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We present an experimental and theoretical investigation of some aspects of the coupling between a premixed laminar quasi-planar flame front and acoustic standing waves in tubes. A multidimensional instability of the front arises from its interaction with the oscillating field of acceleration. This instability can be described by the Clavin–Williams laminar wrinkled flame theory in which the periodic acceleration created by the acoustic field is added to the acceleration due to gravity. As first suggested by Markstein, the resulting equation can be reduced to the Mathieu equation for a parametric oscillator. A cellular instability appears with a finite excitation threshold. This instability is responsible for the spontaneous generation of intense acoustic oscillations observed elsewhere. The value of the acoustic field at the threshold of instability and the wavelength of the cellular structures are measured experimentally for propane flames and are found to be in good agreement with the calculated values. It is also seen, both experimentally and theoretically, that for certain amplitudes of pumping, the parametric mechanism can also stabilize an initially unstable system.

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Description: Combustion is a fascinating phenomenon coupling complex chemistry to transport mechanisms and nonlinear fluid dynamics. This book provides an up-to-date and comprehensive presentation of the nonlinear dynamics of combustion waves and other non-equilibrium energetic systems. The major advances in this field have resulted from analytical studies of simplified models performed in close relation with carefully controlled laboratory experiments. The key to understanding the complex phenomena is a systematic reduction of the complexity of the basic equations. Focusing on this fundamental approach, the book is split into three parts. Part I provides physical insights for physics-oriented readers, Part II presents detailed technical analysis using perturbation methods for theoreticians, and Part III recalls the necessary background knowledge in physics, chemistry and fluid dynamics. This structure makes the content accessible to newcomers to the physics of unstable fronts in flows, whilst also offering advanced material for scientists who wish to improve their knowledge.

This paper presents the first direct experimental measurements of the growth rate of the Darrieus-Landau instability on a planar laminar premixed flame front. Prior to measurements, the intrinsically unstable flame is maintained stable by a novel technique based on the response of the flame to an acoustic parametric forcing. The growth rates of the instability, measured when the forcing is removed, are in agreement with the theoretically predicted values. [S0031-9007(98)05920-1]