Thermoacoustic spontaneous oscillations are now in topics of conversation. Studies on thermoacoustic phenomena, starting with the investigation of the Taconis oscillation, have led to the thermoacoustic theory, which contributed to understanding of the Stirling engine, regenerative refrigerators and the dream pipe. A variety of the thermoacoustic oscillations are classified into open tube type, closed tube type and looped tube type. Geometries of the tube restrict the oscillation frequency. A regenerator (or a stack) in these tubes is a key component. Although the regenerator in the open tube and closed tube is a source of work flow, the regenerator in the looped tube sometimes becomes an amplifier of work flow. Thermodynamic discussion on heat engine indicates that the increment of entropy flow, ΔS, has a decreasing tendency, and thermodynamic discussion on thermoacoustic spontaneous oscillation indicates that nature selects a branch of smallest ΔS. A law of minimizing increment of entropy flow is proposed.
A primitive understanding of fluid oscillation in resonator tube is based on the standing wave approximation. Recent progress in studies on thermoacoustic spontaneous oscillation requires us to make a more realistic image of fluid oscillation in resonator tube. Finite Q-value means some dissipation of work flow in the resonator. Analogous discussion to a transmission line with finite damping successfully leads to empirical equations on the resonance curve and distribution of pressure and velocity amplitudes. The result, however, does not exclude the possibility of negative damping, since this treatment abandons completely information on phase difference between pressure and velocity. The phase difference and the work flow are included in the thermoacoustic theory. Recent progress on experimental techniques makes it possible to observe the phase difference and the work flow, which is rarely discussed in traditional acoustics.
The oscillation of gas in a looped tube is different from that in a non looped tube. Although the oscillation mode in the non looped tube is dominantly decided by boundary conditions at both ends of the tube, the oscillation mode in the looped tube is put under the control of the law of minimum entropy production. The oscillation frequency is near the resonance frequency of the looped tube, if the effect of the branch tube is negligibly small. But if the effect is large enough, a frequency significantly lower than the resonance frequency of the loop is available. The other roles of the branch tube are discussed for both the liquid Stirling engine and the thermoacoustic Stirling engine developed at Los Alamos. Traditional thermoacoustic devices with solid displacers are regarded as variations of a looped tube system with a branch. The final discussion is on the possibility of a looped pulse-tube refrigerator, which is equipped with neither the buffer tank nor the 4-valve controller.