Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

Absolute/Convective Instability Transition in a Backward Facing Step Combustor: Fundamental Mechanism and Influence of Density Gradient

[+] Author and Article Information
Kiran Manoharan

Department of Aerospace Engineering,
Indian Institute of Science,
Bangalore 560012, India
e-mail: kiranm@aero.iisc.ernet.in

Santosh Hemchandra

Department of Aerospace Engineering,
Indian Institute of Science,
Bangalore 560012, India
e-mail: hsantosh@aero.iisc.ernet.in

Reynolds number based on step height and flow velocity at the step.

This is the normal mode form for the flow perturbations.

That is, the eventual state of the flow.

That is, the maxima of the curves in Fig. 5 for each value of δ.

Erickson and Soteriou [43].

Contributed by the Combustion and Fuels Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received June 12, 2014; final manuscript received June 27, 2014; published online September 4, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(2), 021501 (Sep 04, 2014) (11 pages) Paper No: GTP-14-1283; doi: 10.1115/1.4028206 History: Received June 12, 2014; Revised June 27, 2014

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.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


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.
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. [CrossRef]
Huang, Y., and Yang, V., 2009, “Dynamics and Stability of Lean-Premixed Swirl-Stabilized Combustion,” Prog. Energy Combust. Sci., 35(4), pp. 293–364. [CrossRef]
Lieuwen, T. C., 2012, Unsteady Combustor Physics, Cambridge University Press, New York.
O'Connor, J., 2011, “Response of a Swirl-Stabilized Flame to Transverse Acoustic Excitation,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Gaster, M., 1968, “Growth of Disturbances in Both Space and Time,” Phys. Fluids, 11(4), pp. 723–727. [CrossRef]
Huerre, P., and Monkewitz, P. A., 1985, “Absolute and Convective Instabilities in Free Shear Layers,” J. Fluid Mech., 159, pp. 151–168. [CrossRef]
Huerre, P., 2000, “Open Shear Flows,” Perspectives in Fluid Dynamics: A Collective Introduction to Current Research, Cambridge University Press, Cambridge, UK, pp. 159–229.
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. [CrossRef]
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. [CrossRef]
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.
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
McManus, K., Vandsburger, U., and Bowman, C., 1990, “Combustor Performance Enhancement Through Direct Shear Layer Excitation,” Combust. Flame, 82(1), pp. 75–92. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Thibaut, D., and Candel, S., 1998, “Numerical Study of Unsteady Turbulent Premixed Combustion: Application to Flashback Simulation,” Combust. Flame, 113(1), pp. 53–65. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Strykowski, P. J., and Niccum, D. L., 1991, “The Stability of Countercurrent Mixing Layers in Circular Jets,” J. Fluid Mech., 227, pp. 309–343. [CrossRef]
Criminale, W. O., Jackson, T. L., and Joslin, R. D., 2003, Theory and Computation of Hydrodynamic Stability, Cambridge University Press, Cambridge, UK.
Deissler, R. J., 1987, “The Convective Nature of Instability in Plane Poiseuille Flow,” Phys. Fluids, 30(8), pp. 2303–2305. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Schmid, P. J., and Henningson, D. S., eds., 2001, Stability and Transition in Shear Flows, Springer, New York.
Crighton, D., and Gaster, M., 1976, “Stability of Slowly Diverging Jet Flow,” J. Fluid Mech., 77(2), pp. 397–413. [CrossRef]
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.
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. [CrossRef]
Michalke, A., 1964, “On the Inviscid Instability of the Hyperbolic-Tangent Velocity Profile,” J. Fluid Mech., 19(4), pp. 543–556. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Boyd, J. P., ed., 2000, Chebyshev and Fourier Spectral Methods, Dover, Mineola, NY.


Grahic Jump Location
Fig. 3

(a) Base flow velocity profile variation at a location; (b) base flow density profile variation at a location

Grahic Jump Location
Fig. 2

Schematic showing velocity profile variation downstream of the backward facing step combustor

Grahic Jump Location
Fig. 1

Possible mechanisms though which hydrodynamic instability modes can cause combustion instability (a) open loop and (b) closed loop

Grahic Jump Location
Fig. 4

Typical result from temporal stability analysis (a) eigenvalue spectrum and (b) most unstable eigenmode corresponding to the eigenvalue marked with a “+” (α = 2, β = 0.3, δ = 0.15, δw = 0.1, and r = 1). The arrows in (a) point to the physical eigenvalue and its complex conjugate.

Grahic Jump Location
Fig. 5

Variation of ωi with α for the most unstable mode of the shear layer for δ = 0.025, 0.05, and 0.1 (β = 1.0, δw = 0.1, and r = 1). Also shown is the corresponding variation of the canonical KH result for a piecewise constant velocity variation.

Grahic Jump Location
Fig. 6

Spatial variation of the magnitude of the contribution to the fluctuating vorticity production term from the KH mode. The magnitudes for all cases have been normalized by the maximum value for the δ = 0.025 case (β = 1.0, δw = 0.1, and r = 1).

Grahic Jump Location
Fig. 7

Variation of the maximum growth rate, ωi,max with δ for different location of the density variation, yf (r = 0.5, β = 0.3, and δw = 0.1). Also shown is the corresponding constant density r = 1 case for reference.

Grahic Jump Location
Fig. 8

Spatial budget of fluctuating vorticity source terms for two location of the density transition (a) yf = 0.2 and (b) yf = −0.2. The vertical axis on the left of these plots shows magnitudes and the vertical axis on the right shows the phase difference between two source terms (β = 0.3, δ = 0.15, δw = 0.1 and r = 0.5).

Grahic Jump Location
Fig. 10

Transition boundary between absolutely and convectively unstable flows (r = 1, δw = 0.1). The arrows marked AU and CU, respectively, point into regions of absolutely and convectively unstable flow.

Grahic Jump Location
Fig. 9

Spatial budget of fluctuating vorticity source terms for yf = 0.5. The vertical axis on the left is for magnitude values and the vertical axis on the right is for phase difference between the two source terms (β = 0.3, δ = 0.15, δw = 0.1, and r = 0.5). Note that the baroclinic and production terms are misaligned for this case.

Grahic Jump Location
Fig. 11

Comparison between the spatial budget of the production term for fluctuating vorticity at points P and Q in Fig. 10. The magnitude for both cases have been normalized by the maximum value for the δ = 0.25 case (β = 0.3, δw = 0.1, and r = 1).

Grahic Jump Location
Fig. 12

Absolute-convective instability transition boundaries for several locations of the density transition (δw = 0.1 and r = 0.5)

Grahic Jump Location
Fig. 13

Spatial budgets of fluctuating vorticity production and baroclinic source terms at point R in Fig. 12 for (a) yf = 0.2 and (b) yf = 0.6, β = 0.3, δ = 0.3, δw = 0.1, and r = 0.5

Grahic Jump Location
Fig. 14

Variation of the maximum temporal growth rate, ωi.max with δ for the KH mode of the shear layer for varying values of wall boundary layer thickness δw (β = 1.0 and r = 1)

Grahic Jump Location
Fig. 15

Absolute-convective instability transition boundaries for different values of boundary layer thickness, δw(r = 1)



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In