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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.

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Figures

Grahic Jump Location
Fig. 1

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

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Fig. 2

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

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Fig. 3

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

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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.

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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. 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.

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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.

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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).

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Fig. 12

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

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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

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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)

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Fig. 15

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

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