Mean force on a small sphere in a sound field in a viscous fluid

A mean force exerted on a small rigid sphere by a sound wave in a viscous fluid is calculated. The force is expressed as a sum of drag force coming from the external steady flow existing in the absence of the sphere and contributions that are cross products of velocity and velocity derivatives of the incident field. Because of the drag force and an acoustic streaming generated near the sphere, the mean force does not coincide with the acoustic radiation pressure, i.e., the mean momentum flux carried by the sound field through any surface enclosing the sphere. If the sphere radius R is considerably smaller than the viscous wave penetration depth delta, the drag force can give the leading-order contribution (in powers of delta/R) to the mean force and the latter can then be directed against the radiation pressure. In another limit, delta< or =R, the drag force and acoustic streaming play a minor role, and the mean force reduces to the radiation pressure, which can be expressed through source strengths of the scattered sound field. The effect of viscosity can then be significant only if the incident wave is locally plane traveling.     

Acoustic scattering of a high-order Bessel beam by an elastic sphere

The exact analytical solution for the scattering of a generalized (or “hollow”) acoustic Bessel beam in water by an elastic sphere centered on the beam is presented. The far-field acoustic scattering field is expressed as a partial wave series involving the scattering angle relative to the beam axis and the half-conical angle of the wave vector components of the generalized Bessel beam. The sphere is assumed to have isotropic elastic material properties so that the nth partial wave amplitude for plane wave scattering is proportional to a known partial-wave coefficient. The transverse acoustic scattering field is investigated versus the dimensionless parameter ka(k is the wave vector, a radius of the sphere) as well as the polar angle θ for a specific dimensionless frequency and half-cone angle β. For higher-order generalized beams, the acoustic scattering vanishes in the backward (θ = π) and forward (θ = 0) directions along the beam axis. Moreover it is possible to suppress the excitation of certain resonances of an elastic sphere by appropriate selection of the generalized Bessel beam parameters.     

球形粒子在Bessel波束照射下的轴向辐射力计算和分析

通过声散射理论,将水中粒子的Bessel波束声散射场的分波序列(PWS)表达公式加以推广,进而推导出声辐射力的表达公式,获得了液体球及弹性球在Bessel波束下声辐射力的变化规律。通过观察不同散射角形态函数,可发现声辐射力的产生与粒子背向散射抑制程度有关。对于液体球粒子,球壳厚度及材料介质对粒子声辐射力有着重要的影响,同时Bessel波束波锥角越大,产生负声辐射力的可能性越大。对于弹性球和弹性单层壳粒子,声辐射力的产生与其本身的共振特征存在很大的关系。同时,通过改变球壳内介质及壳层厚度的方法,可增加产生的负声辐射力的频率范围及幅值强度.      

Acoustic diffraction by a half-plane in a viscous fluid medium

We consider the diffraction of a time-harmonic acoustic plane wave by a rigid half-plane in a viscous fluid medium. The linearized equations of viscous fluid flow and the no-slip condition on the half-plane are used to derive a pair of disjoint Wiener-Hopf equations for the fluid stresses and velocities. The Wiener-Hopf equations are solved in conjunction with a requirement that the stresses are integrable near the edge of the half-plane. Specific wave components of the scattered velocity field are given analytically. A Padé approximation to the Wiener-Hopf kernel function is used to derive numerical results that show the effect of viscosity on the velocity field in the immediate vicinity of the edge of the half-plane.     

Axial radiation force of a bessel beam on a sphere and direction reversal of the force

An expression is derived for the radiation force on a sphere placed on the axis of an ideal acoustic Bessel beam propagating in an inviscid fluid. The expression uses the partial-wave coefficients found in the analysis of the scattering when the sphere is placed in a plane wave traveling in the same external fluid. The Bessel beam is characterized by the cone angle beta of its plane wave components where beta=0 gives the limiting case of an ordinary plane wave. Examples are found for fluid spheres where the radiation force reverses in direction so the force is opposite the direction of the beam propagation. Negative axial forces are found to be correlated with conditions giving reduced backscattering by the beam. This condition may also be helpful in the design of acoustic tweezers for biophysical applications. Other potential applications include the manipulation of objects in microgravity. Islands in the (ka, beta) parameter plane having a negative radiation force are calculated for the case of a hexane drop in water. Here k is the wave number and a is the drop radius. Low frequency approximations to the radiation force are noted for rigid, fluid, and elastic solid spheres in an inviscid fluid.     

