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.
Measuring second-order time-average pressure
Measurements of the spatial distribution of the time-averaged second-order pressure in a plane standing wave in atmospheric air are reported. Several measurement pitfalls are identified, and solutions are described. These include accounting for slight nonlinearity of the piezoresistive transducer and careful mounting of the transducer. Streaming causes extra complication when a capillary-connected manometer is used. With the proper technique and instrumentation, results are in good agreement with theory.
Velocity of Mass Transport to Model Acoustic Streaming: Numerical Application to Annular Resonators
The acoustic wave propagation in thermo-viscous fluid can generate slow phenomena such as acoustic streaming, by non-linear processes that are mainly confined in the acoustical boundary layers. Considering the fundamental conservation equations for mass, momentum and energy, and splitting the different time scales for acoustic propagation and acoustic streaming, the equations governing the acoustic streaming are presented in a standard form for a weakly compressible flow. The formulation is based upon the velocity of mass transport as variable. The force responsible for acoustic streaming is composed of quadratic terms that account for the combined acoustical density variation or viscosity variation, and particle velocity. The numerical computation of the unsteady Gedeon streaming flow in annular resonator is done as a validation of this formulation.