Circular Piston Research Articles

Nearfield of an electroacoustic transducer, with implications for performance measurement

The spatial structure of the nearfield of an electroacoustic transducer is known to be complicated. This is illustrated by numerical modeling of the nearfield of an ideal planar circular piston in a rigid, infinite baffle. There are implications for performance measurements of electroacoustic transducers including hydrophones in tanks.

Experimental investigation of an oscillating circular piston positive displacement flowmeter: II – Leakage flows and wear tests

Experimental data from an oscillating circular piston positive displacement flowmeter are described which focused on leakage flows and wear. This is the second part of a two part paper on the experimental tests, the first part concerned piston movement and pressure loss. In this paper the leakage across the meter is reported for key parameters including: flow rate, liquid density and viscosity, mass of circular piston, surface coating and length of connection pipes. In addition to the average leakage over a period of time, the leakage past a stationary circular piston was measured during a simulated oscillation. Wear tests were run for both stainless steel and carbon pistons to identify the affected areas of piston and chamber.

Experimental investigation of an oscillating circular piston positive displacement flowmeter: I – Piston movement and pressure losses

Tests of an oscillating circular piston positive displacement flowmeter are described which focused on the effect on pressure drop across the meter of variation in key parameters. These included flow rate, liquid density and viscosity, mass of piston and length of connecting pipes. In addition to the average pressure loss, the pressure loss variation during the oscillation cycle was measured and found to vary with an amplitude dependent on the various parameters. A companion paper reviews data on leakage and wear.

Research on Simulation of Array Directivity Based on MATLAB

According to the theory of underwater acoustic spread and circular piston transducer array, the mathematical model for the directivity of array is created. By means of MATLAB, the accurate expression method for the figure of array directivity is studied, and the characteristic and difference of the simulation curve in various direction are analyzed. It is shown by the application that, to a certain extent, the conclusion has practical value and guide meaning for the directivity simulation and design of the array.

Three curious results of radiation loading calculations

One of the many joys in reading Miguel C. Junger's contributions to the J.A.J.A. and elsewhere, was the physical interpretations that accompanied theoretical results, which were at times unanticipated but always enlightening. In three instances however, he found the task of offering such an explanation particularly challenging. This is documented in his paper Three apparently paradoxical results of sound radiation theory. The specific results are 1. At frequencies above coincidence, the power radiated by a point driven infinite plate exposed to a low impedance fluid is equal to the power radiated by that plate when submerged in a high impedance fluid, 2. At low frequencies, the entrained mass associated with a translating circular piston fully submerged in an acoustic medium is equal to that acting on the piston when it is baffled and exposed to the medium on one side only, and 3. The low frequency admittance of a fluid loaded infinite thin plate driven by a point force exhibits a spring-like reactance,...

Analytical and numerical approximations for the lossy on-axis impulse response of a circular piston

In biological tissues, the frequency dependence of attenuation and speed of sound for ultrasound propagation is described by the power law wave equation, which is a partial differential equation with fractional time derivatives. As demonstrated previously, the time domain Green's function for the power law wave equation combined with the Rayleigh-Sommerfeld integral is an effective reference for calculations of the lossy on-axis impulse response of a circular piston. Using the result obtained from this reference, two different approximations to the lossy on-axis impulse response are evaluated. The first approximation is an analytical expression that is proportional to the difference between two cumulative distribution functions for maximally skewed stable probability densities. The second approximation numerically convolves the lossless impulse response with a maximally skewed stable probability density function. The results show that both approximations achieve relatively small errors. Furthermore, the analytical approximation provides an excellent estimate for the arrival time of the lossy impulse response, whereas the departure time of the lossy impulse response is more difficult to characterize due to the heavy tail of the maximally skewed stable probability density function. Both approximations are rapidly calculated with the STABLE toolbox. [supported in part by NIH Grant R01 EB012079.]

