Dynamic Behavior of Buoyancy-Induced Flame Oscillation Under Swirling Flow by a Use of Nonlinear Time Series Analysis in Combination with Surrogate Data Method

Abstract

The authors experimentally investigated the dynamic behavior of buoyancy-induced flame oscillation under a swirling flow produced by rotating a cylindrical burner tube, focusing on the characterization of the complex dynamics in flame front by a use of nonlinear time series analysis. A Wayland method (R. Wayland et al., 1993), which quantifies the degree of parallelism of trajectories in phase space constructed from time series data of flame front fluctuations, is applied as a sophisticated nonlinear time series analysis in this work. To reveal whether or not the complex dynamics is deterministic chaos, a quantitative method for discussing the null hypothesis that the irregular components of the flame front fluctuations represent a stochastic process (i.e., a surrogate data method; T. Schreiber and A. Schmitz, 1996), is applied in this work. A sophisticated nonlinear time series analysis in combination with a surrogate data method, which has not been widely applied to the study of combustion phenomena, clearly demonstrates that the dynamic behavior undergoes a significant transition from periodic oscillation to low-dimensional deterministic chaos with increasing rotational Reynolds number.

Keywords:

• Buoyancy
• Chaos
• Diffusion flame
• Flickering
• Nonlinear time series analysis
• Surrogate data method
• Swirling flow

ACKNOWLEDGMENTS

Hiroshi Gotoda was partially supported by a Research Grant from the Mazda Foundation, Research Grant from Kurata Hitachi Science Technology Foundation, CASIO Science Foundation, Sasakawa Scientific Research Grant from The Japan Science Society, and a Grant-in-Aid for Young Scientists (B) from the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT). The authors are very grateful to S. Mazubara (Ritsumeikan University) for his assistance in conducting the experiments, and to Junya Okuda (Photron Co) for helping to use the high-speed video camera (Photron Co., FASTCAM SA5) employed in this study.