Experimental study on liquid piston Stirling engine combined with self-rectifying turbine.

A liquid piston Stirling engine is an external combustion engine that uses air and water under atmospheric pressure as its working fluids. Resulting from its uncomplicated design and the capacity to operate under relatively low temperature differentials of less than 100 °C, it has attracted considerable attention in recent years. This paper presents the fundamental characteristics of the liquid piston engine combined with a self-rectifying turbine for the advancement of thermal generators. When the turbine is installed in the water region rather than in the air region, it exhibits unidirectional rotation with a rotational speed directly proportional to the velocity amplitude of the reciprocating axial flow. Additionally, the acoustic impedance within the duct section containing the turbine is determined, demonstrating that the real part of impedance rises with increasing axial velocity, indicating a loss mechanism similar to the minor loss. Furthermore, the installation of the turbine results in a breakdown of symmetry in the engine oscillation mode. To maintain symmetry and improve system design, future developments must consider the installation of a turbine in each unit. These findings can pave the way to the design of liquid piston Stirling engines and their applications in thermal energy conversion.

Time-resolved measurement of acoustic density fluctuations using a phase-shifting Mach-Zehnder interferometer.

Phase-shifting interferometry is one of the optical measurement techniques that improves accuracy and resolution by incorporating a controlled phase shift into conventional optical interferometry. In this study, a four-step phase-shifting interferometer is developed to measure the spatiotemporal distribution of acoustic density oscillations of the gas next to a rigid plate. The experimental apparatus consists of a polarizing Mach-Zehnder interferometer with a polarization camera capable of capturing four polarization directions in one shot image and it is used to measure the magnitude and the phase of density fluctuations through a duct of rectangular cross section connected to a loudspeaker. The results are compared with the well-established thermoacoustic theory describing the thermal coupling between acoustic oscillations and rigid boundaries, and the results show a very good agreement for various ratios of the (frequency-dependent) thermal boundary layer thickness to the plate spacing. This measurement technique could be advantageously employed to analyze more complex heat transfer processes involving the coupling of acoustic oscillations with rigid boundaries.

Study of a thermoacoustic-Stirling engine connected to a piston-crank-flywheel assembly.

This paper deals with the theoretical description of self-sustained oscillations resulting from the coupling of a piston-crank-flywheel assembly with a thermoacoustic-Stirling prime mover. The governing equations of the piston-flywheel motion are coupled to those of the thermoacoustic system, which is described in the time domain through a rational differential operator relating acoustic pressure fluctuations inside the cavity to the piston's velocity. As a result, the complete device is described by means of a fourth-order nonlinear dynamical system and solved numerically. The dynamical behavior of the system is studied as a function of the temperature difference along the thermoacoustic unit, and it is shown that the regime of stable rotations of the flywheel appears through a saddle-node bifurcation above a threshold value of the temperature difference. Moreover, the simulation results show good agreement with experiments.

Observation of thermoacoustic chaotic oscillations in a looped tube.

This study presents experimental observations of chaotic thermoacoustic oscillations induced in a looped tube with respect to both temporal and spatial dimensions and compares them with those in a resonance tube system. The wave propagation directions observed in thermoacoustic systems showing periodic behaviors are confirmed in the chaotic case, from cold to hot sides in the stack in a looped system, and with reflections at the ends of a resonance tube system. Although both systems are similar in their route to chaos and correlation dimensions of the chaotic attractor, a recurrence visualization method reveals differences in the distribution of temporal patterns resulting from the mode competition between the natural frequencies of the systems.

Bifurcation diagram of coupled thermoacoustic chaotic oscillators.

A thermoacoustic chaotic oscillator is a fluid system that presents thermally induced chaotic oscillations of a gas column. This study experimentally reports a bifurcation diagram when two thermoacoustic chaotic oscillators are dissipatively coupled to each other. The two-parameter bifurcation diagram is constructed by varying the frequency mismatch and the coupling strength. Complete chaos synchronization is observed in the region with a frequency mismatch of less than 1% of the uncoupled oscillator. In other regions, synchronization between quasiperiodic oscillations and that between limit-cycle oscillations and amplitude death are observed as well as asynchronous states.

