Research Papers

Influence of Nonaxisymmetric Confinement on the Hydrodynamic Stability of Multinozzle Swirl Flows

[+] Author and Article Information
Harish G. Subramanian

Department of Aerospace Engineering,
Indian Institute of Science,
Bangalore 560012, India
e-mail: gsubramanian@iisc.ac.in

Kiran Manoharan, Santosh Hemchandra

Department of Aerospace Engineering,
Indian Institute of Science,
Bangalore 560012, India

1Corresponding author.

Manuscript received June 30, 2018; final manuscript received July 15, 2018; published online October 4, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(2), 021016 (Oct 04, 2018) (11 pages) Paper No: GTP-18-1410; doi: 10.1115/1.4041080 History: Received June 30, 2018; Revised July 15, 2018

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.

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Fig. 1

Schematic single nozzle swirl stabilized flame flow field

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Fig. 2

Schematics of investigated nonaxisymmetrically confined swirl nozzle configurations (a) single nozzle combustor (b) triple nozzle

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Fig. 3

Base flow velocity and density profiles for the single nozzle case for γ = 0.8 (β = 0.5, N1 = 4, N2 = 2, b1 = b2 = ln(2), rf = 0.78, Nf = 0.2, S = 1.0, N3 = 4.18 and N4 = 0.73)

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Fig. 4

Base flow profiles along the x-axis for the triple nozzle case: (a) axial velocity and density profiles, and, (b) azimuthal velocity profile (β = 0.1, N = 4, γ = 0.3, rf = 1.0, Nf = 0.2, S = 1.0, N3 = 4.18 and N4 = 0.73)

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Fig. 5

Typical variation of |ũz| with x of the most temporally unstable eigenmode for the confined single nozzle case (crosses) (k = 3, ω = 2.047 + 0.878i, AR = 1.0, CR = 2.0, γ = 1.0). Also shown for comparison is the corresponding result for the unconfined case (broken curve). The dotted vertical lines show the positions of the two shear layers in the Uoz profile. Note that for the confined case, the wall is at x = 2.0.

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Fig. 6

Variation of the (a) growth rate (ωi) and (b) oscillation frequency (ωr) with spatial wavenumber (k) of two typical single nozzle eigenmodes for different CR (AR = 1.0). These modes have dominant contributions from m = 0 and m = 2 Fourier components. Corresponding reference results for an unconfined single nozzle are also shown (curves).

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Fig. 7

Variation of the (a) growth rate (ωi) and (b) oscillation frequency (ωr) with spatial wavenumber (k) for two typical single nozzle eigenmodes for different AR (CR = 2.0). These modes have dominant contributions from m = 0 and m = 2 Fourier components. Corresponding reference results for an unconfined single nozzle are also shown (curves).

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Fig. 8

Typical types of eigenmodes for the confined triple nozzle case shown using |ũz| and phase (in deg) ((a) and (b)) middle (k = 3), ((c) and (d)) side (k = 3) and ((e) and (f)) equal (k = 1) with (CR = 2.0, AR = 5.0, d = 2.0). The broken black circles show the position of the ISL. Note that these are all shear layer modes.

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Fig. 9

Variation of ωi with k for the most temporally unstable triple nozzle mode for various values of internozzle spacing (AR = 5.0, CR = 2.0, γ = 1.0). Also shown for reference is the result for the unstable m = 2 mode from the unconfined single nozzle case with ωr similar to that of the triple nozzle case.

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Fig. 10

Variation of ωi with k for the most temporally unstable mode for spacing (a) d = 2.0 and (b) d = 3.0 at various values of density ratio (AR = 5.0, CR = 2.0)

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Fig. 11

Variation of ωoi,max with γ for various confined nozzle cases (symbols, AR = 5.0, CR = 2.0). SN stands for single nozzle. Results from the unconfined single nozzle case (curve) are also shown for reference.

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Fig. 12

Typical variation of eigenvector magnitude, shown using |ũz| along the x-axis for the triple nozzle case (solid curves) at three different nozzle spacings (a) d = 2.0, (b) d = 4.0, and (c) d = 7.0 (AR = 5.0, CR = 2.0, γ = 0.6). These are determined at the (ωo, ko) corresponding to the results shown in Fig. 11. The corresponding result from the unconfined single nozzle is shown for comparison (broken curve) for each case. The vertical broken lines show the position of the nozzle centerlines.

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Fig. 13

Variation of the k+ and k spatial eigenvalue branches along a horizontal contour on the ω plane for a triple nozzle case considered in this study (d = 4.0, γ = 0.3). The contour on the ω plane allows to pass just above the saddle point in the ω plane. The contour in the ω plane extends for a distance of 1.4 on either side of the computed ωo.



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