Stability of the Rijke thermoacoustic oscillation

Abstract

The stability limit of the Rijke oscillation induced from heated wires in a tube with air current is investigated on the basis of the analysis of heat transfer. By developing a general formulation for the thermoacoustic power generation, it is shown that the in-phase component of the fluctuating heat release from a heater with the acoustic pressure can generate the acoustic power. The heat transfer response of an isothermal wire to the particle velocity of an acoustic wave is analyzed numerically by treating the flow as incompressible and two dimensional. The amplitude and phase of the fluctuating heat release are computed and displayed in graphs for various values of the air current velocity and the wire radius normalized by the angular frequency and the thermal diffusivity. The acoustic power generation from a heater wire is expressed in terms of an efficiency factor. It is found that the power generation can be maximized if both the normalized velocity of the air current and the normalized radius of the wire become around unity. By equating the acoustic power generation to the power dissipation in the tube, the limiting condition for the onset of oscillation is obtained for the steady heat input. The theoretical prediction to the stability limit is compared with available experimental data and the good agreement demonstrates a substantial verification of the present analysis.