Descomposición en pistones circulares para la obtención de la radiación acústica de un pistón rectangular

Obtaining pressure radiated by flat surfaces is not a new problem. This problem has studied by the complexity of the topic and its application to design flat speakers. These kind of speakers are the speakers that we use in televisions, ceilings, cinema screens, panels, etc. in this cases usually we have rectangular speakers.The single source model is the simplest model to convert the surface vibration to radiated pressure in a point. This is an easy model but it is very slow, especially when we want calculate at high frequencies. For rectangular surfaces there are models that use relatively complex auxiliary functions. In this case the calculation is accelerated but its implementation is more complicated and is necessary to particularize each situation.This paper presents the decomposition of a rectangular surface in several circular surfaces, by means of area associations, seeking a rapid method based on circular pistons whose behavior is known with an acceptable error in the allocation.

Acoustic beam modeling of ultrasonic transducers and arrays using the impulse response and the discrete representation methods

The impulse response of the velocity potential and the discrete representation methods were used in order to model the acoustic field radiated by ultrasonic transducers and arrays. The first method deals with the calculation of the exact impulse response, in which solutions are possible only for simple geometries, such as the circular piston. The second method is an approximated solution based on the discretization of the acoustic aperture in small elementary areas, each of them radiating a spherical wave. By using circular transducers, which can be considered circular pistons, many simulations comparing the methods were carried out. The relation between the computational cost and the precision was analyzed, thus establishing the time and space discretization levels. The simulations were made using the Matlab software and the results were compared to experimental measurements showing good agreement. The experimental results were obtained using a scanning system. The acoustic field radiated from a 1 MHz circular transducer was measured as well as a 3.5 MHz array of 16 elements both immersed in water. The acoustic field radiated by the array was simulated and measured with focalization on a radius of 30 mm with deflections of 0º and 20º.

Measurement of liquid film thickness by optical fluorescence and its application to an oscillating piston positive displacement flowmeter

The movement of the circular piston in an oscillating piston positive displacement flowmeter is important in understanding the operation of the flowmeter, and the leakage of liquid past the piston plays a key role in the performance of the meter. The clearances between the piston and the chamber are small, typically less than 60 µm. In order to measure this film thickness a fluorescent dye was added to the water passing through the meter, which was illuminated with UV light. Visible light images were captured with a digital camera and analysed to give a measure of the film thickness with an uncertainty of less than 7%. It is known that this method lacks precision unless careful calibration is undertaken. Methods to achieve this are discussed in the paper. The grey level values for a range of film thicknesses were calibrated in situ with six dye concentrations to select the most appropriate one for the range of liquid film thickness. Data obtained for the oscillating piston flowmeter demonstrate the value of the fluorescence technique. The method is useful, inexpensive and straightforward and can be extended to other applications where measurement of liquid film thickness is required.

Evaluation of the power-law impulse response for liver in the time- and frequency-domains

Ultrasound attenuation in biological media often follows a frequency-dependent power-law relationship. Power-law attenuation is accompanied by dispersion in which phase velocity also changes as a function of frequency. The power-law wave equation has exact time- and frequency-domain Green's function solutions that are used in numerical evaluations of the Rayleigh–Sommerfeld diffraction integral. These Green's functions contain stable probability density functions that are evaluated in the time-domain using the STABLE toolbox and in the frequency-domain by evaluating the characteristic function of a stable distribution. The impulse response for a circular piston is evaluated on-axis in the time- and frequency-domain using values for human liver. The results show the accuracy of the time-domain impulse response calculation is dependent upon adequate spatial sampling of the piston face. The frequency-domain impulse response exhibits aliasing caused by wrap around of the heavy tail of the stable distribution. Frequency-domain accuracy is dependent upon the spatial sampling of the piston face and the density of the frequency samples. Numerical evaluations show that the frequency- and time-domain calculations converge to the same result. [This work was supported in part by NIH Grant R01 EB012079.]

Modeling of shear waves generated in a soft solid by a piston

This work is motivated by the transient elastography experiments described by Catheline etal. [J. Am. Stat. Assoc. 105, 2941–2950 (1999)], the purpose of which was to measure the phase speed of shear waves propagating through tissue phantoms. In that work, a small circular piston was used to generate the shear waves, the motion of which was perpendicular to the bounding surface of the sample. The current work is a theoretical investigation of this type of source condition based on the assumption of a linear elastic medium and using an angular spectrum approach to solve for the entire elastic field, both compressional and shear waves, that results from a given velocity distribution at the source plane. Special attention is paid to the velocity field near the source, in particular how the near incompressibility of the tissue-like medium is conducive to the generation of shear waves from such a compressive piston source. For high-frequency excitation, in which the resulting shear wave disturbances are beam-like, the validity of using a parabolic approximation to describe diffraction of the transverse motion of the field in the paraxial region is investigated. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.]

