Triggering of longitudinal combustion instabilities in rocket motors - Nonlinear combustion response

Non-normality and nonlinearity in thermoacoustic instabilities

“…This means that nonnormality helps triggering to occur from pulses that have less energy than that of the unstable periodic solution. The first clues to this behavior could be found in the observation of Wicker et al 18 that most of the energy must be in the first mode and that the phase and frequency content of the pulse is critical. The aim of this article is to explain why this is.…”

“…As well as identifying the unstable limit cycle as a threshold for the onset of triggering, 18 also discovered that the phase and frequency content of the initial pulse is influential. In particular, Wicker et al 18 found that, in order to cause triggering, most of the pulse's energy must be contained in the fundamental acoustic mode.…”

“…Below this amplitude, it will decay back to the stable base flow. 18 Triggering was first reported in solid rockets in the 1960s. 27 The first analyses were performed by Mitchell et al 28 and Zinn and Lores.…”

“…In particular, Wicker et al 18 found that, in order to cause triggering, most of the pulse's energy must be contained in the fundamental acoustic mode. This can be explained by nonlinearity alone.…”

“…16 As well as in the above references, nonlinear heat release has been examined by Refs. [17][18][19][20] Nonlinear heat release rate can cause subcritical bifurcations, whether the gas dynamics are linear or nonlinear. In general, the heat release rate is a function of the velocity and pressure fluctuations.…”