This report describes the operation of a liquid piston engine that uses thermoacoustic spontaneous oscillations of liquid and gas columns connected in series to form a loop. Analysis of the analogous mass-spring model and the numerical calculation based on hydrodynamic equations shows that the natural mode oscillations of the system allow the working gas to execute a Stirling thermodynamic cycle. Numerical results of the operating temperature difference were confirmed from experimentally obtained results.
This study experimentally analyzes the cessation of self-sustained periodic oscillations of gas columns in delay-coupled Rijke tube oscillators. The Rijke tube oscillator comprised an open-ended resonance tube with a Bunsen burner inserted into it. Delay coupling was introduced using acoustic waves propagating through a gas-filled tube with both ends connected to the resonance tubes. Two coupling methods, single- and double-tube coupling, were tested for comparison. A significant reduction in the acoustic amplitude was observed with relatively narrow tubes in double-tube coupling when the tube lengths were equal to half the wavelength and one wavelength of the acoustic waves of the uncoupled oscillator. The experimental results were analyzed using the theoretical model of the delay-coupled Rijke tube oscillators, whose coupling strength varied with the delay time. The present results would be useful in establishing a simple method for suppressing unwanted acoustic oscillations observed in various combustors.
This paper develops a stability analysis for the onset of thermoacoustic oscillations in a gas-filled looped tube with a stack inserted, subject to a temperature gradient. Analysis is carried out based on approximate theories for a thermoviscous diffusion layer derived from the thermoacoustic-wave equation taking account of the temperature dependence of the viscosity and the heat conductivity. Assuming that the stack consists of many pores axially and that the thickness of the diffusion layer is much thicker than the pore radius, the diffusion wave equation with higher-order terms included is applied for the gas in the pores of the stack. For the gas outside of the pores, the theory of a thin diffusion layer is applied. In a section called the buffer tube over which the temperature relaxes from that at the hot end of the stack to room temperature, the effects of the temperature gradient are taken into account. With plausible temperature distributions specified on the walls of the stack and the buffer tube, the solutions to the equations in both theories are obtained and a frequency equation is finally derived analytically by matching the conditions at the junctions between the various sections. Seeking a real solution to the frequency equation, marginal conditions of instability are obtained numerically not only for the one-wave mode but also for the two-wave mode, where the tube length corresponds to one wavelength and two wavelengths, respectively. It is revealed that the marginal conditions depend not only on the thickness of the diffusion layer but also on the porosity of the stack. Although the toroidal geometry allows waves to be propagated in both senses along the tube, it is found that the wave propagating in the sense from the cold to the hot end through the stack is always greater, so that a travelling wave in this sense emerges as a whole. The spatial and temporal variations of excess pressure and mean axial velocity averaged over the cross-section of a flow passage are displayed for the two modes of oscillations at the marginal state. The spatial distribution of mean acoustic energy flux (acoustic intensity) over one period is also shown. It is unveiled that the energy flux is generated only in the stack, and it decays slowly in the other sections by lossy effects due to a boundary layer. Mechanisms for the generation of the acoustic energy flux are also discussed.
Quasiperiodic oscillations can occur in nonequilibrium systems where two or more frequency components are generated simultaneously. Many studies have explored the synchronization of periodic and chaotic oscillations; however, the synchronization of quasiperiodic oscillations has not received much attention. This study experimentally documents forced synchronization of the quasiperiodic state and the internally locked state of a thermoacoustic oscillator system. This system consists of a gas-filled resonance tube with a nonuniform cross-sectional area. The thermoacoustic oscillator was designed and built in such a way that nonlinear interactions between the fundamental acoustic oscillation mode and the third mode of the gas column are controlled by a temperature difference that is locally created in the resonance tube. Bifurcation diagrams were mapped out by changing the forcing strength and frequency. Separated Arnold tongues were found and both modes were entrained to the external force through complete synchronization. A saddle-node bifurcation was observed in the route from partial to complete synchronization when the forcing strength was relatively weak. However, a Hopf (torus-death) bifurcation was observed when the forcing was relatively strong. In the internally locked state, the bifurcation occurred after the internal locking was broken down by the external force.
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