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

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

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

Hydrodynamics of thermal granular convection

A hydrodynamic theory is formulated for buoyancy-driven ("thermal") granular convection, recently predicted in molecular dynamic simulations and observed in experiment. The limit of a dilute flow is considered. The problem is fully described by three scaled parameters. The convection occurs via a supercritical bifurcation, the inelasticity of the collisions being the control parameter. The theory is expected to be valid for small Knudsen numbers and nearly elastic grain collisions.Comment: 4 pages, 4 EPS figures, some details adde

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

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

Onset of thermal convection in a horizontal layer of granular gas

The Navier-Stokes granular hydrodynamics is employed for determining the threshold of thermal convection in an infinite horizontal layer of granular gas. The dependence of the convection threshold, in terms of the inelasticity of particle collisions, on the Froude and Knudsen numbers is found. A simple necessary condition for convection is formulated in terms of the Schwarzschild's criterion, well-known in thermal convection of (compressible) classical fluids. The morphology of convection cells at the onset is determined. At large Froude numbers, the Froude number drops out of the problem. As the Froude number goes to zero, the convection instability turns into a recently discovered phase separation instability.Comment: 6 pages, 6 figures. An extended version. A simple and universal necessary criterion for convection presente

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