Hélène Bailliet

Acoustic streaming in closed thermoacoustic devices

A derivation of acoustic streaming in a steady-state thermoacoustic device is presented in the case of zero second-order time-averaged mass flux across the resonator section (nonlooped device). This yields analytical expressions for the time-independent second-order velocity, pressure gradient, and time-averaged mass flux in a fluid supporting a temperature gradient and confined between widely to closely separated solid boundaries, both in the parallel plate and in the cylindrical tube geometries (two-dimensional problem). From this, streaming can be evaluated in a thermoacoustic stack, regenerator, pulse tube, main resonator of a thermoacoustic device, or in any closed tube that supports a mean temperature gradient, providing only that the acoustic pressure, the longitudinal derivative of the pressure, and the mean temperature variation are known.

Measurements of inner and outer streaming vortices in a standing waveguide using laser doppler velocimetry

Measurements of the axial streaming velocity are performed by means of laser doppler velocimetry in an experimental apparatus consisting of a waveguide having loudspeakers at each end for high intensity sound levels. Streaming is characterized by an appropriate Reynolds number Re(NL), the case Re(NL)<<1 corresponding to the so-called slow streaming and the case Re(NL)>/=1 being referred to as fast streaming. The variation of axial streaming velocity with respect to the transverse coordinate is compared to the available slow streaming theory. Streaming fluid flow is measured both in the core region and in the near wall region. Streaming velocity in the center of the guide agrees reasonably well with the slow streaming theory for small Re(NL) but deviates significantly from such predictions for Re(NL)>20 and its evolution for further increasing Re(NL) is discussed. Then streaming behavior in the near wall region is particularly studied. For Re(NL)<70, two vortices are present across the guide section as predicted by slow streaming theory. Then it appears that, when the Reynolds number is increased, two other vortices become visible in the near wall region. Different stages for the generation and evolution of these inner streaming vortices are presented.

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.

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.

Experimental investigation of acoustic streaming in a cylindrical wave guide up to high streaming Reynolds numbers.

Measurements of streaming velocity are performed by means of Laser Doppler Velocimetry and Particle Image Velociimetry in an experimental apparatus consisting of a cylindrical waveguide having one loudspeaker at each end for high intensity sound levels. The case of high nonlinear Reynolds number ReNL is particularly investigated. The variation of axial streaming velocity with respect to the axial and to the transverse coordinates are compared to available Rayleigh streaming theory. As expected, the measured streaming velocity agrees well with the Rayleigh streaming theory for small ReNL but deviates significantly from such predictions for high ReNL. When the nonlinear Reynolds number is increased, the outer centerline axial streaming velocity gets distorted towards the acoustic velocity nodes until counter-rotating additional vortices are generated near the acoustic velocity antinodes. This kind of behavior is followed by outer streaming cells only and measurements in the near wall region show that inner streaming vortices are less affected by this substantial evolution of fast streaming pattern. Measurements of the transient evolution of streaming velocity provide an additional insight into the evolution of fast streaming.

Fast acoustic streaming in standing waves : Generation of an additional outer streaming cell

Rayleigh streaming in a cylindrical acoustic standing waveguide is studied both experimentally and numerically for nonlinear Reynolds numbers from 1 to 30 [Re(NL)=(U0/c0)(2)(R/δν)(2), with U0 the acoustic velocity amplitude at the velocity antinode, c0 the speed of sound, R the tube radius, and δν the acoustic boundary layer thickness]. Streaming velocity is measured by means of laser Doppler velocimetry in a cylindrical resonator filled with air at atmospheric pressure at high intensity sound levels. The compressible Navier-Stokes equations are solved numerically with high resolution finite difference schemes. The resonator is excited by shaking it along the axis at imposed frequency. Results of measurements and of numerical calculation are compared with results given in the literature and with each other. As expected, the axial streaming velocity measured and calculated agrees reasonably well with the slow streaming theory for small ReNL but deviates significantly from such predictions for fast streaming (ReNL>1). Both experimental and numerical results show that when ReNL is increased, the center of the outer streaming cells are pushed toward the acoustic velocity nodes until counter-rotating additional vortices are generated near the acoustic velocity antinodes.

Development of Laser Techniques for Acoustic Boundary Layer Measurements. Part II: Comparison of LDV and PIV Measurements to Analytical Calculation

The adaptation of Laser Doppler Velocimetry (LDV) and Particle Image Velocimetry (PIV) for acoustic boundary layer measurements is considered. The specificities of acoustic boundary layer are presented and the theoretical expression of acoustic particle velocity is reminded. Appropriate parameters of the PIV system for sound measurements are determined. Results of LDV and PIV measurements of particle velocity profiles in acoustic boundary layers are compared with theoretical predictions based on the literature for different phases along the acoustic period. These results are very satisfactory and show that these two techniques are suitable for acoustic boundary layer measurements.

Development of Laser Techniques for Acoustic Boundary Layer Measurements. Part I: LDV Signal Processing for High Acoustic Displacements

A statistical model of the Laser Doppler signal in the case of pure acoustics is proposed. It appears that two different cases should be considered depending on the ratio of acoustic displacement amplitude to probe volume diameter. The processing of Laser Doppler Velocimetry signal in the case of high particle displacements (with oscillations across the measuring volume) is then considered. A specific signal post-processing strategy is proposed to determine the acoustic frequency, the acoustic velocity amplitude and its phase. First, the acoustic frequency is estimated by means of synchronous analysis weighted by arrival times. Then, the signal is uniformly re-sampled and the phase of the acoustic velocity is calculated. Lastly, a least-square method weighted by local probability density function is used to determine the acoustic velocity amplitude. This method permits an accurate estimation of the three acoustic parameters (frequency, velocity amplitude and phase) even in the adverse conditions induced by the proximity of a wall and is applied to oscillating viscous boundary layer measurements.

Analysis of the Acoustic Flow at an Abrupt Change in Section of an Acoustic Waveguide Using Particle Image Velocimetry and Proper Orthogonal Decomposition

In the vicinity of an abrupt change in cross section, an acoustic wave generates a nonlinear flow. This is investigated experimentally using Particle Image Velocimetry (PIV). The effect of both the acoustic level and the radius of curvature of the abrupt change in section on the flow is studied. At sufficiently high acoustic levels, and past a value of about 0.5 for the Strouhal number, the flow separates and a vortex is formed. Its evolution with the different parameters is studied. Proper Orthogonal Decomposition (POD) is applied to the ensemble of phase-averaged flow fields in the vicinity of the abrupt change. It is used as a means to separate the global acoustic movement from the localized non linear movements induced by it. The quantity of energy flowing from the first (acoustic) mode toward the higher (nonlinear) modes is calculated and is shown to be largely governed by the Strouhal number.