Low-order Network Model of a Duct with Non-Uniform Cross-Section and Varying Mean Temperature in the Presence of Mean Flow

Schaefer, Felicitas; Polifke, Wolfgang

doi:10.2514/6.2019-4376

Cited by 3 publications

(1 citation statement)

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“…Computational low-order acoustic network models have gained much popularity, as the equations for the mean flow and the acoustics can be solved sequentially [2,[5][6][7][8][9][10][11][12][13][14]. As any parametric analysis to identify stability boundaries requires consideration of many cases; analytical solutions that can characterize the acoustic behaviour for any given geometry, mean flow and acoustic boundary conditions offer significant advantages [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Acoustic absorption and generation in ducts of smoothly varying area sustaining a mean flow and a mean temperature gradient

Yeddula,

Gaudron,

Morgans

2021

Preprint

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In ducts with varying cross-sectional area and sustaining a subsonic non-isentropic mean flow, the axially varying flow conditions affect the acoustic energy balance of the system. This is significant in understanding and controlling thermo-acoustic phenomena, particularly in combustors. This work aims at quantifying the acoustic energy change in such configurations, using the acoustic absorption coefficient, ∆. The acoustic response of the duct to acoustic forcing is determined using an analytical model, neglecting the effect of entropy fluctuations on the acoustic field, and subsequently, ∆ is estimated. The model predictions of ∆ are validated using a linearised Euler equations (LEEs) solver. The model was found to be accurate for Mach numbers below 0.25, provided the lower frequency limit set by the analytical solution is satisfied. For conically varying area ducts with linear mean temperature gradient, it was observed that ∆ showed very little dependence on frequency, and that the absolute value of ∆ tended to be maximised when the upstream boundary was anechoic rather than non-anechoic. More importantly, ∆ was also observed to show stronger dependence on the mean temperature gradient than area gradient variation for such configurations.Further parametric and optimisation studies for ∆ revealed a crucial finding that a positive mean temperature gradient, representing a heated duct caused acoustic energy absorption. Similarly, a negative mean temperature gradient, representing a cooled duct caused acoustic energy generation -a key result of this analysis. This behaviour was shown to be consistent with a simplified analysis of the acoustic energy balance. Based on this finding, a linearly proportional reduction in acoustic energy generation was achieved by changing the mean temperature gradient.

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