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.

Frozen sound: An ultra-low frequency and ultra-broadband non-reciprocal acoustic absorber.

The absorption of airborne sound is still a subject of active research, and even more since the emergence of acoustic metamaterials. Although being subwavelength, the screen barriers developed so far cannot absorb more than 50% of an incident wave at very low frequencies (<100 Hz). Here, we explore the design of a subwavelength and broadband absorbing screen based on thermoacoustic energy conversion. The system consists of a porous layer kept at room temperature on one side while the other side is cooled down to a very low temperature using liquid nitrogen. At the absorbing screen, the sound wave experiences both a pressure jump caused by viscous drag, and a velocity jump caused by thermoacoustic energy conversion breaking reciprocity and allowing a one-sided absorption up to 95 % even in the infrasound regime. By overcoming the ordinary low frequency absorption limit, thermoacoustic effects open the door to the design of innovative devices.

Test-bench for the experimental characterization of porous material used in thermoacoustic refrigerators.

The design of thermoacoustic coolers involves an adequate modeling of the thermoacoustic core's performance, which requires, in particular, a precise knowledge of their thermo-physical properties. Materials such as wire mesh stacks, foams, or compressed fibrous media are hard to describe, and their thermo-physical properties are rarely well enough quantified. Moreover, the classical linear thermoacoustic theory is not sufficient to accurately describe the performance of these materials. This paper deals with the experimental performance characterization of various materials for thermoacoustic heat pumping. A dedicated experimental test-bench has been specially developed, which is composed of two loudspeakers placed at opposite ends of a waveguide containing the porous material and a feedback loop to control the acoustic field in the porous material. Its originality is attributable to the possibility of identifying the optimal acoustic field, specific to each material, that maximizes the temperature difference at the ends of the material. Moreover, a specific protocol is implemented to access and compare the thermoacoustic heat flux through various materials at these optimal acoustic fields. Comparison of the experimental and theoretical results shows a reasonable agreement.

Noise and bias in off-axis digital holography for measurements in acoustic waveguides.

This paper discusses noise and bias in the method of holographic interferometry applied to the study of acoustics phenomena. The influence of noise on the measurement of acoustic pressure is described by an analytical approach. Relationships to quantify the minimum measurable fluid density and acoustic pressure are given by taking into account the experimental parameters of the setup. These parameters are related to the spatial bandwidths, number of electrons in pixels, readout noise, and quantization noise. Experimental results show that theoretical relations are relatively close to experimental data and that the lower pressure measurement limit is on the order of 15 Pa for the acoustics pressure. The case of waveguides excited by an internal or external acoustic source is investigated. Specifically, for the case of studies in thermoacoustics, this paper demonstrates that the parasitic coupling of vibrations can be compensated. The proposed method is based on the determination of the amplitude and phase of the parasitic oscillation, requiring a few assumptions related to the physics of the underlying phenomenon. Successful compensation is obtained and yields experimental data in agreement with the theoretical predictions.

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.

Parity-Time symmetric system based on the thermoacoustic effect.

This paper deals with the experimental study of an acoustic Parity-Time (PT) symmetric system based on the thermoacoustic amplification process. Such a system is presented and consists of two acoustic units connected through side branches to a waveguide. One unit contains a thermoacoustic core that provides an acoustic gain which balances the thermal and viscous losses taking place in the second unit. Two control parameters are set to adjust the impedance of the two units and thereby achieve the PT-symmetry condition. The results show that a good balance between gain and loss is achieved within a frequency range from 45 Hz to 60 Hz. The spontaneous PT-symmetry breaking and the existence of exceptional points, which are characteristic of the behavior of PT-symmetric systems, are explored in this frequency range. Moreover, the distance between the two units is shown to be a control parameter to slightly shift the frequency at which the exceptional points occur.

Periodic self-modulation of an electrodynamically driven heated wire near resonance.

A thin nichrome wire driven near resonance by the Lorentz force and heated by an alternating electrical current is a popular lecture demonstration. Due to the convective cooling of the portions of the wire moving with the greatest amplitude, only glowing regions near a velocity node will be visible in a darkened room. Nonlinear effects and the thermal expansion coefficient of the wire displace the wire's tensioning mass. By adiabatic invariance, the work done on or by the vibrating wire, due to the changes in the mass's elevation, causes the natural frequency of the standing wave resonance to be shifted. Competition between the thermal inertia of the wire and the convective heat transfer coefficient introduces an exponential thermal relaxation time so that the amplitude of vibration is dependent on the ratio of the drive frequency to the changing resonance frequency at an earlier (retarded) time. These thermal and kinetic effects are incorporated into three coupled nonlinear ordinary differential equations that are separated by the method of multiple time scales and are solved numerically, reproducing both the spontaneous appearance of stable periodic amplitude modulation and the hysteretic behavior observed with increasing or decreasing of the drive frequency.

Measurements of the impedance matrix of a thermoacoustic core: applications to the design of thermoacoustic engines.

The successful design of a thermoacoustic engine depends on the appropriate description of the processes involved inside the thermoacoustic core (TAC). This is a difficult task when considering the complexity of both the heat transfer phenomena and the geometry of the porous material wherein the thermoacoustic amplification process occurs. An attempt to getting round this difficulty consists in measuring the TAC transfer matrix under various heating conditions, the measured transfer matrices being exploited afterward into analytical models describing the complete apparatus. In this paper, a method based on impedance measurements is put forward, which allows the accurate measurement of the TAC transfer matrix, contrarily to the classical two-load method. Four different materials are tested, each one playing as the porous element allotted inside the TAC, which is submitted to different temperature gradients to promote thermoacoustic amplification. The experimental results are applied to the modeling of basic standing-wave and traveling-wave engines, allowing the prediction of the engine operating frequency and thermoacoustic amplification gain, as well as the optimum choice of the components surrounding the TAC.

Theoretical prediction of the onset of thermoacoustic instability from the experimental transfer matrix of a thermoacoustic core.

The aim of this paper is to propose a method to predict the onset conditions of the thermoacoustic instability for various thermoacoustic engines. As an accurate modeling of the heat exchangers and the stack submitted to a temperature gradient is a difficult task, an experimental approach for the characterization of the amplifying properties of the thermoacoustic core is proposed. An experimental apparatus is presented which allows to measure the transfer matrix of a thermoacoustic core under various heating conditions by means of a four-microphone method. An analytical model for the prediction of the onset conditions from this measured transfer matrix is developed. The experimental data are introduced in the model and theoretical predictions of the onset conditions are compared with those actually observed in standing-wave and traveling-wave engines. The results show good agreement between predictions from the model and experiments.

Measurement of acoustic streaming in a closed-loop traveling wave resonator using laser Doppler velocimetry.

This paper deals with the measurement of acoustic particle velocity and acoustic streaming velocity in a closed-loop waveguide in which a resonant traveling acoustic wave is sustained by two loudspeakers appropriately controlled in phase and amplitude. An analytical model of the acoustic field and a theoretical estimate of the acoustic streaming are presented. The measurement of acoustic and acoustic streaming velocities is performed using laser Doppler velocimetry. The experimental results obtained show that the curvature of the resonator impacts the acoustic velocity and the profile of acoustic streaming. The quadratic dependence of the acoustic streaming velocity on the acoustic pressure amplitude is verified and the measured cross-sectional average streaming velocity is in good agreement with the value predicted by the theoretical estimate.