Acoustic propagation uncertainty in internal wave environments using an ocean-acoustic joint model

An ocean-acoustic joint model is developed for research of acoustic propagation uncertainty in internal wave environments.The internal waves are numerically produced by tidal forcing over a continental slope using an ocean model.Three parameters(i.e.,internal wave,source depth,and water depth)contribute to the dynamic waveguide environments,and result in stochastic sound fields.The sensitivity of the transmission loss(TL)to environment parameters,statistical characteristics of the TL variation,and the associated physical mechanisms are investigated by the Sobol sensitivity analysis method,the Monte Carlo sampling,and the coupled normal mode theory,respectively.The results show that the TL is most sensitive to the source depth in the near field,resulted from the initial amplitudes of higher-order modes;while in middle and far fields,the internal waves are responsible for more than 80%of the total acoustic propagation contribution.In addition,the standard deviation of the TL in the near field and the shallow layer is smaller than those in the middle and far fields and the deep layer.

Three-dimensional acoustic propagation model for shallow waters based on an indirect boundary element method

This work has a two-fold purpose.On the one hand,the theoretical formulation of a three-dimensional(3D)acoustic propagation model for shallow waters with a constant sound speed is presented,based on the boundary element method(BEM),which uses a half-space Green function instead of the more conventional free-space Green function.On the other hand,a numerical implementation is illustrated to explore the formulation in simple idealized cases,controlled by a few parameters,which provides necessary tests for the accuracy and performance of the model.The half-space Green's function,which has been previously used in scattering and diffraction,adds terms to the usual expressions of the integral operators without altering their continuity properties.Verifications against the wavenumber integration solution of the Pekeris waveguide suggest that the model allows an adequate prediction for the acoustic field.Likewise,numerical experiments in relation to the necessary mesh size for the description of the water-marine sediment interface lead to the conclusion that a transmission loss prediction with acceptable accuracy can be obtained with the use of a limited mesh around the desired evaluation region.

ACOUSTIC PROPAGATION IN SHEARED MEAN FLOW USING COMPUTATIONAL AEROACOUSTICS

Acoustic propagation problems in the sheared mean flow are numerically investigated using different acoustic propagation equations , including linearized Euler equations ( LEE ) and acoustic perturbation equations ( APE ) .The resulted acoustic pressure is compared for the cases of uniform mean flow and sheared mean flow using both APE and LEE.Numerical results show that interactions between acoustics and mean flow should be properly considered to better understand noise propagation problems , and the suitable option of the different acoustic equations is indicated by the present comparisons.Moreover , the ability of APE to predict acoustic propagation is validated.APE can replace LEE when the 3-D flow-induced noise problem is solved , thus computational cost can decrease.

Analysis and comparison between two coupled-mode methods for acoustic propagation in range-dependent waveguides

Two coupled-mode methods, namely DGMCM （Direct-Global-Matrix Coupled- Mode Method） and CCMM （Consistent Coupled-Mode Method）, are analyzed and compared. First, both of these two methods provide two-way solutions, and hence they are accurate models. Second, the series of local vertical modes in DGMCM converges as fast as that in CCMM, whereas DGMCM has a more tolerable requirement of the number of segments than CCMM. Third, these two models obtain the field solution by solving the coupled-mode system with different coefficient matrices, in which the computational effort for the required parameters is almost the same. Finally, DGMCM can handle some problems which are difficult for CCMM, such as in a waveguide with a rough bottom, a line source located right on top of a sloping bot- tom, or in the presence of multiple sources. In DGMCM, closed-form expressions for coupling matrices in a two-layer waveguide are given. In addition, the formulation for the line-source problem in plane geometry is derived to update CCMM.

An Application of the Level Set Method to Underwater Acoustic Propagation

An algorithm for computing wavefronts,based on the high frequency approximation to the wave equation,is presented.This technique applies the level set method to underwater acoustic wavefront propagation in the time domain.The level set method allows for computation of the acoustic phase function using established numerical techniques to solve a first order transport equation to a desired order of accuracy.Traditional methods for solving the eikonal equation directly on a fixed grid limit one to only the first arrivals,so these approaches are not useful when multi-path propagation is present.Applying the level set model to the problem allows for the time domain computation of the phase function on a fixed grid,without having to restrict to first arrival times.The implementation presented has no restrictions on range dependence or direction of travel,and offers improved efficiency over solving the full wave equation which under the high frequency assumption requires a large number of grid points to resolve the highly oscillatory solutions.Boundary conditions are discussed,and an approach is suggested for producing good results in the presence of boundary reflections.An efficientmethod to compute the amplitude from the level set method solutions is also presented.Comparisons to analytical solutions are presented where available,and numerical results are validated by comparing results with exact solutions where available,a full wave equation solver,and with wavefronts extracted from ray tracing software.

