Tomoo Kamakura

Acoustic streaming induced in focused Gaussian beams

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.

Model equation for strongly focused finite-amplitude sound beams

A model equation that describes the propagation of sound beams in a fluid is developed using the oblate spheroidal coordinate system. This spheroidal beam equation (SBE) is a parabolic equation and has a specific application to a theoretical prediction on focused, high-frequency beams from a circular aperture. The aperture angle does not have to be small. The theoretical background is basically along the same analytical lines as the composite method (CM) reported previously [B. Ystad and J. Berntsen, Acustica 82, 698-706 (1996)]. Numerical examples are displayed for the amplitudes of sound pressure along and across the beam axis when sinusoidal waves are radiated from the source with uniform amplitude distribution. The primitive approach to linear field analysis is readily extended to the case where harmonic generation in finite-amplitude sound beams becomes significant due to the inherent nonlinearity of the medium. The theory provides the propagation and beam pattern profiles that differ from the CM solution for each harmonic component.

Harmonic generation in finite amplitude sound beams from a rectangular aperture source

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 le...

Theoretical and experimental examination of near-field acoustic levitation

A planar object can be levitated stably close to a piston sound source by making use of acoustic radiation pressure. This phenomenon is called near-field acoustic levitation [Y. Hashimoto et al., J. Acoust. Soc. Am. 100, 2057-2061 (1996)]. In the present article, the levitation distance is predicted theoretically by numerically solving basic equations in a compressible viscous fluid subject to the appropriate initial and boundary conditions. Additionally, experiments are carried out using a 19.5-kHz piston source with a 40-mm aperture and various aluminum disks of different sizes. The measured levitation distance agrees well with the theory, which is different from a conventional theory, and the levitation distance is not inversely proportional to the square root of the surface density of the levitated disk in a strict sense.

Nonlinearly generated spectral components in the nearfield of a directive sound source

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.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.

Time evolution of acoustic streaming from a planar ultrasound source

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.

Sound pressure fields focused using biconcave acoustic lens for normal incidence

The underwater imaging sonar system with an acoustic lens is again receiving considerable attention because it does not require a complex beam-forming circuit. The lens system used in this type of sonar was designed by the ray theory or by a hybrid method of the ray and wave theories. In this report, a basic analysis was performed by an analytical method using a wave theory and by a numerical method using the parabolic equation (PE) method, to determine the convergent characteristics of a biconcave lens. The pressure field focused by the biconcave lens was measured in a water tank. The biconcave lens used in the experiment is made of acrylic resin with a radius of 20 cm and a radius of curvature of 20 cm. Measurements was conducted in a water tank at a frequency of 500 kHz. Sound pressure fields around the focal region measured by the experiments agreed well with the calculated ones by the analytical and PE methods.

Two Model Equations for Describing Nonlinear Sound Beams

This short article is an introductory review and guidance on nonlinear acoustics, the study of which dates back to the 18th century. First, interpretation is made for the meaning and research field of nonlinear acoustics. Second, two typical model equations are presented describing finite-amplitude sound beams radiated in a viscous fluid from unfocused and focused powerful sources with finite apertures. The three basic characteristics of a wave, diffraction, dissipation, and nonlinearity are combined successfully in the model equations. Third, an innovative application referred to as a parametric acoustic array is shortly reviewed. Numerical demonstration shows specifically the sharp directivity of the parametric array.

Feasibility of low-frequency directive sound source with high range resolution using pulse compression technique

The lateral resolution of a parametric acoustic array with narrow directivity is expected to be superior to that of a conventional linear sound source. The range resolution of the parametric array, however, is as low as the resolution of the linear source because of its long wavelength. To improve the range resolution in maintaining a high azimuth resolution for parametric sounds, a pulse compression technique using linear frequency-modulated signals or chirp signals is explored in the present study. The generation of chirp-modulated parametric sounds was experimentally confirmed in water, and then the auto-correlation of the parametric sound demonstrates short pulse widths up to 1/10 of the primary pulse duration. The results reveal that the pulse compression is feasible for a low-frequency parametric sound source with narrow directivity in the same manner as the compression of a linear sound wave.

Buildup of acoustic streaming in focused beams

Using a laser Doppler velocimeter, we measured the buildup velocity of acoustic streaming in water generated from a 2.8 MHz focusing source with a circular aperture along and across the acoustic axis. Steady streaming is established a few seconds after the beam is switched on, and a maximum velocity of about 4 cm/s is observed near the focus. The good agreement of theory and experiment suggests that the numerical calculation method previously developed by the authors is valid within the framework of the present source conditions.