Spatial impulse responses from a flexible baffled circular piston

The theory of orthogonal polynomial (Zernike) expansions of functions on a disk, as used in the diffraction theory of optical aberrations, is applied to obtain (semi-) analytical expressions for the spatial impulse responses arising from a non-uniformly moving, baffled, circular piston. These expressions are in terms of the expansion coefficients of the non-uniformity and the responses of the orthogonal expansion functions. The latter impulse responses have a closed form as finite series involving the Legendre functions and the sinc function. The method is compared with a similar method, proposed by P. R. Stepanishen [J. Acoust. Soc. Am. 70, 1176-1181 (1981)] where zeroth order orthogonal Bessel functions, rather than Zernike polynomials, are used as expansion functions.

Radiation force on absorbing targets and power measurements of a high intensity focused ultrasound (HIFU) source

Based on the analytic expressions for the radiated field of a circular concave piston given by Hasegawa et al., an integral for calculation of the radiation force on a plane absorbing target in a spherically focused field is derived. A general relation between acoustic power P and normal radiation force Fn is obtained under the condition of kr ≫ 1. Numerical computation is carried out by using the symbolic computation program for practically focused sources and absorbing circular targets. The results show that, for a given source, there is a range of target positions where the radiation force is independent of the target’s position under the assumption that the contribution of the acoustic field behind the target to the radiation force can be neglected. The experiments are carried out and confirm that there is a range of target positions where the measured radiation force is basically independent of the target’s position even at high acoustic power (up to 700 W). It is believed that when the radiation force method is used to measure the acoustic power radiated from a focused source, the size of the target must be selected in such a way that no observable sound can be found in the region behind the target.

A relationship between the far field diffraction pattern and the axial pressure radiating from a two-dimensional aperture

The diffraction of an acoustic wave by a two-dimensional aperture produces a sound field that can generally be represented at any point in space as a superposition of a continuum of plane waves. The mathematical formulation that facilitates this representation is known as the angular spectrum of plane waves method. The spectrum, in this representation, is a wavenumber spectrum obtained from a two-dimensional Fourier transform of the acoustic pressure (or velocity) distribution over the surface of the aperture boundary; a quantity which is also known to characterize the Fraunhofer diffraction pattern of the aperture. In this article, the angular spectrum method is used to formulate a mathematical relationship for two-dimensional apertures between the Fraunhofer diffraction pattern and a one-dimensional Fourier transform of the axial pressure. This relationship can be used to rapidly compute the axial pressure profile of the aperture if the boundary condition on the aperture is known and, in some cases, can be used as an inverse method. The approach is demonstrated for the cases of a flat circular piston and a flat rectangular piston undergoing harmonic motion in an infinite, rigid baffle. In the latter case, an analytical solution is also obtained.

Analysis of the modeling of echo responses from circular concavity defects using impulse response and discrete representation methods

In this work the impulse response and the discrete representation method are applied to model the acoustic wave generated by ultrasonic transducers, its interaction with the defect, and the echoes received by the transducer. Several simulations are performed to determine the echo responses arising from a concave circular defect on a plane surface, using a planar circular piston emitting pulses in water. The simulations are calculated using the Matlab software. The effects of defect size and field position on both amplitude and shape of the echo responses are investigated. Moreover, experimental measurements of the acoustic field are compared with the simulations. The experimental results, based on the above-mentioned process, were obtained using 1.6 and 2.25MHz transducers.

Investigation of ultrasonic shock wave propagation and superharmonic field generation in human soft tissues

In this paper, two theoretical methods for the description of non-linear ultrasound wave generated from axis symmetric circular source and propagation in soft human tissues has been described. Burgers' equation was used to model the non-linear propagation of single sinusoidal wave with finite amplitude. In the first method for lossless medium, the analytical solution of Burgers' equation has been achieved by using Fubini method in pre-shock region while weak shock theory was applied in post-shock region. In case of lossy medium, the analytical solution of Burgers' equation was achieved by using linear diffusion equation via Hopf-Cole transformation in pre-shock region and Fay's equation in post-shock region. In the second method, the operator splitting methodology was implemented in which absorption term was solved using Crank Nicholson finite difference (CNFD) method and non-linear term by using analytical method at each step for both lossless and lossy medium. Both the methods were solved using MATLAB. The results have been shown for waveform distortion and shock formation radiated by circular piston source for lossless and lossy tissue mediums. The analytical study of fundamental, second harmonic and superharmonic components variation along the distance of propagation has been studied using both proposed methods and their results have been compared.

