Parametric study on sound radiation from an infinite fluid-filled/semi-submerged cylindrical shell

This work presents the parametric study on the far-field sound pressure radiated from an infinite fluid-filled/semi-submerged cylindrical shell excited by a radial point load. Here, the exterior fluid is non-viscous, isotropic and irrotational coaxial flow. The formula of the radial velocity of the shell in wave-number domain is developed by using the wave-number domain approach (WDA). Then, the analytic expressions are derived for the far-field sound pressure radiating from the shell by using the same method presented in Salaün [Journal of the Acoustical Society of America 90 (1991) 2173]. The influences of parameters such as fluid velocity, structural damping, position of the force, and structural thickness on the far-field sound pressure are investigated. The sound pressure is shown to be very different from the one in the case of a fluid-filled/full-submerged cylindrical shell. Furthermore, it is shown that the pressure and the resonance frequency would increase with the fluid velocity increasing for downstream propagation. The reverse is true for upstream propagation. Moreover, the far-field sound pressure is related to the position and frequency of the excited force. In addition, the influences of structural damping and thickness are shown to be very important.     

Fluid dynamics phenomena induced by power ultrasounds

Propagation of power ultrasound (from 20 to 800 kHz) through a liquid inside a cylindrical reactor initiates acoustic cavitation and also fluid dynamics phenomena such as free surface deformation, convection, acoustic streaming, etc. Mathematical modelling is performed as a new approach to predict where active bubbles are and how intense cavitation is. A calculation based on fluid dynamics equations is undertaken using computational fluid dynamics code; this is of great interest because such code provides not only the pressure field but also velocity and temperature fields. The link between the acoustic pressure and the cavitation field is clearly established. Moreover, the pressure profile near a free surface allows one to predict the shape of the acoustic fountain. The influence of the acoustic fountain on the wave propagation is shown to be important. The convective flow inside a reactor is numerically obtained and agrees well with particle image velocity measurements. Non-linearities arising from the dissipation of the acoustic wave are computed and lead to the calculation of the acoustic streaming. The superimposed velocity field (convective flow and acoustic streaming) succeeds in simulating the bubble behaviour at 500 kHz, for instance.     

An effective quiescent medium for sound propagating through an inhomogeneous,moving fluid

The idea of similarity between acoustic fields in a moving fluid and in a certain "effective" quiescent medium, first put forward by Lord Rayleigh, proved very helpful in understanding and modeling sound propagation in an atmosphere with winds and in an ocean with currents, as well as in other applications involving flows with small velocity compared to sound speed. Known as effective sound speed approximation, the idea is routinely utilized in the contexts of the ray theory, normal mode representation of the sound field, and the parabolic approximation. Despite the wide use of the concept of effective sound speed in acoustics of moving media, no theoretical justification of Rayleigh's idea was published that would be independent of the chosen representation of the sound field and uniformly apply to distinct propagation regimes. In this paper, we present such a justification by reducing boundary conditions and a wave equation governing sound fields in the inhomogeneous moving fluid with a slow flow to boundary conditions and a wave equation in a quiescent fluid with effective sound speed and density. The derivation provides insight into validity conditions of the concept of effective quiescent fluid. Introduction of effective density in conjunction with effective sound speed is essential to ensure accurate reproduction of acoustic pressure amplitude in the effective medium. Effective parameters depend on sound speed, flow velocity, and density of the moving fluid as well as on sound propagation direction. Conditions are discussed under which the dependence on the propagation direction can be avoided or relaxed.     

Guided waves in a circular duct containing an assembly of circular cylinders

This paper provides an analytical scheme to calculate the admissible acoustic propagation modes of fluid in a circular duct containing an assembly of circular cylinders, as might occur in gas-cooled fast breeder reactors and advanced gas-cooled reactors. The duct wall and cylinders are assumed to be stationary, and their axes are assumed to be parallel to each other. The solution to the acoustic wave equation is expressed in a sum of the partial fluid velocity potentials associated with each rod co-ordinate and duct co-ordinate. The technique of transformation of cylindrical wave functions is then used to solve the boundary value problem. Two kinds of acoustic boundary conditions are considered, acoustically hard and acoustically soft, respectively.     

Acoustic signature of a submarine hull under harmonic excitation

The structural and acoustic responses of a submarine under harmonic force excitation are presented. The submarine hull is modelled as a cylindrical shell with internal bulkheads and ring stiffeners. The cylindrical shell is closed by truncated conical shells, which in turn are closed at each end using circular plates. The entire structure is submerged in a heavy fluid medium. The structural responses of the submerged vessel are calculated by solving the cylindrical shell equations of motion using a wave approach and the conical shell equations with a power series solution. The far-field radiated sound pressure is then calculated by means of the Helmholtz integral. The contribution of the conical end closures on the radiated sound pressure for the lowest circumferential mode numbers is clearly observed. Results from the analytical model are compared with computational results from a fully coupled finite element/boundary element model.     

