Experimental investigation of noise induced triggering in thermoacoustic systems Vivekanandan Jegadeesan ⇑ , R.I. Sujith Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600 036, India Available online 20 June 2012 Abstract We experimentally investigate the effect of noise on the stability of a thermoacoustic system operating in a bistable region. The thermoacoustic system chosen for investigation is a ducted non-premixed flame. The system is excited by random fuel flow rate fluctuations which affects the system dynamics as parametric noise. Under the influence of noise, the system undergoes transition from stable to oscillatory state. In par- ticular, transition is observed even when the amplitude of the noise is significantly less than the triggering amplitude of the corresponding deterministic system. While triggering from noise of low amplitudes, phase portraits reveal that the system evolves transiently towards an unstable periodic orbit, before eventually growing to a stable periodic orbit. A stochastic stability map is constructed to represent the probability of the system to undergo transition. It is also observed that the amplitude of the oscillatory state is affected by the noise level. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Noise induced triggering; Non-premixed flame; Stochastic stability; Nonlinear time series analysis; Unstable attractors 1. Introduction Thermoacoustic oscillations occur in a system whenever a positive feedback loop is established between the acoustic field and the unsteady heat release rate in the system [1]. The onset of ther- moacoustic oscillations in a combustion system can be classified into two types: soft and hard excitation. A spontaneous transition from an infin- itesimally small disturbance to self-sustained oscil- lations is referred to as soft excitation or linear instability. This is observed when the operating conditions of the system are varied beyond its linear stability margin, and its occurrence can be predicted using linear stability analysis. A stable combustor (one that does not oscillate spontaneously) can be “triggered” into self-sus- tained oscillation by exciting the system with a finite amplitude disturbance. This phenomenon is referred to as hard excitation or triggering instabil- ity, or subcritical transition to instability in the dynamical systems parlance. During triggering, the thermoacoustic system evolves from a finite amplitude disturbance (a hard excitation) above a threshold amplitude called “triggering ampli- tude” [2]. When the amplitude of the initial condi- tion is less than the triggering amplitude, the system evolves asymptotically to a stable state. The phenomenon of triggering is observed when the system is operating in a hysteresis loop of the stability map. 1540-7489/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.proci.2012.05.003 ⇑ Corresponding author. E-mail addresses: viv041013@gmail.com (V. Jegadee- san), sujith@iitm.ac.in (R.I. Sujith). Available online at www.sciencedirect.com Proceedings of the Combustion Institute 34 (2013) 3175–3183 www.elsevier.com/locate/proci Proceedings of the Combustion Institute