Experimental study on the acoustic propagation and anisotropy of coal rocks

In order to study the propagation laws of acoustic wave of coal samples from the Upper Permian Xuanwei Formation in the east of Yunnan Province,China,under saturated water and dry conditions,the basic physical parameters,acoustic parameters and anisotropic parameters were obtained through the experiments.Based on FFT and wavelet analysis theory,the spectral characteristics of coal samples under different conditions were studied.The results show that physical parameters of coal samples in different directions have different values,that is,the anisotropy of coal samples is obvious.When the coal samples are saturated with water,the acoustic velocities and the attenuation coefficient increase,whereas the dominant frequency decreases.The signal amplitude of the frequency domain significantly decreases,that is,the internal structure of coal samples is damaged.The P-wave velocity and S-wave velocity increase with the increase of the confining pressure,whereas the anisotropy parameters decrease with the increase of the confining pressure.Overall,this study provides the basis to understand basic acoustic information and anisotropy characteristics of coal samples.

Manipulating Backward Propagation of Acoustic Waves by a Periodical Structure

In the backward propagation of acoustic waves, the direction of phase velocity is anti-parallel to that of group velocity. We propose a scheme to manipulate the backward propagation using a periodicM structure. The dynamic backward propagation process is further experimentally observed. It is demonstrated that the oblique incident plane wave moves backward when it travels through the periodical structure and the backward shift can be controlled within a certain range.

Influence of particle packing structure on sound velocity

The anisotropy in the particle systems of different packing structures affects the sound velocity. The acoustic propagation process in four kinds of packing structures（denoted as S45, H60, S90, and D） of two-dimensional granular system is simulated by the discrete element method. The velocity vtof obtained by the time of flight method and the velocity vc obtained from the stiffness tensor of the system are compared. Different sound velocities reflect various packing structures and force distributions within the system. The compression wave velocities of H60 and S90 are nearly the same, and transmit faster than that of D packing structure, while the sound velocity of S45 is the smallest. The shear wave velocities of S45 and H60 are nearly the same, and transmit faster than that of D packing structure. The compression wave velocity is sensitive to the volume fraction of the structure, however, the shear wave velocity is more sensitive to the geometrical structure itself. As the normal stress p is larger than 1 MPa, vtof and vc are almost equal, and the stiffness tensors of various structures explain the difference of sound velocities. When the normal stress is less than 1 MPa, with the coordination number unchanged, the law vtof ∝ p^1/4 still exists. This demonstrates that apart from different power laws between force and deformation as well as the change of the coordination number under different stresses, there are other complicated causes of vtof∝ p^1/4, and an explanation of the deviation from vtof ∝ p^1/6 is given from the perspective of dissipation.

Effects of sediment parameters on the low frequency acoustic wave propagation in shallow water

The integral expression for acoustic field due to a point source in shallow waterwhile sediment is either a liquid or a solid is derived. The synthetic full waveforms are simulatedusing real axis integration and FFF method. The effects of the seabed sediment parametersand center frequency of the source on the low frequency acoustic wave propagation in shallowwater are investigated. The conclusion is that the wave groups received in far field are thoseof the mode waves of the source center frequency. The possibility for inversely deducing thecompressional and shear sound speeds of sediment using the least square optimum through themeasured group velocities of a selected mode at different frequencies is discussed.

The effects of bonding conditions on the propagation of acoustic waves along a cased borehole

Based on the wave equations in cylindrically layered structures and boundary conditions, the frequency equation for axisymmetric guided waves and the expression for sound fields in a cased borehole excited by a monopole or multipole source have been derived. The synthetic full waveforms excited by the monopole and dipole source are simulated using a real axis integration and FFT method. According to the axisymmetric guided wave modes, the synthetic full waveforms and the effects of the interface conditions on the sound field in a cased borehole have been analyzed and studied respectively. Numerical results indicate that it may be difficult to distinguish well bonded, poorly bonded or unbonded intermediate layer between the steel pipe and formation if only using a monopole source or dipole source. To properly estimate the case boundary conditions, a combination of monopole source logging with dipole source logging is suggested.

Numerical method for sound propagation with acoustic shock waves in transonic flow ducts

The fourth order MacCormack scheme with fourth viscous term is used to improve the shocked solutions for sound propagation in varying cross area and hard-wall ducts with transonic flow. The artificial viscous coefficient is given out by an empirical formula. It is shown from three calculation examples of acoustic shock waves that the new method is much better than the second order MacCormack method which is the best one of second order schemes. Moreover, CPU times of both methods are almost the same.