On-off intermittency in coupled chaotic thermoacoustic oscillations.

This paper documents on-off intermittency observed in coupled thermoacoustic chaotic oscillations. Mode competition between two or three oscillation modes engenders chaotic oscillations through quasiperiodic oscillations introduced by a local cross-sectional change in a gas-filled tube. Complete synchronization is then obtained by connecting two thermoacoustic chaotic oscillators via a rigid plate with an orifice. From the analysis of pressure fluctuations, theoretical statistical scaling laws related to the laminar phases, spectral density, and amplitude probability distribution are found to be satisfied in the coupled thermoacoustic oscillators, when the thermoacoustic complete synchronization breaks down through an on-off intermittency route with the decreased orifice size.

Measurements of acoustic particle velocity in a coaxial duct and its application to a traveling-wave thermoacoustic heat engine.

We present theoretical solutions, based on linear acoustic theory, for axial acoustic particle velocity in an annular region of a coaxial duct. The solutions are expressed in terms of two non-dimensional parameters h/δ(ν) and R; h and δ(ν), respectively, represent the half of the spacing between two concentric ducts and the characteristic length given by kinematic viscosity of the gas and angular frequency of acoustic oscillations, and R is the radius ratio of the ducts. The validity of the solutions was verified by direct measurements using a laser Doppler velocimeter. The present results are applied to measurements of the acoustic power distribution in a traveling wave thermoacoustic engine with a coaxial duct, which provides experimental evidence for acoustic power feedback in the coaxial duct.

Observation of thermoacoustic shock waves in a resonance tube.

This paper reports thermally induced shock waves observed in an acoustic resonance tube. Self-sustained oscillations of a gas column were created by imposing an axial temperature gradient on the short stack of plates installed in the resonance tube filled with air at atmospheric pressure. The tube length and axial position of the stack were examined so as to make the acoustic amplitude of the gas oscillations maximum. The periodic shock wave was observed when the acoustic pressure amplitude reached 8.3 kPa at the fundamental frequency. Measurements of the acoustic intensity show that the energy absorption in the stack region with the temperature gradient tends to prevent the nonlinear excitation of harmonic oscillations, which explains why the shock waves had been unfavorable in the resonance tube thermoacoustic systems.

Acoustical power amplification and damping by temperature gradients.

Ceperley proposed a concept of a traveling wave heat engine ["A pistonless Stirling engine-The traveling wave heat engine," J. Acoust. Soc. Am. 66, 1508-1513 (1979).] that provided a starting point of thermoacoustics today. This paper verifies experimentally his idea through observation of amplification and strong damping of a plane acoustic traveling wave as it passes through axial temperature gradients. The acoustic power gain is shown to obey a universal curve specified by a dimensionless parameter ωτα; ω is the angular frequency and τα is the relaxation time for the gas to thermally equilibrate with channel walls. As an application of his idea, a three-stage acoustic power amplifier is developed, which attains the gain up to 10 with a moderate temperature ratio of 2.3.

Observation of traveling thermoacoustic shock waves (L).

Shock waves were explored in the thermoacoustic spontaneous gas oscillations occurring in a gas column with a steep temperature gradient. The results show that a periodic shock occurs in the traveling wave mode in a looped tube but not in the standing wave mode in a resonator. Measurements of the harmonic components of the acoustic intensity reveal a clear difference between them. The temperature gradient acts as an acoustic energy source for the harmonic components of the shock wave in the traveling wave mode but as an acoustic energy sink of the second harmonic in the standing wave mode.

Observation of energy cascade creating periodic shock waves in a resonator.

