Guillaume Penelet

Experimental investigation of transient nonlinear phenomena in an annular thermoacoustic prime-mover: observation of a double-threshold effect

Thermoacoustic engines have been subjected to numerous studies for the past 10 years. Our current research is focused on the transient regime in an annular thermoacoustic prime-mover. It appears that several nonlinear phenomena can play a role in the amplification and saturation regimes. Indeed, acoustically induced conductivity, forced convection due to acoustic streaming, minor loss phenomenon, and saturation due to harmonic generation can be quoted among the others. The experiments presented here show for the first time a double-threshold phenomenon during the amplification regime. The first threshold, which corresponds to the setting of the thermoacoustic instability, is followed by a saturation regime. Then after a time delay, without any changes in the control parameters, a second threshold corresponding to an additional amplification has been observed.

On the Use of a Complex Frequency for the Description of Thermoacoustic Engines

In this paper, a formulation is proposed to describe the process of thermoacoustic amplification in thermoacoustic engines. This formulation is based on the introduction of a complex frequency which is calculated from the transfer matrices of the thermoacoustic core and its surrounding components. The real part of this complex frequency represents the frequency of self-sustained acoustic oscillations, while its imaginary part characterizes the amplification/attenuation of the wave due to the thermoacoustic process. This formalism can be applied to any type of thermoacoustic engine including stack-based or regenerator-based systems as well as straight, closed loop or coaxial duct geometries. It can be applied to the calculation of the threshold of thermoacoustic instability, but it is also well-suited for the description of the transient regime of wave amplitude growth and saturation due to non linear processes. All of the above mentioned aspects are described in this paper.

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.

Synchronization of a thermoacoustic oscillator by an external sound source

Since the pioneering work of Christiaan Huygens on the sympathy of pendulum clocks, synchronization phenomena have been widely observed in nature and science. In this paper, we describe a simple experiment, with a thermoacoustic oscillator driven by a loudspeaker, which exhibits several aspects of synchronization. Both the synchronization region of leading order around the oscillators natural frequency f0 and regions of higher order (around f0∕2 and f0∕3) are measured as functions of the loudspeaker voltage and frequency. We also show that increasing the coupling between the loudspeaker and the oscillator gives rise under some circumstances to the death of self-sustained oscillations (quenching). Moreover, two additional set of experiments are performed: the first investigates a feedback loop in which the signal captured by the microphone is delivered to the loudspeaker through a phase-shifter; the second investigates the nontrivial interaction between the loudspeaker and the oscillator when the latter a...

Active control of thermoacoustic amplification in an annular engine

In this paper, a new method is proposed to control the thermoacoustic amplification in thermoacoustic engines. This method, based on the active control of the spatial distribution of the acoustic field by means of auxiliary acoustic sources, is applied here to an annular thermoacoustic engine. Two auxiliary acoustic sources are used to tune the spatial distribution of the sound field in the engine in such a way that the thermal-to-acoustic energy conversion occurring into the thermoacoustic core is maximized. An experimental study of this device is proposed, which should be considered as a proof-of-concept study, aiming at demonstrating that the addition of auxiliary acoustic sources can be used advantageously to improve the efficiency of thermoacoustic engines. The overall device is characterized below and above the onset of thermoacoustic instability. It is demonstrated that below the onset of thermoacoustic instability, there exists an optimum phase shift between the auxiliary sources which maximizes the acoustic power available in the annular waveguide. When the device is operated above the onset of thermoacoustic instability, it is demonstrated that the appropriate tuning of the two auxiliary sources enables to improve significantly the acoustic work produced into the engine (compared to the case without active control), that the additional output acoustic power is significantly larger than the input electric power supplied to the acoustic sources, and that the overall efficiency of the engine is thus significantly increased. A discussion about the applicability of this new method for the improvement of actual, high power thermoacoustic engines is also provided.

Experimental and theoretical study of the dynamics of self-sustained oscillations in a standing wave thermoacoustic engine

A model for the description of the transient regime leading to steady-state sound in a quarter-wavelength thermoacoustic prime mover is proposed, which is based on the description of the unsteady heat transfer in the system, coupled with an ordinary differential equation describing wave amplitude growth/attenuation. The equations are derived by considering a cross-sectional averaged temperature distribution along the resonator, and by assuming that both the characteristic time associated with heat diffusion through the stack and that associated with the thermoacoustic amplification are much larger than the acoustic period. Attention is here focused on the only mechanism of saturation due to heat transport by sound within the stack. The numerical solving of the governing equations leads to the prediction of the transient regime, which is compared with experimental results for several values of the heat power supplied to the system and for several positions of the stack in the resonator. The model reproduce...

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.

Active control of thermoacoustic amplification in a thermo-acousto-electric engine

In this paper, a new approach is proposed to control the operation of a thermoacoustic Stirling electricity generator. This control basically consists in adding an additional acoustic source to the device, connected through a feedback loop to a reference microphone, a phase-shifter, and an audio amplifier. Experiments are performed to characterize the impact of the feedback loop (and especially that of the controlled phase-shift) on the overall efficiency of the thermal to electric energy conversion performed by the engine. It is demonstrated that this external forcing of thermoacoustic self-sustained oscillations strongly impacts the performance of the engine, and that it is possible under some circumstances to improve the efficiency of the thermo-electric transduction, compared to the one reached without active control. Applicability and further directions of investigation are also discussed.

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.

Account of heat convection by Rayleigh streaming in the description of wave amplitude growth and stabilization in a standing wave thermoacoustic prime-mover.

This study focuses on the transient regime of wave amplitude growth and stabilization occuring into a standing wave thermoacoustic engine. Experiments are performed on a standing wave thermoacoustic oscillator. They show that the transient regime leading to steady state sound exhibits complicated dynamics, like the systematic overshoot of wave amplitude before its final stabilization, and the spontaneous and periodic switch on/off of the thermoacoustic instability at constant heat power supply. A simplified model is presented which describes wave amplitude growth from the coupled equations governing thermoacoustic amplification and unsteady heat transfer. In this model, the assumption of a one-dimensional temperature profile is retained and the equations describing heat transfer through the thermoacoustic core are coupled to that describing wave amplitude growth. These equations include the simplified description of two processes saturating wave amplitude growth, i.e. thermoacoustic heat pumping by acoust...