Structural and acoustic responses of a fluid-loaded cylindrical hull with structural discontinuities

This paper studies the low frequency vibrational behaviour and radiated sound of a submarine hull under axial excitation. The submarine is modelled as a fluid-loaded cylindrical shell with internal bulkheads and ring-stiffeners and closed at each end by circular plates. A smeared approach is used to model the ring stiffeners. The external pressure acting on the hull due to the fluid loading is calculated using an infinite model and is shown to be a good approximation at low frequencies. The radiated sound pressure is obtained by considering the finite cylindrical hull to be extended by two semi-infinite rigid baffles. The sound pressure is then only due to the radial displacement of the cylindrical shell, without taking into account the scattering at the finite ends. The main aim of this paper is to observe the influence of the various complicating effects such as the bulkheads, ring-stiffeners and fluid loading on the structural and acoustic responses of the finite cylindrical shell. Results from the analytical models presented in this paper are compared to the computational results from finite element and boundary element models.     

Acoustic radiation from the submerged circular cylindrical shell treated with active constrained layer damping

Based on the transfer matrix method of exploring the circular cylindrical shell treated with active constrained layer damping(i.e., ACLD), combined with the analytical solution of the Helmholtz equation for a point source, a multi-point multipole virtual source simulation method is for the first time proposed for solving the acoustic radiation problem of a submerged ACLD shell. This approach, wherein some virtual point sources are assumed to be evenly distributed on the axial line of the cylindrical shell, and the sound pressure could be written in the form of the sum of the wave functions series with the undetermined coefficients, is demonstrated to be accurate to achieve the radiation acoustic pressure of the pulsating and oscillating spheres respectively. Meanwhile, this approach is proved to be accurate to obtain the radiation acoustic pressure for a stiffened cylindrical shell. Then, the chosen number of the virtual distributed point sources and truncated number of the wave functions series are discussed to achieve the approximate radiation acoustic pressure of an ACLD cylindrical shell. Applying this method, different radiation acoustic pressures of a submerged ACLD cylindrical shell with different boundary conditions, different thickness values of viscoelastic and piezoelectric layer, different feedback gains for the piezoelectric layer and coverage of ACLD are discussed in detail. Results show that a thicker thickness and larger velocity gain for the piezoelectric layer and larger coverage of the ACLD layer can obtain a better damping effect for the whole structure in general. Whereas, laying a thicker viscoelastic layer is not always a better treatment to achieve a better acoustic characteristic.     

The effect of flow on the piston problem of acoustics

A compressible fluid, bounded on one side by an infinite plane, flows with constant subsonic speed U parallel to the plane, and acoustic disturbances are caused by a small amplitude vibration of a circular piston set in the plane. The effect of the mean flow on this classical radiation problem is investigated and the distant field is expressed in elementary form. For the compact piston, whose radius is small compared with a wavelength, it is confirmed (in agreement with earlier work) that the distant field is not simply that of a point source with strength equal to the displaced volume flux since the piston has an additional blockage effect on the mean flow. The total excess energy flow is calculated for the compact piston with any subsonic mean flow (and also for the non-compact piston with low Mach number mean flow) and is compared with that for the complementary problem of a moving piston in a quiescent fluid. Since this is the previous problem referred to a reference frame that moves with the mean flow, the pressure and velocity fluctuations are as before, but the energy balance is different since the drag force on the piston does work in the latter case.     

Equations for finite-difference, time-domain simulation of sound propagation in moving inhomogeneous media and numerical implementation

Finite-difference, time-domain (FDTD) calculations are typically performed with partial differential equations that are first order in time. Equation sets appropriate for FDTD calculations in a moving inhomogeneous medium (with an emphasis on the atmosphere) are derived and discussed in this paper. Two candidate equation sets, both derived from linearized equations of fluid dynamics, are proposed. The first, which contains three coupled equations for the sound pressure, vector acoustic velocity, and acoustic density, is obtained without any approximations. The second, which contains two coupled equations for the sound pressure and vector acoustic velocity, is derived by ignoring terms proportional to the divergence of the medium velocity and the gradient of the ambient pressure. It is shown that the second set has the same or a wider range of applicability than equations for the sound pressure that have been previously used for analytical and numerical studies of sound propagation in a moving atmosphere. Practical FDTD implementation of the second set of equations is discussed. Results show good agreement with theoretical predictions of the sound pressure due to a point monochromatic source in a uniform, high Mach number flow and with Fast Field Program calculations of sound propagation in a stratified moving atmosphere.     

