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

This paper presents an analytical/numerical study of the effects of the mean flow on thermoacoustic instabilities. Simple quasi-1D configurations such as a 1D premixed flame in a duct connected to a nozzle are considered in order to investigate to what extent the frequency of oscillation and growth rate are modified when the Mach number is not zero. It is demonstrated that the zero Mach number assumption for the mean flow can lead to significant errors, especially when the mean flow is not isentropic, a condition which is always met in combustion applications. The analysis confirms that terms involving the mean velocity may contribute to the disturbance energy equation as much as the flame forcing ('Rayleigh') term. Besides, the net effect of the non zero Mach number terms on the stability of the modes strongly depends on both the boundary conditions and the flame response. For moderate Mach number values of order 0.05, the errors made by assuming that the mean flow is at rest are large enough to change the stability of the frequencies of interest in an academic combustor.

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