Analysis of heat-driven oscillations of gas flows

The case treated is that of a straight tube open at both ends and provided with a hot wire gauze composed of a thin spirally wound metallic wire. The general form of the characteristic equation governing the excitation of sound when air is forced to flow through the tube was derived in a previous paper. A discussion now follows of the transfer functions of the hot wire gauze and the dissipation of acoustic energy in the tube; it is shown that a first-order solution of the characteristic equation can be obtained that accounts for the main features of the Rijke-tube phenomenon, viz. that excitation of the fundamental frequency of the tube occurs only when the hot wire gauze is in the entrance half of the tube, and that maximum excitation occurs when it is located at about one fifth of the tube length from the entrance. Neutral curves for the fundamental frequency are calculated which show that for excitation to occur the Strouhal number of the hot wire should have a value within a critical range. This means that to any given dimensions of the tube and the wire gauze there corresponds a critical range of values of the mean velocity of the gas flow outside which there should be no sound generation. Finally neutral curves for the first overtone are presented that show that there are two positions of the wire gauze that give rise to excitation of this harmonic.