Characteristics of the vibrational power flow propagation in a submerged periodic ring-stiffened cylindrical shell

By using space-harmonic analysis method, the characteristics of the vibrational power flow propagation in an infinite periodic ring-stiffened cylindrical shell immersed in water are studied. The harmonic motion of the shell and the sound pressure field in the fluid are described by Flügge shell equations and Helmholtz equation, respectively, and four kinds of the rings’ forces and moments are considered. Along the shell axial direction, the propagation of the power flow carried by different internal forces (moments) of the shell wall can be obtained, thus the total power flow in the shell wall and the ratios of the component power flow carried by different shell internal forces (moments) to the total power flow are also studied. It is found that characteristics of the vibrational power flow propagation vary with different circumferential modes order and different frequencies. Moreover, the presence of the stiffeners and structural damping will greatly influence the results.     

The Force Acting on a Cylinder in a Ring Flow of a Viscous Fluid with a Small Eccentric Displacement

A system consisting of two circular cylinders one inside the other with parallel axes is considered. The outer cylinder of radius R₂ is fixed, and the inner cylinder of radius R₁ rotates with a sufficiently large angular velocity. The region between the cylinders is filled with an incompressible viscous fluid and, in the case of coaxial cylinders, Couette flow along circular trajectories arises. Upon an eccentric small displacement of the axis of the inner cylinder, the symmetry of the flow is disturbed and a force exerted on the inner cylinder by the fluid is created. Within the ideal fluid model, the force depends linearly on the transverse velocities and accelerations of the cylinder. In a viscous fluid, the force depends on the previous motion of the cylinder. It is expressed in terms of the velocity functional by analogy with the Basset force acting on a ball moving in a viscous fluid with a variable velocity.     

Axially symmetric vibrations of fluid-filled poroelastic circular cylindrical shells

Employing Biot's theory of wave propagation in liquid saturated porous media, axially symmetric vibrations of fluid-filled and empty poroelastic circular cylindrical shells of infinite extent are investigated for different wall-thicknesses. Let the poroelastic cylindrical shells are homogeneous and isotropic. The frequency equation of axially symmetric vibrations each for a pervious and an impervious surface is derived. Particular cases when the fluid is absent are considered both for pervious and impervious surfaces. The frequency equation of axially symmetric vibrations propagating in a fluid-filled and an empty poroelastic bore, each for a pervious and an impervious surface is derived as a limiting case when ratio of thickness to inner radius tends to infinity as the outer radius tends to infinity. Cut-off frequencies when the wavenumber is zero are obtained for fluid-filled and empty poroelastic cylindrical shells both for pervious and impervious surfaces. When the wavenumber is zero, the frequency equation of axially symmetric shear vibrations is independent of nature of surface, i.e., pervious or impervious and also it is independent of presence of fluid in the poroelastic cylindrical shell. Non-dimensional phase velocity for propagating modes is computed as a function of ratio of thickness to wavelength in absence of dissipation. These results are presented graphically for two types of poroelastic materials and then discussed. In general, the phase velocity of an empty poroelastic cylindrical shell is higher than that of a fluid-filled poroelastic cylindrical shell.The phase velocity of a fluid-filled bore is higher than that of an empty poroelastic bore. Previous results are shown as a special case of present investigation. Results of purely elastic solid are obtained.     

基于高速摄像实验的开放腔体圆柱壳入水空泡流动研究

基于高速摄像方法,针对入水空泡流动特征和机理,进行了开放腔体圆柱壳垂直入水实验研究.通过对实验现象的观测,发现开放腔体圆柱壳入水运动会形成波动流动和云化流动两种流动方式,结合影像数据,分别描述了两种流动状态下的空泡形态特征,并获得了空泡波动参数的变化规律;对比不同入水速度实验,分析了入水速度对入水空泡流动方式和流动参数的影响;依据流体力学基本理论,分析了入水空泡波动和云化现象的形成机理.结果表明:随入水速度增加,入水空泡依次呈现波动和云化两种流动状态,波动频率与入水速度无关,闭合发生时间随入水速度增加而减小,与Froude数呈线性关系;入水导致开放空腔内部气体涨缩,引起开放端压力场和速度场周期性扰动,空泡截面扩展程度出现差异,形成空泡波动现象;空泡闭合后尾部形成回射流,回射流触及空泡壁面引起壁面流动转捩,形成空泡云化现象.     

Low frequency pressure waves in a vapor-liquid medium with a fixed layer of spherical particles

The features of the propagation of low-frequency pressure waves in a liquid-vapor flow through a layer of close-packed spherical solid particles have been studied. Principal measurements have been performed at two pressure values, mainly 0.2 and 0.6 MPa; in a cylindrical channel using lead balls sized 3 and 8 mm. The experimental results allowed defining the characteristic parameters and conditions providing that the wave’s propagation velocity coincides with the thermodynamic equilibrium’s acoustic speed in the vapor-liquid mixture. The results show the dispersive nature of the acoustic speed in the vapor-liquid medium.     