Nonlinear excitation of periodic shock waves in high-amplitude standing waves was studied from measurements of the acoustic intensity. A gas column of atmospheric air in a cylindrical resonator was driven sinusoidally by an oscillating piston at the fundamental resonance frequency. Acoustic pressure and axial acoustic particle velocity were simultaneously measured and decomposed into the Fourier components, from which the intensity associated with each of the oscillating modes in the resonator was determined. This letter reports the energy cascade from the driven mode to the second harmonic in the periodic shock waves in the resonator.

Experimental verification of a two-sensor acoustic intensity measurement in lossy ducts.

Two-sensor method proposed by Fusco et al. ["Two-sensor power measurements in lossy ducts," J. Acoust. Soc. Am. 91, 2229-2235 (1992)] is a novel technique that determines acoustic intensity of a gas column in a wide duct from measurements of pressure based on the boundary layer approximation. For further development of this method, its validity is experimentally tested through comparison with the direct method measuring the pressure and the velocity simultaneously, and its formulation is modified to include the narrow duct range where the duct radius is smaller than the viscous boundary layer thickness of the gas. It is shown that the modified two-sensor method enables quick and accurate evaluation of the acoustic intensity seamlessly from narrow to wide duct ranges.

Acoustic intensity measurement in a narrow duct by a two-sensor method.

The use of two pressure sensors [Fusco et al., J. Acoust. Soc. Am. 91, 2229 (1992)] makes it possible to determine the acoustic intensity of a gas column in a duct, but the application of this method was limited to wide ducts. In this letter, the formulation of the method is modified to include narrow ducts where the duct radius is as small as the viscous boundary layer thickness of the gas. The validity of this method is shown by comparison with the direct measurements of the pressure and velocity.

Determination of a response function of a thermocouple using a short acoustic pulse.

This paper reports on an experimental technique to determine a response function of a thermocouple using a short acoustic pulse wave. A pulse of 10 ms is generated in a tube filled with 1 bar helium gas. The temperature is measured using the thermocouple. The reference temperature is deduced from the measured pressure on the basis of a laminar oscillating flow theory. The response function of the thermocouple is obtained as a function of frequency below 50 Hz through a comparison between the measured and reference temperatures.

Energy flow measurements in acoustic waves in a duct.

Where, how much and how efficiently the energy conversion takes place in a regenerator of a thermoacoustic engine are expressed using the axial distribution of acoustic work flow and heat flow. As a first step in determining the energy flows inside the regenerator, measuring methods of the work flow are briefly described and the experimental results in an acoustic resonator are shown. Applicability of these methods to the regenerator is discussed.

Measurement of the Q value of an acoustic resonator.

A cylindrical acoustic resonator was externally driven at the first resonance frequency by a compression driver. The acoustic energy stored in the resonator and the power dissipated per unit time were evaluated through the simultaneous measurements of acoustic pressure and velocity, in order to determine the Q value of the resonator. The resulting Q value, being employed as a measure of the damping in a resonator, was obtained as 36. However, the Q value determined from a frequency response curve known as a conventional technique turned out to be 25, which is 30% less than that obtained in the present method. By further applying these two methods in the case of a resonator having an acoustic load inside, we present an accurate measurement of the Q value of the resonator by making full use of its definition.

Experimental demonstration of thermoacoustic energy conversion in a resonator.

Using thermoacoustic energy conversions, both amplification and damping of acoustic intensity are demonstrated. A differentially heated regenerator is installed near the velocity node of the resonator and thereby a high specific acoustic impedance and a traveling wave phase are obtained. It is shown that the gain of acoustic intensity resulting from the traveling wave energy conversion reaches 1.7 in a positive temperature gradient and 0.3 in a negative gradient. When the regenerator is replaced with a stack, it is found that the gain reaches 2.3, exceeding the temperature ratio (=1.9) of both ends of the stack. This is brought about by the addition of standing wave energy conversion. The present results would contribute to the development of new acoustic devices using thermoacoustic energy conversion.