Hydrodynamic instabilities of the flow field in lean premixed gas turbine combustors can generate velocity perturbations that wrinkle and distort the flame sheet over length scales that are smaller than the flame length. The resultant heat release oscillations can then potentially result in combustion instability. Thus, it is essential to understand the hydrodynamic instability characteristics of the combustor flow field in order to understand its overall influence on combustion instability characteristics. To this end, this paper elucidates the role of fluctuating vorticity production from a linear hydrodynamic stability analysis as the key mechanism promoting absolute/convective instability transitions in shear layers occurring in the flow behind a backward facing step. These results are obtained within the framework of an inviscid, incompressible, local temporal and spatio-temporal stability analysis. Vorticity fluctuations in this limit result from interaction between two competing mechanisms—(1) production from interaction between velocity perturbations and the base flow vorticity gradient and (2) baroclinic torque in the presence of base flow density gradients. This interaction has a significant effect on hydrodynamic instability characteristics when the base flow density and velocity gradients are colocated. Regions in the space of parameters characterizing the base flow velocity profile, i.e., shear layer thickness and ratio of forward to reverse flow velocity, corresponding to convective and absolute instability are identified. The implications of the present results on understanding prior experimental studies of combustion instability in backward facing step combustors and hydrodynamic instability in other flows such as heated jets and bluff body stabilized flames is discussed.

References

References
1.
Lieuwen
,
T. C.
,
Yang
,
V.
, and
Lu
,
F. K.
,
2005
,
Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms and Modeling
(Progress in Astronautics and Aeronautics, Vol. 201),
American Institute of Aeronautics and Astronautics
, Reston, VA.
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
.10.1016/j.pecs.2005.10.002
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
.10.1016/j.pecs.2009.01.002
4.
Lieuwen
,
T. C.
,
2012
,
Unsteady Combustor Physics
,
Cambridge University Press, New York
.
5.
O'Connor
,
J.
,
2011
, “
Response of a Swirl-Stabilized Flame to Transverse Acoustic Excitation
,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.
6.
Schuller
,
T.
,
Ducruix
,
S.
,
Durox
,
D.
, and
Candel
,
S.
,
2002
, “
Modeling Tools for the Prediction of Premixed Flame Transfer Functions
,”
Proc. Combust. Inst.
,
29
(
1
), pp.
107
113
.10.1016/S1540-7489(02)80018-9
7.
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
), pp.
21
34
.10.1016/S0010-2180(03)00042-7
8.
Preetham
,
H. S.
, and
Lieuwen
,
T.
,
2008
, “
Dynamics of Laminar Premixed Flames Forced by Harmonic Velocity Disturbances
,”
J. Propul. Power
,
24
(
6
), pp.
1390
1402
.10.2514/1.35432
9.
Gaster
,
M.
,
1968
, “
Growth of Disturbances in Both Space and Time
,”
Phys. Fluids
,
11
(
4
), pp.
723
727
.10.1063/1.1691990
10.
Huerre
,
P.
, and
Monkewitz
,
P. A.
,
1985
, “
Absolute and Convective Instabilities in Free Shear Layers
,”
J. Fluid Mech.
,
159
, pp.
151
168
.10.1017/S0022112085003147
11.
Huerre
,
P.
,
2000
, “
Open Shear Flows
,”
Perspectives in Fluid Dynamics: A Collective Introduction to Current Research
,
Cambridge University
Press,
Cambridge, UK
, pp.
159
229
.
12.
Ghoniem
,
A. F.
,
Annaswamy
,
A.
,
Wee
,
D.
,
Yi
,
T.
, and
Park
,
S.
,
2002
, “
Shear Flow Driven Combustion Instability: Evidence, Simulation and Modeling
,”
Proc. Combust. Inst.
,
29
(1), pp.
53
60
.10.1016/S1540-7489(02)80011-6
13.
Armaly
,
B. F.
,
Durst
,
F.
,
Pereira
,
J. C. F.
, and
Schonung
,
B.
,
1983
, “
Experimental and Theoretical Investigation of Backward-Facing Step Flow
,”
J. Fluid Mech.
,
127
(
2
), pp.
473
496
.10.1017/S0022112083002839
14.
Denham
,
M.
, and
Patrick
,
M.
,
1974
, “
Laminar Flow Over a Downstream-Facing Step in a Two-Dimensional Flow Channel
,”
Trans. Inst. Chem. Eng.
,
52
(
4
), pp.
361
367
.
15.
Eaton
,
J. K.
, and
Johnstone
,
J. P.
,
1980
, “
An Evaluation of Data for the Backward-Facing Step Flow
,” Conference on Complex Turbulent Flows, Stanford University, Stanford, CA, Sept. 3–6.
16.
Nadge
,
P. M.
, and
Govardhan
,
R.
,
2014
, “
High Reynolds Number Flow Over a Backward-Facing Step: Structure of the Mean Separation Bubble
,”
Exp. Fluids
,
55
(
1
), pp.
1
22
.10.1007/s00348-013-1657-5
17.
Beaudoin
,
J.-F.
,
Cadot
,
O.
