An Analytical Investigation Characterizing the Application of Single Frequency Acoustic Modulation for High Frequency Combustion Instability Suppression

Cranford, Jacob; Bennewitz, John W.; Rani, Sarma L.; Frederick, Robert A.

doi:10.2514/6.2014-3679

50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference 2014

DOI: 10.2514/6.2014-3679

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An Analytical Investigation Characterizing the Application of Single Frequency Acoustic Modulation for High Frequency Combustion Instability Suppression

Jacob Cranford¹,

John W. Bennewitz²,

Sarma L. Rani³

et al.

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2015

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Cited by 2 publications

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“…The model predictions were in agreement with the modal frequencies and stability observed in the experiments of Yu et al [5]. Consequently, the current study adopts the approach derived by Rani and Rani [4] to perform a one-dimensional (1-D) modal analysis of the acoustically modulated combustor configuration considered in the accompanying experimental study [6].…”

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confidence: 72%

Combustion Instability Control Through Acoustic Modulation at the Inlet Boundary: Analysis

Bennewitz

Rani

Cranford

et al. 2015

Journal of Propulsion and Power

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A linear modal analysis is undertaken to investigate the effects of acoustic modulation at the inlet boundary on the longitudinal instability modes of a dump combustor. This study complements an accompanying experimental investigation that demonstrates combustion instability control through single-frequency acoustic modulation at the inlet [Bennewitz, J. W., Frederick, R. A., Jr., Cranford, J. T., Lineberry, D. M., "Combustion Instability Control Through Acoustic Modulation at the Inlet Boundary: Experiments," Journal of Propulsion and Power (to be published)]. The modal analysis employs acoustically consistent matching conditions instead of the conventional mass, momentum, and energy balances. A specific impedance boundary condition at the inlet is derived through a mass-spring-damper model of a speaker diaphragm that provides the acoustic modulation. The speaker model constants are obtained from an apparatus consisting of a speaker attached to a short hard-wall-terminated duct. At first, the modal analysis is shown to predict a naturally unstable first longitudinal mode in the absence of acoustic modulation, consistent with the spontaneously excited combustion instability mode observed experimentally. Subsequently, a detailed investigation involving variation of the modulation frequency from 0 to 2500 Hz and a mean combustor temperature from 1248 to 1685 K demonstrates the unstable to stable transition of a 2300-2500 Hz first longitudinal mode. The model-predicted mode stability transition is consistent with experimental observations, thereby supporting the premise that inlet acoustic modulation is a means to control high-frequency combustion instabilities. From the modal analysis, it may be deduced that the inlet impedance provides a damping mechanism for instability suppression. Nomenclature A = speaker diaphragm area, m 2 A = amplitudes of the longitudinal mode propagating in the positive and negative x directions, Pa B = electromagnetic speaker B field, T b = speaker diaphragm damping coefficient, N · s∕m c = mean sound speed, m∕s d dphgm = diaphragm diameter, cm F = force, N f acous;sys = acoustic system resonant frequency of the speaker constant determination test facility, Hz f mech;spk = mechanical resonance of the speaker, Hz G amp = amplifier gain Hf = speaker model frequency response function, m∕s · A I = current, A k = axial wave numbers of the longitudinal mode propagating in the positive and negative x directions, 1∕m L const;sys = length of the speaker constant determination test facility, cm M = mean flow Mach number m = speaker diaphragm mass, kg N = number of speaker diaphragm voice coil turns p 0 spk = acoustic pressure at the speaker diaphragm, Pa p 0 = acoustic pressure fluctuations, Pa p= mean pressure, Pa T comb = average combustor temperature measured from the four thermocouples located within the chamber, K u 0 spk = acoustic velocity at the speaker diaphragm, m∕s u 0 = acoustic velocity fluctuations, m∕s u = mean velocity, m∕s Z = impedance, Pa · m∕s β = region index κ = speaker diaphr...

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supporting

confidence: 72%

Combustion Instability Control Through Acoustic Modulation at the Inlet Boundary: Analysis

Bennewitz

Rani

Cranford

et al. 2015

Journal of Propulsion and Power

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Combustion Instability Control Through Acoustic Modulation at the Inlet Boundary: Experiments

Bennewitz

Frederick

Cranford

et al. 2015

Journal of Propulsion and Power

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An Analytical Investigation Characterizing the Application of Single Frequency Acoustic Modulation for High Frequency Combustion Instability Suppression

Cited by 2 publications

References 6 publications

Combustion Instability Control Through Acoustic Modulation at the Inlet Boundary: Analysis

Combustion Instability Control Through Acoustic Modulation at the Inlet Boundary: Analysis

Combustion Instability Control Through Acoustic Modulation at the Inlet Boundary: Experiments

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