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.
Influences of a temperature gradient and fluid inertia on acoustic streaming in a standing wave.
Following the experimental method of Thompson and Atchley [J. Acoust. Soc. Am. 117, 1828-1838 (2005)] laser Doppler anemometry (LDA) is used to investigate the influences of a thermoacoustically induced axial temperature gradient and of fluid inertia on the acoustic streaming generated in a cylindrical standing-wave resonator filled with air driven sinusoidally at a frequency of 308 Hz. The axial component of Lagrangian streaming velocity is measured along the resonator axis and across the diameter at acoustic-velocity amplitudes of 2.7, 4.3, 6.1, and 8.6 m/s at the velocity antinodes. The magnitude of the axial temperature gradient along the resonator wall is varied between approximately 0 and 8 K/m by repeating measurements with the resonator either surrounded by a water jacket, suspended within an air-filled tank, or wrapped in foam insulation. A significant correlation is observed between the temperature gradient and the behavior of the streaming: as the magnitude of the temperature gradient increases, the magnitude of the streaming decreases and the shape of the streaming cell becomes increasingly distorted. The observed steady-state streaming velocities are not in agreement with any available theory.
Nonlinear effect of the inertia of the fluid on acoustic streaming in cylindrical guides
Acoustic streaming is the mean flow created by a high sound level wave. Classical treatment [J. W. S. Rayleigh, Philos. Trans. R. Soc. London 175, 1–21 (1884)] considers that in cylindrical guides a standing acoustic wave creates a symmetrical toroidal vortex (slow streaming) due to the action of Reynolds stress forcing resisted by viscosity. A perturbation method followed by a time averaging applied to the conservation equations leads to the equations describing the behavior of the mean flow velocity in a cylindrical air‐filled guide. According to a dimensional analysis, the effect of the fluid inertia cannot be neglected if the streaming becomes perceptible. This effect, previously studied for free or semi‐infinite space, is controlled in the case of a waveguide by the dimensionless parameter Renl=M2/Sh2 (M and Sh are the acoustic Mach number and the Shear number). Numerical resolution of this nonlinear system of equations (Newton–Raphson method) is performed using nonslip conditions on the tube wall an...