,
Aider
,
J.-L.
, and
Wesfreid
,
J. E.
,
2004
, “
Three-Dimensional Stationary Flow Over a Backward-Facing Step
,”
Eur. J. Mech. B
,
23
(
1
), pp.
147
155
.10.1016/j.euromechflu.2003.09.010
18.
Cohen
,
J. M.
, and
Bennett
, Jr.,
J. C.
,
1996
, “
An Experimental Study of the Transient Flow Over a Backward-Facing Step
,”
AIAA
Paper No. 96-0322. 10.2514/6.1996-322
19.
Schäfer
,
F.
,
Breuer
,
M.
, and
Durst
,
F.
,
2009
, “
The Dynamics of the Transitional Flow Over a Backward-Facing Step
,”
J. Fluid Mech.
,
623
(
1
), pp.
85
119
.10.1017/S0022112008005235
20.
Ghia
,
K.
,
Osswald
,
G.
, and
Ghia
,
U.
,
1989
, “
Analysis of Incompressible Massively Separated Viscous Flows Using Unsteady Navier–Stokes Equations
,”
Int. J. Numer. Methods Fluids
,
9
(
8
), pp.
1025
1050
.10.1002/fld.1650090809
21.
Williams
,
P.
, and
Baker
,
A.
,
1997
, “
Numerical Simulations of Laminar Flow Over a 3D Backward-Facing Step
,”
Int. J. Numer. Methods Fluids
,
24
(
11
), pp.
1159
1183
.10.1002/(SICI)1097-0363(19970615)24:11<1159::AID-FLD534>3.0.CO;2-R
22.
Kaiktsis
,
L.
,
Karniadakis
,
G. E.
, and
Orszag
,
S. A.
,
1991
, “
Onset of Three-Dimensionality, Equilibria, and Early Transition in Flow Over a Backward-Facing Step
,”
J. Fluid Mech.
,
231
, pp.
501
528
.10.1017/S0022112091003488
23.
Kaiktsis
,
L.
,
Karniadakis
,
G. E.
, and
Orszag
,
S. A.
,
1996
, “
Unsteadiness and Convective Instabilities in Two-Dimensional Flow Over a Backward-Facing Step
,”
J. Fluid Mech.
,
321
(
1
), pp.
157
187
.10.1017/S0022112096007689
24.
Barkley
,
D.
,
Gomes
,
M. G. M.
, and
Henderson
,
R. D.
,
2002
, “
Three-Dimensional Instability in Flow Over a Backward-Facing Step
,”
J. Fluid Mech.
,
473
, pp.
167
190
.10.1017/S002211200200232X
25.
Blackburn
,
H.
,
Barkley
,
D.
, and
Sherwin
,
S. J.
,
2008
, “
Convective Instability and Transient Growth in Flow Over a Backward-Facing Step
,”
J. Fluid Mech.
,
603
, pp.
271
304
.10.1017/S0022112008001109
26.
Keller
,
J.
,
Vaneveld
,
L.
,
Korschelt
,
D.
,
Hubbard
,
G.
,
Ghoniem
,
A.
,
Daily
,
J.
, and
Oppenheim
,
A.
,
1982
, “
Mechanism of Instabilities in Turbulent Combustion Leading to Flashback
,”
AIAA J.
,
20
(
2
), pp.
254
262
.10.2514/3.51073
27.
Cohen
,
J. M.
, and
Anderson
,
T. J.
,
1996
, “
Experimental Investigation of Near-Blowout Instabilities in a Lean, Premixed Step Combustor
,”
AIAA
Paper No. 96-0819.10.2514/6.96-0819
28.
McManus
,
K.
,
Vandsburger
,
U.
, and
Bowman
,
C.
,
1990
, “
Combustor Performance Enhancement Through Direct Shear Layer Excitation
,”
Combust. Flame
,
82
(
1
), pp.
75
92
.10.1016/0010-2180(90)90079-7
29.
De Zilwa
,
S.
,
Uhm
,
J.
, and
Whitelaw
,
J.
,
2000
, “
Combustion Oscillations Close to the Lean Flammability Limit
,”
Combust. Sci. Technol.
,
160
(
1
), pp.
231
258
.10.1080/00102200008935804
30.
Najm
,
H. N.
, and
Ghoniem
,
A. F.
,
1991
, “
Numerical Simulation of the Convective Instability in a Dump Combustor
,”
AIAA J.
,
29
(
6
), pp.
911
919
.10.2514/3.10678
31.
Yu
,
K. H.
,
Trouve
,
A.
, and
Daily
,
J. W.
,
1991
, “
Low-Frequency Pressure Oscillations in a Model Ramjet Combustor
,”
J. Fluid Mech.
,
232
, pp.
47
72
.10.1017/S0022112091003622
32.
Najm
,
H. N.
, and
Ghoniem
,
A. F.
,
1994
, “
Coupling Between Vorticity and Pressure Oscillations in Combustion Instability
,”
J. Propul. Power
,
10
(
6
), pp.
769
776
.10.2514/3.23814
33.
Thibaut
,
D.
, and
Candel
,
S.
