Nonaxisymmetric interaction of a spherical radiator in a fluid-filled permeable borehole

The Biot theory of poroelasticity along with the proper cylindrical/spherical wave-field transformations are used to investigate general (nonaxisymmetric) harmonic radiation from a spherical surface vibrating at the center of a fluid-filled circular cylindrical cavity embedded within a fluid-saturated porous elastic formation. This configuration, which is a realistic idealization of an acoustic logging tool suspended in a fluid-filled borehole, is of practical importance with a multitude of possible applications in seismic engineering and geophysics. The analytical results are illustrated with numerical examples in which the spherical source suspended at the center of a water-filled borehole embedded within water-saturated soils of distinct frame properties (i.e., soft or stiff soils), is excited in vibrational modes of various orders. The basic acoustic and elastic field quantities such as the resistive/reactive components of the modal acoustic radiation impedance load as well as the radial displacement and stress components induced within the surrounding formation for a pulsating (n = 0), an oscillating (n = 1), and a quadrupole-like (n = 2) spherical source are evaluated and discussed for representative values of the parameters characterizing the system. Special attention is paid to the effects of source excitation frequency, size, surface velocity profile, and internal impedance as well as soil type on the modal impedance values and the displacement/stress amplitudes. Limiting cases are considered and fair agreements with well-known solutions are obtained.     

Dynamic interaction of a spherical radiator in a fluid-filled cylindrical borehole within a poroelastic formation

Harmonic acoustic radiation from a modally oscillating spherical source positioned at the center of a fluid-filled cylindrical cavity embedded within a fluid-saturated porous elastic formation is studied in an exact manner. The formulation utilizes the Biot theory of dynamic poroelasticity along with the cylindrical to spherical wave-field transformations, and the pertinent boundary conditions to obtain a closed-form series solution. The analytical results are illustrated with a numerical example in which the spherical source, with its polar axis oriented along the main axis of a water-filled borehole and embedded within a water-saturated Ridgefield sandstone formation, is excited in vibrational modes of various orders. The magnitude of the reflected component of acoustic pressure along the axis of the borehole for a pulsating (n = 0), an oscillating (n = 1), and also a multipole (n = 0–3) spherical source as a function of the excitation frequency is calculated and discussed for representative values of the parameters characterizing the system. Special attention is paid to the effects of source excitation frequency, size, surface velocity profile, and internal impedance as well as borehole interface permeability condition on the reflected pressure magnitudes. Limiting cases are considered and fair agreements with well-known solutions are obtained.     

Modal acoustic impedance force on a spherical source near a rigid interface

The modal acoustic radiation load on a spherical surface undergoing angularly periodic axisymmetric harmonic vibrations while immersed in an acoustic halfspace with a rigid (infinite impedance) planar boundary is analyzed in an exact fashion using the classical technique of separation of variables. The formulation utilizes the appropriate wave field expansions, the classical method of images and the appropriate translational addition theorem to simulate the relevant boundary conditions for the given configuration. The associated acoustic field quantities such as the modal impedance matrix and the modal acoustic radiation force acting on the spherical surface are determined. The analytical results are illustrated with a numerical example in which the spherical surface, excited in vibrational modes of various orders, is immersed near an impervious rigid wall. The presented solution could eventually be used to validate those obtained by numerical approximation techniques.     

Harmonic radiation from a liquid-filled spherical acoustic lens with an internal eccentric spherical source

Radiation of sound from a modally vibrating shell-encapsulated (eccentric) spherical source is analyzed in an exact manner using the classical method of separation of variables. The proposed model is a realistic idealization of a spherical acoustic lens with focal point inside the lens when used as a sound projector. The analytical results are illustrated with a numerical example in which the modal acoustic radiation impedance load on the source and the radiated far-field pressure are evaluated for representative values of the parameters characterizing the system. Numerical results clearly illustrate that in addition to frequency, surface velocity distribution and eccentricity of the source, the dynamic interaction of the encapsulating shell can be of great consequence in sound radiation.     

Acoustic radiation force of a solid elastic sphere immersed in a cylindrical cavity filled with ideal fluid

An expression for the acoustic radiation force function on a solid elastic spherical particle placed in an infinite rigid cylindrical cavity filled with an ideal fluid is deduced when the incident wave is a plane progressive wave propagated along the cylindrical axis. The acoustic radiation force of the spherical particle with different materials was computed to validate the theory. The simulation results demonstrate that the acoustic radiation force changes demonstrably because of the influence of the reflective acoustic wave from the cylindrical cavity. The sharp resonance peaks, which result from the resonance of the fluid-filled cylindrical cavity, appear at the same positions in the acoustic radiation force curve for the spherical particle with different radii and materials. Relative radius, which is the ratio of the sphere radius and the cylindrical cavity radius, has more influence on acoustic radiation force. Moreover, the negative radiation forces, which are opposite to the progressive directions of the plane wave, are observed at certain frequencies.     