Fast MATLAB-based ultrasound simulation software: Transient calculations.

The FOCUS software package quickly calculates transient pressure fields generated by ultrasound phased arrays. This software is useful for visualizing pressure wave propagation in the nearfield region, and the results are directly applicable to beamforming evaluations and phased array design for diagnostic and therapeutic applications. FOCUS includes support for transient pressure calculations with single transducers, including flat circular and rectangular pistons as well as spherically focused shells, and arrays of flat circular and rectangular transducers. Routines to calculate time delays for focusing the arrays are also included with the software. Transient calculations are performed with a combination of the fast nearfield method and time space decomposition, which achieves rapid convergence to reduce the numerical error while significantly reducing the computation time. Within the FOCUS software, time space decomposition is implemented with a simplified approach that decreases the overhead and reduces the computational complexity. The advantages of FOCUS over competing approaches include short computation times and small numerical errors. Examples of the supported element and array geometries will be shown, and sample codes will be provided. Transient pressure fields computed with FOCUS and with FIELD II are compared, and results show that, for the same peak error value, FOCUS is several times faster for calculations in the nearfield region.

Fast MATLAB-based ultrasound simulation software: Time harmonic calculations.

A library of fast C++ routines is created for MATLAB simulations of time harmonic pressures generated by ultrasound phased arrays. These programs are included in the recently released FOCUS software package, where FOCUS is an acronym for “fast object-oriented C++ ultrasound simulator.” FOCUS is intended for large scale phased array simulations, characterizations of beamforming strategies, and analysis of new phased array designs. This software supports nearfield simulations of individual flat circular and rectangular pistons and focused spherical shells. Routines for pressure calculations with flat and curved phased array geometries consisting of circular and rectangular elements are also included. Within the FOCUS program, time harmonic simulations are performed with a combination of the fast nearfield method and the angular spectrum approach. Comparisons of errors and computation times with competing programs are evaluated for single element and phased array calculations, and results show that, for the same peak error value, FOCUS achieves an order of magnitude or more reduction in the computation time in large phased array simulations.

Estimation of the sound pressure field of a baffled uniform elliptically shaped transducer

In this paper an alternative approach to estimate the sound field of an elliptically shaped transducer in an infinite baffle is described. The method is based on a singular value decomposition of a propagating matrix which is computed through a division of the vibrating surface into a finite number of small circular piston sources flush-mounted on the elliptical surface. This decomposition is combined with the volume velocity vector on the discretized surface to obtain the sound pressure field. Numerical examples for both on-axis sound pressure and directivity are presented for the uniform elliptical piston transducer and they are in good agreement with the results given by other methods.

Material properties from acoustic radiation force step response

An ultrasonic technique for estimating viscoelastic properties of hydrogels, including engineered biological tissues, is being developed. An acoustic radiation force is applied to deform the gel locally while Doppler pulses track the induced movement. The system efficiently couples radiation force to the medium through an embedded scattering sphere. A single-element, spherically-focused, circular piston element transmits a continuous-wave burst to suddenly apply and remove a radiation force to the sphere. Simultaneously, a linear array and spectral Doppler technique are applied to track the position of the sphere over time. The complex shear modulus of the gel was estimated by applying a harmonic oscillator model to measurements of time-varying sphere displacement. Assuming that the stress-strain response of the surrounding gel is linear, this model yields an impulse response function for the gel system that may be used to estimate material properties for other load functions. The method is designed to explore the force-frequency landscape of cell-matrix viscoelasticity. Reported measurements of the shear modulus of gelatin gels at two concentrations are in close agreement with independent rheometer measurements of the same gels. Accurate modulus measurements require that the rate of Doppler-pulse transmission be matched to a priori estimates of gel properties.