On acoustic radiation by a rigid object in a fluid flow

A problem of sound radiation by an absolutely rigid object, moving with respect to the surrounding fluid, is considered on the basis of the Lighthill's equation for aerodynamic sound. An integral representation of the radiated acoustic field is utilized, where the field is characterized as the sum of three fields, generated by a volume distribution of monopoles and by distributions of monopoles and dipoles on the surface of the rigid object. It is shown that, due to a discontinuity of Lighthill's stress tensor on the rigid boundary, a layer of surface divergence of hydrodynamic stresses on the boundary must be taken into account when evaluating the volume integral over Lighthill's quadrupole sources. When the contribution of the surface divergence is included in the solution of Lighthill's equation, amplitudes of the monopole and dipole sound radiated by the rigid object are shown to depend on the potential components of the normal velocity and the pressure on the rigid surface. The obtained solution is compared with Curle's solution for this problem, which establishes that the sound radiation by a rigid object is determined by the force exerted by the object upon the fluid. Both solutions are applied to two known problems of sound scattering and radiation by a rigid sphere in variable pressure and velocity fields. It is shown that predictions based on the obtained solution are equivalent to the results known from literature, whereas Curle's solution gives predictions contradicting the known results. It is also shown that the Ffowcs Williams and Hawkings equation, which coincides with Curle's equation for an immoveable rigid object, does not lead to the correct predictions as well.     

Receiving sensitivity and transmitting voltage response of a fluid loaded spherical piezoelectric transducer with an elastic coating

A method is presented to determine the response of a spherical acoustic transducer that consists of a fluid-filled piezoelectric sphere with an elastic coating embedded in infinite fluid to electrical and plane-wave acoustic excitations. The exact spherically symmetric, linear, differential, governing equations are used for the interior and exterior fluids, and elastic and piezoelectric materials. Under acoustic excitation and open circuit boundary condition, the equation governing the piezoelectric sphere is homogeneous and the solution is expressed in terms of Bessel functions. Under electrical excitation, the equation governing the piezoelectric sphere is inhomogeneous and the complementary solution is expressed in terms of Bessel functions and the particular integral is expressed in terms of a power series. Numerical results are presented to illustrate the effect of dimensions of the piezoelectric sphere, fluid loading, elastic coating and internal material losses on the open-circuit receiving sensitivity and transmitting voltage response of the transducer.     

Acoustic scattering by a rigid elliptic cylinder in a slightly viscous medium

A complete solution is obtained for the two-dimensional diffraction of a time-harmonic acoustic plane wave by an impenetrable elliptic cylinder in a viscous fluid. Arbitrary size, ellipticity, and angle of incidence are considered. The linearized equations of viscous flow are used to write down expressions for the dilatation and vorticity in terms of products of radially and angular dependent Mathieu functions. The no-slip condition on the rigid boundary then determines the coefficients. The resulting computations are facilitated by recently developed library routines for complex input parameters. The solution for the circular cylinder serves as a guide and a differently constructed solution for the strip is also given. Typical results in the "resonant" range of dimensionless wave number, displaying the surface vorticity and the far-field scattering pattern are included, with the latter allowing comparison with the inviscid case.     

On the effect of viscosity in scattering from partially coated infinite cylinders

This paper considers the two-dimensional problem of scattering of a plane wave incident on an infinite cylinder that is coated with strips of pressure-release material extending over quadrants on the illuminated and shadowed sides, with the remainder of the surface considered to be rigid. Transitions from soft to rigid surfaces correspond to discontinuous boundary conditions. Ideal fluid theory predicts an infinite pressure gradient at these transitions, which suggests that viscous effects may be significant. The present work is a quantitative analysis of the global effect on acoustic scattering of viscosity effects arising in the vicinity of the discontinuity. The analysis represents the scattered field in terms of acoustic and vortical contributions. Both contributions are represented by series expansions in terms of azimuthal harmonics and associated cylindrical wave functions. The amplitudes of these harmonics are determined by satisfying a pair of discontinuous boundary conditions. Results obtained by using the method of weighted residuals are shown to be less accurate than those obtained from a collocation procedure. The results for surface pressure and farfield directivity indicate that viscous effects are important only if the Reynolds number is extremely small.     

