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Research Papers

Thermoacoustic Instability Model With Porous Media: Linear Stability Analysis and the Impact of Porous Media

[+] Author and Article Information
Cody S. Dowd

Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: cdowd33@vt.edu

Joseph W. Meadows

Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: jwm84@vt.edu

Manuscript received June 22, 2018; final manuscript received July 6, 2018; published online December 3, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(4), 041017 (Dec 03, 2018) (13 pages) Paper No: GTP-18-1313; doi: 10.1115/1.4041025 History: Received June 22, 2018; Revised July 06, 2018

Lean premixed (LPM) combustion systems are susceptible to thermoacoustic instability, which occurs when acoustic pressure oscillations are in phase with the unsteady heat release rates. Porous media has inherent acoustic damping properties and has been shown to mitigate thermoacoustic instability; however, theoretical models for predicting thermoacoustic instability with porous media do not exist. In the present study, a one-dimensional (1D) model has been developed for the linear stability analysis of the longitudinal modes for a series of constant cross-sectional area ducts with porous media using a n-Tau flame transfer function (FTF). By studying the linear regime, the prediction of acoustic growth rates and subsequently the stability of the system is possible. A transfer matrix approach is used to solve for acoustic perturbations of pressure and velocity, stability growth rate, and frequency shift without and with porous media. The Galerkin approximation is used to approximate the stability growth rate and frequency shift, and it is compared to the numerical solution of the governing equations. Porous media is modeled using the following properties: porosity, flow resistivity, effective bulk modulus, and structure factor. The properties of porous media are systematically varied to determine the impact on the eigenfrequencies and stability growth rates. Porous media is shown to increase the stability domain for a range of time delays (Tau) compared to similar cases without porous media.

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Figures

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Fig. 1

Canonical series of ducts with operating conditions. Dashed line represents flame location.

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Fig. 2

Variation of normalized growth rate with normalized convective time delay (fnτ), where fn is the homogeneous frequency

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Fig. 3

Representative combustor domain

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Fig. 4

Representative results for (a) structure factor and (b) effective bulk modulus prediction with trend lines

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Fig. 5

Attenuation constant results for the order of magnitude analysis for varying PIM parameters

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Fig. 6

The 3/4 wave (a) and (c) acoustic pressure and (b) and (d) acoustic velocity mode shapes, for cases without PIM (a) and (b) and with PIM (c) and (d). (- - - represents start of dump plane and – - - – represents end of PIM).

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Fig. 7

The 3/4 wave acoustic velocity mode shape (a) without PIM and (b) with PIM

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Fig. 8

The 5/4 wave (a) and (c) acoustic pressure and (b) and (d) acoustic velocity mode shapes, for cases without PIM (a) and (b) and with PIM (c) and (d) (- - - represents start of dump plane and – - - – represents end of PIM)

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Fig. 9

(a) Normalized frequency and (b) normalized growth rate for various PIM locations for 3/4 mode. Circled location represents nominal PIM location.

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Fig. 10

(a) Normalized frequency and (b) normalized growth rate for various PIM locations for 5/4 mode. Circled location represents nominal PIM location.

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Fig. 11

The 3/4 wave (a) acoustic pressure and (b) acoustic velocity mode shapes (--- represents start of dump plane and –- - – represents end of PIM)

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Fig. 12

Normalized growth rates for various normalized convective time delays and interaction indexes

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Fig. 13

Stability map comparison for cases without PIM and with PIM with flame

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Fig. 14

Comparison of cases without and with PIM for the stability map, utilizing the transfer matrix and Galerkin approximation approaches

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Fig. 15

(a) Normalized frequency and (b) normalized growth rate for change in porosity

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Fig. 16

(a) Variation in structure factor with change in porosity and (b) flow resistivity

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Fig. 17

(a) Normalized frequency and (b) normalized growth rate for change in flow resistivity

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