,
1998
, “
Numerical Study of Unsteady Turbulent Premixed Combustion: Application to Flashback Simulation
,”
Combust. Flame
,
113
(
1
), pp.
53
65
.10.1016/S0010-2180(97)00196-X
34.
Altay
,
H. M.
,
Speth
,
R. L.
,
Hudgins
,
D. E.
, and
Ghoniem
,
A. F.
,
2009
, “
Flame–Vortex Interaction Driven Combustion Dynamics in a Backward-Facing Step Combustor
,”
Combust. Flame
,
156
(
5
), pp.
1111
1125
.10.1016/j.combustflame.2009.02.003
35.
Wee
,
D.
,
Yi
,
T.
,
Annaswamy
,
A.
, and
Ghoniem
,
A. F.
,
2004
, “
Self-Sustained Oscillations and Vortex Shedding in Backward-Facing Step Flows: Simulation and Linear Instability Analysis
,”
Phys. Fluids
,
16
(
9
), pp.
3361
3373
.10.1063/1.1773091
36.
Strykowski
,
P. J.
, and
Niccum
,
D. L.
,
1991
, “
The Stability of Countercurrent Mixing Layers in Circular Jets
,”
J. Fluid Mech.
,
227
, pp.
309
343
.10.1017/S0022112091000137
37.
Criminale
,
W. O.
,
Jackson
,
T. L.
, and
Joslin
,
R. D.
,
2003
,
Theory and Computation of Hydrodynamic Stability
,
Cambridge University Press, Cambridge, UK
.
38.
Deissler
,
R. J.
,
1987
, “
The Convective Nature of Instability in Plane Poiseuille Flow
,”
Phys. Fluids
,
30
(
8
), pp.
2303
2305
.10.1063/1.866118
39.
Emerson
,
B.
,
O'Connor
,
J.
,
Juniper
,
M.
, and
Lieuwen
,
T.
,
2012
, “
Density Ratio Effects on Reacting Bluff-Body Flow Field Characteristics
,”
J. Fluid Mech.
,
706
, pp.
219
250
.10.1017/jfm.2012.248
40.
Raynal
,
L.
,
Harison
,
J.
,
Faver-Marinet
,
M.
, and
Binder
,
G.
,
1996
, “
The Oscillatory Instability of Plane Variabledensity Jets
,”
Phys. Fluids
,
8
(
4
), pp.
993
1006
.10.1063/1.868877
41.
Srinivasan
,
V.
,
Halberg
,
M.
, and
Strykowski
,
P.
,
2010
, “
Viscous Linear Stability of Axisymmetric Low-Density Jets: Parameters Influencing Absolute Instability
,”
Phys. Fluids
,
22
(
2
), p.
024103
.10.1063/1.3306671
42.
Yu
,
M.-H.
, and
Monkewitz
,
P. A.
,
1990
, “
The Effect of Nonuniform Density on the Absolute Instability of Two-Dimensional Inertial Jets and Wakes
,”
Phys. Fluids A
,
2
(
7
), pp.
1175
1181
.10.1063/1.857618
43.
Erickson
,
R.
, and
Soteriou
,
M.
,
2011
, “
The Influence of Reactant Temperature on the Dynamics of Bluff Body Stabilized Premixed Flames
,”
Combust. Flame
,
158
(
12
), pp.
2441
2457
.10.1016/j.combustflame.2011.05.006
44.
Schmid
,
P. J.
, and
Henningson
,
D. S.
, eds.,
2001
,
Stability and Transition in Shear Flows
,
Springer
,
New York
.
45.
Crighton
,
D.
, and
Gaster
,
M.
,
1976
, “
Stability of Slowly Diverging Jet Flow
,”
J. Fluid Mech.
,
77
(
2
), pp.
397
413
.10.1017/S0022112076002176
46.
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
.
47.
Monkewitz
,
P. A.
,
Huerre
,
P.
, and
Chomaz
,
J.-M.
,
1993
, “
Global Linear Stability Analysis of Weakly Non-Parallel Shear Flows
,”
J. Fluid Mech.
,
251
, pp.
1
20
.10.1017/S0022112093003313
48.
Michalke
,
A.
,
1964
, “
On the Inviscid Instability of the Hyperbolic-Tangent Velocity Profile
,”
J. Fluid Mech.
,
19
(4), pp.
543
556
.10.1017/S0022112064000908
49.
Kyle
,
D. M.
, and
Sreenivasan
,
K. R.
,
1991
, “
The Instability and Breakdown of a Round Variable-Density Jet
,”
J. Fluid Mech.
,
249
, pp.
619
664
.10.1017/S0022112093001314
50.
Michael
,
G.
,
Obrist
,
D.
, and
Kleiser
,
L.
,
2013
, “
Linear Stability and Acoustic Characteristics of Compressible, Viscous, Subsonic Coaxial Jet Flow
,”
Phys. Fluids
,
25
(
8
), p.
084102
.10.1063/1.4816368
51.
Boyd
,
J. P.
, ed.,
2000
,
Chebyshev and Fourier Spectral Methods
,
Dover
,
Mineola, NY
.
You do not currently have access to this content.