Interaction between coherent flow oscillations and the premixed flame sheet in combustors can result in coherent unsteadiness in the global heat release response. These coherent flow oscillations can either be self-excited (e.g., the precessing vortex core) or result from the hydrodynamic response of the flow field to acoustic forcing. Recent work has focused on understanding the various instability modes and fundamental mechanisms that control hydrodynamic instability in single nozzle swirl flows. However, the effect of multiple closely spaced nozzles as well as the nonaxisymmetric nature of the confinement imposed by the combustor liner on swirl nozzle flows remains as yet unexplored. We study the influence of internozzle spacing and nonaxisymmetric confinement on the local temporal and spatiotemporal stability characteristics of multinozzle flows in this paper. The base flow model for the multinozzle case is constructed by superposing contributions from a base flow model for each individual nozzle. The influence of the flame is captured by specifying a spatially varying base flow density field. The nonaxisymmetric local stability problem is posed in terms of a parallel base flow with spatial variations in the two directions perpendicular to the streamwise direction. We investigate the case of a single nozzle and three nozzles arranged in a straight line within a rectangular combustor. The results show that geometric confinement imposed by the combustor walls has a quantitative impact on the eigenvalues of the hydrodynamic modes. Decreasing nozzle spacing for a given geometric confinement configuration makes the flow more unstable. The presence of an inner shear layer (ISL) stabilized flame results in an overall stabilization of the flow instability. We also discuss qualitatively, the underlying vorticity dynamics mechanisms that influence the characteristics of instability modes in triple nozzle flows.

References

References
1.
Lefebvre
,
A. H.
,
1998
,
Gas Turbine Combustion
,
CRC Press
, Boca Raton, FL.
2.
Syred
,
N.
,
2006
, “
A Review of Oscillation Mechanisms and the Role of the Precessing Vortex Core (PVC) in Swirl Combustion Systems
,”
Prog. Energy Combust. Sci.
,
32
(
2
), pp.
93
161
.
3.
Huang
,
Y.
, and
Yang
,
V.
,
2009
, “
Dynamics and Stability of Lean-Premixed Swirl-Stabilized Combustion
,”
Prog. Energy Combust. Sci.
,
35
(
4
), pp.
293
364
.
4.
Lieuwen
,
T. C.
,
2012
,
Unsteady Combustor Physics
,
Cambridge University Press
, New York.
5.
Oberleithner
,
K.
,
Sieber
,
M.
,
Nayeri
,
C.
,
Paschereit
,
C.
,
Petz
,
C.
,
Hege
,
H.-C.
,
Noack
,
B.
, and
Wygnanski
,
I.
,
2011
, “
Three-Dimensional Coherent Structures in a Swirling Jet Undergoing Vortex Breakdown: Stability Analysis and Empirical Mode Construction
,”
J. Fluid Mech.
,
679
, pp.
383
414
.
6.
Oberleithner
,
K.
,
Stöhr
,
M.
,
Im
,
S. H.
,
Arndt
,
C. M.
, and
Steinberg
,
A. M.
,
2015
, “
Formation and Flame-Induced Suppression of the Precessing Vortex Core in a Swirl Combustor: Experiments and Linear Stability Analysis
,”
Combust. Flame
,
162
(
8
), pp.
3100
3114
.
7.
Terhaar
,
S.
,
Oberleithner
,
K.
, and
Paschereit
,
C.
,
2014
, “
Key Parameters Governing the Precessing Vortex Core in Reacting Flows: An Experimental and Analytical Study
,”
Proc. Combust. Inst.
,
35
(3), pp. 3347–3354.
8.
Manoharan
,
K.
,
Hansford
,
S.
,
O'Connor
,
J.
, and
Hemchandra
,
S.
,
2015
, “
Instability Mechanism in a Swirl Flow Combustor: Precession of Vortex Core and Influence of Density Gradient
,”
ASME
Paper No. GT2015-42985.
9.
Tammisola
,
O.
, and
Juniper
,
M.
,
2016
, “
Coherent Structures in a Swirl Injector at Re = 4800 by Nonlinear Simulations and Linear Global Modes
,”
J. Fluid Mech.
,
792
, pp.
620
657
.
10.
O'Connor
,
J.
,
2011
, “
Response of a Swirl-Stabilized Flame to Transverse Acoustic Excitation
,”
Ph.D. thesis
, Georgia Institute of Technology, Atlanta, GA.https://smartech.gatech.edu/handle/1853/43756
11.
O' Connor
,
J.
, and
Lieuwen
,
T.
,
2012
, “
Recirculation Zone Dynamics of a Transversely Excited Swirl Flow and Flame
,”
Phys. Fluids
,
24
(
7
), p.
075107
.
12.
Bellows
,
B. D.
,
Bobba
,
M. K.
,
Forte
,
A.
,
Seitzman
,
J. M.
, and
Lieuwen
,
T.
,
2007
, “
Flame Transfer Function Saturation Mechanisms in a Swirl-Stabilized Combustor
,”
Proc. Combust. Inst.
,
31
(
2
), pp.
3181
3188
.
13.
O'Connor
,
J.
,
Acharya
,
V.
, and
Lieuwen
,
T.
,
2015
, “
Transverse Combustion Instabilities: Acoustic, Fluid Mechanic, and Flame Processes
,”
Prog. Energy Combust. Sci.
,
49
, pp.
1
39
.
14.
Manoharan
,
K.
, and
Hemachandra
,
S.
,
2014
, “
Absolute/Convective Instability Transition in a Backward Facing Step Combustor: Fundamental Mechanism and Influence of Density Gradient
,”
ASME J. Eng. Gas Turbines Power
,
137
(
2
), p.
