Two-dimensional numerical simulations of nonlinear acoustic streaming in standing waves

Numerical simulations of compressible Navier–Stokes equations in closed two-dimensional channels are performed. A plane standing wave is excited inside the channel and the associated acoustic streaming is investigated for high intensity waves, in the nonlinear streaming regime. Significant distortion of streaming cells is observed, with the centers of streaming cells pushed toward the end-walls. The mean temperature evolution associated with the streaming motion is also investigated

Etude numérique du vent acoustique non linéaire dans un résonateur à ondes stationnaires

Le vent acoustique associé aux ondes stationnaires dans un résonateur rectangulaire est étudié pour des nombres de Reynolds non-linéaires croissants, par résolution numérique des équations de Navier-Stokes compressibles moyennées sur une période. Pour des vitesses acoustiques assez grandes, des chocs sont visibles. Lorsque le Reynolds non linéaire augmente, les centres des tourbillons sont repoussés vers les parois latérales du tube. Ce résultat est en accord avec plusieurs résultats expérimentaux existants qui divergent des modèles linéaires

Acoustically induced thermal effects on Rayleigh streaming

The present study focuses on acoustically induced thermal effects on Rayleigh streaming inside a resonator. Firstly, we consider the effect of the transverse (or wall-normal) mean temperature gradient on the acoustic streaming flow generated by a standing wave between two parallel plates. Analytical expressions for acoustic quantities are developed and used to express the sources of linear streaming. The influence of a transverse temperature variation on the streaming velocity is clearly identified through a term proportional to the temperature difference and to the square of the half-width of the guide. This term modifies the Rayleigh streaming pattern and may generate an additional vortex. On the other hand, the longitudinal (or wall-parallel) temperature difference is calculated as a cumulated effect of thermoacoustic heat transport in the fluid, heat conduction in the wall and heat convection of the air outside the resonator. At high acoustic levels, heat is significantly convected by the streaming flow and the resulting transverse temperature difference is proportional to the longitudinal temperature difference. Combining these expressions brings out a new criterion parameter for the nonlinear Reynolds number (ReNL) characterizing the transition in streaming patterns at high acoustic levels. This result explains previous experimental and numerical observations of the streaming flow dynamics at high acoustic amplitudes, under different temperature boundary conditions, and can provide a powerful prediction tool for streaming pattern transitions

Inertial effects on acoustic Rayleigh streaming flow: Transient and established regimes

The effect of inertia on Rayleigh streaming generated inside a cylindrical resonator where a mono-frequency standing wave is imposed, is investigated numerically and experimentally. To this effect, time evolutions of streaming cells in the near wall region and in the resonator core are analyzed. An analogy with the lid-driven cavity in a cylindrical geometry is presented in order to analyze the physical meanings of the characteristic times. Inertial effects on the established streaming flow pattern are then investigated numerically using a code solving the time averaged Navier–Stokes compressible equations, where a mono-frequency acoustic flow field is used to compute the source terms. It is shown that inertia of streaming cannot be considered as the leading phenomenon to explain the mutation of streaming at high acoustic levels

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. 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

Acoustic and streaming velocity components in a resonant waveguide at high acoustic levels

Rayleigh streaming is a steady flow generated by the interaction between an acoustic wave and a solid wall, generally assumed to be second order in a Mach number expansion. Acoustic streaming is well known in the case of a stationary plane wave at low amplitude: it has a half-wavelength spatial periodicity and the maximum axial streaming velocity is a quadratic function of the acoustic velocity amplitude at antinode. For higher acoustic levels, additional streaming cells have been observed. Results of laser Doppler velocimetry measurements are here compared to direct numerical simulations. The evolution of axial and radial velocity components for both acoustic and streaming velocities is studied from low to high acoustic amplitudes. Two streaming flow regimes are pointed out, the axial streaming dependency on acoustics going from quadratic to linear. The evolution of streaming flow is different for outer cells and for inner cells. Also, the hypothesis of radial streaming velocity being of second order in a Mach number expansion, is not valid at high amplitudes. The change of regime occurs when the radial streaming velocity amplitude becomes larger than the radial acoustic velocity amplitude, high levels being therefore characterized by nonlinear interaction of the different velocity components