Three methods for analyzing forced vibration of a fluid-filled cylindrical shell

The forced vibration of an infinite elastic circular cylindrical shell filled with fluid is studied. Three methods are employed to analyze the forced vibration problem of this shell-fluid coupled system, that is, wave propagation approach (wave mode superposition), theorem of residues and a numerical integral method. In order to explain these methods more explicitly, before being used to investigate the vibration of an infinite fluid-filled elastic circular cylindrical shell, all these three methods are employed firstly to analyze the forced vibration problem of an infinite beam and an infinite elastic circular cylindrical shell in vacuo. Advantage and disadvantage of these three methods are discussed and their interesting relationship is revealed. That is, to any circumferential wavenumber and frequency of the external force, there is an unchangeable relationship between the general coordinates of various waves in the wave propagation approach and the residuals in the theorem of residues.     

径向声子晶体隔声特性*

该文构造了由两种匀质材料交替分布的径向声子晶体柱壳模型。首先,针对声波在其中的轴对称传播情况进行了理论分析,建立了声波由内向外传播的传递矩阵,进而导出了声压透射系数和隔声量表达式。采用数值分析的方法系统地讨论了径向声子晶体柱壳的隔声特性,并与单一材质柱壳的传播规律进行对比分析,其次,借助有限元仿真分析的手段对数值结果进行了验证。最后,详细分析了内外流体的特性阻抗对径向声子晶体柱壳隔声特性的影响,得到了相应的参数影响规律。研究表明,径向声子晶体柱壳存在声波带隙,导致其在带隙范围内的隔声效果远远优于单材质柱壳,并且该结构的固有特性突破了质量定律的限制;声波带隙内表面局域态现象出现与否由内外声场和结构场共同决定。     

Energy trapping in power transmission through a circular cylindrical elastic shell by finite piezoelectric transducers

We study the transmission of electric energy through a circular cylindrical elastic shell by acoustic wave propagation and piezoelectric transducers. Our mechanics model consists of a circular cylindrical elastic shell with finite piezoelectric patches on both sides of the shell. A theoretical analysis using the equations of elasticity and piezoelectricity is performed. A trigonometric series solution is obtained. Output voltage and transmitted power are calculated. Confinement and localization of the vibration energy (energy trapping) is studied which can only be understood from analyzing finite transducers. It is shown that when thickness-twist mode is used the structure shows energy trapping with which the vibration can be confined to the transducer region. It is also shown that energy trapping is sensitive to the geometric and physical parameters of the structure.     

Finite-element modeling of an acoustic cloak for three-dimensional flexible shells with structural excitation

A finite-element model for three-dimensional acoustic cloaks in both cylindrical and spherical coordinates is presented. The model is developed through time-harmonic analysis to study pressure and velocity field distributions as well as the cloak’s performance. The model developed accounts for the fluid-structure interaction of thin fluid-loaded shells. A plane strain model is used for the thin shell. Mechanical harmonic excitation is applied to the fluid-loaded shell to investigate the effect of mechanical oscillation of the shell on the performance of the acoustic cloak. In developing this model, a deeper insight into the acoustic cloak phenomena presented by Cummer and Shurig in 2007 is presented. Different nonlinear coordinate transformations are presented to study their effect on the acoustic cloak performance.     

Recovering the acoustic Green's function from ambient noise cross correlation in an inhomogeneous moving medium

We study long-range correlation of diffuse acoustic noise fields in an arbitrary inhomogeneous, moving fluid. The flow reversal theorem is used to show that the cross-correlation function of ambient noise provides an estimate of a combination of the Green's functions corresponding to sound propagation in opposite directions between the two receivers. Measurements of the noise cross correlation allow one to quantify flow-induced acoustic nonreciprocity and evaluate both spatially averaged flow velocity and sound speed between the two points.     

Investigation of flow features and acoustic radiation of a round cavity

In this work, the interaction between a boundary layer and a circular cylindrical cavity is studied. Experimental pressure and velocity results for a cavity of diameter 10 cm and depth ranging from 10 to 15 cm are described, for flow velocities between 50 and 110 m s^?1. This flow configuration is found to generate intense discrete depth- and flow-dependent tones, resulting in modes similar in appearance to Rossiter modes found in shallow rectangular cavities. Differences between the cylindrical cavity's mean flow and that of a similarly sized rectangular cavity are highlighted. The development of the shear layer is quantified, in terms of thickening and of velocity statistics profiles. Radial and azimuthal acoustic modes are observed in the acoustic field inside the cavity. A feedback model based on the coupled behaviour of the fundamental acoustic depth mode of the cavity and the large scale dynamics of the shear layer is constructed, and its response is compared to experimental data. A good qualitative agreement between available data and modeled behaviour is observed, allowing the two acoustic modes found in this work to be attributed to the interaction of the shear layer with the cavity's fundamental depth mode.