Nonlinear/chaotic behaviour in thermo-acoustic instability

Abstract

This paper is concerned with the dynamic system nonlinear behaviour encountered in classical thermo-acoustic instability. The Poincaré map is adopted to analyse the stability of a simple non-autonomous system considering a harmonic oscillation behaviour for the combustion environment. The bifurcation diagram of a one-mode model is obtained where the analysis reveals a variety of chaotic behaviours for some select ranges of the bifurcation parameter. The bifurcation parameter and the corresponding period of a two-mode dynamic model are calculated using both analytical and numerical methods. The results computed by different methods are in good agreement. In addition, the dependence of the bifurcation parameter and the period on all the relevant coefficients in the model is investigated in depth. IntroductionVarious devices including aerospace propulsion, gas turbines, domestic boilers and radiant heaters, frequently suffer from combustion instability. It is widely recognised that the thermo-acoustic instability results from the interaction of heat release within a combustion chamber with pressure/velocity oscillations related to the chamber acoustics. Generally, the amplitude of pressure oscillation within a chamber will increase if the heat-release energy is transferred with the appropriate phase to an acoustic field, as illustrated in Rayleigh's seminal work on thermo-acoustic instability known as Rayleigh's Criterion [1]. Chu [2] proposed a more comprehensive criterion, as a generalised form of Rayleigh's criterion, considering the effect of boundary conditions and viscous dissipation, in addition to the exchange of energy between combustion and the acoustic waves. Chu's criterion reveals that thermo-acoustic instability occurs if the net energy gain from combustion exceeds the sum of the energy losses across the boundary and due to dissipation. Consequently, the amplitude of pressure fluctuations increase initially and then reach a plateau, viz., the limit cycle, owing to nonlinear effects. Therefore, it is of paramount importance to pay attention to system nonlinearities resulting in thermo-acoustic instability.In the past, the various nonlinear behaviours concerning thermo-acoustic instability have been investigated experimentally, analytically and computationally by a number of authors [3][4][5][6][7][8][9][10][11][12][13][14]. Culick [3,4] put forward a second-order nonlinear dynamic model using

Intermittency route to self-excited chaotic thermoacoustic oscillations

“…The first evidence of chaos in a self-excited thermoacoustic system was reported by Keanini, Yu & Daily (1989), who used phase-space reconstruction to identify a strange attractor in the pressure oscillations of a ramjet combustor. The next two decades, however, saw only isolated reports of chaos in thermoacoustics (Sterling 1993;Fichera, Losenno & Pagano 2001;Lei & Turan 2009). It was not until the most recent decade that widespread evidence of chaos began to emerge, facilitated by the advent of more sophisticated analysis tools based on dynamical systems theory and complex networks (Juniper & Sujith 2018).…”

Route to chaos for combustion instability in ducted laminar premixed flames

“…Jahnke and Culick 8 have reported the possibility of quasi-periodic thermoacoustic oscillations through their numerical continuation analysis of a solid rocket motor. Sterling 12 and later Lei and Turan 13 have reported chaotic oscillations through numerical bifurcation analysis of premixed combustors with different models for combustion processes. In experiments, Fichera et al 14 have reported chaotic dynamics of heat release rate fluctuations in a lean gas turbine combustor.…”

Nonlinear self-excited thermoacoustic oscillations of a ducted premixed flame: bifurcations and routes to chaos

“…These studies do not assume a priori that the system reaches period-1 oscillations (Culick 1971;Margolis 1993;Sterling 1993;Jahnke & Culick 1994;Lei & Turan 2009;Stow & Dowling 2009). These studies show that the influence of harmonics and the interaction between different modes can be modelled with the time-domain approach.…”