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.

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.