Acoustic field in a borehole within fluid formations with a horizontal interface

The acoustic field in a cylindrical borehole embedded in a horizontally layered infinite medium is studied. The modes in each layer are found to consist of continuous as well as discrete ones, the orthogonality and completeness of which are proven. The relevant weights associated with the two kinds of modes are determined by solving a set of integral equations deduced from the boundary conditions at the layer interface. This technique is not limited to low frequencies, but applies well to frequencies prevailing in typical logging environment. Reflection, transmission and coupling coefficients of different modes are evaluated. The numerical results are verified by comparison with the method of real axis integration (RAI) and the hybrid mehtod proposed by Tsang [“Transient acoustic waves in a fluid-filled borehole with a horizontal bed boundary separating two solid formations”, J. Acoust. Soc. Am. 81, 844–853 (1987)]. The scaled laboratory experiments are carried out and the corresponding results are presented for comparison with the numerical computation.     

Axial acoustic radiation force on a rigid cylinder near an impedance boundary for on-axis Gaussian beam

This work presents a theoretical model to calculate the acoustic radiation force on a rigid cylindrical particle immersed in an ideal fluid near a boundary for an on-axis Gaussian beam. An exact solution of the axial acoustic radiation force function is derived for a cylindrical particle by applying the translation addition theorem of cylindrical Bessel function. We analyzed the effects of the impedance boundary on acoustic radiation force of a rigid cylinder immersed in water near an impedance boundary with particular emphasis on the radius of the rigid cylinder and the distance from the cylinder center to impedance boundary. Simulation results reveal that the existence of particle trapping behavior depends on the choice of nondimensional frequency as well as the offset distance from the impedance boundary. The value of the radiation force function varies when the cylinder lies at the different position of the on-axis Gaussian beam. For the particle with different radius, the acoustic radiation force functions vary significantly with frequency. This study provides a theoretical basis for acoustic manipulation, which may benefit to the improvement and development of the acoustic control technology.     

External shock loading on a submerged fluid-filled cylindrical shell

The interaction between a submerged fluid-filled elastic circular cylindrical shell and an external shock wave is considered. The study focuses on the internal acoustic field. A linear formulation of the problem is considered. A semi-analytical solution is obtained and used to simulate the interaction. A variety of phenomena are observed in the internal fluid, including the reflection and focusing of the internal acoustic wave as well as the radiation into the fluid of elastic waves propagating in the shell. Throughout the paper, the results of numerical simulations are compared with available experimental data, and a good agreement is observed. The solution developed appears to be suitable for use as a benchmark. Engineering relevance of the phenomena observed is discussed.     

Acoustic radiation force on an elastic cylinder in a Gaussian beam near an impedance boundary

Acoustic radiation force (ARF) is studied by considering an infinite elastic cylinder near an impedance boundary when the cylinder is illuminated by a Gaussian beam. The surrounding fluid is an ideal fluid. Using the method of images and the translation-addition theorem for the cylindrical Bessel function, the resulting sound field including the incident wave, its reflection from the boundary, the scattered wave from the elastic cylinder, and its image are expressed in terms of the cylindrical wave function. Then, we deduce the exact equations of the axial and transverse ARFs. The solutions depend on the cylinder position, cylinder material, beam waist, reflection coefficient, distance from the impedance boundary, and absorption in the cylinder. To analyze the effects of the various factors intuitively, we simulate the radiation force for non-absorbing elastic cylinders made of stainless steel, gold, and beryllium as well as for an absorbing elastic cylinder made of polyethylene, which is a well-known biomedical polymer. The results show that the impedance boundary, cylinder material, absorption in the cylinder, and cylinder position in the Gaussian beam significantly affect the magnitude and direction of the force. Both stable and unstable equilibrium regions are found. Moreover, a larger beam waist broadens the beam domain, corresponding to non-zero axial and transverse ARFs. More importantly, negative ARFs are produced depending on the choice of the various factors. These results are particularly important for designing acoustic manipulation devices operating with Gaussian beams.     

