Bifurcation structure of the flame oscillation

TL;DR

This study combines simulation and experiments to analyze the bifurcation structure of flame oscillations, revealing hysteresis, bistability, and the influence of fuel-inlet diameter on oscillation characteristics.

Contribution

It provides the first combined simulation and experimental analysis of flame bifurcation structure, demonstrating the subcritical Andronov-Hopf bifurcation in flame oscillations.

Findings

Hysteresis and bistability observed in simulations.

Switching between stationary and oscillatory states in experiments.

Amplitude increases and frequency decreases with larger fuel-inlet diameter.

Abstract

A flame exhibits a limit-cycle oscillation, which is called "flame flickering" or "puffing", in a certain condition. We investigated the bifurcation structure of the flame oscillation in both simulation and experiment. We performed a two-dimensional hydrodynamic simulation by employing the flame sheet model. We reproduced the flame oscillation and investigated the parameter dependences of the amplitude and frequency on the fuel-inlet diameter. We also constructed an experimental system, in which we could finely vary the fuel-inlet diameter, and we investigated the diameter-dependences of the amplitude and frequency. In our simulation, we observed the hysteresis and bistability of the stationary and oscillatory states. In our experiments, we observed the switching between the stationary and oscillatory states. As fluctuations can induce the switching in the bistable system, switching observed in our experiments suggested the bistability of the two states. Therefore, we concluded that the oscillatory state appeared from the stationary state through the subcritical Andronov-Hopf bifurcation in both the simulation and experiment. The amplitude was increased and the frequency was decreased as the fuel-inlet diameter was increased. In addition, we visualized the vortex structure in our simulation and discussed the effect of the vortex on the flame dynamics.