Eckart-type acoustic streaming induced in confined sound beams from a piston source is examined in water theoretically and experimentally. Axisymmetric flow equations with a spatially distributed driving force in the beams are based on the continuity equation and the Navier–Stokes equation in a viscous, incompressible fluid. They are solved numerically by the stream-function vorticity method [T. Kamakura et al., J. Acoust. Soc. Am. 97, 2740–2746 (1995)]. Experiments are conducted using a 5-MHz planar transducer with a 9.5-mm radius aperture. All measurements of the streaming velocities are carried out by a laser Doppler velocimeter and are compared with the numerical computations including the enhancement of the force due to finite-amplitude sound distortion. These measurements agree well with the theoretical prediction. It is noted that diffraction of sound beams plays an important role in the generation of streaming, particularly in the early stage. Consistency between experiments and computations suggests that both acoustic and hydrodynamic nonlinearities should be taken into account in the present observation system.
Axisymmetric flow equations for a viscous incompressible fluid are transformed into the vorticity transport and Poisson’s equations. They are numerically solved via a finite difference method imposing appropriate initial and boundary conditions. A model source of 1-cm radius and 5-cm focal length with Gaussian amplitude distribution radiates 5-MHz ultrasound beams in water. Numerical examples are shown for buildup of acoustic streaming along and across the acoustic axis. Evidently, hydrodynamic nonlinearity has an essential effect on the streaming generation in comparison with a linear flow case; the nonlinearity reduces the streaming velocity in the focal and prefocal region, whereas it tends to accelerate the flow in the postfocal region.
Theoretical analysis and some experiments are performed on nonlinearly generated harmonic components in bounded sound beams emitted from a rectangular aperture source. The Khokhlov–Zabolotskaya–Kuznetsov equation, which takes account of nonlinearity, dissipation, and diffraction effects in the beams, is numerically solved by means of the alternating direction implicit difference method. Using a planar source of size 24×44 cm, axial sound pressures and beam patterns of the first three harmonics are measured in air for initially sinusoidal ultrasounds of 25- and 30-kHz frequency, and are compared with the theory. They are in relatively good agreement. Deformation of the source face from circular to rectangular shape results in the unclear appearance of pressure peaks and dips with propagation. Within the framework of these studies, the harmonic pressure levels in the far field are almost the same as from a circular aperture source with equal face area and equal initial pressure, independent of the source levels.
Nonlinear propagation of sound waves generated by a directive ultrasound source in air is discussed theoretically and experimentally. The circular source of 21 cm in radius consists of 1410 small PZT bimorph transducers, whose resonance frequency is 28 kHz. For a single-frequency wave excitation, sound pressures of the fundamental, second, and third harmonics are measured and are compared with the numerical results using a method of Aanonsen et al. [J. Acoust. Soc. Am. 75, 749–768 (1984)]. Extending their initial condition to the case of a two-frequency wave excitation, propagation curves and beam patterns of the difference frequency sound are obtained and compared with the measured data. All observations quantitatively agree very well with the numerical calculation. Nonlinear attenuation of spectral components by increasing the source pressure is clearly confirmed.
Due to the inherent nonlinearity of the medium, finite amplitude ultrasound interacts with itself and generates some secondary waves in the sound beam. The parametric loudspeaker, making use of this phenomenon, has a sharp directivity and might be applied to a speech transmission system under the limited environment. In this paper, a numerical analysis method available for high sound pressure levels, where the nonlinear interactions of ultrasound become greatly active, can be used successfully to theoretically design the parametric loudspeaker. It is reported that the numerical computations agree well with the experiments by a circular aperture projector of radius 21 cm and carrier frequency 27 kHz. To develop the parametric loudspeaker for practical uses, the problems on harmonic distortions and the physiological effect on human being must be solved. Based on the theoretical prediction, the reasonable solutions for such problems are considered in accordance with appropriate primary wave modulations.
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