Combustion-Acoustic Interaction of a Flat Flame Burner System Enclosed Within an Open Tube

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Abstract
Previous theories of flame/acoustic interaction have successfully modelled the coupling of acoustic oscillations with combustion zone fluctuations of a flat flame. These theories are now extended to include the effect of (a) finite tube length both upstream and downstream of the burner and (b) the impedance of the burner itself. The inclusion of these effects has led to realistic modelling of some experiments conducted in recent years. In particular it is found that all important is the impedance of the acoustic wave just downstream of the flame. Due to the interaction of the acoustic disturbance with diffusive effects within the combustion zone (which effects are now on the same time scale as an acoustic time period), the phase difference between the pressure and velocity fluctuations can change sign. It is this phenomenon which will precipitate acoustic resonance for flames with upstream and/or downstream ports. A particular mode, determined by the geometry of the system, will induce a positive or negative phase-shift in the downstream impedance of the signal. Depending on the value of this phase-shift, resonance will or will not occur. For some situations it is well known that acoustic amplification can take place. The theory presented here is used to confirm that amplification of acoustic signals of low frequency can occur for a burner with an upstream port, although the exact value of amplification will depend on the way the impedance of the burner varies with frequency.