021501
.
15.
Smith
,
T.
,
Emerson
,
B.
,
Chterev
,
I.
,
Noble
,
D. R.
, and
Lieuwen
,
T.
,
2016
, “
Flow Dynamics in Single and Multi-Nozzle Swirl Flames
,”
ASME
Paper No. GT2016-57755
.
16.
Chomaz
,
J.-M.
,
Huerre
,
P.
, and
Redekopp
,
L. G.
,
1991
, “
A Frequency Selection Criterion in Spatially Developing Flows
,”
Stud. Appl. Math.
,
84
(
2
), pp.
119
144
.
17.
Monkewitz
,
P. A.
,
Huerre
,
P.
, and
Chomaz
,
J.-M.
,
1993
, “
Global Linear Stability Analysis of Weakly Non-Parallel Shear Flows
,”
J. Fluid Mech.
,
251
(
1
), pp.
1
20
.
18.
Juniper
,
M. P.
, and
Pier
,
B.
,
2015
, “
The Structural Sensitivity of Open Shear Flows Calculated With a Local Stability Analysis
,”
Eur. J. Mech.-B
,
49
, pp.
426
437
.
19.
Gallaire
,
F.
, and
Chomaz
,
J.-M.
,
2003
, “
Instability Mechanisms in Swirling Flows
,”
Phys. Fluids
,
15
(
9
), pp.
2622
2639
.
20.
Gaster
,
M.
,
1968
, “
Growth of Disturbances in Both Space and Time
,”
Phys. Fluids
,
11
(
4
), pp.
723
727
.
21.
Huerre
,
P.
, and
Monkewitz
,
P. A.
,
1985
, “
Absolute and Convective Instabilities in Free Shear Layers
,”
J. Fluid Mech.
,
159
(
1
), pp.
151
168
.
22.
Huerre
,
P.
, and
Rossi
,
M.
,
2005
, “
Hydrodynamic Instabilities in Open Flows
,”
Hydrodynamics and Nonlinear Instabilities
,
P.
Manneville
and
C.
Godrèche
, eds.,
Cambridge University Press
,
Cambridge, UK
, pp.
81
288
.
23.
Smith
,
T. E.
,
Chterev
,
I. P.
,
Emerson
,
B. L.
,
Noble
,
D. R.
, and
Lieuwen
,
T. C.
,
2017
, “
Comparison of Single- and Multinozzle Reacting Swirl Flow Dynamics
,”
J. Propul. Power
,
34
(2), pp.
384
394
.
24.
Boyd
,
J. P.
, ed.,
2000
,
Chebyshev and Fourier Spectral Methods
,
Dover Publications
,
Mineola, NY
.
25.
Bayliss
,
A.
, and
Turkel
,
E.
,
1992
, “
Mappings and Accuracy for Chebyshev Pseudo-Spectral Approximations
,”
J. Comput. Phys.
,
101
(
2
), pp.
349
359
.
26.
Hernandez
,
V.
,
Roman
,
J. E.
, and
Vidal
,
V.
,
2005
, “
SLEPc: A Scalable and Flexible Toolkit for the Solution of Eigenvalue Problems
,”
ACM Trans. Math. Software
,
31
(
3
), pp.
351
362
.
27.
Deissler
,
R. J.
,
1987
, “
The Convective Nature of Instability in Plane Poiseuille Flow
,”
Phys. Fluids
,
30
(
8
), pp.
2303
2305
.
28.
Schmid
,
P. J.
, and
Henningson
,
D. S.
,
2001
,
Stability and Transition in Shear Flows
, Vol.
142
,
Springer Verlag
, New York.
29.
Preetham
,
Santosh, H.
, and
Lieuwen
,
T.
,
2008
, “
Dynamics of Laminar Premixed Flames Forced by Harmonic Velocity Disturbances
,”
J. Propul. Power
,
24
(
6
), pp.
1390
1402
.
30.
Schuller
,
T.
,
Durox
,
D.
, and
Candel
,
S.
,
2003
, “
A Unified Model for the Prediction of Laminar Flame Transfer Functions: Comparisons Between Conical and v-Flame Dynamics
,”
Combust. Flame
,
134
(
1–2
), pp.
21
34
.
31.
Acharya, V.
,
Shreekrishna, Shin, D.-H.
, and
Lieuwen, T.
,
2012
, “
Swirl Effects on Harmonically Excited, Premixed Flame Kinematics
,”
Combust. Flame
,
159
(
3
), pp.
1139
1150
.
32.
Kirthy
,
S. K.
,
Hong
,
S.
,
Shanbhogue
,
S.
,
Ghoniem
,
A. F.
, and
Hemchandra
,
S.
,
2016
, “
Role of Shear Layer Instability in Driving Pressure Oscillations in a Backward Facing Step Combustor
,”
ASME
Paper No. GT2016-57322
.
33.
Taamallah
,
S.
,
Shanbhogue
,
S. J.
, and
Ghoniem
,
A. F.
,
2016
, “
Turbulent Flame Stabilization Modes in Premixed Swirl Combustion: Physical Mechanism and Karlovitz Number-Based Criterion
,”
Combust. Flame
,
166
, pp.
19
33
.
34.
Moeck
,
J. P.
,
Bourgouin
,
J.-F.
,
Durox
,
D.
,
Schuller
,
T.
, and
Candel
,
S.
,
2012
, “
Nonlinear Interaction Between a Precessing Vortex Core and Acoustic Oscillations in a Turbulent Swirling Flame
,”
Combust. Flame
,
159
(
8
), pp.
2650
2668
.
You do not currently have access to this content.