Analyse expérimentale des effets non linéaires dans les systèmes thermoacoustiques

Les phénomènes non linéaires présents dans les systèmes thermoacoustiques sont responsables de l'apparition des écoulements continus secondaires qui se superposent aux oscillations acoustiques dominantes, pénalisant l'efficacité des systèmes. L'objectif de cette étude est de caractériser le champ acoustique dans un résonateur contenant un générateur d'onde thermoacoustique et de mettre en évidence les écoulements secondaires. Nous avons mesuré le champ de vitesse par vélocimétrie par images de particules (PIV). Les premières mesures, désordonnées par rapport à la période acoustique, ont permis de reconstruire la composante acoustique sur une période, en réordonnant les vitesses suivant leur phase avec une technique de projection par décomposition en valeurs singulières (SVD) Le calcul du champ de vitesse moyenné en temps montre l'existence d'un écoulement continu. Le deuxième type de mesures, synchronisées aux mesures de pression, apportent une meilleure précision sur les écoulements secondaires. L'estimation de la vitesse acoustique est en accord avec la théorie linéaire

Une approche mécanicienne des phénomènes non linéaires en thermoacoustique

It is organized in three chapters, followed by a selection of articles. In the fist chapter, the study of acoustic streaming flow, generated by the interaction between an acoustic wave and a solid wall, is presented. The first work is experimental, on a thermoacoustic system, followed by analyses of acoustic streaming dynamics through models and numerical simulations, from low to high acoustic amplitudes. The second chapter is devoted to the numerical study of thermoacoustic wave generators. In the last chapter is presented the study of natural convection flows in thermoacoustic systems, in which the resonator is a differentially heated fluid/porous cavity.Ce mémoire synthétise mes travaux de recherche sur des phénomènes non linéaires en thermoacoustique. Il est structuré en trois chapitres, suivis d’une sélection d’articles. Le premier chapitre porte sur l’étude du streaming acoustique, engendré par l’interaction entre une onde acoustique et une paroi. La première étude est expérimentale dans un système thermoacoustique, suivie d’une étude de modélisation et simulation en guides d’ondes, à faible et fort niveaux acoustiques. Le deuxième chapitre porte sur la modélisation et simulation des moteurs thermoacoustiques. Le dernier chapitre présente l’étude des écoulements de convection naturelle dans les systèmes thermoacoustiques, dont le résonateur est une cavité fluide/poreuse, différentiellement chauffée

A numerical model of thermoacoustic heat pumping inside a compact cavity

This paper presents a numerical study of thermoacoustic heat pumping along a stack of solid plates placed inside a compact cavity submitted to an oscillating flow. Velocity and pressure fields are controlled by two acoustic sources: a main “pressure” source monitoring the fluid compression and expansion phases, and a secondary “velocity” source generating the oscillating fluid motion. Numerical simulations are performed with an “in-house” code solving Navier–Stokes equations under a Low Mach number approximation in a two-dimensional geometry. In the linear regime, thermoacoustic heat pumping is correctly described with this model for different sets of parameters such as thermo-physical properties of the stack plates, amplitude of pressure oscillation or of the velocity source, phase shift between both sources. Numerical results on the normalized temperature difference established between the ends of stack plates are in excellent agreement with analytical estimates and experimental results published in the literature. Several configurations corresponding to different thermal conditions applied on the outside wall and an inside separation plate are then considered. If the separation plate is adiabatic, temperature varies linearly along the stack, recovering classical linear theory’s results. If the separation plate is thermally conductive, the model, providing detailed description of local heat and mass transfer, shows that the temperature field becomes fully two-dimensional and thermoacoustic heat pumping is less efficient. The model is well adapted to explore the influence of local heat transfer constraints on the heat pump efficiency and thus well suited for detailed analyses of more complex mechanisms such as buoyancy effects