Recurrence networks to study dynamical transitions in a turbulent combustor

Abstract

Thermoacoustic instability and lean blowout are the major challenges faced when a gas turbine combustor is operated under fuel lean conditions. The dynamics of thermoacoustic system is the result of complex nonlinear interactions between the subsystems-turbulent reactive flow and the acoustic field of the combustor. In order to study the transitions between the dynamical regimes in such a complex system, the time series corresponding to one of the dynamic variables is transformed to an ε-recurrence network. The topology of the recurrence network resembles the structure of the attractor representing the dynamics of the system. The transitions in the thermoacoustic system are then captured as the variation in the topological characteristics of the network. We show the presence of power law degree distribution in the recurrence networks constructed from time series acquired during the occurrence of combustion noise and during the low amplitude aperiodic oscillations prior to lean blowout. We also show the absence of power law degree distribution in the recurrence networks constructed from time series acquired during the occurrence of thermoacoustic instability and during the occurrence of intermittency. We demonstrate that the measures derived from recurrence network can be used as tools to capture the transitions in the turbulent combustor and also as early warning measures for predicting impending thermoacoustic instability and blowout.

Network broadcast analysis and control of turbulent flows

“…The Lagrangian motion of fluid elements has been used to quantify interactions in fluid flows (Ser-Giacomi et al 2015;Iacobello et al 2019). Time series of fluid-flow properties have been considered to establish visibility graphs and recurrence networks, extracting dynamical features of complex flows (Godavarthi et al 2017;Scarsoglio, Cazzato & Ridolfi 2017). Network analysis has been used to study triadic interactions in turbulent flows (Gürcan 2017) and to model vortical interactions in Lagrangian and Eulerian settings (Nair & Taira 2015;Taira, Nair & Brunton 2016;Gopalakrishnan Meena, Nair & Taira 2018).…”

Early warning signals indicate a critical transition in Betelgeuse

“…This pattern of return times is known to change near critical transitions (Wissel 1984), which reflects as changes in RQA measures. RQA measures have been used for the characterization of system dynamics in different domains such as climate studies (Zhao et al 2011), physiological data analysis (Acharya et al 2011;Marwan et al 2002), stock markets (Bastos & Caiado 2011), and engineering (Godavarthi et al 2017). They have been particularly useful for the identification of dynamical transitions, including periodic-chaos and chaoschaos transitions, as well as intermittent states (Marwan et al 2013;Godavarthi et al 2017).…”

Bayesian Machine Learning for the Prognosis of Combustion Instabilities From Noise

“…Similarly, Nair and colleagues [15] show the disappearance of the multifractal signature of combustion noise as it transitions to instability and note that measures such as the Hurst exponent can serve as an early warning of thermoacoustic instabilities. A follow-up study by Godavarthi et al [16] looks at measures derived from recurrence networks as instability precursors. Kobayashi et al [17] use a modified version of the permutation entropy to detect a precursor of the frequency-mode-shift in their staged aircraft engine model combustor before the amplification of pressure fluctuations.…”