Submerged fluid-filled cylindrical shell subjected to a shock wave: Fluid–structure interaction effects

A submerged fluid-filled circular cylindrical shell subjected to a shock wave propagating in the external fluid is considered. The study focuses on a number of acoustic and structural effects taking place during the interaction. Specifically, the influence of the acoustic phenomena in the fluid on the stress–strain state of the shell is analysed using two different visualization techniques. The effect that the parameters of the shell have on the internal acoustic field is addressed as well, and the ‘shock transparency’ of various shells is discussed. Special attention is paid to the analysis of the contribution of the terms in the shell equations representing bending stiffness, and the limits of applicability of the membrane theory of thin shells are discussed in the fluid–structure interaction context. The possibility of cavitation in the internal fluid is investigated, and the effect that cavitation could have on the structural dynamics of the shell is discussed. The present paper is a follow-up of the author's earlier study of the interaction between fluid-filled cylindrical shells and external shock waves.     

Acoustic radiation force on a rigid cylinder in an off-axis Gaussian beam near an impedance boundary

The exact equations of the axial and transverse acoustic radiation force functions of a Gaussian beam arbitrarily incident on an infinite rigid cylinder close to an impedance boundary and immersed in an ideal fluid are deduced by expressing the incident wave, the scattering wave and the boundary reflected wave in terms of the cylindrical wave function. The effects of the beam waist, the sound reflection coefficient, the cylinder position and the distance from the impedance boundary on the acoustic radiation force are studied using numerical simulations. The simulation results show that the amplitude of the acoustic radiation force function increases with beam width. Moreover, the values of the acoustic radiation force in both the axial and transverse directions reach those of a plane wave when the beam width is considerably larger than the wavelength of the Gaussian beam. The properties of the impedance boundary and the position of the cylinder in the Gaussian beam have a considerable effect on the magnitude and direction of the force. The simulation results, particularly in the case of a transverse force, indicate the presence of a negative acoustic radiation force that is related to the nondimensional frequency and position of the cylinder in the Gaussian beam.     

Vibroacoustic responses of a heavy fluid loaded cylindrical shell excited by a turbulent boundary layer

A fully coupled structural–acoustic model of a cylindrical shell under external turbulent boundary layer excitation is herein developed. The numerical process requires computation of the wall pressure cross spectral density function as well as sensitivity functions for the fluid-loaded cylindrical shell. A semi-empirical model from literature is used to describe the wall pressure field induced by the turbulent boundary layer in the wavenumber–frequency domain. An analytical expression of the wall pressure field for a flat surface is adapted to describe the wall pressure field for a cylindrical surface. Circumferential sensitivity functions are derived using a wavenumber-point reciprocity principle. Results for the near-field and far-field acoustic pressure spectra are presented. Contributions of individual circumferential modes to the acoustic pressure spectra are examined, showing distinct trends below and above the ring frequency. The proposed method is computationally efficient and provides an effective approach to investigate vibroacoustic responses for maritime platforms.     

孔隙地层中声波诱导的电磁场测井响应模拟

声电效应测井过程中,当充流体井中发射的声波传播至井外时,在孔隙地层中引起含带电离 子的孔隙流体相对于固体骨架流动,导致电磁场. 在忽略转换电磁场对声场影响的条件下,先采用Biot-Rosenbaum模型计算孔隙地层中的 声场,再计算声波诱导的电场和磁场. 计算结果表明,有伴随纵波波群和横波波群的电磁场、有伴随斯通利波的电磁场,还有微弱的 临界折射电磁波. 计算还表明: 接收器偏离井轴越远,电场和磁场的强度越大; 在井壁处,磁场强度的波形与轴向电场强度的波形相似.     

Sound radiation of a functionally graded material cylindrical shell in water by mobility method

Based on the fundamental dynamic equations of functionally graded material (FGM) cylindrical shell, this paper investigates the sound radiation of vibrational FGM shell in water by mobility method. This model takes into account the exterior fluid loading due to the sound press radiated by the FGM shell. The FGM cylindrical shell was excited by a harmonic line radial force uniformly distributing along the generator. The FGM shell equations of motion, the Helmholtz equation in the exterior fluid medium and the continuity equation at fluid-shell interface are used in this vibroacoustic problem. The expressions of sound radiation efficiency and sound field of the FGM shell have been derived by mobility method. Radiation efficiency, modal mobility and the directivity pattern of the sound field are solved numerically. In particular, radiation efficiency and directivity pattern with various power law index are analyzed.     