Acoustic scattering mechanism and noise attenuation of circumferentially non-uniform liner with spectral-wave guide method

In this paper,a model is established with application of the spectral-wave guide method,which has higher accuracy and can serve as a rapid calculation tool for sound transmission calculations.Based on this calculation model,some numerical results of circumferentially non-uniform lined annular/circular ducts are carried out,and some physical mechanisms can be discovered.The numerical results show that periodical impedance distributions along the circumferential direction will lead to discontinuous scattered modes with regular spacing;and mirror-symmetric structure liner will converge the energy of opposite modes.Relying on this mechanism,the potential of acoustic scattering can be further developed by suppressing lower or enhancing higher order modes with expressly designed segmented liner configurations.In particular,the intrinsic mechanism of mode redistribution brought about by the non-uniform liner can be subtly utilized to attenuate broadband noise.The present work indeed shows that circumferentially non-uniform liner is conducive to the reduction of the practical broadband sound source.Furthermore,the effects of nonuniform flow are considered in the model,then distinction of noise attenuation and scattered modes energy in different flows is shown.A possible mechanism is proposed that refraction effects in complex flows lead to the distinction.These works show that the current model has profound potential and availability for the research and designs of circumferentially non-uniform liner.

Temporal and spatial characteristics of monopole acoustic energy dominated by unsteady thermodynamic cavitating flow

The acoustic propagation characteristics of the cavitating flow are essential for the noise suppression, but were not well studied. In the current paper, a new technique concerning the propagation path of the monopole acoustic energy is presented and two typical thermodynamic cavitation modes (the inertial and thermal modes) are selected to investigate the effect of the cavity shedding dynamics on the acoustic propagation path. In the inertial mode, the temporal variation and the spatial distributions of the monopole acoustic energy as well as the divergence of the monopole acoustic pressure are both more powerful and concentrated than that in the thermal mode. The acoustic propagation path in the thermal mode strictly satisfies the feature of the convective amplification, while there exists another propagation direction close to the normal direction of the foil surface in the inertial mode. Furthermore, the occurrence of the normal direction propagation will make the path deviate from the convective direction.

Numerical Boundary Conditions for Specular Reflection in a Level-Sets-Based Wavefront Propagation Method

We study the simulation of specular reflection in a level set method implementation for wavefront propagation in high frequency acoustics using WENO spatial operators.To implement WENO efficiently andmaintain convergence rate,a rectangular grid is used over the physical space.When the physical domain does not conformto the rectangular grid,appropriate boundary conditions to represent reflection must be derived to apply at grid locations that are not coincident with the reflecting boundary.A related problem is the extraction of the normal vectors to the boundary,which are required to formulate the reflection condition.A separate level set method is applied to pre-compute the boundary normals which are then stored for use in the wavefront method.Two approaches to handling the reflection boundary condition are proposed and studied:one uses an approximation to the boundary location,and the other uses a local reflection principle.The second method is shown to produce superior results.

Simulation of Propagating Acoustic Wavefronts with Random Sound Speed

A method for simulating acoustic wavefronts propagating under random sound speed conditions is presented.The approach applies a level set method to solve the Eikonal equation of high frequency acoustics for surfaces of constant phase,instead of tracing rays.The Lagrangian nature often makes full-field ray solutions difficult to reconstruct.The level set method captures multiple-valued solutions on a fixed grid.It is straightforward to represent other sources of uncertainty in the input data using this model,which has an advantage over Monte Carlo approaches in that it yields an expression for the solution as a function of random variables.

A variational principle analysis of surface acoustic waves propagating under periodic metal grating with finite thickness

A theoretical method is presented,which analyzes properties of surface acoustic waves propagating on metallic gratings with finite thickness by combining finite element method with variational principle on surface acoustic waves propagating on periodic metal gratings. Based on D.P.Chen and Haus theory,a finite element method is used to investigate the effects of metallic gratings upon the propagation of surface acoustic waves.The coupling-of-modes parameters contributed by mechanical loading are expressed by the matrix derived from the finite element method.Consequently D.P.Chen and Haus theory can also be applied to analyze the properties of surface acoustic waves propagating on metallic gratings with finite thickness and arbitrary shape.Finally,the characteristics of surface acoustic waves propagating under gold and aluminum or silver gratings on a few piezoelectric crystals are studied.Numerical results of the coupling-of-modes parameters of the surface acoustic waves are obtained.