Interaction of a spherical acoustic wave with an elastic spherical shell

The interaction of a spherical acoustic wave with an elastic spherical shell is treated analytically. The solution includes the coupling between the acoustic sound field and vibration of the shell with any degree of fluid loading. The formulation for the far-field acoustic pressure is derived in terms of natural spherical wave functions, the properties of the acoustic medium, and the material constants of the shell. The far acoustic field is computed for a thin aluminum shell and several sound source locations over a large range of ka, where k is the wavenumber, and a is the shell radius. It is shown that the acoustic pressure depends significantly on whether the shell is in air or is submerged in water, particularly when the sound source is very near the surface. In air, the sound field of the shell is nearly identical to that of a rigid sphere but, in water, the shell is more compliant, which results in a damped radiation field that is characterized by vibrational resonances throughout the range of frequencies considered. As the sound sources is moved further away from the surface, however, this resonance response decreases very rapidly, and the sound field corresponds more closely to that of the shell in air.     

Radiation pressure on an inclusion with a given scattering amplitude in an arbitrary external field

A method is proposed for calculating the radiation pressure forces that act on a body characterized by a given scattering amplitude and positioned in an ideal liquid in an arbitrary acoustic field. The efficiency of the method is tested by two examples: a fluid sphere in a spherical wave and a similar sphere in the field of a traveling wave with a Gaussian amplitude distribution. The agreement with the results obtained earlier by other methods is demonstrated.     

A characterization of the scattered acoustic intensity field in the resonance region for simple spheres

The properties of the scattered acoustic vector fields generated by simple spheres illuminated by monotonic continuous wave (CW) plane waves are investigated. Analytical solutions are derived from general acoustic pressure scattering models and analyzed for wave numbers in the resonance region. Of particular interest is the understanding of the characteristics of the scattered acoustic vector field in the near-to-far-field transition region. The separable active and reactive components of the acoustic intensity are used to investigate the structural features of the scattered field components. Numerical results are presented for the near and transition regions for a rigid sphere. A method of mapping nulls in the scattered intensity field components is described. The analysis is then extended to include a simple fluid-filled boundary and finally the evacuated thin-walled shell. Near field acoustic intensity field structures are compared against mechanical material properties of vacuous shells. The ability to extract scattered field features is illustrated with measurements obtained from a recent in-air experiment using an anechoic chamber and acoustic vector sensor probes to measure the scattered acoustic vector field from rigid spheres.     

Acoustic radiation force of a quasi-Gaussian beam imparted to a solid spherical scatterer in a fluid

The radiation force generated upon the scattering of a quasi-Gaussian acoustic beam on a homo-geneous elastic sphere in a fluid is investigated. It is shown that the force depends nonmonotonically on the ratio between the sphere’s diameter and the beam’s waist. For a given beam power, the radiation force has its maximum value when the diameters are roughly egual to each other. This is due to the resonant excitation of shear waves on the sphere’s surface under the impact of acoustic wave in the surrounding fluid.     

充水有限长圆柱薄壳声散射:Ⅰ.理论

研究水中充水有限长圆柱薄壳的声散射。采用弹性薄壳理论结合边界条件导出了有限长圆柱薄壳倾斜入射时散射声场的解析解,内部充水的作用反映在系统总阻抗中增加了内部流体阻抗。数值计算表明,在反向散射声场中,刚性散射部分仅在正横附近有比较大的贡献,而斜入射时起主要作用的是弹性散射部分。散射波相速度频散曲线的计算表明,与内部真空的情况相比内部充水后除正横附近的纵波和剪切波以外,增加了一组内部流体引起的附加波,其对散射声场贡献非常重要。在计算的频率-角度谱图中,内部流体附加波呈现"碗"形共振曲线。      

Acoustic scattering by a modified Werner method

A modified integral Werner method is used to calculate pressure scattered by an axisymmetric body immersed in a perfect and compressible fluid subject to a harmonic acoustic field. This integral representation is built as the sum of a potential of a simple layer and a potential of volume. It is equivalent to the exterior Helmholtz problem with Neumann boundary condition for all real wave numbers of the incident acoustic field. For elastic structure scattering problems, the modified Werner method is coupled with an elastodynamic integral formulation in order to account for the elastic contribution of the displacement field at the fluid/structure interface. The resulting system of integral equations is solved by the collocation method with a quadratic interpolation. The introduction of a weighting factor in the modified Werner method decreases the number of volume elements necessary for a good convergence of results. This approach becomes very competitive when it is compared with other integral methods that are valid for all wave numbers. A numerical comparison with an experiment on a tungsten carbide end-capped cylinder allows a glimpse of the interesting possibilities for using the coupling of the modified Werner method and the integral elastodynamic equation used in this research.     

