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Large-activation-energy theory for premixed combustion under the influence of enthalpy fluctuations

Published online by Cambridge University Press:  14 May 2010

XUESONG WU  and
PARVIZ MOIN
XUESONG WU
Affiliation:
Department of Mathematics, Imperial College London SW7 2AZ, UK
PARVIZ MOIN
Affiliation:
Department of Mechanical Engineering, Stanford University, CA 94305, USA
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Abstract

This paper presents a mathematical theory for premixed combustion under the influence of enthalpy fluctuations in the oncoming fresh mixture. On the basis of the assumptions of large activation energy and small Mach number, an analysis of the thermal, hydrodynamic and acoustic regions of a flame is performed to derive an interactive system that describes, on the first-principles basis, the intricate coupling between the flame and its spontaneously emitted acoustic waves. The system, in its general form, is strongly nonlinear and requires a numerical attack. In this paper, it is employed to analyse several fundamental physical processes in relatively simple cases in order to provide useful insights into the role of enthalpy fluctuations in combustion. First, the linear response of the flame to two- or three-dimensional small-amplitude enthalpy fluctuations is considered, and they are found to generate hydrodynamic motion. Secondly, enthalpy fluctuations are shown to radiate sound waves through their interaction with the flame. Thirdly, enthalpy fluctuations and the sound waves emitted by them modify the flame stability, and the analysis shows that a moderate level of enthalpy fluctuation may cause a strong subharmonic parametric instability. Finally, in the small-heat-release limit, an extended Michelson–Sivashinsky equation is derived to describe the nonlinear evolution of the flame under the influence of both the imposed enthalpy fluctuations and the induced acoustic waves. Numerical solutions suggest that the flame evolves into a time-periodic state and acquires a curved profile, which primarily vibrates in the longitudinal direction, while its overall shape remains almost unaltered.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 655 , 25 July 2010 , pp. 3 - 37
Copyright
Copyright © Cambridge University Press 2010

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