On Flame Resonance in Tubes

Abstract

This short communication applies a recently developed theory of moderate frequency flame-acoustic interaction to the classical experimental configuration of a flame resonating in a tube.It has been well known ever since the early experiments of Lord Raylcigh, that a flame (or just a hot porous gauzes— as used by Rijke) produces a loud “ gauze tone” due to the effect of the impedance of the flame/ gauze system on the progress of the acoustic waves up and down the tube. It is the significant change in the phase of the velocity of the acoustic disturbance which is all important in the resonance which occurs, The change in velocity is governed by a “ velocity transfer function” V which in general will be a function of the type of flame and geometry used.

A theory has already been developed which exploits the largeness of activation energy 0 ₁ and also the smallness of Mach number M. to find an analytical expression for V. Thus for any flame/tube configuration, a prediction of the change in velocity of the acoustic disturbance across the combustion region can be made and an estimate given as to the amplification (or damping) of a particular frequency.

The theory is applied to predicting where the flame should sit in a constant length tube in order to cause most amplification of the gauze tone. It is found that there is very good agreement with the experimental finding, that the greatest amplification always occurs when the flame is in the lower quadrant of the tube. The fluctuating heat transfer of the flame/ gauze system is there found to cause the greatest resonance with acoustic waves.