Scattering of pulsed Rayleigh surface waves by a cylindrical cavity

A pulsed Rayleigh surface wave of prescribed shape is incident on a cylindrical cavity which is parallel to both the plane free surface and the plane wave front. Multiple reflections at the cylindrical and plane free surface are considered and the resulting displacements and stress components are calculated in the surrounding of the cavity by approximately summing infinite double sums. Use is made of the stationary loading case simulated by a periodic train of wave pulses and its time Fourier series representation and of expansions of all incident and reflected waves in terms of cylindrical wave functions. For reflection, the free surface of the half-space is approximated by a fictitious convex (or concave) cylindrical surface of “large” radius. The wave pattern due to a single pulse loading is constructed from the stationary solution by enforcing homogeneous initial conditions in the half-space ahead of the single loading pulse and by prescribing a wide spacing in the periodically set-forth train of pulses. The numerical results for stresses and dynamic stress magnification factors are especially useful for the interpretation of recent measurements in dynamic photoelasticity.     

Analytical solution of radiation sound pressure of double cylindrical shells in fluid medium

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Modeling and simulation of an acoustic well stimulation method

This paper presents a mathematical model and a numerical procedure to simulate an acoustic well stimulation (AWS) method for enhancing the permeability of the rock formation surrounding oil and gas wells. The AWS method considered herein aims to exploit the well-known permeability-enhancing effect of mechanical vibrations in acoustically porous materials, by transmitting time-harmonic sound waves from a sound source device—placed inside the well—to the well perforations made into the formation. The efficiency of the AWS is assessed by quantifying the amount of acoustic energy transmitted from the source device to the rock formation in terms of the emission frequency and the well configuration. A simple methodology to find optimal emission frequencies for a given well configuration is presented. The proposed model is based on the Helmholtz equation, a sound-hard boundary condition at the casing, and an impedance boundary condition that effectively accounts for the porous solid–fluid interaction at the interface between the rock formation and the well perforations. Exact non-reflecting boundary conditions derived from Dirichlet-to-Neumann maps are utilized to truncate the circular cylindrical waveguides considered in the model. The resulting boundary value problem is then numerically solved by means of the finite element method. A variety of numerical examples are presented in order to demonstrate the effectiveness of the proposed procedure for finding optimal emission frequencies.     

Scattering of acoustic waves from a point source over an impedance wedge

In this work we study diffraction of a spherical acoustic wave due to a point source, by an impedance wedge In the exterior of the wedge the acoustic pressure satisfies the stationary wave (Helmholtz) equation and classical impedance boundary conditions on two faces of the wedge, as well as Meixner’s condition at the edge and the radiation conditions at infinity. Solution of the boundary value problem is represented by a Weyl type integral and its asymptotic behavior is discussed. On this way, we derive various components in the far field interpreting them accordingly and discussing their physical meaning.     

Forced Convective Cooling via Acoustic Streaming in a Narrow Channel Established by a Vibrating Piezoelectric Bimorph

Forced convection in a narrow channel is investigated both numerically and experimentally. The flow field is established through the mechanism of acoustic streaming. This is accomplished by high frequency vibration of one of the channel walls, which is composed of a piezoelectric bimorph. In the numerical computations, the Navier-Stokes equations are decomposed into the acoustic equations and the streaming equations by the perturbation method. The acoustic field is first numerically obtained, which provides the driving force for the streaming field. The streaming field and the associated temperature field are then obtained numerically. Heat losses from a heat source are measured to determine the efficiency of this as a cooling method. The air-flow patterns in the channel between the heat source and the bimorph actuator are visualized using the particle tracking velocimetry. The visualization clearly shows that vortical streaming (acoustic streaming) can be induced by bimorph vibration, which enhances heat transfer between the heat source and the surrounding air. The temperature decreases obtained computationally and experimentally are in good agreement.     

阶梯圆柱形耦合声场的特征正交-里兹法建模及声学特性分析

针对阶梯圆柱形耦合声场建模问题,提出基于特征正交-里兹能量原理的声学建模方法.该方法利用二维特征正交多项式和周向傅里叶级数表征阶梯圆柱形耦合声场子分段的声压函数,从能量角度考虑邻近子声场间声学连续性条件,并结合里兹法获得耦合声场的声学特性.基于本建模方法对不同分段的耦合声场开展声学特性分析,结果表明,本建模方法在保证计算准确性的基础上有效提高了计算效率,且对任意阶梯分段的圆柱形耦合声场普遍适用;圆柱形耦合声场固有频率会随着腔体外径增大而普遍增大,而腔深的影响规律相反;降低声学边界阻抗可抑制声学响应幅值,为此类声场的噪声控制提供了设计依据.