Modelling of Circumferential Modal Coupling Due to Helmholtz Resonators

Abstract

Lean premixed prevaporised (LPP) combustion can reduce NOx emissions from gas turbines, but often leads to combustion instability. Acoustic waves produce fluctuations in heat release, for instance by perturbing the fuel-air ratio or flame shape. These heat fluctuations will in turn generate more acoustic waves and in some situations self-sustained oscillations can result. A linear model for thermoacoustic oscillations in LPP combustors is described. A thin annular geometry is assumed and so circumferential modes are included but radial dependence is ignored. The formulation is in terms of a network of modules such as straight ducts and area changes. At certain operating conditions, the flow is predicted to be unstable, with linear waves growing in amplitude. Helmholtz resonators can be used to absorb acoustic energy and, when carefully designed and installed at appropriate locations, can stabilise the flow. Helmholtz resonators are included in the model. Connecting a Helmholtz resonator to an annular duct destroys the axisymmetry of the geometry. This results in coupling of the circumferential modes which must be calculated. The model is used to investigate the best arrangement of resonators around the circumference of an annular duct to achieve maximum damping of a circumferential oscillation.

About the Zero Mach Number Assumption in the Calculation of Thermoacoustic Instabilities

“…However, even when they confirm that a combustor is unstable, LES calculations do not say why and how to control its instability. Besides, because of its intrinsic nature (full three-dimensional resolution of the unsteady Navier-Stokes equations), LES remains very CPU demanding, even on today's computers, (b) Low-order methods where the geometry of the combustor is modelled by a network of homogeneous (constant density) 1D or 2D axisymmetric acoustic elements where the acoustic problem can be solved analytically [17][18][19][20][21][22]. Jump relations are used to connect all these elements, enforcing pressure continuity and flow rate conservation and accounting for the dilatation induced by the infinitely thin flame, if any.…”

Acoustic Models for Cooled Helmholtz Resonators

“…It is worth noting that the effect of hot-gas penetration from the combustor into the neck of the resonator at large oscillation amplitudes has been found to alter the sound absorption performance of the HR [13,14]. However, the effect of the HR-combustor temperature difference on the acoustic (and entropy) waves in the combustor is also highly relevant [10,15], and has not been considered in previous studies [4,10,16].…”

Prediction of Combustion Noise for an Aeroengine Combustor

“…(12)(13)(14)(15)(16) one recognises that the local wave number spectrum for the heat release rate, E q (κ), is determined by the mean quantities. To obtain the frequency spectrum ψ q (ω) required for the acoustic power spectrum, Hirsch et al 5 followed Tennekes and Lumley 23 by requiring that the spectral energy content in the corresponding scales is conserved, i.e.…”

“…Now the local frequency spectrum of the heat release rate ψ q (ω) = κE q (κ)/ω is obtained by combining Eqs. (12)(13)(14)(15)(16)(17)(18). Moreover, it has been suggested in previous studies 12,28 that the correlation volume is V cor = 8 3 cor over the flame brush and cor ≈ δ T , the flame brush thickness.…”