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Gas Turbines: Aircraft Engine

Analytical Analysis of Indirect Combustion Noise in Subcritical Nozzles

[+] Author and Article Information
Alexis Giauque1

 Department of Computational Fluid Dynamics and Aeroacoustics, Onera–The French Aerospace Lab, Châtillon, France 92322alexis.giauque@onera.fr

Maxime Huet, Franck Clero

 Department of Computational Fluid Dynamics and Aeroacoustics, Onera–The French Aerospace Lab, Châtillon, France 92322

1

Corresponding author.

J. Eng. Gas Turbines Power 134(11), 111202 (Sep 21, 2012) (8 pages) doi:10.1115/1.4007318 History: Received March 09, 2012; Revised July 02, 2012; Published September 20, 2012; Online September 21, 2012

This article revisits the problem of indirect combustion noise in nozzles of finite length. The analytical model proposed by Moase for indirect combustion noise is rederived and applied to subcritical nozzles having shapes of increasing complexity. This model is based on the equations formulated by Marble and Candel for which an explicit solution is obtained in the subsonic framework. The discretization of the nozzle into n elementary units of finite length implies the determination of 2n integration constants for which a set of linear equations is provided in this article. The analytical method is applied to configurations of increasing complexity. Analytical solutions are compared to numerical results obtained using SUNDAY (a 1D nonlinear Euler solver in temporal space) and CEDRE (3D Navier–Stokes flow solver). Excellent agreement is found for all configurations thereby showing that acceleration discontinuities at the boundaries between adjacent elements do not influence the actual acoustic transfer functions. The issue of nozzle compactness is addressed. It is found that in the subcritical domain, spectral results should be nondimensionalized using the flow-through-time of the entire nozzle. Doing so, transfer functions of nozzles of different lengths are successfully compared and a compactness criterion is proposed that writes ω*0Ldζ/u(ζ)<1 where L is the axial length of the nozzle. Finally, the entropy wave generator (EWG) experimental setup is considered. Analytical results are compared to the results reported by Howe. Both models give similar trends and show the important role of the rising time of the fluctuating temperature front on the amplitude of the indirect acoustic emission. The experimental temperature profile and the impedance coefficients at the inlet and outlet are introduced into the analytical formulation. Results show that the indirect combustion noise mechanism is not alone responsible for the acoustic emission in the subcritical case.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

General shape of the nozzle geometry proposed by Sigman and Zinn [21]

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Figure 2

Schematics of the considered configurations and velocity profiles (gas is air; inlet temperature is 300 K except for case 5)

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Figure 3

(a) Case 1: transfer functions in a converging nozzle; (b) case 2: transfer functions in a diverging nozzle. P1-/σ: ▪ compact limit [4], — analytical solution, □ numerical solution (SUNDAY). P2+/σ: ● compact limit [4], – – analytical solution, ○ numerical solution (SUNDAY). Nonreflective inlet and outlet (Z1 = -1, Z2 = 1).

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Figure 4

(a) Case 3: converging diverging nozzle; (b) case 4: converging diverging nozzle with pipe. Transfer functions: P1-/σ: — analytical solution, □ numerical solution (SUNDAY); P2+/σ: – – analytical solution, ○ numerical solution (SUNDAY). Nonreflective inlet and outlet (Z1 = -1, Z2 = 1).

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Figure 5

(a) Axial velocity profile in the nozzle; (b) case 5: converging diverging nozzle of arbitrary shape. Transfer functions: P1-/σ: — analytical method, □ numerical solution (CEDRE); P2+/σ: – – analytical method, ○ numerical solution (CEDRE). Nonreflective inlet and outlet (Z1 = -1, Z2 = 1).

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Figure 6

Bake [10] experimental setup: evolution of TF+ with Mach number at the throat; (a) gain, (b) phase: — M=0.5, — — — M=0.6, – – – M=0.7, - - - -  M=0.75, . . . . . M=0.8, . . . . . . M=0.9, ○ SUNDAY (Mthroat=0.75), ▪ compact limit [4]. Nonreflective inlet and outlet (Z1 = -1, Z2 = 1).

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Figure 7

Bake [10] experimental setup: (a) example of temperature fluctuation considered in this study (here Δt = 10 ms), (b) corresponding analytical pressure pulse at the outlet. Nonreflective inlet and outlet (Z1 = -1, Z2 = 1).

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Figure 8

Evolution of the acoustic pressure maximum level at nozzle outlet with respect to the throat Mach number: ♦ Bake [10]; Howe’s model [9] with: — Δt = 30 ms, — — — Δt = 3 ms, – – – Δt = 0.3 ms, - - - - Δt = 0 ms. Present analytical method with: ▪ Δt = 30 ms, ● Δt = 10 ms, ▴ Δt = 3 ms. Nonreflective inlet and outlet (Z1 = -1, Z2 = 1).

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Figure 9

Evolution of the acoustic pressure maximum level at nozzle outlet with respect to the throat Mach number (nonreflective inlet and outlet): ♦ Bake [10]; ▪ analytical method with nonreflective inlet and outlet (Z1 = -1, Z2 = 1); ▴ analytical method with partially-reflective inlet and outlet; ● numerical results (SUNDAY) with nonreflective inlet and outlet

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