wiley-Blackwell
, Hoboken, NJ.
Copyright © 2016 by ASME
You do not currently have access to this content.