Comparison of Open and Choked Premixed Combustor Exits During Thermoacoustic Limit Cycle

Abstract

This paper compares the thermoacoustic limit cycles of a premixed laboratory combustor with acoustically open and choked exits. It is shown that the form of the downstream boundary condition can have a significant effect on the combustion chamber acoustics, with both the dominant limit cycle frequencies and the acoustic mode shapes being very different for the different combustor exits. The fundamental limit cycle frequency with the choked exit in place agrees closely with that determined by the convective time scales of entropy disturbances, as argued by other authors. A novel experimental method is then developed to examine the acoustic response of an arbitrary duct termination to incident pressure and entropy perturbations, and used to measure the response of the combustor downstream boundary condition during thermoacoustic limit cycle. The reflection coefficient for the acoustically open exit matches closely the classical result for zero mean flow. It is also shown that a choked nozzle downstream of the flame generates significant sound due to the interaction of the convected entropy perturbation with the nozzle. This final result is qualitatively in keeping with an existing analytic boundary condition for a choked nozzle, even though quantitative agreement is not observed. Reasons for this discrepancy are then suggested. Nomenclature A = Fourier transform of the nondimensional incident pressure fluctuation AR = downstream nozzle area ratio a = amplitude of the incident nondimensional pressure fluctuation B = Fourier transform of the nondimensional reflected pressure fluctuation b = amplitude of the reflected nondimensional pressure fluctuation C ij = real part of the cross-spectral density between i and j c = speed of sound c p = specific heat at constant pressure f = frequency H = transfer function k = wave number L = length of rig downstream of the flame holder M = Mach number n = mode number P = Fourier transform of the nondimensional pressure fluctuation p = pressure Q ij = imaginary part of the cross-spectral density between i and j R = reflection coefficient S = Fourier transform of the nondimensional entropy fluctuation S ij = cross-spectral density between i and j s = entropy, amplitude of the nondimensional entropy fluctuation T = temperature, Fourier transform of the nondimensional temperature, measurement period t = time u = velocity x = spatial coordinate = ratio of specific heats = density = equivalence ratio ! = angular frequency Subscripts H = hot flow quantity i = incident n = mode number p = pressure r = reflected s = entropy 1,2,. . . = measurement location, transfer function number Modifiers g = mean component of the quantity g g 0 = fluctuating component of the quantity g g = complex conjugate of the complex number g

Thermoacoustic limit cycles in a premixed laboratory combustor with open and choked exits

“…MacQuisten and Dowling [40] reported a strong low-frequency instability in their combustor when the exit was choked, and speculated that this was the cause. Hield and Brear [42] also observed a similar low-frequency instability, and showed experimentally that the conversion of incident entropy disturbances to upstream travelling sound can be significant.…”

“…Whilst thermoacoustic instability has been studied extensively in premixed combustors over the last few decades, most studies have concentrated on combustors with acoustically open exits. The effect of a choked exit nozzle has received less attention [40][41][42]. This is an important omission, given that some of those studies that have been carried out suggest that a choked exit nozzle can have a strong effect on the system stability [3,40,42,43], and that most in service combustors feature a choked, or nearly choked, nozzle downstream of the combustion chamber.…”

Response of a conical, laminar premixed flame to low amplitude acoustic forcing – A comparison between experiment and kinematic theories

“…The time delay between the PMT and hot-wire signals was calculated using a cross correlation Method [11,37]. The phase of the flame transfer function was then defined as ϕ = 2πfτ where τ (s) is the heat release time delay relative to the upstream velocity forcing [17,38].…”

“…Further, the essential physics of thermoacoustic instabilities are not entirely understood [6,7]. This is mostly due to the complexities involved in the interactions between premixed flames and sound waves [9,10] and, to some extent, the effects of system boundaries [11,12].…”

On the dissipation and dispersion of entropy waves in heat transferring channel flows

“…There is now a body of experimental [21,22] and theoretical [23,24,11] works showing that entropy noise could influence the thermoacoustic instability of laboratory scale combustors. Yet, the studies conducted in real engines revealed much less effects [25,26].…”