Modeling the influence of interactions on different variables in a turbulent thermoacoustic system

TL;DR

This paper introduces a reduced-order model for turbulent thermoacoustic systems that captures how local interactions influence global oscillatory behavior, reproducing complex dynamics like chaos, bifurcation, and multifractality.

Contribution

The novel model uses nonlinear oscillators with variable forcing terms to represent local-global interactions, accurately simulating complex thermoacoustic phenomena.

Findings

Reproduces multifractal characteristics of acoustic fluctuations

Captures transition from chaos to order via scaling laws

Models emergence of periodicity and bifurcation in heat release

Abstract

Turbulent reacting flows confined to ducts are plagued by thermoacoustic instability, a state in which a positive feedback between flow, flame and acoustic perturbations leads to the emergence of catastrophically high-amplitude oscillatory dynamics in the sound and global heat release rate fluctuations. Modeling the interdependence between local interactions and the global emergence of order in such spatially extended complex systems is exacting. Here, we present a novel reduced-order model to capture the influence of the local interactions on the variables exhibiting global emergence of order in a turbulent reacting flow system. We represent each variable that exhibits global oscillatory instability as an oscillator with a cubic nonlinearity. The oscillator is driven by a forcing term that represents the holistic influence of the inter-subsystem interactions on the global behavior. The forcing term essentially couples the local interactions and the globally emergent dynamics in the model. Further, the influence of the inter-subsystem interactions on the behavior of each subsystem is different. Therefore, we use different forcing terms for each variable inspired by the physical interactions in the system. The nonlinear oscillators representing the acoustic and the heat release rate oscillations are hence forced using Wiener and Markov-modulated Poisson processes, respectively. Using this approach, we are able to reproduce (i) the multifractal characteristics of acoustic pressure fluctuations during chaotic dynamics, (ii) the loss of multifractality through the experimentally observed scaling law behavior during the transition from chaos to order and (iii) the emergence of periodicity and bifurcation in heat release rate dynamics.