Pierrick Lotton

Nonlinear System Identification Using Exponential Swept-Sine Signal

In this paper, we propose a method for nonlinear system (NLS) identification using a swept-sine input signal and based on nonlinear convolution. The method uses a nonlinear model, namely, the nonparametric generalized polynomial Hammerstein model made of power series associated with linear filters. Simulation results show that the method identifies the nonlinear model of the system under test and estimates the linear filters of the unknown NLS. The method has also been tested on a real-world system: an audio limiter. Once the nonlinear model of the limiter is identified, a test signal can be regenerated to compare the outputs of both the real-world system and its nonlinear model. The results show good agreement between both model-based and real-world system outputs.

Acoustic power flow measurement in a thermoacoustic resonator by means of laser Doppler anemometry (L.D.A.) and microphonic measurement

Abstract Acoustic power flow measurements in the resonator of a thermoacoustic refrigerator are described. The technique of measurement is based on particle velocity measurement by laser Doppler anemometry (L.D.A.) together with microphonic acoustic pressure measurement. The calibration procedure is explained and results of measurements are compared with analytical results. The L.D.A. technique permits the measurement of acoustic power flow at almost any position and for almost any working frequency in the resonator of thermoacoustic devices.

Acoustic streaming in annular thermoacoustic prime-movers

The theory of acoustic streaming in an annular thermoacoustic prime-mover is developed. It is predicted that above the threshold for traveling wave excitation the device considered (which does not contain any moving parts or externally imposed pressure gradients) produces circulation of fluid. The heat flux carried by this directional mass flow inside the thermoacoustic stack exceeds (or is comparable with) the heat flux associated with the acoustically induced increase of thermal diffusivity of the gas. The effects investigated are important for optimization of the performance of thermoacoustic devices.

Interaction of counterpropagating acoustic waves in media with nonlinear dissipation and in hysteretic media

Abstract The interaction of sound waves travelling in the opposite directions in media with quadratic nonlinearity is analyzed theoretically. It is well-known that quadratic elastic nonlinearity does not provide an effective interaction of counterpropagating acoustic waves. One of the research results presented here is rather expected. It consists of the prediction that in media with quadratic nonlinear dissipation a wave travelling in one direction induces additional attenuation of a wave travelling in the opposite direction. A more interesting result is the prediction that in media with hysteretic quadratic nonlinearity a strong sound wave travelling in one direction induces amplification of a weak sound wave travelling in the opposite direction. The threshold of the stimulated backscattering of acoustic waves in the hysteretic media is evaluated. Possible applications include thermoacoustics and acoustic diagnostics of micro-inhomogeneous materials.

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.

Enhancement of the Q of a nonlinear acoustic resonator by active suppression of harmonics

Finite-amplitude stationary acoustic waves in a closed resonator subjected to simultaneous excitation at fundamental frequency and its second harmonic are analyzed in the frame of the second-order nonlinear theory. The conditions when the dual-frequency excitation leads to a quality factor Q higher than in the case of a single-frequency excitation are derived. The Q enhancement can be explained in terms of active suppression of cascade processes of the generation of higher harmonics. The second harmonic generated in the resonator is compensated by the second harmonic radiated by the piston. Suppression of higher harmonics also can be explained as being due to effective down conversion of energy from the second harmonic to the fundamental wave in the nonlinear parametric process.

Thermal wave harmonics generation in the hydrodynamical heat transport in thermoacoustics

It is demonstrated that the temperature oscillations near the edge of the thermoacoustic stack are highly anharmonic even in the case of harmonic acoustic oscillations in the thermoacoustic engines. In the optimum regime for the acoustically induced heat transfer, the amplitude of the second harmonic of the temperature oscillations is comparable to that of the fundamental frequency.

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.

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.

Acoustic streaming related to minor loss phenomenon in differentially heated elements of thermoacoustic devices

It is demonstrated that the differentially heated stack, the heart of all thermoacoustic devices, provides a source of streaming additional to those associated with Reynolds stresses in quasi-unidirectional gas flow. This source of streaming is related to temperature-induced asymmetry in the generation of vortices and turbulence near the stack ends. The asymmetry of the hydrodynamic effects in an otherwise geometrically symmetric stack is due to the temperature difference between stack ends. The proposed mechanism of streaming excitation in annular thermoacoustic devices operates even in the absence of thermo-viscous interaction of sound waves with resonator walls.