Statistical characteristics of pressure oscillations in a premixed combustor

This paper describes an investigation of the statistical characteristics of self-excited and noise-driven pressure oscillations in a premixed combustor. This work was motivated by observations that certain characteristics of these oscillations appear random and cannot be entirely characterized within a deterministic framework (e.g., spontaneous, noise-induced transitions of the combustor from stable to unstable operation or cycle-to-cycle variations in the oscillating pressure). In an effort to elucidate these stochastic elements, we performed an analysis of cycle-to-cycle variations in combustor pressure whose results are described in this paper. Data obtained from our combustor shows that the probability density function of the amplitude of these oscillations transitions from a Rayleigh to a Gaussian-type distribution as the combustor moves from stable to unstable operation. These data also show that the instability phase is nearly uniformly distributed; i.e., there is no phase value with maximum probability of occurrence. We also describe a theoretical analysis of the statistical features of a non-linear combustor model that is forced by random noise. Solutions of this model are presented and shown to be in agreement with measured data. The good agreement between the predictions and measured data suggest that the analysis presented in this paper provides a useful framework for interpreting many other apparently random features of combustor stability characteristics; for example, cyclic variability, “fuzziness” in stability boundaries, or noise-induced transitions.