A parametric acoustic instability in premixed flames

Abstract

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.

DNS of Intrinsic ThermoAcoustic modes in laminar premixed flames

“…(18) may be satisfied only in a restricted frequency range, within which the phase criterion arg (F(ω)) = π (Eq. (16)) must also be satisfied to trigger an unstable ITA mode 7 .…”

On-shell description of unsteady flames

“…In particular, it prevents the development of singularities of the front shape such as the edge points which would occur otherwise [15], leading to discontinuities in the values of the flow variables or their derivatives. That λ c often exceeds the actual thickness of the flame preheat zone significantly [16] has yet another virtue: the Reynolds number based on λ c and the fuel properties is typically over ∼ 10 2 , and hence is fairly large when based upon the width (> λ c or ≫ λ c ) of the channel where the flame studied below is meant to propagate. It then makes sense to model the flame as a surface (or line in 2-D) equipped with a local λ c -dependent propagation law, and embedded in ideal fluid flows.…”

Onset mechanism of primary acoustic instability in downward-propagating flames

“…He reported four distinct regimes of downward-propagating flames in a tube: (1) a curved flame with no acoustic sound just after ignition; (2) a primary acoustic instability with a flat flame surface when the flame has reached the lower half of the tube; (3) a violent secondary acoustic instability with a corrugated flame; and (4) turbulent flame. The secondary acoustic instability has been distinctly studied experimentally [2,3]. The physical initiation mechanism of this instability is periodic acceleration of the flame separating dense and tenuous regions, which is similar to Faraday instability [4].…”

“…An analytical analysis of this mechanism was further performed by Pelcé and Rochwerger [11] in connection with the experiments conducted by Searby [1]. They studied the coupling with variation in the flame surface area produced by the presence of an initial curved structure due to D-L instability and demonstrated that the growth rate of the primary acoustic instability is proportional to (ak) 2 , where a is an amplitude and k is a wave number of the curved flame. For this study, they used a more complete model for flame dynamics that adopted stability limits of the D-L instability [9] and gravity effects into the problem in order to estimate a situation close to that of real propagating flames.…”