Theoretical and numerical calculations for the time-averaged acoustic force and torque acting on a rigid cylinder of arbitrary size in a low viscosity fluid

In this paper, theoretical calculations as well as numerical simulations are performed for the time-averaged acoustic force and torque on a rigid cylinder of arbitrary size in a fluid with low viscosity, i.e., the acoustic boundary layer is thin compared to the cylinder radius. An exact analytical solution and its approximation are proposed in the form of an infinite series including Bessel functions. These solutions can be evaluated easily by a mathematical software package such as mathematica and matlab. Three types of incident waves, plane traveling wave, plane standing wave, and dual orthogonal standing waves, are investigated in detail. It is found that for a small particle, the viscous effects for an incident standing wave may be neglected but those for an incident traveling wave are notable. A nonzero viscous torque is experienced by the rigid cylinder when subjected to dual orthogonal standing waves with a phase shift even when the cylinder is located at equilibrium positions without imposed acoustic forces. Furthermore, numerical simulations are carried out based on the FVM algorithm to verify the proposed theoretical formulas. The theoretical results and the numerical ones agree with each other very well in all the cases considered.     

近似声斗篷的多层介质覆盖水中弹性球壳的声散射

对水中弹性球壳的低频覆盖层消声效果和消声机理进行研究。声斗篷(Acoustic cloak)是各向异性的超常材料,根据有效介质近似理论(Effective MediumApproximationTheory),采用各向同性多层介质近似各向异性材料的声斗篷,推导出覆盖多层介质水中弹性球壳散射声场的解析表达式,计算了弹性球壳覆盖多层介质前后的散射形态函数、谐振模态以及声场分布,分析了覆盖前后球壳的声散射特性和声传播机理。研究表明,覆盖层内的声波在多层介质之间的声传播方向发生改变,声场形成弯曲变形,声能流绕过目标,这不仅极大的降低了低频散射强度,而且使到达弹性体表面的声场强度非常小,散射频响中除了0阶子波产生的第一个谐振峰外,无法激发弹性球壳的其它谐振模态,有效的抑制弹性球壳的谐振散射。      

Acoustic scattering from a fluid-filled finite cylindrical shell in water:Ⅰ.Theory

Acoustic scattering from a submerged fluid-filled finite cylindrical shell insonified by an incident plane wave was studied.The analytic solutions of the scattering field are derived using the elastic thin shell theory with the boundary conditions.The fluid-filled impedance,due to the effect of internal fluid,must add to the impedance of the system.The results show that in the backscattering field,rigid scattering has a large contribution only on the broadside and elastic scattering play a major role when oblique incidence.The dispersion curves of the phase velocity show that comparing with the internal vacuum condition,except the contribution by longitudinal wave and shear wave near the broadside a series of the additional waves caused by the internal fluid is added which have great contribution to the scattering field.Bowl-shape resonance curves are presented in the frequency-angle spectrum as the contribution of the internal fluid waves.     

楔形理想波导中球体散射的镜像方法

应用镜像原理和球波函数加法公式,把楔形理想波导中球体的散射声场等效为无界空间中多球体散射声场,镜像解析解与边界元数值结果相同,可以作为边界随水平距离变化波导中目标散射数值方法的标准解。比较无界空间和楔形理想波导中球体散射声场空间分布特征,结果表明:楔形理想波导中球体的散射声场在水平和倾斜边界反射;散射声场沿楔形理想波导下坡方向的衰减在相同的水平距离下小于无界空间的情况,散射声场在楔形理想波导上坡的空间分布受到限制。     

Scattering of a Bessel beam by a sphere

The exact scattering by a sphere centered on a Bessel beam is expressed as a partial wave series involving the scattering angle relative to the beam axis and the conical angle of the wave vector components of the Bessel beam. The sphere is assumed to have isotropic material properties so that the nth partial wave amplitude for plane wave scattering is proportional to a known partial-wave coefficient. The scattered partial waves in the Bessel beam case are also proportional to the same partial-wave coefficient but now the weighting factor depends on the properties of the Bessel beam. When the wavenumber-radius product ka is large, for rigid or soft spheres the scattering is peaked in the backward and forward directions along the beam axis as well as in the direction of the conical angle. These properties are geometrically explained and some symmetry properties are noted. The formulation is also suitable for elastic and fluid spheres. A partial wave expansion of the Bessel beam is noted.