The mechanics of vibrating flames in tubes

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Abstract
A mechanism of flame vibration is proposed which depends upon the instability of a reacting gas with respect to wave motion. A flame, steadily advancing down a tube, is represented by a narrow section of reacting gas bounded on either side by non-reacting gases at appropriate temperatures. By matching the derivatives of the velocity potentials of the reacting gas and the non-reacting gases at the two interfaces the dynamical properties of the flame are investigated. Relative values of the intensities of the possible acoustic modes, as well as their frequencies, are calculated and are shown to be in general agreement with observations. The pressure oscillations at the end of a closed tube in the unburnt gases are investigated and it is shown how such measurements can provide an experimental determination of the rate of growth of the amplitudes of the permissible modes of vibration.

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